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Symmetry Breaking of Partially PT-Symmetric Solitons in Fractional Diffraction Systems
Yuanbo Zhai, Rujiang Li, and Pengfei Li
ObjectiveFractional diffraction effects and various novel phenomena produced by parity-time (PT) symmetric optics systems have become research hotspots in the field of optics. A large amount of theoretical research has proven the existence of the optical soliton in the fractional nonlinear Schr?dinger equation containing PT-symmetric potentials. However, the existence, stability, and dynamics of partially PT-symmetric solitons in non-Hermitian nonlinear optical waveguides with fractional diffraction effect have not been explored yet. The phenomenon and mechanism of spontaneous symmetry breaking of the partially PT-symmetric solitons are still unclear. Meanwhile, the obtained research results provide new insights into the propagation and controlling of the partially PT-symmetric solitons in the non-Hermitian nonlinear optical waveguides with fractional diffraction.MethodsWe numerically solve partially PT-symmetric soliton solutions and asymmetric solutions. Specifically, the accelerated imaginary time evolution method is used to solve the stationary fractional nonlinear Schr?dinger equation. Two types of solutions are obtained. The first type is the partially PT-symmetric solitons with real propagation constants, and the second is the asymmetric solutions with complex propagation constants. Then, the solutions of the perturbation are linearized through linear stability analysis, and the eigenvalue problem of the perturbation modes is transformed into the spectral space by using the Fourier collocation method. The spectrum of the eigenvalue problem of the perturbation modes is numerically solved. The propagations of the partially PT-symmetric solitons and the asymmetric solutions are numerically simulated using the split-step Fourier method. Finally, the obtained results are compared with the results of linear stability analysis.Results and DiscussionsFirst, two types of solutions are confirmed to exist in the fractional nonlinear Schr?dinger equation with the partially PT-symmetric potential. The first type of solution is the partially PT-symmetric solitons with real propagation constants, and the second type of solution is the asymmetric solutions with complex propagation constants. The results are shown in Fig. 2 and Fig. 3, respectively. Then, the critical power of the symmetry breaking bifurcation point of the partially PT-symmetric solitons is numerically determined and verified with the linear stability analysis, and the results are shown in Fig. 4(c) and Fig. 5(b), respectively. The reduction of the Lévy index from 2 to 1 causes the critical power of the spontaneous symmetry breaking for the partially PT-symmetric solitons to decrease from 1.6 to 0.4. The numerical simulations of the transmissions of the partially PT-symmetric solitons and the asymmetric solutions are shown in Fig. 6, Fig. 7, and Fig. 8, respectively. It is found that the stable partially PT-symmetric solitons obtained by linear stability analysis are robust, as shown in Fig. 6. The amplitude oscillates periodically during the propagations for the unstable partially PT-symmetric solitons in Fig. 7. In Fig. 8, the amplitude and light field distribution of the asymmetric solution change significantly.ConclusionsIn summary, the partially PT-symmetric optical solitons and spontaneous symmetry breaking phenomenon in the fractional nonlinear Schr?dinger equation are numerically studied. The research results show that there exist partially PT-symmetric solitons. The soliton power exceeds the critical value, and the partially PT-symmetric solitons turn into the asymmetric state. The enhanced fractional diffraction effect weakens the stability of the partially PT-symmetric solitons, and then spontaneous symmetry breaking occurs under the smaller soliton power. The critical power of the partially PT-symmetric soliton decreases to 0.409, when the Lévy index decreases to 1. The stable partially PT-symmetric solitons are robust and can be transmitted stably up to 1000 times the diffraction length, even in the presence of the perturbation. The research results of this work may be used to control optical solitons in the non-Hermitian nonlinear optical waveguides with fractional diffraction. ObjectiveFractional diffraction effects and various novel phenomena produced by parity-time (PT) symmetric optics systems have become research hotspots in the field of optics. A large amount of theoretical research has proven the existence of the optical soliton in the fractional nonlinear Schr?dinger equation containing PT-symmetric potentials. However, the existence, stability, and dynamics of partially PT-symmetric solitons in non-Hermitian nonlinear optical waveguides with fractional diffraction effect have not been explored yet. The phenomenon and mechanism of spontaneous symmetry breaking of the partially PT-symmetric solitons are still unclear. Meanwhile, the obtained research results provide new insights into the propagation and controlling of the partially PT-symmetric solitons in the non-Hermitian nonlinear optical waveguides with fractional diffraction.MethodsWe numerically solve partially PT-symmetric soliton solutions and asymmetric solutions. Specifically, the accelerated imaginary time evolution method is used to solve the stationary fractional nonlinear Schr?dinger equation. Two types of solutions are obtained. The first type is the partially PT-symmetric solitons with real propagation constants, and the second is the asymmetric solutions with complex propagation constants. Then, the solutions of the perturbation are linearized through linear stability analysis, and the eigenvalue problem of the perturbation modes is transformed into the spectral space by using the Fourier collocation method. The spectrum of the eigenvalue problem of the perturbation modes is numerically solved. The propagations of the partially PT-symmetric solitons and the asymmetric solutions are numerically simulated using the split-step Fourier method. Finally, the obtained results are compared with the results of linear stability analysis.Results and DiscussionsFirst, two types of solutions are confirmed to exist in the fractional nonlinear Schr?dinger equation with the partially PT-symmetric potential. The first type of solution is the partially PT-symmetric solitons with real propagation constants, and the second type of solution is the asymmetric solutions with complex propagation constants. The results are shown in Fig. 2 and Fig. 3, respectively. Then, the critical power of the symmetry breaking bifurcation point of the partially PT-symmetric solitons is numerically determined and verified with the linear stability analysis, and the results are shown in Fig. 4(c) and Fig. 5(b), respectively. The reduction of the Lévy index from 2 to 1 causes the critical power of the spontaneous symmetry breaking for the partially PT-symmetric solitons to decrease from 1.6 to 0.4. The numerical simulations of the transmissions of the partially PT-symmetric solitons and the asymmetric solutions are shown in Fig. 6, Fig. 7, and Fig. 8, respectively. It is found that the stable partially PT-symmetric solitons obtained by linear stability analysis are robust, as shown in Fig. 6. The amplitude oscillates periodically during the propagations for the unstable partially PT-symmetric solitons in Fig. 7. In Fig. 8, the amplitude and light field distribution of the asymmetric solution change significantly.ConclusionsIn summary, the partially PT-symmetric optical solitons and spontaneous symmetry breaking phenomenon in the fractional nonlinear Schr?dinger equation are numerically studied. The research results show that there exist partially PT-symmetric solitons. The soliton power exceeds the critical value, and the partially PT-symmetric solitons turn into the asymmetric state. The enhanced fractional diffraction effect weakens the stability of the partially PT-symmetric solitons, and then spontaneous symmetry breaking occurs under the smaller soliton power. The critical power of the partially PT-symmetric soliton decreases to 0.409, when the Lévy index decreases to 1. The stable partially PT-symmetric solitons are robust and can be transmitted stably up to 1000 times the diffraction length, even in the presence of the perturbation. The research results of this work may be used to control optical solitons in the non-Hermitian nonlinear optical waveguides with fractional diffraction.
Acta Optica Sinica
- Publication Date: Mar. 10, 2024
- Vol. 44, Issue 5, 0519002 (2024)
Multiple Breathers of AB System Under Background of Elliptic Functions
Weiyue Xiong, Haiqiang Zhang, and Hui Yao
ObjectiveFor current nonlinear physical systems, nonlinear optical fibers serve as a mature nonlinear experimental platform in experimental science. As a type of nonlinear wave with periodic evolution or periodic distribution structure, breathers have become one of the research hotspots in nonlinear optical systems. As the demand for long-distance and high-capacity fiber optic communication increases, the dynamic properties of breathers are receiving increasing attention. Studying the breather solutions for the AB system is of great significance for better understanding long-distance transmission without shape changing in fiber optic communication. In the context of the periodic solution of the AB system, we focus on the breathers of the system. By studying the interactions between two breathers, it is found that the collision between breathers is elastic, which means that breathers can be transported over long distances without changing their shapes. The results obtained in this article will help to understand the dynamics and interactions of breathers under periodic backgrounds in nonlinear optics.MethodsVia the Darboux transformation method in soliton theory, multi-breather solutions for the AB system were constructed under the elliptic function background. With the help of Matlab software, the spatiotemporal structure of the breathers was plotted, and the nonlinear dynamic characteristics of these breathers were further analyzed. Firstly, elliptic function solutions of the AB system were solved by the modified squared wave (MSW) function approach and the traveling wave transformation. Then, we obtained the basic solution to the Lax pair corresponding to the seed solution to the Jacobi elliptic function. Based on the elliptic function transformation formulas and the integral formulas, the potential function solution could be expressed in terms of the Weierstrass elliptic function. Secondly, by the once-iterated Darboux transformation, three types of breather solutions under the elliptic function background were constructed including the general breather (GB), the Kuznetsov-Ma breather (KMB), and the Akhmediev breather (AB). In addition, we analyzed the dynamic behaviors of these three kinds of breathers and presented their three-dimensional spatiotemporal structures. By the twice-iterated Darboux transformation, the spatiotemporal structure of the interaction between a GB and a KMB under the dn background was investigated, as well as the interaction between two GBs under the cn background.Results and DiscussionsAs an important integrable model, the AB system can be used to describe various nonlinear phenomena in many physical fields such as the quantum field theory, weak nonlinear dispersive water wave, and nonlinear optics. It is meaningful to solve various types of solutions of this model to describe the propagation of nonlinear waves. As far as we know, the breather solutions for the AB system have not been constructed under the elliptic function background. In the context of the periodic solution to the elliptic function in the AB system, the basic solution to the Lax pair of the system is obtained using the MSW function. Using the Darboux transformation method, multiple breathers are constructed under the elliptic function background. Based on the expressions of the breather solutions, the dynamic characteristics of three types of breathers are discussed, including the GB, the KMB, and the AB (Figs. 1 and 2). Finally, the spatiotemporal structure of the interaction between a GB and a KMB under the dn background is investigated (Fig. 3), as well as the interaction between two GBs under the cn background (Fig. 4). It is found that collisions between breathers are elastic, which means that breathers can be transmitted over long distances without changing their shapes. These theoretical research results contribute to exploring the practical physical significance and applications of breathers in nonlinear optics.ConclusionsBased on the elliptic function formulas, we derive the explicit expressions of the first- and second-order breather solutions under the backgrounds of the dn and cn elliptic functions using the Darboux iteration algorithm. By analyzing the dynamic characteristics of three types of breathers and studying the spatiotemporal structure of multi-breather interactions under the dn and cn backgrounds, we find that the collision of GBs and the collision between GB and KMB in the AB system are both elastic, and the breathers do not undergo any shape change during their propagation. This discovery is of great significance for understanding the propagation characteristics of breathers and further elucidating their ability to complete long-distance transmission without changing their shapes. This research will help to understand the dynamics and interactions of breathers under the periodic background from fluid dynamics to nonlinear optics. ObjectiveFor current nonlinear physical systems, nonlinear optical fibers serve as a mature nonlinear experimental platform in experimental science. As a type of nonlinear wave with periodic evolution or periodic distribution structure, breathers have become one of the research hotspots in nonlinear optical systems. As the demand for long-distance and high-capacity fiber optic communication increases, the dynamic properties of breathers are receiving increasing attention. Studying the breather solutions for the AB system is of great significance for better understanding long-distance transmission without shape changing in fiber optic communication. In the context of the periodic solution of the AB system, we focus on the breathers of the system. By studying the interactions between two breathers, it is found that the collision between breathers is elastic, which means that breathers can be transported over long distances without changing their shapes. The results obtained in this article will help to understand the dynamics and interactions of breathers under periodic backgrounds in nonlinear optics.MethodsVia the Darboux transformation method in soliton theory, multi-breather solutions for the AB system were constructed under the elliptic function background. With the help of Matlab software, the spatiotemporal structure of the breathers was plotted, and the nonlinear dynamic characteristics of these breathers were further analyzed. Firstly, elliptic function solutions of the AB system were solved by the modified squared wave (MSW) function approach and the traveling wave transformation. Then, we obtained the basic solution to the Lax pair corresponding to the seed solution to the Jacobi elliptic function. Based on the elliptic function transformation formulas and the integral formulas, the potential function solution could be expressed in terms of the Weierstrass elliptic function. Secondly, by the once-iterated Darboux transformation, three types of breather solutions under the elliptic function background were constructed including the general breather (GB), the Kuznetsov-Ma breather (KMB), and the Akhmediev breather (AB). In addition, we analyzed the dynamic behaviors of these three kinds of breathers and presented their three-dimensional spatiotemporal structures. By the twice-iterated Darboux transformation, the spatiotemporal structure of the interaction between a GB and a KMB under the dn background was investigated, as well as the interaction between two GBs under the cn background.Results and DiscussionsAs an important integrable model, the AB system can be used to describe various nonlinear phenomena in many physical fields such as the quantum field theory, weak nonlinear dispersive water wave, and nonlinear optics. It is meaningful to solve various types of solutions of this model to describe the propagation of nonlinear waves. As far as we know, the breather solutions for the AB system have not been constructed under the elliptic function background. In the context of the periodic solution to the elliptic function in the AB system, the basic solution to the Lax pair of the system is obtained using the MSW function. Using the Darboux transformation method, multiple breathers are constructed under the elliptic function background. Based on the expressions of the breather solutions, the dynamic characteristics of three types of breathers are discussed, including the GB, the KMB, and the AB (Figs. 1 and 2). Finally, the spatiotemporal structure of the interaction between a GB and a KMB under the dn background is investigated (Fig. 3), as well as the interaction between two GBs under the cn background (Fig. 4). It is found that collisions between breathers are elastic, which means that breathers can be transmitted over long distances without changing their shapes. These theoretical research results contribute to exploring the practical physical significance and applications of breathers in nonlinear optics.ConclusionsBased on the elliptic function formulas, we derive the explicit expressions of the first- and second-order breather solutions under the backgrounds of the dn and cn elliptic functions using the Darboux iteration algorithm. By analyzing the dynamic characteristics of three types of breathers and studying the spatiotemporal structure of multi-breather interactions under the dn and cn backgrounds, we find that the collision of GBs and the collision between GB and KMB in the AB system are both elastic, and the breathers do not undergo any shape change during their propagation. This discovery is of great significance for understanding the propagation characteristics of breathers and further elucidating their ability to complete long-distance transmission without changing their shapes. This research will help to understand the dynamics and interactions of breathers under the periodic background from fluid dynamics to nonlinear optics.
