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Physical Optics|634 Article(s)
Generation and Manipulation of Tunable Chiral Structured Light Beams
Wenni Ye, Juntao Hu, Zhihao Ying, Yishu Wang, and Yixian Qian
ObjectiveVortex beam (VB) has attracted great attention due to its unique optical properties including a helical wavefront, phase singularity, and ability to carry orbital angular momentum (OAM) of l? per photon, where l is the topological charge, and ? is the reduced Planck constant. VBs have been widely used in super-resolution imaging, laser microfabrication, optical manipulation, and ultra-large capacity optical communication. Especially, OAM can twist molten material and can be used for chiral nanostructure microfabrication. In recent years, chiral structured light fields with twisted intensity distribution and OAM have attracted great research interest due to their advantages in optical microfabrication. Alonzo et al. constructed a spiral cone phase using the product of the spiral phase and cone phase and generated a spiral cone light field with chiral intensity distribution. Subsequently, Li et al. proposed a spiral light field with an automatic focusing effect by a power-exponential phase. However, these structures of chiral optical fields are simple. Therefore, generating a flexible and tunable chiral structured light field becomes important. However, the generation of flexible chiral light fields remains challenging. In this paper, we proposed a simple and efficient approach for generating tunable chiral structured beams (TCSB), which exhibited flexible adjustability and multi-ring chiral structures. Such light fields would be beneficial to flexible chiral structure micromachining, optical manipulation, and optical communications.MethodsWe proposed and generated a TCSB by constructing an annular phase (AP) which consisted of multiple annular sub-phases (ASPs). Specifically, every sub-phase was constructed by introducing an equiphase and radial phase based on a classical spiral phase, and then a monocyclic TCSB was generated by imposing such ASP on an incident Gaussian beam. The number and direction of the twisted intensity lobes were flexibly and individually controlled by manipulating the topological charge, equiphase, and radial phase. Moreover, we used multiple ASPs to generate multi-ring chiral optical fields, which could be more flexible in practical applications. Experimentally, chiral light fields could be generated by phase modulation and observed via the CCD, as described in Fig. 5.Results and DiscussionsThe structures of the tunable chiral beams can be flexibly manipulated by controlling the topological charge (Fig. 6). The number and direction of the twisted intensity lobes are determined by the number and sign of the topological charge. By controlling the equal phase, the twisted lobe direction can be arbitrarily controlled (Fig. 9). More complex chiral structured beams with three-ring and four-ring structures are constructed, and this validates the effectiveness of our proposed approach. Additionally, the equal phase gradient is employed to control dynamically the rotation of the light fields (Video 1). The advantage of this rotation also makes this chiral beam beneficial for twisting transiently molten matter, machining complex chiral nanostructures, and sorting multiple particles.ConclusionsIn summary, we have developed an effective method to generate TCSBs by multiple ASPs. The properties of the twisting lobes, including the twisting directions, lobe orientations, and lobe number can be freely manipulated by controlling the topological charge sign, magnitude, and equiphase, respectively. Our findings offer a novel promising technology to manufacture chiral microstructures. Moreover, the flexible TCSBs also provide an innovative method for optical manipulation and optical communications. ObjectiveVortex beam (VB) has attracted great attention due to its unique optical properties including a helical wavefront, phase singularity, and ability to carry orbital angular momentum (OAM) of l? per photon, where l is the topological charge, and ? is the reduced Planck constant. VBs have been widely used in super-resolution imaging, laser microfabrication, optical manipulation, and ultra-large capacity optical communication. Especially, OAM can twist molten material and can be used for chiral nanostructure microfabrication. In recent years, chiral structured light fields with twisted intensity distribution and OAM have attracted great research interest due to their advantages in optical microfabrication. Alonzo et al. constructed a spiral cone phase using the product of the spiral phase and cone phase and generated a spiral cone light field with chiral intensity distribution. Subsequently, Li et al. proposed a spiral light field with an automatic focusing effect by a power-exponential phase. However, these structures of chiral optical fields are simple. Therefore, generating a flexible and tunable chiral structured light field becomes important. However, the generation of flexible chiral light fields remains challenging. In this paper, we proposed a simple and efficient approach for generating tunable chiral structured beams (TCSB), which exhibited flexible adjustability and multi-ring chiral structures. Such light fields would be beneficial to flexible chiral structure micromachining, optical manipulation, and optical communications.MethodsWe proposed and generated a TCSB by constructing an annular phase (AP) which consisted of multiple annular sub-phases (ASPs). Specifically, every sub-phase was constructed by introducing an equiphase and radial phase based on a classical spiral phase, and then a monocyclic TCSB was generated by imposing such ASP on an incident Gaussian beam. The number and direction of the twisted intensity lobes were flexibly and individually controlled by manipulating the topological charge, equiphase, and radial phase. Moreover, we used multiple ASPs to generate multi-ring chiral optical fields, which could be more flexible in practical applications. Experimentally, chiral light fields could be generated by phase modulation and observed via the CCD, as described in Fig. 5.Results and DiscussionsThe structures of the tunable chiral beams can be flexibly manipulated by controlling the topological charge (Fig. 6). The number and direction of the twisted intensity lobes are determined by the number and sign of the topological charge. By controlling the equal phase, the twisted lobe direction can be arbitrarily controlled (Fig. 9). More complex chiral structured beams with three-ring and four-ring structures are constructed, and this validates the effectiveness of our proposed approach. Additionally, the equal phase gradient is employed to control dynamically the rotation of the light fields (Video 1). The advantage of this rotation also makes this chiral beam beneficial for twisting transiently molten matter, machining complex chiral nanostructures, and sorting multiple particles.ConclusionsIn summary, we have developed an effective method to generate TCSBs by multiple ASPs. The properties of the twisting lobes, including the twisting directions, lobe orientations, and lobe number can be freely manipulated by controlling the topological charge sign, magnitude, and equiphase, respectively. Our findings offer a novel promising technology to manufacture chiral microstructures. Moreover, the flexible TCSBs also provide an innovative method for optical manipulation and optical communications.
Acta Optica Sinica
- Publication Date: Apr. 25, 2024
- Vol. 44, Issue 8, 0826002 (2024)
Measurement Method of Aspherical Synchronous Annular Subaperture Interferometry
Yuan Su, Ailing Tian, Hongjun Wang, Bingcai Liu, Xueliang Zhu, Siqi Wang, Kexin Ren, and Yuwen Zhang
ObjectiveAspherical optical elements are widely employed in optical systems due to their large degree of design freedom, and the surface shape accuracy of the elements directly affects the performance of the optical system, but the normal aberration properties result in difficult detection of aspherical surfaces. Annular subaperture stitching interferometry is non-null interferometry for detecting the surface shape of aspherical surfaces, does not need to completely compensate for the normal aberration of aspherical surfaces, but relies on high-precision mechanical motion mechanisms and complex positional error algorithms. Therefore, we propose a method for synchronous annular subaperture interferometry (SASI) to synchronously obtain the interference pattern of two subapertures. Meanwhile, SASI does not need a complex motion mechanism and can increase the dynamic direct detection range of aspherical surfaces by the interferometer to some extent. Furthermore, it can effectively improve the detection speed and reduce the influence of motion error on measurement accuracy.MethodsWe adopt the theoretical analysis and the combination of simulations and experiments to carry out this research. Firstly, according to the Nyquist sampling theorem, the theory of the SASI method is analyzed to determine the focal distance principle, and the reference unified model is built by coordinate change and Zemax assisted modeling to realize the surface shape reconstruction. Secondly, the measurement of SASI is simulated and verified, the Zemax is adopted to assist in building the measurement system model, and the interference images obtained by the SASI method and interferometer direct detection are simulated respectively. Additionally, the fringe density of the two interference images is compared, and the aspherical surface shape is reconstructed in the simulated measurement experiments to verify the correctness of the SASI method. Finally, we actually measure the aspherical surface and obtain the interference pattern, and the aspherical surface is placed in the best position and measured directly with the interferometer. Furthermore, the interference fringes measured by SASI method are compared with the result of Luphoshcan method, which can further verify the correctness and validity of the SASI.Results and DiscussionsOur SASI method can accomplish the detection of aspherical surfaces without a complex motion mechanism, and it can also increase the dynamic range of the interferometer for direct detection of aspherical surfaces to a certain extent. Firstly, the SASI theory is analyzed, and a unified model is proposed for reconstructing the surface shape. Secondly, simulation experiments are carried out to detect the surface shape of an asphere with a vertex radius of curvature of 250 mm and an aperture of 80 mm. The simulation results show that the density of interferometric fringe patterns obtained by the SASI is reduced compared with that obtained by the interferometer (Fig. 4). Meanwhile, by adopting the proposed baseline unified model, the reconstructed surface shape results with the original surface shape of the residual PV of 0.0282λ, RMS of 0.0045λ are shown in Fig. 6, which initially verifies the validity of the proposed method. Secondly, the aspherical surface with vertex curvature radius of 317 mm and aperture of 90 mm is measured experimentally, and the density of the SASI method is still reduced compared with that of the interferometer directly detecting the same asphere (Fig. 8). Additionally, in Fig. 9 and Table 3, comparison of the reconstructed surface shape with the Luphoshcan result shows that PV is 0.0362λ and RMS is 0.0091λ of absolute surface error, and the residual deviation of the surface shape is 0.0926λ (PV) and 0.0098λ (RMS), which further verifies the correctness of the proposed SASI method.ConclusionsThe proposed SASI method can effectively realize the surface shape detection of aspherical surfaces. On the one hand, the method does not need to move the interferometer or the element to be measured, which utilizes a bifocal lens to form two measurement wavefronts to match different subaperture of the aspherical surface, and then realizes the synchronized annular band subaperture interferometry of the aspherical surface. Finally, this simplifies the measurement device, shortens the measurement time, and reduces the effect of the motion error on the measurement accuracy. On the other hand, this method increases the dynamic range of the interferometer for direct detection of aspherical surfaces to a certain extent. Combined with the aspherical surface example of the SASI method for simulation and measurement experiments to verify the SASI method, the density of interferometric fringe pattern under the detection of the SASI method is significantly reduced. Additionally, the results of the surface reconstruction are consistent with the actual surface results, which further verifies the correctness and validity of the proposed SASI method. ObjectiveAspherical optical elements are widely employed in optical systems due to their large degree of design freedom, and the surface shape accuracy of the elements directly affects the performance of the optical system, but the normal aberration properties result in difficult detection of aspherical surfaces. Annular subaperture stitching interferometry is non-null interferometry for detecting the surface shape of aspherical surfaces, does not need to completely compensate for the normal aberration of aspherical surfaces, but relies on high-precision mechanical motion mechanisms and complex positional error algorithms. Therefore, we propose a method for synchronous annular subaperture interferometry (SASI) to synchronously obtain the interference pattern of two subapertures. Meanwhile, SASI does not need a complex motion mechanism and can increase the dynamic direct detection range of aspherical surfaces by the interferometer to some extent. Furthermore, it can effectively improve the detection speed and reduce the influence of motion error on measurement accuracy.MethodsWe adopt the theoretical analysis and the combination of simulations and experiments to carry out this research. Firstly, according to the Nyquist sampling theorem, the theory of the SASI method is analyzed to determine the focal distance principle, and the reference unified model is built by coordinate change and Zemax assisted modeling to realize the surface shape reconstruction. Secondly, the measurement of SASI is simulated and verified, the Zemax is adopted to assist in building the measurement system model, and the interference images obtained by the SASI method and interferometer direct detection are simulated respectively. Additionally, the fringe density of the two interference images is compared, and the aspherical surface shape is reconstructed in the simulated measurement experiments to verify the correctness of the SASI method. Finally, we actually measure the aspherical surface and obtain the interference pattern, and the aspherical surface is placed in the best position and measured directly with the interferometer. Furthermore, the interference fringes measured by SASI method are compared with the result of Luphoshcan method, which can further verify the correctness and validity of the SASI.Results and DiscussionsOur SASI method can accomplish the detection of aspherical surfaces without a complex motion mechanism, and it can also increase the dynamic range of the interferometer for direct detection of aspherical surfaces to a certain extent. Firstly, the SASI theory is analyzed, and a unified model is proposed for reconstructing the surface shape. Secondly, simulation experiments are carried out to detect the surface shape of an asphere with a vertex radius of curvature of 250 mm and an aperture of 80 mm. The simulation results show that the density of interferometric fringe patterns obtained by the SASI is reduced compared with that obtained by the interferometer (Fig. 4). Meanwhile, by adopting the proposed baseline unified model, the reconstructed surface shape results with the original surface shape of the residual PV of 0.0282λ, RMS of 0.0045λ are shown in Fig. 6, which initially verifies the validity of the proposed method. Secondly, the aspherical surface with vertex curvature radius of 317 mm and aperture of 90 mm is measured experimentally, and the density of the SASI method is still reduced compared with that of the interferometer directly detecting the same asphere (Fig. 8). Additionally, in Fig. 9 and Table 3, comparison of the reconstructed surface shape with the Luphoshcan result shows that PV is 0.0362λ and RMS is 0.0091λ of absolute surface error, and the residual deviation of the surface shape is 0.0926λ (PV) and 0.0098λ (RMS), which further verifies the correctness of the proposed SASI method.ConclusionsThe proposed SASI method can effectively realize the surface shape detection of aspherical surfaces. On the one hand, the method does not need to move the interferometer or the element to be measured, which utilizes a bifocal lens to form two measurement wavefronts to match different subaperture of the aspherical surface, and then realizes the synchronized annular band subaperture interferometry of the aspherical surface. Finally, this simplifies the measurement device, shortens the measurement time, and reduces the effect of the motion error on the measurement accuracy. On the other hand, this method increases the dynamic range of the interferometer for direct detection of aspherical surfaces to a certain extent. Combined with the aspherical surface example of the SASI method for simulation and measurement experiments to verify the SASI method, the density of interferometric fringe pattern under the detection of the SASI method is significantly reduced. Additionally, the results of the surface reconstruction are consistent with the actual surface results, which further verifies the correctness and validity of the proposed SASI method.