Acta Optica Sinica
- Publication Date: Mar. 10, 2024
- Vol. 44, Issue 5, 0519001 (2024)
Passive Q-Switched Laser Based on Zinc Indium Sulfide Nanoflowers
Yixuan Zhu, Luyang Tong, Yangjian Cai, Lina Zhao, and Liren Zheng
ObjectivePulse lasers have a wide range of applications in the medical treatment, communication, material processing, and other fields. Saturable absorber (SA) is a key element in triggering pulse operation, which can switch between different absorption states and produce ultrafast lasers on ultrafast timelines. In the past few years, various two-dimensional materials have been applied to ultrafast laser research, such as graphene, transition metal oxides, topological insulators, black phosphorus, and MXenes. The transition metal dichalcogenides (TMDs) put transition metals (Mo, W, Ti, Re, Hf) sandwiched between two chalcogenides (S, Se, Te) planes. This structure has reliable optical, mechanical, and electronic properties. It has become a new two-dimensional material. As SA, TMDs are widely used in pulse lasers, such as MoS2, ReS2, and WS2. However, TMDs typically have a high saturation light intensity (tens of GW/cm2). Ternary metal sulfides (TMSs) nanomaterials have been explored by many researchers due to their ultra-wideband nonlinear optical response, high carrier mobility, and excellent air stability. The TMSs ZnIn2S4 (ZIS) has a layered structure composed of two-dimensional [S-Zn-S-In-S-In-S] layers with tunable electronic and optical properties. Compared with traditional binary metal sulfides such as CdS and Sb2S3, ZIS has the advantages of low toxicity, good chemical stability, simple preparation method, and abundant sources. In terms of optical properties, ZIS has a high optical absorption coefficient and strong optical stability. In addition, the charge transport characteristics of ZIS are changed due to the presence of abundant sulfur vacancies. It is necessary to study the layered ZIS with sulfur vacancies as efficient SA.MethodsIn this paper, we synthesize ZIS nanoflowers with sulfur vacancies by solution method. The morphology, phase structure, and ultraviolet-visible (UV-Vis) diffuse reflection spectra of ZIS nanoflowers are analyzed by scanning electron microscopy (SEM), X-ray diffraction (XRD), and ultraviolet-visible-near infrared (UV-Vis-NIR) spectra. The nonlinear SA characteristics of ZIS are studied by the Z-scan method, and the optical performance and nonlinear optical response of ZIS are verified by constructing a pulsed laser experimental setup. Finally, the passive Q-switched laser output based on ZIS is realized.Results and DiscussionsWe represent the characteristics of ZIS nanoflowers and show SEM images of ZIS-SA in Figs. 1(a) and (b), XRD spectrum of ZIS-SA in Fig. 1(c), absorptance of the ZIS-SA in Fig. 1(d), and EPR spectroscopy of the ZIS-SA in Fig. 1(e). As shown in Fig. 2, we verify the optical properties of the SA. The fitting results show that the saturation intensity of the ZIS-SA is 675 MW/cm2 and the modulation depth is 7.8%. Second, we verify the modulation performance of ZIS as SA in pulsed lasers. Fig. 3 shows the schematic of the 1 μm pulsed laser experimental setup. Fig. 4 shows the output performance of the passive Q-switched laser. As shown in Fig. 4(a), when the pump power is 5.31 W, the continuous output power reaches 2.67 W. Passive Q-switched laser is achieved by inserting SA and adjusting its position in the cavity so that the SA is in the best position. When the pump power is 4.10 W, a stable Q-switched pulse can be obtained. When the pump power is increased to 5.31 W, the maximum output power of the laser is 240 mW. As shown in Fig. 4(b), with an increase in pump power, the pulse repetition rate gradually increases and the pulse width decreases. When the pump power increases from 4.10 W to 5.31 W, and the pulse repetition rate frequency increases from 594.6 kHz to 629.08 kHz, and the pulse width decreases from 560 ns to 388 ns. As shown in Fig. 4(c), single pulse energy and peak power of the Q-switched laser. It can be seen that the peak power and single pulse energy increase with the growing pump power. When the pump power is 5.31 W, the single pulse energy is 0.38 μJ, and the corresponding peak power is 0.98 W. As shown in Fig. 5, we record the shortest pulse at different time scales. Fig. 5(a) shows the pulse sequence at a 20 μs time scale, and Fig. 5(b) shows the pulse sequence at a 2 μs time scale. The minimum pulse width is 388 ns. As shown in Fig 6, we measure the beam quality M2 factors. The transverse beam quality factor (Mx2) is 1.83 and the longitudinal beam quality factor (My2) is 1.65 which indicate that the Q-switched pulse laser has a high beam quality.ConclusionsTwo-dimensional zinc sulfide indium nanoflowers are synthesized by solution method. The Q-switched Nd∶YVO4 laser was realized by ZIS as SA. When the maximum pump power is 5.31 W, the maximum pulse repetition rate frequency of the pulsed laser is 629.08 kHz, the pulse width is 388 ns, and the maximum average output power is 240 mW. The corresponding single pulse energy and peak power are 0.38 μJ and 0.98 W. The results show that although the band gap of indium zinc sulfide is 2.32 eV and its absorption edge is located at 534 nm, the presence of sulfur vacancies introduces intermediate energy levels in the near-infrared band and enhances its light absorption. Therefore, the nanomaterials of indium zinc sulfide can still exhibit good saturation absorption characteristics in the near-infrared region. The laser with a high repetition rate and short pulse width can be obtained by ZIS as SA in the laser resonator. Therefore, zinc indium sulfide nanomaterials have a good application prospect in Q-switched pulse lasers. ObjectivePulse lasers have a wide range of applications in the medical treatment, communication, material processing, and other fields. Saturable absorber (SA) is a key element in triggering pulse operation, which can switch between different absorption states and produce ultrafast lasers on ultrafast timelines. In the past few years, various two-dimensional materials have been applied to ultrafast laser research, such as graphene, transition metal oxides, topological insulators, black phosphorus, and MXenes. The transition metal dichalcogenides (TMDs) put transition metals (Mo, W, Ti, Re, Hf) sandwiched between two chalcogenides (S, Se, Te) planes. This structure has reliable optical, mechanical, and electronic properties. It has become a new two-dimensional material. As SA, TMDs are widely used in pulse lasers, such as MoS2, ReS2, and WS2. However, TMDs typically have a high saturation light intensity (tens of GW/cm2). Ternary metal sulfides (TMSs) nanomaterials have been explored by many researchers due to their ultra-wideband nonlinear optical response, high carrier mobility, and excellent air stability. The TMSs ZnIn2S4 (ZIS) has a layered structure composed of two-dimensional [S-Zn-S-In-S-In-S] layers with tunable electronic and optical properties. Compared with traditional binary metal sulfides such as CdS and Sb2S3, ZIS has the advantages of low toxicity, good chemical stability, simple preparation method, and abundant sources. In terms of optical properties, ZIS has a high optical absorption coefficient and strong optical stability. In addition, the charge transport characteristics of ZIS are changed due to the presence of abundant sulfur vacancies. It is necessary to study the layered ZIS with sulfur vacancies as efficient SA.MethodsIn this paper, we synthesize ZIS nanoflowers with sulfur vacancies by solution method. The morphology, phase structure, and ultraviolet-visible (UV-Vis) diffuse reflection spectra of ZIS nanoflowers are analyzed by scanning electron microscopy (SEM), X-ray diffraction (XRD), and ultraviolet-visible-near infrared (UV-Vis-NIR) spectra. The nonlinear SA characteristics of ZIS are studied by the Z-scan method, and the optical performance and nonlinear optical response of ZIS are verified by constructing a pulsed laser experimental setup. Finally, the passive Q-switched laser output based on ZIS is realized.Results and DiscussionsWe represent the characteristics of ZIS nanoflowers and show SEM images of ZIS-SA in Figs. 1(a) and (b), XRD spectrum of ZIS-SA in Fig. 1(c), absorptance of the ZIS-SA in Fig. 1(d), and EPR spectroscopy of the ZIS-SA in Fig. 1(e). As shown in Fig. 2, we verify the optical properties of the SA. The fitting results show that the saturation intensity of the ZIS-SA is 675 MW/cm2 and the modulation depth is 7.8%. Second, we verify the modulation performance of ZIS as SA in pulsed lasers. Fig. 3 shows the schematic of the 1 μm pulsed laser experimental setup. Fig. 4 shows the output performance of the passive Q-switched laser. As shown in Fig. 4(a), when the pump power is 5.31 W, the continuous output power reaches 2.67 W. Passive Q-switched laser is achieved by inserting SA and adjusting its position in the cavity so that the SA is in the best position. When the pump power is 4.10 W, a stable Q-switched pulse can be obtained. When the pump power is increased to 5.31 W, the maximum output power of the laser is 240 mW. As shown in Fig. 4(b), with an increase in pump power, the pulse repetition rate gradually increases and the pulse width decreases. When the pump power increases from 4.10 W to 5.31 W, and the pulse repetition rate frequency increases from 594.6 kHz to 629.08 kHz, and the pulse width decreases from 560 ns to 388 ns. As shown in Fig. 4(c), single pulse energy and peak power of the Q-switched laser. It can be seen that the peak power and single pulse energy increase with the growing pump power. When the pump power is 5.31 W, the single pulse energy is 0.38 μJ, and the corresponding peak power is 0.98 W. As shown in Fig. 5, we record the shortest pulse at different time scales. Fig. 5(a) shows the pulse sequence at a 20 μs time scale, and Fig. 5(b) shows the pulse sequence at a 2 μs time scale. The minimum pulse width is 388 ns. As shown in Fig 6, we measure the beam quality M2 factors. The transverse beam quality factor (Mx2) is 1.83 and the longitudinal beam quality factor (My2) is 1.65 which indicate that the Q-switched pulse laser has a high beam quality.ConclusionsTwo-dimensional zinc sulfide indium nanoflowers are synthesized by solution method. The Q-switched Nd∶YVO4 laser was realized by ZIS as SA. When the maximum pump power is 5.31 W, the maximum pulse repetition rate frequency of the pulsed laser is 629.08 kHz, the pulse width is 388 ns, and the maximum average output power is 240 mW. The corresponding single pulse energy and peak power are 0.38 μJ and 0.98 W. The results show that although the band gap of indium zinc sulfide is 2.32 eV and its absorption edge is located at 534 nm, the presence of sulfur vacancies introduces intermediate energy levels in the near-infrared band and enhances its light absorption. Therefore, the nanomaterials of indium zinc sulfide can still exhibit good saturation absorption characteristics in the near-infrared region. The laser with a high repetition rate and short pulse width can be obtained by ZIS as SA in the laser resonator. Therefore, zinc indium sulfide nanomaterials have a good application prospect in Q-switched pulse lasers.