Acta Optica Sinica
- Publication Date: Apr. 25, 2024
- Vol. 44, Issue 8, 0826001 (2024)
Beam Shaping Algorithm Based on High-Order Quasi-Discrete Hankel Transform
Hui Yu, Xinhui Ding, Dawei Li, Qiong Zhou, Lü Fengnian, and Xingqiang Lu
ObjectiveIn the realm of beam shaping, diffractive optical elements (DOEs) can manipulate the laser intensity distribution by altering the laser phase through microstructures. Beam shaping algorithms play a significant role in the design of diffractive optical elements. Specifically, the most representative is the Gerchberg-Saxton (GS) algorithm proposed by R.W. Gerchberg and W.O. Saxton. It involves an iterative process of performing a Fourier transform between the input plane and output plane, while simultaneously imposing known constraints on both planes. To enhance the convergence effect of the algorithm, an input-output algorithm and the phase-mixture algorithm have been developed based on the GS algorithm. In recent years, there have been advancements in mixed-region amplitude freedom algorithms, particularly those demonstrating superior convergence effects in the signal region, as well as offset mixed-region amplitude-freedom algorithms. Global optimization algorithms, such as the feedback GSGA (Gerchberg-Saxton genetic algorithm) and the last place elimination GSGA, have also gained attraction. These algorithms are derived from the GS algorithm. However, the phase complexity of these designs is high, presenting significant challenges to the physical processing of DOEs. Furthermore, as the number of limiting conditions increases, the computational time required also escalates, especially for the feedback GSGA and last place elimination GSGA.MethodsTo optimize time efficiency and reduce phase complexity, we discover that in conventional laser applications, the use of the Hankel transform is more effective than the Fourier transform in numerical calculations when both the incident beam and target beam exhibit circular symmetry. We introduce a beam shaping algorithm, the pQDHT-GS algorithm, for a circularly symmetric beam system based on the GS algorithm. The implementation process is based on the characteristic that the Hankel transform is solely related to the radial coordinate. This is achieved by iteratively alternating between the input plane and output plane to perform the Hankel transform. We employ a quadratic surface type phase as the initial phase, select a Gaussian beam with a full width at half maximum of 2 mm as the input light source, set an iteration time of 500, and use sample numbers of 512×512 (where the sample number in the pQDHT-GS algorithm is 1×256). We then apply this algorithm and the traditional GS algorithm to shape the incident beam into a circular Airy (CA) beam, Bessel beam, and Laguerre-Gaussian (LG) beam respectively. We compare the root mean square error and energy utilization efficiency of these two algorithms. Subsequently, we set the LG beam as the target beam, adjust the iteration times to 500 and 1000, and sample numbers to 512×512 and 1024×1024 respectively, to further analyze the computational performance of both algorithms. Furthermore, we evaluate the shaping performance of the pQDHT-GS algorithm by using the CA beam as the target beam in our experimental system.Results and DiscussionsIn terms of the phase distribution of DOEs, the phase calculated by the GS algorithm exhibits rotational symmetry, and it contains some high-frequency components. In contrast, the phase of DOEs computed by the pQDHT-GS algorithm displays circular symmetry, simplifying the DOEs structure and reducing processing complexity. When examining the intensity distribution at the focal plane (output plane), both algorithms exhibit superior intensity profiles. However, compared to the results obtained from the GS algorithm, the shaping beam output calculated by the pQDHT-GS algorithm is smoother (Fig. 3). In identical conditions, the pQDHT-GS algorithm achieves rapid convergence within fewer iterations and saves computational time (approximately 100 times) (Table 2). Furthermore, experimental results indicate that the shaping beam intensity distribution aligns closely with the target beam intensity distribution, with consistent light intensity curve trends. The shaping beam exhibits noticeable burrs, with a root mean square error of 0.545 and an energy utilization efficiency of 78.07%. After being filtered, these burrs are substantially reduced, and the light intensity curve distribution becomes smoother, exhibiting a root mean square error of 0.491 and an energy utilization efficiency of 78.14% (Fig. 6).ConclusionsIn this study, we introduce a beam-shaping algorithm based on the pQDHT proposed for the circularly symmetric beam system. This approach achieves the circular symmetry of the DOEs structure by substituting the Fourier transform in the conventional GS algorithm with the Hankel transform. We select the CA beam, the Bessel beam, and the LG beam as target beams. A numerical simulation method is employed to juxtapose and assess the performance of both the GS algorithm and the pQDHT-GS algorithm in terms of shaping outcomes. Our findings indicate that, in comparison to the GS algorithm, the pQDHT-GS algorithm converges rapidly with fewer iterations. Moreover, it refines the intensity of the output-shaped beam, ensuring that the DOEs phase exhibit a circular symmetry distribution and thereby simplifying processing. Given that the pQDHT-GS algorithm requires significantly fewer sampling points than the GS algorithm, it significantly reduces matrix operation time, leading to nearly two orders of magnitude reduced computational time. Conclusive experiments on the CA beam validate the efficacy of this method. In conclusion, the pQDHT-GS algorithm exhibits rapid and precise capabilities in circular symmetric beam shaping, holding significant implications for the design and processing of DOEs. Its potential applications extend to various areas of beam shaping, including the choice of initial phase values through the integration of global search algorithms, deep learning, neural networks, and other intelligent algorithms. Furthermore, its utility is evident in designing phase plates within large aperture lasers. Future research will further explore this area. ObjectiveIn the realm of beam shaping, diffractive optical elements (DOEs) can manipulate the laser intensity distribution by altering the laser phase through microstructures. Beam shaping algorithms play a significant role in the design of diffractive optical elements. Specifically, the most representative is the Gerchberg-Saxton (GS) algorithm proposed by R.W. Gerchberg and W.O. Saxton. It involves an iterative process of performing a Fourier transform between the input plane and output plane, while simultaneously imposing known constraints on both planes. To enhance the convergence effect of the algorithm, an input-output algorithm and the phase-mixture algorithm have been developed based on the GS algorithm. In recent years, there have been advancements in mixed-region amplitude freedom algorithms, particularly those demonstrating superior convergence effects in the signal region, as well as offset mixed-region amplitude-freedom algorithms. Global optimization algorithms, such as the feedback GSGA (Gerchberg-Saxton genetic algorithm) and the last place elimination GSGA, have also gained attraction. These algorithms are derived from the GS algorithm. However, the phase complexity of these designs is high, presenting significant challenges to the physical processing of DOEs. Furthermore, as the number of limiting conditions increases, the computational time required also escalates, especially for the feedback GSGA and last place elimination GSGA.MethodsTo optimize time efficiency and reduce phase complexity, we discover that in conventional laser applications, the use of the Hankel transform is more effective than the Fourier transform in numerical calculations when both the incident beam and target beam exhibit circular symmetry. We introduce a beam shaping algorithm, the pQDHT-GS algorithm, for a circularly symmetric beam system based on the GS algorithm. The implementation process is based on the characteristic that the Hankel transform is solely related to the radial coordinate. This is achieved by iteratively alternating between the input plane and output plane to perform the Hankel transform. We employ a quadratic surface type phase as the initial phase, select a Gaussian beam with a full width at half maximum of 2 mm as the input light source, set an iteration time of 500, and use sample numbers of 512×512 (where the sample number in the pQDHT-GS algorithm is 1×256). We then apply this algorithm and the traditional GS algorithm to shape the incident beam into a circular Airy (CA) beam, Bessel beam, and Laguerre-Gaussian (LG) beam respectively. We compare the root mean square error and energy utilization efficiency of these two algorithms. Subsequently, we set the LG beam as the target beam, adjust the iteration times to 500 and 1000, and sample numbers to 512×512 and 1024×1024 respectively, to further analyze the computational performance of both algorithms. Furthermore, we evaluate the shaping performance of the pQDHT-GS algorithm by using the CA beam as the target beam in our experimental system.Results and DiscussionsIn terms of the phase distribution of DOEs, the phase calculated by the GS algorithm exhibits rotational symmetry, and it contains some high-frequency components. In contrast, the phase of DOEs computed by the pQDHT-GS algorithm displays circular symmetry, simplifying the DOEs structure and reducing processing complexity. When examining the intensity distribution at the focal plane (output plane), both algorithms exhibit superior intensity profiles. However, compared to the results obtained from the GS algorithm, the shaping beam output calculated by the pQDHT-GS algorithm is smoother (Fig. 3). In identical conditions, the pQDHT-GS algorithm achieves rapid convergence within fewer iterations and saves computational time (approximately 100 times) (Table 2). Furthermore, experimental results indicate that the shaping beam intensity distribution aligns closely with the target beam intensity distribution, with consistent light intensity curve trends. The shaping beam exhibits noticeable burrs, with a root mean square error of 0.545 and an energy utilization efficiency of 78.07%. After being filtered, these burrs are substantially reduced, and the light intensity curve distribution becomes smoother, exhibiting a root mean square error of 0.491 and an energy utilization efficiency of 78.14% (Fig. 6).ConclusionsIn this study, we introduce a beam-shaping algorithm based on the pQDHT proposed for the circularly symmetric beam system. This approach achieves the circular symmetry of the DOEs structure by substituting the Fourier transform in the conventional GS algorithm with the Hankel transform. We select the CA beam, the Bessel beam, and the LG beam as target beams. A numerical simulation method is employed to juxtapose and assess the performance of both the GS algorithm and the pQDHT-GS algorithm in terms of shaping outcomes. Our findings indicate that, in comparison to the GS algorithm, the pQDHT-GS algorithm converges rapidly with fewer iterations. Moreover, it refines the intensity of the output-shaped beam, ensuring that the DOEs phase exhibit a circular symmetry distribution and thereby simplifying processing. Given that the pQDHT-GS algorithm requires significantly fewer sampling points than the GS algorithm, it significantly reduces matrix operation time, leading to nearly two orders of magnitude reduced computational time. Conclusive experiments on the CA beam validate the efficacy of this method. In conclusion, the pQDHT-GS algorithm exhibits rapid and precise capabilities in circular symmetric beam shaping, holding significant implications for the design and processing of DOEs. Its potential applications extend to various areas of beam shaping, including the choice of initial phase values through the integration of global search algorithms, deep learning, neural networks, and other intelligent algorithms. Furthermore, its utility is evident in designing phase plates within large aperture lasers. Future research will further explore this area.