Acta Optica Sinica
- Publication Date: Feb. 25, 2024
- Vol. 44, Issue 4, 0419001 (2024)
Design of Optical Frequency Comb Based on Dual-Frequency Pumped Normal Dispersion Silicon-Riched Silicon Nitride Microresonator
Yanan Yang, Rong Gao, Chenyi Zhan, Ding Li, Yi Deng, Zixiao Wang, Kun Liang, and Suchun Feng
ObjectiveGeneration schemes of optical frequency combs mainly include mode-locked laser, electro-optic modulation comb, nonlinear supercontinuum-based comb, and nonlinear Kerr microresonator comb. Compared with other generation methods of optical frequency combs, the Kerr microresonator comb is considered a new type of coherent light source that features unique and promising advantages of lower power consumption and whole system integratability.The Kerr microresonator pumped in the anomalous group velocity dispersion (GVD) regime leads to the dissipative Kerr soliton comb. The dissipative soliton states are sometimes inaccessible due to the intracavity thermal dynamics and therefore require special tricks to align the pump laser and the resonances in soliton formation. These approaches need benchtop laser sources and complex control protocols, which are not suitable for integrated photonic systems. Furthermore, due to the small temporal overlap between the driving continuum wave laser and the ultrashort pulse, the pump-to-comb conversion efficiency is rather low. Meanwhile, Kerr comb pumped in the normal GVD regime has the benefits including relatively easy access to high pump-to-comb conversion efficiency, large pump frequency detuning range for comb generation, and lower power falloffs within the spectral region of interest which are more ideal for optical communications. Since there is no modulation instability (MI) in the normal GVD regime, the most prevalent method to generate a normal GVD comb is to modify the microresonator dispersion via mode splitting. Common mode splitting mechanisms contain mode coupling to different polarization modes, spatial modes, injection locking, and auxiliary resonator modes. However, the above-mentioned methods are quite complicated. Another method to generate a normal GVD comb can be achieved by pump direct modulation or electro-optic pulse generator based on electro-optic intensity and phase modulators at the resonator free spectral range (FSR), but the electro-optic pulse generator is quite bulky. The phase-locked dual-frequency laser can be regarded as a pulse pump laser source with a wide pulse duration, which can be realized by an integrated DFB laser.Silicon nitride is widely applied to nonlinear optics. It has an ultra-broad transparency window, low intrinsic loss, and a refractive index that allows for moderate optical field confinement in waveguides. However, fabricating thick films with high yield is challenging owing to the large tensile stress in as-deposited stoichiometric silicon nitride films, which can result in the formation of cracks crossing the photonic devices. An alternative way to overcome the high tensile stress is varying the composition of the material itself. In particular, silicon-riched silicon nitride can dramatically reduce the film stress. Silicon-riched silicon nitride waveguides also have a higher nonlinear Kerr coefficient and refractive index than stoichiometric silicon nitride, but the normal GVD comb based on the silicon-riched silicon nitride has not been reported. Thus, we propose a generation scheme of optical frequency combs by adopting a phase-locked dual-frequency laser-pumped normal dispersion silicon-riched silicon nitride microresonator. The proposed optical frequency comb has potential applications in astronomy, optical communication, and microwave photonics.MethodsFirstly, the flat normal dispersion in the 1550 nm band is realized via dispersion engineering of the silicon-riched silicon nitride microresonator by the finite element method mode solver. The effective mode field area of the TE0 fundamental mode at 1550 nm in the optimized silicon-riched silicon nitride waveguide is about 1.005 μm2, and the nonlinear coefficient is about 4.587 W-1·m-1. Meanwhile, the dispersion parameters of the microresonator with 100 GHz free spectral range (FSR) are also optimized. Then, the optical frequency comb generation pumped by a phase-locked dual-frequency laser based on the normal dispersion silicon-riched silicon nitride microresonator is simulated by employing the Lugiato Lefever equation (LLE). The evolution process of the optical frequency comb in time and frequency domains related to the laser pump detuning is studied. Additionally, the effects of several parameters on the performance of the optical frequency comb are also investigated.Results and DiscussionsThe silicon-riched silicon nitride waveguide structure with optimized normal dispersion and nonlinear coefficient is obtained by dispersion engineering (Fig. 1). The dispersion parameters such as resonant mode frequency spacing D1/(2π), second-order dispersion D2/(2π), third-order dispersion D3/(2π), dispersion parameter Dint/(2π) of a microresonator with bending radius of 206.5 μm are also obtained (Fig. 2). The schematic diagram of the optical frequency comb generated via phase-locked dual-frequency laser pumped normal dispersion silicon-riched silicon nitride microresonator is shown (Fig. 3). The optical frequency comb generation is simulated by the LLE. The time-frequency evolution process of the optical frequency comb in time and frequency domains related to the pump detuning is studied (Fig. 4). The optical frequency comb in the normal GVD regime can be generated within a relatively large pump detuning range. The laser pump detuning is intrinsically linked to the intensity filling rate of a pulse state. When the pump detuning increases, the pulse becomes narrow with a broad corresponding spectrum. The effects of several parameters such as the pump power, the power proportion of the dual-frequency laser, microresonator waveguide loss, microresonator dispersion, and the frequency interval of dual-frequency laser on the performance of the optical frequency comb are also investigated. The following conclusions can be obtained by the simulation. Firstly, under the higher laser pump power, the pump detuning range for the optical frequency comb generation becomes larger and the pulse peak power under the same pulse intensity filling rate increases, with a wider corresponding spectrum (Fig. 5). Secondly, the power proportion of dual-frequency laser has little influence on optical frequency comb generation (Fig. 6). Thirdly, when the microresonator waveguide loss is larger, the pump detuning range for optical frequency comb generation becomes smaller, and the pulse peak power under the same pulse intensity filling rate decreases (Fig. 7). Fourthly, with the increasing absolute dispersion value, the spectrum bandwidth of the optical frequency comb under the same pulse intensity filling rate reduces obviously (Fig. 8). Finally, the frequency spacing of the optical frequency comb can be tuned via changing the frequency spacing of the phase-locked dual-frequency laser with integral multiple of FSR (Fig. 9).ConclusionsWe propose a generation scheme of optical frequency combs by adopting a phase-locked dual-frequency laser-pumped normal dispersion silicon-riched silicon nitride microresonator. By optimizing the structure of silicon-riched silicon nitride microresonator and dispersion engineering, an optical frequency comb with bandwidth from 1520 nm to 1580 nm is realized via the simulation. The time-frequency evolution process of optical frequency comb generation is analyzed. The simulation results show that a dual-frequency pumped optical frequency comb in the normal GVD regime can be generated within a relatively large pump detuning range, which will benefit long-term comb stabilization and real applications. Additionally, the effects on the performance of optical frequency combs such as the pump power, the power proportion of the dual-frequency laser, microresonator waveguide loss, microresonator dispersion, and the frequency interval of dual-frequency lasers are also studied. Our study shows that silicon-riched silicon nitride waveguides have potential benefits for the 1550 nm broadband optical frequency comb based on normal dispersion nonlinear optical microresonator. ObjectiveGeneration schemes of optical frequency combs mainly include mode-locked laser, electro-optic modulation comb, nonlinear supercontinuum-based comb, and nonlinear Kerr microresonator comb. Compared with other generation methods of optical frequency combs, the Kerr microresonator comb is considered a new type of coherent light source that features unique and promising advantages of lower power consumption and whole system integratability.The Kerr microresonator pumped in the anomalous group velocity dispersion (GVD) regime leads to the dissipative Kerr soliton comb. The dissipative soliton states are sometimes inaccessible due to the intracavity thermal dynamics and therefore require special tricks to align the pump laser and the resonances in soliton formation. These approaches need benchtop laser sources and complex control protocols, which are not suitable for integrated photonic systems. Furthermore, due to the small temporal overlap between the driving continuum wave laser and the ultrashort pulse, the pump-to-comb conversion efficiency is rather low. Meanwhile, Kerr comb pumped in the normal GVD regime has the benefits including relatively easy access to high pump-to-comb conversion efficiency, large pump frequency detuning range for comb generation, and lower power falloffs within the spectral region of interest which are more ideal for optical communications. Since there is no modulation instability (MI) in the normal GVD regime, the most prevalent method to generate a normal GVD comb is to modify the microresonator dispersion via mode splitting. Common mode splitting mechanisms contain mode coupling to different polarization modes, spatial modes, injection locking, and auxiliary resonator modes. However, the above-mentioned methods are quite complicated. Another method to generate a normal GVD comb can be achieved by pump direct modulation or electro-optic pulse generator based on electro-optic intensity and phase modulators at the resonator free spectral range (FSR), but the electro-optic pulse generator is quite bulky. The phase-locked dual-frequency laser can be regarded as a pulse pump laser source with a wide pulse duration, which can be realized by an integrated DFB laser.Silicon nitride is widely applied to nonlinear optics. It has an ultra-broad transparency window, low intrinsic loss, and a refractive index that allows for moderate optical field confinement in waveguides. However, fabricating thick films with high yield is challenging owing to the large tensile stress in as-deposited stoichiometric silicon nitride films, which can result in the formation of cracks crossing the photonic devices. An alternative way to overcome the high tensile stress is varying the composition of the material itself. In particular, silicon-riched silicon nitride can dramatically reduce the film stress. Silicon-riched silicon nitride waveguides also have a higher nonlinear Kerr coefficient and refractive index than stoichiometric silicon nitride, but the normal GVD comb based on the silicon-riched silicon nitride has not been reported. Thus, we propose a generation scheme of optical frequency combs by adopting a phase-locked dual-frequency laser-pumped normal dispersion silicon-riched silicon nitride microresonator. The proposed optical frequency comb has potential applications in astronomy, optical communication, and microwave photonics.MethodsFirstly, the flat normal dispersion in the 1550 nm band is realized via dispersion engineering of the silicon-riched silicon nitride microresonator by the finite element method mode solver. The effective mode field area of the TE0 fundamental mode at 1550 nm in the optimized silicon-riched silicon nitride waveguide is about 1.005 μm2, and the nonlinear coefficient is about 4.587 W-1·m-1. Meanwhile, the dispersion parameters of the microresonator with 100 GHz free spectral range (FSR) are also optimized. Then, the optical frequency comb generation pumped by a phase-locked dual-frequency laser based on the normal dispersion silicon-riched silicon nitride microresonator is simulated by employing the Lugiato Lefever equation (LLE). The evolution process of the optical frequency comb in time and frequency domains related to the laser pump detuning is studied. Additionally, the effects of several parameters on the performance of the optical frequency comb are also investigated.Results and DiscussionsThe silicon-riched silicon nitride waveguide structure with optimized normal dispersion and nonlinear coefficient is obtained by dispersion engineering (Fig. 1). The dispersion parameters such as resonant mode frequency spacing D1/(2π), second-order dispersion D2/(2π), third-order dispersion D3/(2π), dispersion parameter Dint/(2π) of a microresonator with bending radius of 206.5 μm are also obtained (Fig. 2). The schematic diagram of the optical frequency comb generated via phase-locked dual-frequency laser pumped normal dispersion silicon-riched silicon nitride microresonator is shown (Fig. 3). The optical frequency comb generation is simulated by the LLE. The time-frequency evolution process of the optical frequency comb in time and frequency domains related to the pump detuning is studied (Fig. 4). The optical frequency comb in the normal GVD regime can be generated within a relatively large pump detuning range. The laser pump detuning is intrinsically linked to the intensity filling rate of a pulse state. When the pump detuning increases, the pulse becomes narrow with a broad corresponding spectrum. The effects of several parameters such as the pump power, the power proportion of the dual-frequency laser, microresonator waveguide loss, microresonator dispersion, and the frequency interval of dual-frequency laser