Acta Optica Sinica
- Publication Date: Apr. 10, 2024
- Vol. 44, Issue 7, 0726001 (2024)
Ring Nesting Phenomenon Analysis in Common-Path Tolansky Interference
Yefeng Ouyang, Zijie Xu, Baowu Zhang, Ling Zhu, Zhenyuan Fang, Xianhuan Luo, and Yi Sun
ObjectiveThe thickness measurement method based on dual-channel light directly radiating on the two end faces of the thickness sample has gradually become an international hotspot. This is because the measurement results are only related to the end face characteristics of the thickness sample, the measurement optical path and environmental parameters, and the influence of the auxiliary agent, radiation, with the internal optical path of the thickness sample in the traditional method excluded. Among these, Tolansky interferometry features both angle and thickness measurements, which provides a new possibility for research into high-precision thickness measurement methods for double-end faces. Additionally, this means that the series radius of the interference concentric ring is adopted to calculate the measured thickness. In the thickness measurement using the common-path Tolansky interference scheme, the image of the interference concentric ring has an obvious ring nesting phenomenon, and even misaligned nesting occurs. This phenomenon will affect the image recognition accuracy of the radius and interfere with the subsequent thickness measurement results. Therefore, it is important to investigate technical schemes to eliminate or suppress this phenomenon in thickness measurements using the common-path Tolansky interference scheme.MethodsBased on the dual-beam interference principle of the point light source, the Tolansky interference image is displayed by MATLAB virtual simulations. Then the experimental pictures of whether the interference concentric rings are different or not are displayed via the common-path Tolansky interferometer and the dual-arm optical path structure experimental system similar to the Michelson interferometer. That means there is an interference loop nesting in the former, and no interference loop nesting in the latter. After a detailed study, it is found that the biggest difference between the two systems is the existence of a multi-faceted structure of the common-path Tolansky. Additionally, the laser will reflect multiple times between these faces, while the dual-arm optical path structure similar to the Michelson interferometer does not have this multiple reflection phenomenon.Given this, based on the geometrical optics principle, we employ the multiple reflection method to carry out theoretical analysis and formula derivation and obtain the expression of optical path difference and interference intensity different from double beam interference. Meanwhile, the correlation relationship between the beam intensity after multiple reflections and the incident light intensity of the interference spectrometer, the transmittance Kt, the reflectivity Kr, and the reflectivity K of the mirror is acquired. Thus, a new simulation model of interference concentric rings is obtained. On this basis, the interference concentric ring is simulated by MATLAB. The simulation results show that the interference concentric rings obtained based on the multiple reflection theory are in good agreement with the experimental images in terms of the structure and intensity profile, which also confirms the correctness of the theory. Given the strong correlation between the beam intensity after multiple reflections and the parameters of incident light intensity, transmittance Kt, reflectivity Kr, and reflectivity K, the interference concentric ring images with different collocations of these parameters are further virtually studied. The results show that by adjusting the transmittance and reflectivity of the interferometric spectroscope and the reflectivity of the interferometric mirror, the nesting phenomenon can be suppressed.Based on the theoretical analysis and virtual simulation, interference spectrometers with different spectral ratios and interference mirrors with different reflectivities are replaced in the common-path Tolansky interference experimental system to realize different collocations among these parameters. The experimental results are in good agreement with the virtual simulation results, which verify the proposed method for suppressing the nesting phenomenon.Results and DiscussionsWe propose an analysis method of multiple reflections among multiple planes, and obtain the expression of optical path difference and interference intensity different from double beam interference. Meanwhile, the correlation between the beam intensity after multiple reflections and the incident light intensity of the interference spectrometer, transmittance Kt, reflectivity Kr, and reflectivity K of the reflector is obtained. Thus, a new simulation model of an interference concentric ring is obtained, with the theory of common-path Tolansky interference analysis perfected.Based on a new theoretical basis, a method to suppress the nesting phenomenon of the interference ring is proposed to suppress the phenomenon by reasonably adjusting the transmittance, reflectance of the interference spectrometer, and reflectivity of the interference mirror. Finally, a guarantee is provided for accurate extraction of the series ring radius by the common-path Tolansky interference thickness measurement technology.ConclusionsThe nesting or misplaced nesting of the common-path Tolansky interference ring causes bifurcation and ambiguity in each interference ring, which not only changes the interference level at the center of the circle, but also affects the recognition accuracy of each ring radius. As a result, there will be errors in the measured thickness inversion via the ring radius, which is unfavorable for accurate thickness measurement using the common-path Tolansky interference. The MATLAB virtual simulation and experimental results show that the nesting phenomenon comes from multiple reflections among multiple surfaces, and the intensity of the reflected light beam can be quickly weakened by adjusting the transmittance and reflectance of the interference spectroscope and the reflectivity of the interference mirror reasonably. Finally, the interference result is approximately double beam interference, and the nesting phenomenon is effectively restrained. This provides a guarantee for accurate radius extraction of the common-path Tolansky interference concentric ring series and accurate thickness measurements. ObjectiveThe thickness measurement method based on dual-channel light directly radiating on the two end faces of the thickness sample has gradually become an international hotspot. This is because the measurement results are only related to the end face characteristics of the thickness sample, the measurement optical path and environmental parameters, and the influence of the auxiliary agent, radiation, with the internal optical path of the thickness sample in the traditional method excluded. Among these, Tolansky interferometry features both angle and thickness measurements, which provides a new possibility for research into high-precision thickness measurement methods for double-end faces. Additionally, this means that the series radius of the interference concentric ring is adopted to calculate the measured thickness. In the thickness measurement using the common-path Tolansky interference scheme, the image of the interference concentric ring has an obvious ring nesting phenomenon, and even misaligned nesting occurs. This phenomenon will affect the image recognition accuracy of the radius and interfere with the subsequent thickness measurement results. Therefore, it is important to investigate technical schemes to eliminate or suppress this phenomenon in thickness measurements using the common-path Tolansky interference scheme.MethodsBased on the dual-beam interference principle of the point light source, the Tolansky interference image is displayed by MATLAB virtual simulations. Then the experimental pictures of whether the interference concentric rings are different or not are displayed via the common-path Tolansky interferometer and the dual-arm optical path structure experimental system similar to the Michelson interferometer. That means there is an interference loop nesting in the former, and