on the performance of the optical frequency comb are also investigated. The following conclusions can be obtained by the simulation. Firstly, under the higher laser pump power, the pump detuning range for the optical frequency comb generation becomes larger and the pulse peak power under the same pulse intensity filling rate increases, with a wider corresponding spectrum (Fig. 5). Secondly, the power proportion of dual-frequency laser has little influence on optical frequency comb generation (Fig. 6). Thirdly, when the microresonator waveguide loss is larger, the pump detuning range for optical frequency comb generation becomes smaller, and the pulse peak power under the same pulse intensity filling rate decreases (Fig. 7). Fourthly, with the increasing absolute dispersion value, the spectrum bandwidth of the optical frequency comb under the same pulse intensity filling rate reduces obviously (Fig. 8). Finally, the frequency spacing of the optical frequency comb can be tuned via changing the frequency spacing of the phase-locked dual-frequency laser with integral multiple of FSR (Fig. 9).ConclusionsWe propose a generation scheme of optical frequency combs by adopting a phase-locked dual-frequency laser-pumped normal dispersion silicon-riched silicon nitride microresonator. By optimizing the structure of silicon-riched silicon nitride microresonator and dispersion engineering, an optical frequency comb with bandwidth from 1520 nm to 1580 nm is realized via the simulation. The time-frequency evolution process of optical frequency comb generation is analyzed. The simulation results show that a dual-frequency pumped optical frequency comb in the normal GVD regime can be generated within a relatively large pump detuning range, which will benefit long-term comb stabilization and real applications. Additionally, the effects on the performance of optical frequency combs such as the pump power, the power proportion of the dual-frequency laser, microresonator waveguide loss, microresonator dispersion, and the frequency interval of dual-frequency lasers are also studied. Our study shows that silicon-riched silicon nitride waveguides have potential benefits for the 1550 nm broadband optical frequency comb based on normal dispersion nonlinear optical microresonator.
Acta Optica Sinica
- Publication Date: Feb. 10, 2024
- Vol. 44, Issue 3, 0319005 (2024)
Edge-Enhanced Upconversion Detection Enabled by Spatial-Complex Amplitude Modulation on Pump Beams
Jiaqi Jiang, Xiu Yao, Chunyu Li, Bo Zhao, Baosen Shi, and Zhihan Zhu
ObjectiveEdge-enhanced upconversion detection is a technique to enhance the geometric edges of a target and convert infrared (or terahertz, etc.) targets into the visible spectrum by nonlinear optics. Utilizing this technique for identifying and retrieving edge information within images can substantially mitigate computational burdens in image processing. This is of paramount significance in areas like machine vision, bio-imaging, and related disciplines. However, previous studies have predominantly focused on the "spiral phase contrast" resulting from nonlinear phase transfer and neglected the influence of nonlinear amplitude modulation on targets. The latter is determined by the pump amplitude distribution and the spatial overlap between the pumps and signals, both of which control the spatial spectrum distribution of upconversion images. We theoretically and experimentally investigate the effect of spatial-complex amplitude modulation of pumps on upconversion target based on edge-enhanced upconversion detection caused by amplitude bandpass filtering and spiral phase contrast, followed by analyzing quantum efficiency differences. Finally, based on research findings, we provide practical recommendations for multiple typical scenarios.MethodsThe principle of edge-enhanced upconversion detection (Fig. 1) allows for spatial filtering operations on the signal spatial spectrum by utilizing the spatial amplitude distribution and spiral phase of the pump via parametric nonlinear interactions. This process influences the outcomes of edge-enhanced upconversion detection, thus bringing an improved and more refined detection method. The nonlinear optics platform described by us is based on non-degenerate sum-frequency generation with type-0 phase matching (Fig. 2). Initially, the Laguerre-Gaussian (LG01) beam is employed as the pump beam, which has circular amplitude distribution and spiral phase similar to previous research. Subsequently, a hollow beam with the same spatial amplitude distribution is adopted as the pump beam, and only amplitude spatial filtering is applied to the signal. By comparing the differences between the imaging results and a reference, we can investigate the effect of the spiral phase on edge enhancement. Additionally, Gaussian and super-Gaussian vortex beams carrying spiral phase are employed as pump beam sources to examine how different spatial amplitude distributions of vortex beams affect both imaging results and quantum efficiency in an upconversion detection system.Results and DiscussionsTheoretical and experimental imaging results are compared and analyzed for the pump with four different spatial-complex amplitude distributions under two beam waist radii (Fig. 3). Specifically, when the LG01 beam is utilized as the pump beam, bandpass filtering, and spiral phase modulation are simultaneously applied to the target spatial spectrum, which leads to rounded edge distribution of the upconversion image. Additionally, an increase in the pump beam waist radius reduces the conversion of low-frequency components and sharper edges in the upconversion image. On the other hand, the hollow beam only applies amplitude bandpass filtering on the spatial spectrum of the target, enhancing regions with intensity gradients. In contrast, Gaussian vortex beams exhibit higher conversion efficiency for low-frequency components compared to high-frequency ones, thereby bringing smoother edge profiles for upconversion images. When the waist of the Gaussian vortex beam expands, due to the conversion of a greater proportion of high-frequency components, the low-pass filtering effect on the original image is diminished. Consequently, the contour width of the upconversion image becomes more pronounced. Lastly, super-Gaussian vortex beam has uniform spatial amplitude distribution that converts all spectral components equally, leading to nonlinear spiral phase contrast results close to linear ones.The quantum efficiency corresponding to these four pump beams at identical peak amplitudes and two beam waist radii is obtained (Fig. 4). Since the spectral energy of the image is predominantly concentrated in the low-frequency range, the super-Gaussian vortex beam overlaps most extensively with the spatial spectrum of the signal image, which brings the highest nonlinear conversion efficiency. Importantly, under intense pumping, a pump light characterized by super-Gaussian amplitude can attain the theoretical quantum efficiency upper limit of 100%. The quantum efficiency of the Gaussian vortex beam is surpassed only by the super-Gaussian vortex beam. In contrast, the nonlinear conversion efficiency of the LG01 pump light is comparatively inferior.ConclusionsThe results indicate that the utilization of a circular beam with a spiral phase as the pump light can obtain an upconversion image with enhanced edge sharpness. This technique is particularly suitable for scenarios where precise extraction of the target edge is desired. Conversely, a hollow beam outperforms a circular beam with a spiral phase in preserving more image features. Super-Gaussian vortex beams exhibit the highest quantum efficiency and approach theoretical limits under intense pumping. As a result, when efficient conversion of weak signals is necessary, the utilization of super-Gaussian vortex beam is recommended. On the other hand, the Gaussian vortex beams can be employed to smooth the target edge. It is important to note that Gaussian and super-Gaussian vortex beams are not spatial eigenmodes, whose transverse structures are propagation variants. Thus, imaging should be conducted on the pump light carrying the spiral phase to the signal image spectrum plane and then achieve superior enhancement of the upconversion target edge. ObjectiveEdge-enhanced upconversion detection is a technique to enhance the geometric edges of a target and convert infrared (or terahertz, etc.) targets into the visible spectrum by nonlinear optics. Utilizing this technique for identifying and retrieving edge information within images can substantially mitigate computational burdens in image processing. This is of paramount significance in areas like machine vision, bio-imaging, and related disciplines. However, previous studies have predominantly focused on the "spiral phase contrast" resulting from nonlinear phase transfer and neglected the influence of nonlinear amplitude modulation on targets. The latter is determined by the pump amplitude distribution and the spatial overlap between the pumps and signals, both of which control the spatial spectrum distribution of upconversion images. We theoretically and experimentally investigate the effect of spatial-complex amplitude modulation of pumps on upconversion target based on edge-enhanced upconversion detection caused by amplitude bandpass filtering and spiral phase contrast, followed by analyzing quantum efficiency differences. Finally, based on research findings, we provide practical recommendations for multiple typical scenarios.MethodsThe principle of edge-enhanced upconversion detection (Fig. 1) allows for spatial filtering operations on the signal spatial spectrum by utilizing the spatial amplitude distribution and spiral phase of the pump via parametric nonlinear interactions. This process influences the outcomes of edge-enhanced upconversion detection, thus bringing an improved and more refined detection method. The nonlinear optics platform described by us is based on non-degenerate sum-frequency generation with type-0 phase matching (Fig. 2). Initially, the Laguerre-Gaussian (LG01) beam is employed as the pump beam, which has circular amplitude distribution and spiral phase similar to previous research. Subsequently, a hollow beam with the same spatial amplitude distribution is adopted as the pump beam, and only amplitude spatial filtering is applied to the signal. By comparing the differences between the imaging results and a reference, we can investigate the effect of the spiral phase on edge enhancement. Additionally, Gaussian and super-Gaussian vortex beams carrying spiral phase are employed as pump beam sources to examine how different spatial amplitude distributions of vortex beams affect both imaging results and quantum efficiency in an upconversion detection system.Results and DiscussionsTheoretical and experimental imaging results are compared and analyzed for the pump with four different spatial-complex amplitude distributions under two beam waist radii (Fig. 3). Specifically, when the LG01 beam is utilized as the pump beam, bandpass filtering, and spiral phase modulation are simultaneously applied to the target spatial spectrum, which leads to rounded edge distribution of the upconversion image. Additionally, an increase in the pump beam waist radius reduces the conversion of low-frequency components and sharper edges in the upconversion image. On the other hand, the hollow beam only applies amplitude bandpass filtering on the spatial spectrum of the target, enhancing regions with intensity gradients. In contrast, Gaussian vortex beams exhibit higher conversion efficiency for low-frequency components compared to high-frequency ones, thereby bringing smoother edge profiles for upconversion images. When the waist of the Gaussian vortex beam expands, due to the conversion of a greater proportion of high-frequency components, the low-pass filtering effect on the original image is diminished. Consequently, the contour width of the upconversion image becomes more pronounced. Lastly, super-Gaussian vortex beam has uniform spatial amplitude distribution that converts all spectral components equally, leading to nonlinear spiral phase contrast results close to linear ones.The quantum efficiency corresponding to these four pump beams at identical peak amplitudes and two beam waist radii is obtained (Fig. 4). Since the spectral energy of the image is predominantly concentrated in the low-frequency range, the super-Gaussian vortex beam overlaps most extensively with the spatial spectrum of the signal image, which brings the highest nonlinear conversion efficiency. Importantly, under intense pumping, a pump light characterized by super-Gaussian amplitude can attain the theoretical quantum efficiency upper limit of 100%. The quantum efficiency of the Gaussian vortex beam is surpassed only by the super-Gaussian vortex beam. In contrast, the nonlinear conversion efficiency of the LG01 pump light is comparatively inferior.ConclusionsThe results indicate that the utilization of a circular beam with a spiral phase as the pump light can obtain an upconversion image with enhanced edge sharpness. This technique is particularly suitable for scenarios where precise extraction of the target edge is desired. Conversely, a hollow beam outperforms a circular beam with a spiral phase in preserving more image features. Super-Gaussian vortex beams exhibit the highest quantum efficiency and approach theoretical limits under intense pumping. As a result, when efficient conversion of weak signals is necessary, the utilization of super-Gaussian vortex beam is recommended. On the other hand, the Gaussian vortex beams can be employed to smooth the target edge. It is important to note that Gaussian and super-Gaussian vortex beams are not spatial eigenmodes, whose transverse structures are propagation variants. Thus, imaging should be conducted on the pump light carrying the spiral phase to the signal image spectrum plane and then achieve superior enhancement of the upconversion target edge.