no interference loop nesting in the latter. After a detailed study, it is found that the biggest difference between the two systems is the existence of a multi-faceted structure of the common-path Tolansky. Additionally, the laser will reflect multiple times between these faces, while the dual-arm optical path structure similar to the Michelson interferometer does not have this multiple reflection phenomenon.Given this, based on the geometrical optics principle, we employ the multiple reflection method to carry out theoretical analysis and formula derivation and obtain the expression of optical path difference and interference intensity different from double beam interference. Meanwhile, the correlation relationship between the beam intensity after multiple reflections and the incident light intensity of the interference spectrometer, the transmittance Kt, the reflectivity Kr, and the reflectivity K of the mirror is acquired. Thus, a new simulation model of interference concentric rings is obtained. On this basis, the interference concentric ring is simulated by MATLAB. The simulation results show that the interference concentric rings obtained based on the multiple reflection theory are in good agreement with the experimental images in terms of the structure and intensity profile, which also confirms the correctness of the theory. Given the strong correlation between the beam intensity after multiple reflections and the parameters of incident light intensity, transmittance Kt, reflectivity Kr, and reflectivity K, the interference concentric ring images with different collocations of these parameters are further virtually studied. The results show that by adjusting the transmittance and reflectivity of the interferometric spectroscope and the reflectivity of the interferometric mirror, the nesting phenomenon can be suppressed.Based on the theoretical analysis and virtual simulation, interference spectrometers with different spectral ratios and interference mirrors with different reflectivities are replaced in the common-path Tolansky interference experimental system to realize different collocations among these parameters. The experimental results are in good agreement with the virtual simulation results, which verify the proposed method for suppressing the nesting phenomenon.Results and DiscussionsWe propose an analysis method of multiple reflections among multiple planes, and obtain the expression of optical path difference and interference intensity different from double beam interference. Meanwhile, the correlation between the beam intensity after multiple reflections and the incident light intensity of the interference spectrometer, transmittance Kt, reflectivity Kr, and reflectivity K of the reflector is obtained. Thus, a new simulation model of an interference concentric ring is obtained, with the theory of common-path Tolansky interference analysis perfected.Based on a new theoretical basis, a method to suppress the nesting phenomenon of the interference ring is proposed to suppress the phenomenon by reasonably adjusting the transmittance, reflectance of the interference spectrometer, and reflectivity of the interference mirror. Finally, a guarantee is provided for accurate extraction of the series ring radius by the common-path Tolansky interference thickness measurement technology.ConclusionsThe nesting or misplaced nesting of the common-path Tolansky interference ring causes bifurcation and ambiguity in each interference ring, which not only changes the interference level at the center of the circle, but also affects the recognition accuracy of each ring radius. As a result, there will be errors in the measured thickness inversion via the ring radius, which is unfavorable for accurate thickness measurement using the common-path Tolansky interference. The MATLAB virtual simulation and experimental results show that the nesting phenomenon comes from multiple reflections among multiple surfaces, and the intensity of the reflected light beam can be quickly weakened by adjusting the transmittance and reflectance of the interference spectroscope and the reflectivity of the interference mirror reasonably. Finally, the interference result is approximately double beam interference, and the nesting phenomenon is effectively restrained. This provides a guarantee for accurate radius extraction of the common-path Tolansky interference concentric ring series and accurate thickness measurements.
Acta Optica Sinica
- Publication Date: Mar. 10, 2024
- Vol. 44, Issue 5, 0526001 (2024)
Reversible Control System for Continuous Variable Light Field Polarization State
Jinliang Zhang, Liang Wu, Jieli Yan, Zhihui Yan, and Xiaojun Jia
ObjectiveQuantum teleportation can transfer arbitrary unknown quantum states between two distant users with the help of quantum entanglement, thereby facilitating the construction of quantum networks, implementation of quantum logic operations, and advancement in quantum computing. Continuous variable (CV) polarized light field is an important quantum resource, with advantages such as high efficiency in preparation, transmission, and measurement. It is suitable for long-distance quantum state transmission and can directly interact with atomic nodes. Therefore, it is desired to implement a quantum teleportation network of the CV polarized light field. However, the precise control and transformation of the polarization state of the light field are key to the quantum teleportation of an arbitrary CV polarization state. Quantum teleportation of the CV polarization state requires reversible control, enabling transformation from any arbitrary polarization state to a predetermined state for quantum teleportation, followed by restoration to the initial polarization state. Nevertheless, existing studies on polarization control primarily focus on unidirectional control, which fails to meet these requirements. This scheme intends to realize reversible precise regulation of any polarization state of the light field and achieve effective conversion between the initial polarization state and the predetermined polarization state.MethodsThe amplitude-division polarization measurement method and the wave plate polarization controller are employed in this paper to achieve polarization measurement and reversible control. The field-programmable gate array (FPGA) and host computer are utilized for control optimization and information display. First, a combination of half wave plate (HWP) and quarter wave plate (QWP) is used to generate incident field polarization states uniformly distributed on the Poincare sphere. Second, an amplitude-division polarization measurement system consisting of the partial polarization beam splitter, polarization beam splitter, HWP, and QWP is employed to spatially modulate the incident polarization state of the light field. Full Stokes parameters are measured in real time through inversion, which are then converted into azimuth and elliptic frequency. Additionally, based on the obtained polarization measurement information, a wave plate polarization controller comprising of HWP and QWP is used to convert arbitrary polarizations into preset polarizations and restore the initial polarizations, thereby enabling reversible control over the polarization state of the light field. Finally, communication between the systems for both polarization measurement and control is realized by combining FPGA with the host computer, while an optimization algorithm designed specifically for controlling errors caused by optical systems enhances control accuracy.Results and DiscussionsThe reversible control system for the polarization state of the light field exhibits precise measurement and effective manipulation of polarization. The azimuth is measured by rotating HWP to generate linearly polarized light. The average error between the measured result and the theoretical value is 0.543°. The ellipticity is measured by rotating the QWP to produce different degrees of ellipticity polarization. The average error between the measured results and the theoretical value is 0.432°. The aforementioned results of the polarization azimuth and elliptic ratio measurements demonstrate the precise effectiveness of the polarization measurement system, thereby providing valuable test outcomes for the polarization control component. Through the forward polarization control of the incident polarized light field by QWP 1 and HWP 1, the azimuth of the converted linearly polarized light is close to 90°, and the average error is 0.474°. The forward polarization control successfully achieves precise and efficient conversion from the arbitrary polarization state to the predetermined target polarization state, with the measured value closely approximating the set value. The average error of the azimuth is 0.636°, and the average error of the ellipticity is 0.479° for the inverse polarization control of the incident polarized state by HWP 2 and QWP 2. The reverse polarization control successfully achieves accurate and efficient conversion from the preset polarization state to the initial incident polarization state, resulting in a restored polarization state that closely approximates the initial polarization state.ConclusionsThe measurement and reversible control of the polarization state of the optical field are realized by using the amplitude split polarization measurement method and the wave plate polarization control method. Algorithm optimization and semi-open-loop structure design have been employed to achieve an average measurement error of less than 0.543° for any polarization state. Furthermore, the average preset conversion error is less than 0.474° and the average reduced conversion error is less than 0.636° for any polarization control conversion. The system can realize the effective conversion between the initial and the preset polarization states, which provides key technical support for the efficient quantum teleportation of the CV polarization state. Using an optical fiber system and free space is the main way to realize the long-distance transmission of quantum states. A quantum key distribution of 200 km can be achieved by maintaining a polarization offset in the optical fiber. Free space is not sensitive to polarization, so the polarization state can be easily and directly realized for long-distance quantum communication. This scheme can realize the efficient conversion between the initial and preset polarization state of the light field, so it is of great research significance for the long-distance state transmission in free space or long-distance optical fiber quantum state transmission combined with the bias-preserving controller. ObjectiveQuantum teleportation can transfer arbitrary unknown quantum states between two distant users with the help of quantum entanglement, thereby facilitating the construction of quantum networks, implementation of quantum logic operations, and advancement in quantum computing. Continuous variable (CV) polarized light field is an important quantum resource, with advantages such as high efficiency in preparation, transmission, and measurement. It is suitable for long-distance quantum state transmission and can directly interact with atomic nodes. Therefore, it is desired to implement a quantum teleportation network of the CV polarized light field. However, the precise control and transformation of the polarization state of the light field are key to the quantum teleportation of an arbitrary CV polarization state. Quantum teleportation of the CV polarization state requires reversible control, enabling transformation from any arbitrary polarization state to a predetermined state for quantum teleportation, followed by restoration to the initial polarization state. Nevertheless, existing studies on polarization control primarily focus on unidirectional control, which fails to meet these requirements. This scheme intends to realize reversible precise regulation of any polarization state of the light field and achieve effective conversion between the initial polarization state and the predetermined polarization state.MethodsThe amplitude-division polarization measurement method and the wave plate polarization controller are employed in this paper to achieve polarization measurement and reversible control. The field-programmable gate array (FPGA) and host computer are utilized for control optimization and information display. First, a combination of half wave plate (HWP) and quarter wave plate (QWP) is used to generate incident field polarization states uniformly distributed on the Poincare sphere. Second, an amplitude-division polarization measurement system consisting of the partial polarization beam splitter, polarization beam splitter, HWP, and QWP is employed to spatially modulate the incident polarization state of the light field. Full Stokes parameters are measured in real time through inversion, which are then converted into azimuth and elliptic frequency. Additionally, based on the obtained polarization measurement information, a wave plate polarization controller comprising of HWP and QWP is used to convert arbitrary polarizations into preset polarizations and restore the initial polarizations, thereby enabling reversible control over the polarization state of the light field. Finally, communication between the systems for both polarization measurement and control is realized by combining FPGA with the host computer, while an optimization algorithm designed specifically for controlling errors caused by optical systems enhances control accuracy.Results and DiscussionsThe reversible control system for the polarization state of the light field exhibits precise measurement and effective manipulation of polarization. The azimuth is measured by rotating HWP to generate linearly polarized light. The average error between the measured result and the theoretical value is 0.543°. The ellipticity is measured by rotating the QWP to produce different degrees of ellipticity polarization. The average error between the measured results and the theoretical value is 0.432°. The aforementioned results of the polarization azimuth and elliptic ratio measurements demonstrate the precise effectiveness of the polarization measurement system, thereby providing valuable test outcomes for the polarization control component. Through the forward polarization control of the incident polarized light field by QWP 1 and HWP 1, the azimuth of the converted linearly polarized light is close to 90°, and the average error is 0.474°. The forward polarization control successfully achieves precise and efficient conversion from the arbitrary polarization state to the predetermined target polarization state, with the measured value closely approximating the set value. The average error of the azimuth is 0.636°, and the average error of the ellipticity is 0.479° for the inverse polarization control of the incident polarized state by HWP 2 and QWP 2. The reverse polarization control successfully achieves accurate and efficient conversion from the preset polarization state to the initial incident polarization state, resulting in a restored polarization state that closely approximates the initial polarization state.ConclusionsThe measurement and reversible control of the polarization state of the optical field are realized by using the amplitude split polarization measurement method and the wave plate polarization control method. Algorithm optimization and semi-open-loop structure design have been employed to achieve an average measurement error of less than 0.543° for any polarization state. Furthermore, the average preset conversion error is less than 0.474° and the average reduced conversion error is less than 0.636° for any polarization control conversion. The system can realize the effective conversion between the initial and the preset polarization states, which provides key technical support for the efficient quantum teleportation of the CV polarization state. Using an optical fiber system and free space is the main way to realize the long-distance transmission of quantum states. A quantum key distribution of 200 km can be achieved by maintaining a polarization offset in the optical fiber. Free space is not sensitive to polarization, so the polarization state can be easily and directly realized for long-distance quantum communication. This scheme can realize the efficient conversion between the initial and preset polarization state of the light field, so it is of great research significance for the long-distance state transmission in free space or long-distance optical fiber quantum state transmission combined with the bias-preserving controller.