Acta Optica Sinica
- Publication Date: Feb. 10, 2024
- Vol. 44, Issue 3, 0319001 (2024)
Tunable Broadband Terahertz Wave Generation Based on Optical Rectification Effect of Shaped Ultrashort Laser Pulses Interacting with GaSe Crystal
Qiangshuang Li, Changming Sun, Shuzhen Fan, and Haiwei Du
ObjectiveTerahertz wave refers to the electromagnetic wave whose frequency and wavelength are in the ranges of 0.1-10.0 THz and 30-3000 μm, respectively. Throughout the entire electromagnetic spectrum, the terahertz band is located between electronics and optical bands, so it is also called the "terahertz gap". Terahertz wave has some special properties due to its special band, such as low energy, high penetration, and transient. With the development of research and the maturity of technology, terahertz wave has shown bright application prospects in material science, biomedicine, imaging, and communication in recent years. Broadband terahertz radiation source is an important basis for spectral technology in the terahertz band. Therefore, it is of great significance to develop broadband terahertz radiation sources. Since GaSe crystal has a high light transmission and a small absorption coefficient, it has a good application in the generation and detection of broadband terahertz radiation. In this study, GaSe crystal is used to generate tunable broadband terahertz pulses through the optical rectification effect, which provides new ideas for the generation of tunable broadband terahertz pulse radiation.MethodsIn light of nonlinear optics, this paper studies the tunable broadband terahertz radiation generated through the optical rectification effect of shaped ultrashort laser pulses interacting with GaSe crystal, and the process is simulated by numerical calculations. It is found that by adjusting the laser spectrum component with a 4F shaping system, some components whose wavelengths are greater than λ1 in the frequency domain are blocked and truncated. Different shaped ultrashort laser pulses are obtained by varying the value of λ1. The adjustable shaped pulses and the optical rectification effect of GaSe crystal can be utilized to produce tunable broadband terahertz radiation. This scheme makes the center frequency of the terahertz pulse modulated from the high frequency to the low frequency, and the bandwidth is also changed.Results and DiscussionsThe terahertz radiation from GaSe crystal with different pulse durations is given by numerical methods (Fig. 2). Tunable terahertz pulses pumped by the shaped ultrashort laser pulses with a duration of 50 fs and a center wavelength of 800 nm are obtained, and their properties are given in detail. When the cutoff wavelength λ1 is changed, the center frequency and bandwidth (full width at half maximum) of the generated terahertz pulses are also changed accordingly (Fig. 3 and Fig. 4). In the shaping process, some energy of the laser pulse is lost. More energy of the pump pulse is lost at a smaller cutoff wavelength (Fig. 5). When half of the energy is blocked, the lost energy accounts for half of the total energy. Such energy loss also results in the energy loss of the resulting terahertz pulses (Fig. 6). The smaller the cutoff wavelength is, the smaller the terahertz pulse energy is. The proposed method is simple and feasible, and can change the envelope of the high-peak-power laser pulse without requiring any light modulator, thus avoiding the damage of the high-peak-power laser pulse to the modulator. Such pulse shaping methods provide a good theoretical reference for future experimental studies.ConclusionsIn summary, this paper presents a simple way to generate tunable terahertz pulse radiation by using the optical rectification effect of shaped ultrashort laser pulses on the GaSe crystal. The pump laser spectrum component in the 4F shaping system is shielded by an opaque baffle so that the high-peak-power laser pulse can be shaped, and the envelope of the laser pulse and the terahertz spectrum distribution generated by it can be changed. It is found that the center frequency and bandwidth of the generated terahertz pulse can be adjusted by changing the cutoff wavelength. This idea might offer new methods to generate tunable broadband terahertz pulses based on the optical rectification effect of GaSe crystal, which provides a good reference for related experiments. ObjectiveTerahertz wave refers to the electromagnetic wave whose frequency and wavelength are in the ranges of 0.1-10.0 THz and 30-3000 μm, respectively. Throughout the entire electromagnetic spectrum, the terahertz band is located between electronics and optical bands, so it is also called the "terahertz gap". Terahertz wave has some special properties due to its special band, such as low energy, high penetration, and transient. With the development of research and the maturity of technology, terahertz wave has shown bright application prospects in material science, biomedicine, imaging, and communication in recent years. Broadband terahertz radiation source is an important basis for spectral technology in the terahertz band. Therefore, it is of great significance to develop broadband terahertz radiation sources. Since GaSe crystal has a high light transmission and a small absorption coefficient, it has a good application in the generation and detection of broadband terahertz radiation. In this study, GaSe crystal is used to generate tunable broadband terahertz pulses through the optical rectification effect, which provides new ideas for the generation of tunable broadband terahertz pulse radiation.MethodsIn light of nonlinear optics, this paper studies the tunable broadband terahertz radiation generated through the optical rectification effect of shaped ultrashort laser pulses interacting with GaSe crystal, and the process is simulated by numerical calculations. It is found that by adjusting the laser spectrum component with a 4F shaping system, some components whose wavelengths are greater than λ1 in the frequency domain are blocked and truncated. Different shaped ultrashort laser pulses are obtained by varying the value of λ1. The adjustable shaped pulses and the optical rectification effect of GaSe crystal can be utilized to produce tunable broadband terahertz radiation. This scheme makes the center frequency of the terahertz pulse modulated from the high frequency to the low frequency, and the bandwidth is also changed.Results and DiscussionsThe terahertz radiation from GaSe crystal with different pulse durations is given by numerical methods (Fig. 2). Tunable terahertz pulses pumped by the shaped ultrashort laser pulses with a duration of 50 fs and a center wavelength of 800 nm are obtained, and their properties are given in detail. When the cutoff wavelength λ1 is changed, the center frequency and bandwidth (full width at half maximum) of the generated terahertz pulses are also changed accordingly (Fig. 3 and Fig. 4). In the shaping process, some energy of the laser pulse is lost. More energy of the pump pulse is lost at a smaller cutoff wavelength (Fig. 5). When half of the energy is blocked, the lost energy accounts for half of the total energy. Such energy loss also results in the energy loss of the resulting terahertz pulses (Fig. 6). The smaller the cutoff wavelength is, the smaller the terahertz pulse energy is. The proposed method is simple and feasible, and can change the envelope of the high-peak-power laser pulse without requiring any light modulator, thus avoiding the damage of the high-peak-power laser pulse to the modulator. Such pulse shaping methods provide a good theoretical reference for future experimental studies.ConclusionsIn summary, this paper presents a simple way to generate tunable terahertz pulse radiation by using the optical rectification effect of shaped ultrashort laser pulses on the GaSe crystal. The pump laser spectrum component in the 4F shaping system is shielded by an opaque baffle so that the high-peak-power laser pulse can be shaped, and the envelope of the laser pulse and the terahertz spectrum distribution generated by it can be changed. It is found that the center frequency and bandwidth of the generated terahertz pulse can be adjusted by changing the cutoff wavelength. This idea might offer new methods to generate tunable broadband terahertz pulses based on the optical rectification effect of GaSe crystal, which provides a good reference for related experiments.
Acta Optica Sinica
- Publication Date: Mar. 10, 2023
- Vol. 43, Issue 5, 0519001 (2023)
Ultrashort Chirped Pulse Amplification in Fiber Based on Deep Learning
Hao Sui, Hongna Zhu, yan Zhang, Bin Luo, and Xihua Zou
Results and Discussions Specifically, the prediction precision in the four cases is discussed. As training epochs increase, network weights are gradually optimized, and the prediction error of the deep convolutional neural network is gradually reduced. After training for 10000 rounds, the normalized errors on the testing sets in the four cases are all smaller than 1×10-7 (Fig. 4 and Fig. 6). Even in the most complex case (different initial pulse power, width, and chirp), excellent visual agreement is achieved between the predicted pulse propagations and the real ones where all the temporal distributions include details. The prediction error is mainly concentrated in the propagation range after 350 m and is distributed in the range of the pulse peak, with a maximum value smaller than 10 mW (Fig. 7). In conclusion, the normalized root-mean-square errors of the 500 testing samples are smaller than 0.0584. The results show that the proposed network can predict the process of ultrashort CPA under complex initial pulse conditions with high precision. Furthermore, the computation efficiency of the proposed DL method is investigated and compared with that of the traditional split-step Fourier method. The computation time of the proposed DL method for 500 independent samples is less than 1/10 that of the traditional split-step Fourier method, demonstrating that the DL method has clear advantages over the conventional approach in computation efficiency.ObjectiveFiber optical parametric chirped pulse amplification (FOPCPA) is a widely studied ultrashort pulse amplification technique. The FOPCPA can provide excellent gain bandwidth and achieve ultrashort pulse amplification with a more compact and stable system design. The basic principle of the operation relies on a degenerate phase-matched four-wave mixing process involving one strong narrow-bandwidth pump wave, a weak stretched signal, and a generated idler wave. The FOPCPA process can be described by the nonlinear Schrodinger equation. However, the FOPCPA system is highly sensitive to the initial parameters and fiber parameters. Consequently, the traditional numerical methods (i.e., split-step Fourier method and finite-difference method) of analyzing the ultrashort CPA in an FOPCPA system require a huge amount of computation and become less efficient. Nowadays, deep learning (DL) methods have been developed to model and predict nonlinear pulse dynamics and thereby reap the benefits of purely data-driven methods without any underlying governing equations. This study focuses on modeling the ultrashort CPA in fiber by a DL method. The proposed method is expected to broaden the application of DL methods in the prediction of laser behavior and provide an alternative for studying the characteristics of ultrashort pulses in fiber.MethodsA deep convolutional neural network is constructed in the present study. This network contains three parts: five convolutional blocks, a reshaping layer, and three fully connected layers (Fig. 3). Each convolutional block contains a one-dimensional (1d) convolutional layer, a batch normalization layer, a rectified linear unit activation function, and a 1d max pooling layer. The intensity distribution of the initial chirped pulse is used as the input of the neural network. After five convolutional blocks and three fully connected layers, the predicted ultrashort pulse propagation is obtained. For better feature extraction, the real and imaginary parts of the initial pulse are simultaneously used as the input of the deep convolutional neural network. The weights and biases of the proposed network are updated by the back-propagation of the root-mean-square error between the predicted pulse propagation intensity and the ground truth. In the training phase, this study uses the Adam optimizer and sets the learning rate of the network to 0.0001. The whole program is implemented in the Pytorch framework with a 2080Ti GPU. Four cases are considered to test the performance of the proposed network (Table 2). In all these cases, the training sets and testing sets are independent of each other, namely that no duplicate samples are used.ConclusionsIn this study, a DL method is employed to model ultrashort CPA in fiber. A deep convolutional neural network that consists of convolutional blocks and fully connected layers is designed to predict ultrashort pulse propagation under different initial parameters with high precision. Specifically, the paper analyzes the propagation characteristics of the chirped ultrashort pulse and the influence of initial chirp on pulse evolution. The prediction precision and computation efficiency of the proposed method are further studied under different initial pulse parameters. Without compromising generality, the study selects the case of different initial pulse power, width, and chirp to present the testing results. The results show that the neural network constructed performs well in both prediction precision and computation efficiency. On 500 independent testing samples, the proposed deep convolutional neural network achieves normalized root-mean-square errors smaller than 0.0584 and takes less than 1/10 the computation time of the traditional split-step Fourier method. The proposed method extends the application of DL methods in laser technologies and ultrafast optics and provides an alternative for modeling ultrashort pulse propagation in fiber. Results and Discussions Specifically, the prediction precision in the four cases is discussed. As training epochs increase, network weights are gradually optimized, and the prediction error of the deep convolutional neural network is gradually reduced. After training for 10000 rounds, the normalized errors on the testing sets in the four cases are all smaller than 1×10-7 (Fig. 4 and Fig. 6). Even in the most complex case (different initial pulse power, width, and chirp), excellent visual agreement is achieved between the predicted pulse propagations and the real ones where all the temporal distributions include details. The prediction error is mainly concentrated in the propagation range after 350 m and is distributed in the range of the pulse peak, with a maximum value smaller than 10 mW (Fig. 7). In conclusion, the normalized root-mean-square errors of the 500 testing samples are smaller than 0.0584. The results show that the proposed network can predict the process of ultrashort CPA under complex initial pulse conditions with high precision. Furthermore, the computation efficiency of the proposed DL method is investigated and compared with that of the traditional split-step Fourier method. The computation time of the proposed DL method for 500 independent samples is less than 1/10 that of the traditional split-step Fourier method, demonstrating that the DL method has clear advantages over the conventional approach in computation efficiency.ObjectiveFiber optical parametric chirped pulse amplification (FOPCPA) is a widely studied ultrashort pulse amplification technique. The FOPCPA can provide excellent gain bandwidth and achieve ultrashort pulse amplification with a more compact and stable system design. The basic principle of the operation relies on a degenerate phase-matched four-wave mixing process involving one strong narrow-bandwidth pump wave, a weak stretched signal, and a generated idler wave. The FOPCPA process can be described by the nonlinear Schrodinger equation. However, the FOPCPA system is highly sensitive to the initial parameters and fiber parameters. Consequently, the traditional numerical methods (i.e., split-step Fourier method and finite-difference method) of analyzing the ultrashort CPA in an FOPCPA system require a huge amount of computation and become less efficient. Nowadays, deep learning (DL) methods have been developed to model and predict nonlinear pulse dynamics and thereby reap the benefits of purely data-driven methods without any underlying governing equations. This study focuses on modeling the ultrashort CPA in fiber by a DL method. The proposed method is expected to broaden the application of DL methods in the prediction of laser behavior and provide an alternative for studying the characteristics of ultrashort pulses in fiber.MethodsA deep convolutional neural network is constructed in the present study. This network contains three parts: five convolutional blocks, a reshaping layer, and three fully connected layers (Fig. 3). Each convolutional block contains a one-dimensional (1d) convolutional layer, a batch normalization layer, a rectified linear unit activation function, and a 1d max pooling layer. The intensity distribution of the initial chirped pulse is used as the input of the neural network. After five convolutional blocks and three fully connected layers, the predicted ultrashort pulse propagation is obtained. For better feature extraction, the real and imaginary parts of the initial pulse are simultaneously used as the input of the deep convolutional neural network. The weights and biases of the proposed network are updated by the back-propagation of the root-mean-square error between the predicted pulse propagation intensity and the ground truth. In the training phase, this study uses the Adam optimizer and sets the learning rate of the network to 0.0001. The whole program is implemented in the Pytorch framework with a 2080Ti GPU. Four cases are considered to test the performance of the proposed network (Table 2). In all these cases, the training sets and testing sets are independent of each other, namely that no duplicate samples are used.ConclusionsIn this study, a DL method is employed to model ultrashort CPA in fiber. A deep convolutional neural network that consists of convolutional blocks and fully connected layers is designed to predict ultrashort pulse propagation under different initial parameters with high precision. Specifically, the paper analyzes the propagation characteristics of the chirped ultrashort pulse and the influence of initial chirp on pulse evolution. The prediction precision and computation efficiency of the proposed method are further studied under different initial pulse parameters. Without compromising generality, the study selects the case of different initial pulse power, width, and chirp to present the testing results. The results show that the neural network constructed performs well in both prediction precision and computation efficiency. On 500 independent testing samples, the proposed deep convolutional neural network achieves normalized root-mean-square errors smaller than 0.0584 and takes less than 1/10 the computation time of the traditional split-step Fourier method. The proposed method extends the application of DL methods in laser technologies and ultrafast optics and provides an alternative for modeling ultrashort pulse propagation in fiber.
Acta Optica Sinica
- Publication Date: Feb. 10, 2023
- Vol. 43, Issue 3, 0319001 (2023)
Optical Nonlinear Enhancement and Dynamics of Bi Doped Chalcogenide Glass Films
Tongtong Wang, Jianxing Zhao, Yinghao Cao, Nannan Gong, Yinglin Song, and Jianhong Zhou
ObjectiveFinding materials with third-order nonlinearity is one of the most important research areas in the field of optical materials. Because of its high refractive index, high nonlinearity, and adjustable properties with components, chalcogenide glass has obtained many excellent results in all optical switching, optical limiting, optical communication, and other fields. Ultrafast dynamics is the exploration of the microscopic state of materials, and the change of the state of microscopic particles is the direct cause of the change in the macroscopic properties of materials. The study of ultrafast dynamics can observe the change of microscopic particle motion, clarify the mechanism of optical nonlinearity, and obtain the dynamics parameters. However, studies on the ultrafast dynamics of chalcogenide glass are still lacking. Therefore, on the basis of enhancing the nonlinearity of chalcogenide glass, the ultrafine dynamic process of chalcogenide glass is discussed in this paper, which provides an important reference for further understanding of its optical nonlinearity mechanism and developing related devices.MethodsThe experimental samples in this paper were prepared by co-evaporation technique. In the evaporation process, we set different evaporation rates of Ge28Sb12Se60(GSS) powder and Bi particles to obtain (Ge28Sb12Se60)100-xBix chalcogenide glass films with different Bi content and thickness of 50 nm. The elemental composition of each sample with a specific composition was measured by energy disperse spectroscopy (EDS). The transmission and absorption spectra of each sample in the wavelength range of 400-2000 nm were measured and calculated using a UV-3150 spectrometer. The optical band gap (Eg) of the prepared sample is calculated according to the classical Tauc equation, and the nonlinear absorption coefficient of the sample is measured at 532 nm by the picosecond Z-scan method. Finally, the effect of Bi doping on the ultrafast dynamics process of GSS in chalcogenide glass was investigated by the PO pump-probe method and the introduction of a three-energy level system. The optical nonlinear mechanism was studied, and the related dynamics parameters were obtained.Results and DiscussionsIn the wavelength range of 400-2000 nm, with the increase in Bi element content from 0% to 19.4%, the transmission curve (Fig. 3) of the samples decreases significantly and accompanies by redshift, while the absorption curve (Fig. 3) of the samples increases gradually, and the absorption coefficients in the visible wavelength region (the strong absorption region) reach the magnitude of 104-105 cm-1. The results of the calculation of Tauc's equation show that the optical band gap of the samples decreases from 1.81 eV to 1.14 eV with the increase in Bi content (Table 2), which is caused by the broadening of the energy band of the samples and the decrease in the cohesive energy of the system. The nonlinear absorption curves of the samples obtained from the picosecond Z-scan experiment all show a "valley" shape (Fig. 5), which is a typical feature of the reverse saturation absorption behavior, and the increase in Bi doping leads to the decrease in the "valley depth", which indicates that Bi doping plays an obvious enhancement role in the nonlinear absorption. Finally, the maximum nonlinear absorption coefficient β=3.78×10-6 m/W is obtained, which is nearly four times higher than that of the original chalcogenide glass (GSS) film. Subsequently, the absorption dynamics curves of the samples obtained by the PO pump-probe method (Fig. 7) demonstrate that the optical nonlinear absorption mechanism of the samples is excited state absorption, and the doping of Bi elements leads to an increase in the first excited state absorption cross-section of the samples up to the order of 10-19, which is the main reason for the enhancement of the nonlinear absorption, and it leads to the increase in the excited state lifetimes.ConclusionsGSS thin films with different Bi contents were prepared by co-evaporation technique, and their transmission and absorption spectra showed a trend of redshift. It was found that the inclusion of Bi element significantly enhanced the reverse saturation absorption characteristics of GSS, and its nonlinear absorption coefficient β increased from 0.98×10-6 m/W to 3.78×10-6 m/W, which enhanced nearly four times. The enhancement effect was realized by broadening the energy band and reducing the cohesive energy of the system after doping Bi into the GSS system, thus reducing the optical band gap. On this basis, the ultrafast dynamics were investigated by using the PO pump-probe technique and introducing a simplified three-energy-level system. The measured dynamics curves show no "sharp valley" at the zero moment and a long trailing tail afterward, indicating that the nonlinear absorption mechanism of the Bi doped GSS film was excited state absorption, and the excited state lifetime was on the order of ns. The specific value of the first excited state absorption cross section of the samples was also obtained, which reached the order of 10-19, and the doping of Bi elements, which were less electronegative and weakly electron-binding, increased to achieve the nonlinear enhancement. These results provide a valuable reference for the study of ultrafast dynamics of chalcogenide glass and the development of chalcogenide glass-related photonics devices. ObjectiveFinding materials with third-order nonlinearity is one of the most important research areas in the field of optical materials. Because of its high refractive index, high nonlinearity, and adjustable properties with components, chalcogenide glass has obtained many excellent results in all optical switching, optical limiting, optical communication, and other fields. Ultrafast dynamics is the exploration of the microscopic state of materials, and the change of the state of microscopic particles is the direct cause of the change in the macroscopic properties of materials. The study of ultrafast dynamics can observe the change of microscopic particle motion, clarify the mechanism of optical nonlinearity, and obtain the dynamics parameters. However, studies on the ultrafast dynamics of chalcogenide glass are still lacking. Therefore, on the basis of enhancing the nonlinearity of chalcogenide glass, the ultrafine dynamic process of chalcogenide glass is discussed in this paper, which provides an important reference for further understanding of its optical nonlinearity mechanism and developing related devices.MethodsThe experimental samples in this paper were prepared by co-evaporation technique. In the evaporation process, we set different evaporation rates of Ge28Sb12Se60(GSS) powder and Bi particles to obtain (Ge28Sb12Se60)100-xBix chalcogenide glass films with different Bi content and thickness of 50 nm. The elemental composition of each sample with a specific composition was measured by energy disperse spectroscopy (EDS). The transmission and absorption spectra of each sample in the wavelength range of 400-2000 nm were measured and calculated using a UV-3150 spectrometer. The optical band gap (Eg) of the prepared sample is calculated according to the classical Tauc equation, and the nonlinear absorption coefficient of the sample is measured at 532 nm by the picosecond Z-scan method. Finally, the effect of Bi doping on the ultrafast dynamics process of GSS in chalcogenide glass was investigated by the PO pump-probe method and the introduction of a three-energy level system. The optical nonlinear mechanism was studied, and the related dynamics parameters were obtained.Results and DiscussionsIn the wavelength range of 400-2000 nm, with the increase in Bi element content from 0% to 19.4%, the transmission curve (Fig. 3) of the samples decreases significantly and accompanies by redshift, while the absorption curve (Fig. 3) of the samples increases gradually, and the absorption coefficients in the visible wavelength region (the strong absorption region) reach the magnitude of 104-105 cm-1. The results of the calculation of Tauc's equation show that the optical band gap of the samples decreases from 1.81 eV to 1.14 eV with the increase in Bi content (Table 2), which is caused by the broadening of the energy band of the samples and the decrease in the cohesive energy of the system. The nonlinear absorption curves of the samples obtained from the picosecond Z-scan experiment all show a "valley" shape (Fig. 5), which is a typical feature of the reverse saturation absorption behavior, and the increase in Bi doping leads to the decrease in the "valley depth", which indicates that Bi doping plays an obvious enhancement role in the nonlinear absorption. Finally, the maximum nonlinear absorption coefficient β=3.78×10-6 m/W is obtained, which is nearly four times higher than that of the original chalcogenide glass (GSS) film. Subsequently, the absorption dynamics curves of the samples obtained by the PO pump-probe method (Fig. 7) demonstrate that the optical nonlinear absorption mechanism of the samples is excited state absorption, and the doping of Bi elements leads to an increase in the first excited state absorption cross-section of the samples up to the order of 10-19, which is the main reason for the enhancement of the nonlinear absorption, and it leads to the increase in the excited state lifetimes.ConclusionsGSS thin films with different Bi contents were prepared by co-evaporation technique, and their transmission and absorption spectra showed a trend of redshift. It was found that the inclusion of Bi element significantly enhanced the reverse saturation absorption characteristics of GSS, and its nonlinear absorption coefficient β increased from 0.98×10-6 m/W to 3.78×10-6 m/W, which enhanced nearly four times. The enhancement effect was realized by broadening the energy band and reducing the cohesive energy of the system after doping Bi into the GSS system, thus reducing the optical band gap. On this basis, the ultrafast dynamics were investigated by using the PO pump-probe technique and introducing a simplified three-energy-level system. The measured dynamics curves show no "sharp valley" at the zero moment and a long trailing tail afterward, indicating that the nonlinear absorption mechanism of the Bi doped GSS film was excited state absorption, and the excited state lifetime was on the order of ns. The specific value of the first excited state absorption cross section of the samples was also obtained, which reached the order of 10-19, and the doping of Bi elements, which were less electronegative and weakly electron-binding, increased to achieve the nonlinear enhancement. These results provide a valuable reference for the study of ultrafast dynamics of chalcogenide glass and the development of chalcogenide glass-related photonics devices.
Acta Optica Sinica
- Publication Date: Dec. 10, 2023
- Vol. 43, Issue 23, 2319001 (2023)
Unidirectional Electromagnetically Induced Transparency-Like Effect with Electrically Switchable Excitation Port
Jia Ran, Siwen Zhang, Wenchang Wang, Honggang Hao, Fei Tan, and Yongqiang Chen
MethodsWe take Rogers RT5880 copper-clad substrate with a thickness of 1.57 mm as the substrate of the microstrip cavity and CRLH-TLs. The thickness of the copper layer is 0.035 mm. A Fabry-Perot (FP) cavity is formed inside a microstrip line. Two SRRs are placed in the cavity and located at the antinode and node of the electromagnetic field in the FP cavity respectively to construct a unidirectional EIT-like structure. The excitation port of the EIT-like effect is determined by the sequence of the antinode and node in the FP cavity. Tunable composite right/left-handed transmission lines (CRLH-TLs) loaded with varactors are added at the two ends of the FP cavity (marked as left and right CRLH-TLs respectively) to change the electromagnetic field distribution in the cavity. By optimizing all parameters, the electrical lengths of CRLH-TLs are quarter wavelength and half wavelength respectively under different bias voltages. Therefore, since the distribution of the nodes and antinodes in the cavity can be switched by changing the electric length of the CRLH-TLs, the sequence of the antinode and node where the two split ring resonators (SRRs) lie in the cavity is also switched, which leads to a switched EIT-like excitation port. Finally, a sample is fabricated and tested to validate the unidirectional EIT-like effect with the electrically switchable excitation port.Results and DiscussionsThis structure realizes the unidirectional EIT-like effect to bring a unidirectional reflection with high contrast ratio. It is validated both in simulation and experiments that the contrast ratio of the unidirectional reflection can reach more than 95%, and the excitation port of the unidirectional EIT-like effect is determined by the sequence of nodes and antinodes in the FP cavity. The capacitance of the varactors in the CRLH-TLs varies along with the bias voltage. Thus, different bias voltages are simulated by setting different capacitance values. In case I, the capacitance of varactors in the left CRLH-TLs is set as 2.5 pF (Csl=2.5 pF) and that in the right is set as 1.5 pF (Csr=1.5 pF). The magnitude of the reflection coefficient of port 1 S11 and port 2 S22 at 3.97 GHz are 0.007 and 0.538 respectively, showing that the EIT-like effect is only excited through port 1. Case II has swapped the capacitance of the varactors in the right and left CRLH-TLs units. Thus the reflection spectra S11 and S22 will also be exchanged due to the geometric symmetry of the switchable EIT-like effect. At last, the excitation port of the EIT-like effect has been switched to port 2, indicating that switching the bias voltage can achieve a unidirectional EIT-like effect with an electrically switchable excitation port (Fig. 2). When the capacitance of the varactors is set as 1.5 pF and 2.5 pF, the transmission amplitudes of the CRLH-TLs are both larger than 0.7 and ∠S21 are close to -90° and -180° at 3.97 GHz respectively (Fig. 3). Since the transmission phase difference between the CRLH-TLs units with the capacitance of 2.5 pF and 1.5 pF is -90°, once the capacitance of the varactors in the left and right CRLH-TLs is exchanged, the sequence of the nodes and antinodes in the FP cavity is reversed. As a result, the port to excite the unidirectional EIT-like effect is switched (Fig. 4). For the fabricated sample, when the bias voltage on the left and right sides of the CRLH-TLs are V1=0 V and V2=6 V respectively, only when the wave is incident from port 1, the EIT-like effect can be excited. Through exchanging the bias voltages, the unidirectional EIT-like excitation port is switched. This shows that the structure can achieve a unidirectional EIT-like effect with an electrically switchable excitation port.ObjectiveUnidirectional electromagnetically induced transparency-like effect is a special kind of EIT-like effect, which is caused by its asymmetric structure. The EIT-like effect can be excited by the asymmetric structure only when a wave is incident from a certain port. The unidirectional EIT-like effect plays a significant role in realizing directional reflection and transmission and is crucial in unidirectional invisibility. With the development of tunable metamaterials, various kinds of reconfigurable metamaterials are also proposed to realize a tunable EIT-like effect. However, the dynamically switchable unidirectional EIT-like effect has been barely reported. The excitation port of the unidirectional EIT-like effect is usually fixed and determined by the structure topology. To realize a reflection-type unidirectional EIT-like effect, an electrically switchable excitation port based on tunable CRLH-TLs and a two-port microstrip cavity embedded with two SRRs is proposed. The reflection-type EIT-like effect can only be excited when an electromagnetic wave is incident from a certain port. The contrast ratio of the asymmetric reflection coefficient of the two ports in our paper reaches 98.7%. On this basis, the coupling between the microstrip cavity and the SRRs is dynamically modulated by the tunable CRLH-TLs, thereby changing the excitation port of the unidirectional EIT-like effect. Finally, a unidirectional EIT-like effect with an electrically switchable excitation port is achieved, and the applications of the EIT-like effect in optical storage, optical modulation, sensing, and other fields are promoted.ConclusionsWe propose a reflection-type unidirectional EIT-like effect with an electrically switchable excitation port, and validate it in simulation and experiments. To switch the excitation port of the unidirectional EIT-like effect, our paper reverses the sequence of nodes and antinodes in the FP cavity by changing the bias voltages of CRLH-TLs on both sides of the cavity. This unidirectional EIT-like effect with an electrically switchable excitation port provides a feasible scheme for tunable asymmetric EIT-like effects and is expected to be applied in directional reflection and multifunctional unidirectional stealth devices. MethodsWe take Rogers RT5880 copper-clad substrate with a thickness of 1.57 mm as the substrate of the microstrip cavity and CRLH-TLs. The thickness of the copper layer is 0.035 mm. A Fabry-Perot (FP) cavity is formed inside a microstrip line. Two SRRs are placed in the cavity and located at the antinode and node of the electromagnetic field in the FP cavity respectively to construct a unidirectional EIT-like structure. The excitation port of the EIT-like effect is determined by the sequence of the antinode and node in the FP cavity. Tunable composite right/left-handed transmission lines (CRLH-TLs) loaded with varactors are added at the two ends of the FP cavity (marked as left and right CRLH-TLs respectively) to change the electromagnetic field distribution in the cavity. By optimizing all parameters, the electrical lengths of CRLH-TLs are quarter wavelength and half wavelength respectively under different bias voltages. Therefore, since the distribution of the nodes and antinodes in the cavity can be switched by changing the electric length of the CRLH-TLs, the sequence of the antinode and node where the two split ring resonators (SRRs) lie in the cavity is also switched, which leads to a switched EIT-like excitation port. Finally, a sample is fabricated and tested to validate the unidirectional EIT-like effect with the electrically switchable excitation port.Results and DiscussionsThis structure realizes the unidirectional EIT-like effect to bring a unidirectional reflection with high contrast ratio. It is validated both in simulation and experiments that the contrast ratio of the unidirectional reflection can reach more than 95%, and the excitation port of the unidirectional EIT-like effect is determined by the sequence of nodes and antinodes in the FP cavity. The capacitance of the varactors in the CRLH-TLs varies along with the bias voltage. Thus, different bias voltages are simulated by setting different capacitance values. In case I, the capacitance of varactors in the left CRLH-TLs is set as 2.5 pF (Csl=2.5 pF) and that in the right is set as 1.5 pF (Csr=1.5 pF). The magnitude of the reflection coefficient of port 1 S11 and port 2 S22 at 3.97 GHz are 0.007 and 0.538 respectively, showing that the EIT-like effect is only excited through port 1. Case II has swapped the capacitance of the varactors in the right and left CRLH-TLs units. Thus the reflection spectra S11 and S22 will also be exchanged due to the geometric symmetry of the switchable EIT-like effect. At last, the excitation port of the EIT-like effect has been switched to port 2, indicating that switching the bias voltage can achieve a unidirectional EIT-like effect with an electrically switchable excitation port (Fig. 2). When the capacitance of the varactors is set as 1.5 pF and 2.5 pF, the transmission amplitudes of the CRLH-TLs are both larger than 0.7 and ∠S21 are close to -90° and -180° at 3.97 GHz respectively (Fig. 3). Since the transmission phase difference between the CRLH-TLs units with the capacitance of 2.5 pF and 1.5 pF is -90°, once the capacitance of the varactors in the left and right CRLH-TLs is exchanged, the sequence of the nodes and antinodes in the FP cavity is reversed. As a result, the port to excite the unidirectional EIT-like effect is switched (Fig. 4). For the fabricated sample, when the bias voltage on the left and right sides of the CRLH-TLs are V1=0 V and V2=6 V respectively, only when the wave is incident from port 1, the EIT-like effect can be excited. Through exchanging the bias voltages, the unidirectional EIT-like excitation port is switched. This shows that the structure can achieve a unidirectional EIT-like effect with an electrically switchable excitation port.ObjectiveUnidirectional electromagnetically induced transparency-like effect is a special kind of EIT-like effect, which is caused by its asymmetric structure. The EIT-like effect can be excited by the asymmetric structure only when a wave is incident from a certain port. The unidirectional EIT-like effect plays a significant role in realizing directional reflection and transmission and is crucial in unidirectional invisibility. With the development of tunable metamaterials, various kinds of reconfigurable metamaterials are also proposed to realize a tunable EIT-like effect. However, the dynamically switchable unidirectional EIT-like effect has been barely reported. The excitation port of the unidirectional EIT-like effect is usually fixed and determined by the structure topology. To realize a reflection-type unidirectional EIT-like effect, an electrically switchable excitation port based on tunable CRLH-TLs and a two-port microstrip cavity embedded with two SRRs is proposed. The reflection-type EIT-like effect can only be excited when an electromagnetic wave is incident from a certain port. The contrast ratio of the asymmetric reflection coefficient of the two ports in our paper reaches 98.7%. On this basis, the coupling between the microstrip cavity and the SRRs is dynamically modulated by the tunable CRLH-TLs, thereby changing the excitation port of the unidirectional EIT-like effect. Finally, a unidirectional EIT-like effect with an electrically switchable excitation port is achieved, and the applications of the EIT-like effect in optical storage, optical modulation, sensing, and other fields are promoted.ConclusionsWe propose a reflection-type unidirectional EIT-like effect with an electrically switchable excitation port, and validate it in simulation and experiments. To switch the excitation port of the unidirectional EIT-like effect, our paper reverses the sequence of nodes and antinodes in the FP cavity by changing the bias voltages of CRLH-TLs on both sides of the cavity. This unidirectional EIT-like effect with an electrically switchable excitation port provides a feasible scheme for tunable asymmetric EIT-like effects and is expected to be applied in directional reflection and multifunctional unidirectional stealth devices.
Acta Optica Sinica
- Publication Date: Nov. 10, 2023
- Vol. 43, Issue 21, 2119001 (2023)
Storage and Retrieval of Optical Soliton in N-Type Quantum Well EIT Medium Under High-Order Effects
Mingjun Hu, Denglong Wang, Yaoyong Dong, and Jianwen Ding
ObjectiveAs soliton can travel over long distance without attenuation and shape change due to the interplay balance between dispersion and nonlinearity in nonlinear media, it becomes a good information carrier in quantum information processing and transmission. Till now, the research on the storage and retrieval of optical soliton mainly focuses on ultra-cold atomic electromagnetic induction transparency (EIT) media. This is mainly because ultra-cold atomic systems can generate strong nonlinear effects under low light excitation. However, for practical applications, it is a great challenge to accurately control the optical soliton storage in the atomic EIT media due to the low temperature approaching to absolute zero and rarefaction. Fortunately, with the mature semiconductor quantum production technology, quantum wells have extensive application prospect in quantum information processing and transmission. Thus, we study the storage and retrieval of optical soliton in the GaAs/AlGaAs double quantum well EIT system.MethodsBased on the current experiments, we first propose an N-type four-level asymmetrical semiconductor GaAs/AlGaAs double quantum well EIT model. Subsequently, the interaction properties between the optical field and semiconductor quantum wells in the system are studied by a semi-classical theory. The physical properties of the optical field are described by the Maxwell equation, while the semiconductor quantum well is described by the Bloch equation of quantum mechanics. Therefore, the Maxwell-Bloch (M-B) equations which govern the linear absorption and nonlinear propagating properties of the system are obtained. Generally, the analytic solution of the M-B equations cannot be obtained directly. Thereby, M-B equations are solved approximately by adopting a multiple-scale method. Correspondingly, the soliton solution [Eq. (63)] is chosen as the initial condition, and the M-B equations are numerically simulated by the Runge-Kutta method to explore the storage and retrieval of the probe pulse.Results and DiscussionsThrough the above methods, when the second control field is turned off, the linear absorption curve of the system exhibits a Lorentz absorption peak whatever the first control field changes [Fig. 2 (a)]. Fig. 2 (b) shows that when the second control field is only turned on, which means that the first control field is turned off, there is a single transparent window, and the width of the single transparent window becomes wider with the increasing strength of the second control field. When both the control fields are turned on, the double transparent window will occur, and the width of the double transparent windows is wider with the rising strength of any control field [Fig. 2 (c)]. Interestingly, after both the control fields are turned on, the double EIT windows show symmetrical distribution regardless of whether the strengths of the two control fields are equal or not [Fig. 2 (c)]. For the nonlinear case, Fig. 3 shows that with the low-order effect being considered, the optical soliton cannot propagate stably over a long distance with attenuation. The soliton instability is from the high-order dispersion of the system. After the high-order effects are only considered, the formed optical soliton can propagate stably over long distances (Fig. 4). Furthermore, Fig. 5 indicates that the optical soliton can be stored and retrieved by switching off and on the control fields, and the storage and retrieval fidelity of the optical soliton is higher than that of the ordinary optical pulse. Moreover, the amplitude of the stored optical soliton can be modulated by the strength of the control field. Specifically, when only the second control field is turned on, the amplitude of the stored optical soliton increases with the rising strength of the second control field [Fig. 6 (a)]. When both the control fields are turned on, the amplitude of the stored optical soliton rises with the increasing strength of the second control field under the unchanged first control field. However, if the second control field keeps unchanged, the amplitude of the stored optical soliton decreases with the increasing strength of the first control field [Fig. 6 (b)].ConclusionsIn this paper, we propose an N-type four-level asymmetrical semiconductor double quantum well EIT model. Subsequently, we obtain the M-B equations governing the linear and nonlinear properties of the system through the semi-classical theory combined with the multiple-scale method. When both the control fields are turned on, the linear absorption curve of the system exhibits double EIT windows. Interestingly, the double EIT windows show symmetrical distribution regardless of whether the strengths of the two control fields are equal or not. For the nonlinear case, only after the high-order effects are considered, the formed optical soliton can propagate stably over long distances, and the optical soliton can be stored and retrieved by switching off and on the control fields. Meanwhile, the amplitude of the stored optical soliton can be modulated by the strength of the control field. When the first control field keeps unchanged, the amplitude of the stored optical soliton increases with the rising strength of the second control field. However, the amplitude of the stored optical soliton decreases with the increasing strength of the first control field under the unchanged second control field. The results can improve the fidelity for the storage and retrieval of quantum information in semiconductor quantum well devices. ObjectiveAs soliton can travel over long distance without attenuation and shape change due to the interplay balance between dispersion and nonlinearity in nonlinear media, it becomes a good information carrier in quantum information processing and transmission. Till now, the research on the storage and retrieval of optical soliton mainly focuses on ultra-cold atomic electromagnetic induction transparency (EIT) media. This is mainly because ultra-cold atomic systems can generate strong nonlinear effects under low light excitation. However, for practical applications, it is a great challenge to accurately control the optical soliton storage in the atomic EIT media due to the low temperature approaching to absolute zero and rarefaction. Fortunately, with the mature semiconductor quantum production technology, quantum wells have extensive application prospect in quantum information processing and transmission. Thus, we study the storage and retrieval of optical soliton in the GaAs/AlGaAs double quantum well EIT system.MethodsBased on the current experiments, we first propose an N-type four-level asymmetrical semiconductor GaAs/AlGaAs double quantum well EIT model. Subsequently, the interaction properties between the optical field and semiconductor quantum wells in the system are studied by a semi-classical theory. The physical properties of the optical field are described by the Maxwell equation, while the semiconductor quantum well is described by the Bloch equation of quantum mechanics. Therefore, the Maxwell-Bloch (M-B) equations which govern the linear absorption and nonlinear propagating properties of the system are obtained. Generally, the analytic solution of the M-B equations cannot be obtained directly. Thereby, M-B equations are solved approximately by adopting a multiple-scale method. Correspondingly, the soliton solution [Eq. (63)] is chosen as the initial condition, and the M-B equations are numerically simulated by the Runge-Kutta method to explore the storage and retrieval of the probe pulse.Results and DiscussionsThrough the above methods, when the second control field is turned off, the linear absorption curve of the system exhibits a Lorentz absorption peak whatever the first control field changes [Fig. 2 (a)]. Fig. 2 (b) shows that when the second control field is only turned on, which means that the first control field is turned off, there is a single transparent window, and the width of the single transparent window becomes wider with the increasing strength of the second control field. When both the control fields are turned on, the double transparent window will occur, and the width of the double transparent windows is wider with the rising strength of any control field [Fig. 2 (c)]. Interestingly, after both the control fields are turned on, the double EIT windows show symmetrical distribution regardless of whether the strengths of the two control fields are equal or not [Fig. 2 (c)]. For the nonlinear case, Fig. 3 shows that with the low-order effect being considered, the optical soliton cannot propagate stably over a long distance with attenuation. The soliton instability is from the high-order dispersion of the system. After the high-order effects are only considered, the formed optical soliton can propagate stably over long distances (Fig. 4). Furthermore, Fig. 5 indicates that the optical soliton can be stored and retrieved by switching off and on the control fields, and the storage and retrieval fidelity of the optical soliton is higher than that of the ordinary optical pulse. Moreover, the amplitude of the stored optical soliton can be modulated by the strength of the control field. Specifically, when only the second control field is turned on, the amplitude of the stored optical soliton increases with the rising strength of the second control field [Fig. 6 (a)]. When both the control fields are turned on, the amplitude of the stored optical soliton rises with the increasing strength of the second control field under the unchanged first control field. However, if the second control field keeps unchanged, the amplitude of the stored optical soliton decreases with the increasing strength of the first control field [Fig. 6 (b)].ConclusionsIn this paper, we propose an N-type four-level asymmetrical semiconductor double quantum well EIT model. Subsequently, we obtain the M-B equations governing the linear and nonlinear properties of the system through the semi-classical theory combined with the multiple-scale method. When both the control fields are turned on, the linear absorption curve of the system exhibits double EIT windows. Interestingly, the double EIT windows show symmetrical distribution regardless of whether the strengths of the two control fields are equal or not. For the nonlinear case, only after the high-order effects are considered, the formed optical soliton can propagate stably over long distances, and the optical soliton can be stored and retrieved by switching off and on the control fields. Meanwhile, the amplitude of the stored optical soliton can be modulated by the strength of the control field. When the first control field keeps unchanged, the amplitude of the stored optical soliton increases with the rising strength of the second control field. However, the amplitude of the stored optical soliton decreases with the increasing strength of the first control field under the unchanged second control field. The results can improve the fidelity for the storage and retrieval of quantum information in semiconductor quantum well devices.
Acta Optica Sinica
- Publication Date: Oct. 10, 2023
- Vol. 43, Issue 19, 1919001 (2023)
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