Acta Optica Sinica
- Publication Date: May. 25, 2024
- Vol. 44, Issue 10, 1026035 (2024)
Propagation Control of Circular Swallowtail Beams in Atmospheric Turbulence
Nana Liu, Peilong Hong, Yuxuan Ren, and Yi Liang
ObjectiveLight absorption and scattering pose great challenges to applications such as atmospheric optical communication and biological optical manipulation. Exploring special beams with minimal influence has been a research hotspot in light field manipulation. Currently, a mainstream method is to shape the beam by wavefront shaping to restore its light field. However, this method is quite complex and requires pre-calibration of the scattering process and restoration via complex algorithms, which increases the difficulty. Therefore, we directly look for a more robust beam that can reduce the light field distortion in complex environments. Meanwhile, we investigate the propagation characteristics of circular swallowtail beams with autofocusing properties in atmospheric turbulence. By analyzing the distortion and intensity fluctuations of the beam in complex environments, we study circular swallowtail beams' propagation in resisting turbulence scattering. Finally, theoretical support is provided for selecting beams that are stable and have high focal intensity and effective propagation in complex environments.MethodsWe utilize the Kolmogorov turbulence theory to model turbulence strength, and employ a modified power spectral density and the multi-phase screen method to simulate turbulence. The turbulence magnitude indicates the level of turbulent disturbance. Initially, we adopt the multi-phase screen method to simulate the propagation of beams in turbulence. Then, we observe the propagation process and perform statistical analysis of instantaneous intensity at the focal point. In experiments, an alcohol lamp and tin foil are leveraged to mimic turbulence conditions. The beam passes above the tin foil during monitoring beam disturbance via a CCD camera. Additionally, we calculate the scintillation index (SI) of the circular swallowtail beam using simulations to observe intensity fluctuations. Finally, we analyze variations in SI and autofocusing factor with parameters of the circular swallowtail beam, providing a quantitative analysis for selecting appropriate parameters.Results and DiscussionsAs turbulence increases, the propagation quality of the swallowtail beam decreases, leading to beam drift and scintillation. By optimizing the beam scale factor and initial transverse position, the autofocusing stability can be improved. Theoretical studies have shown that circular swallowtail beams with strong autofocusing ability perform better in turbulence. This characteristic is attributed to the self-healing ability of swallowtail beams, which allows the beams to quickly restore their intensity distribution to a state close to the original after encountering obstacles. Specifically, based on catastrophe diffraction theory, the self-accelerating propagation properties of swallowtail and Airy beams arise from catastrophe caustics. Catastrophe caustics are regions where light intensity reaches the maximum, and are closely associated with stable“singularities”, also known as caustics. The structural stability of caustics is an inherent feature of catastrophe beams. The results demonstrate that circular swallowtail beams have advantages in resisting turbulence scattering, providing important options for optical communication, optical trapping, and light field manipulation in complex environments.ConclusionsWe analyze the propagation of beams after passing through turbulence, the longitudinal offset at the focal point, and the statistical distribution of the focal intensity position. The results indicate that circular swallowtail beams with strong self-healing abilities exhibit excellent robustness, with relatively small intensity distortion and fluctuations. Furthermore, by studying the SI variation with propagation distance, it is observed that circular swallowtail beams with strong autofocusing abilities are less disturbed, with lighter scintillation and advantages in intensity stability. Finally, by parameter scanning, a series of circular swallowtail beams with the same focal length but different size factors w and control radius parameters r0 are identified. The autofocusing factor and SI are calculated for these beams. It is observed that the SI initially decreases and then increases with w and r0, while the autofocusing factor (K) simultaneously increases and then decreases. The research results not only provide a solid basis for regulating the propagation characteristics of circular swallowtail beams in turbulence but also theoretical support for selecting stable, high focal intensity, thus effectively propagating beams in complex environments. ObjectiveLight absorption and scattering pose great challenges to applications such as atmospheric optical communication and biological optical manipulation. Exploring special beams with minimal influence has been a research hotspot in light field manipulation. Currently, a mainstream method is to shape the beam by wavefront shaping to restore its light field. However, this method is quite complex and requires pre-calibration of the scattering process and restoration via complex algorithms, which increases the difficulty. Therefore, we directly look for a more robust beam that can reduce the light field distortion in complex environments. Meanwhile, we investigate the propagation characteristics of circular swallowtail beams with autofocusing properties in atmospheric turbulence. By analyzing the distortion and intensity fluctuations of the beam in complex environments, we study circular swallowtail beams' propagation in resisting turbulence scattering. Finally, theoretical support is provided for selecting beams that are stable and have high focal intensity and effective propagation in complex environments.MethodsWe utilize the Kolmogorov turbulence theory to model turbulence strength, and employ a modified power spectral density and the multi-phase screen method to simulate turbulence. The turbulence magnitude indicates the level of turbulent disturbance. Initially, we adopt the multi-phase screen method to simulate the propagation of beams in turbulence. Then, we observe the propagation process and perform statistical analysis of instantaneous intensity at the focal point. In experiments, an alcohol lamp and tin foil are leveraged to mimic turbulence conditions. The beam passes above the tin foil during monitoring beam disturbance via a CCD camera. Additionally, we calculate the scintillation index (SI) of the circular swallowtail beam using simulations to observe intensity fluctuations. Finally, we analyze variations in SI and autofocusing factor with parameters of the circular swallowtail beam, providing a quantitative analysis for selecting appropriate parameters.Results and DiscussionsAs turbulence increases, the propagation quality of the swallowtail beam decreases, leading to beam drift and scintillation. By optimizing the beam scale factor and initial transverse position, the autofocusing stability can be improved. Theoretical studies have shown that circular swallowtail beams with strong autofocusing ability perform better in turbulence. This characteristic is attributed to the self-healing ability of swallowtail beams, which allows the beams to quickly restore their intensity distribution to a state close to the original after encountering obstacles. Specifically, based on catastrophe diffraction theory, the self-accelerating propagation properties of swallowtail and Airy beams arise from catastrophe caustics. Catastrophe caustics are regions where light intensity reaches the maximum, and are closely associated with stable“singularities”, also known as caustics. The structural stability of caustics is an inherent feature of catastrophe beams. The results demonstrate that circular swallowtail beams have advantages in resisting turbulence scattering, providing important options for optical communication, optical trapping, and light field manipulation in complex environments.ConclusionsWe analyze the propagation of beams after passing through turbulence, the longitudinal offset at the focal point, and the statistical distribution of the focal intensity position. The results indicate that circular swallowtail beams with strong self-healing abilities exhibit excellent robustness, with relatively small intensity distortion and fluctuations. Furthermore, by studying the SI variation with propagation distance, it is observed that circular swallowtail beams with strong autofocusing abilities are less disturbed, with lighter scintillation and advantages in intensity stability. Finally, by parameter scanning, a series of circular swallowtail beams with the same focal length but different size factors w and control radius parameters r0 are identified. The autofocusing factor and SI are calculated for these beams. It is observed that the SI initially decreases and then increases with w and r0, while the autofocusing factor (K) simultaneously increases and then decreases. The research results not only provide a solid basis for regulating the propagation characteristics of circular swallowtail beams in turbulence but also theoretical support for selecting stable, high focal intensity, thus effectively propagating beams in complex environments.
Acta Optica Sinica
- Publication Date: May. 25, 2024
- Vol. 44, Issue 10, 1026034 (2024)
Generation of Spatial Spherical Focused Spots Based on Reverse Radiation of Dipole Antenna
Junjie Wang, Yanfang Yang, Ying He, Qi Li, and Kunfeng Wang
ObjectiveTo solve the problem that the traditional method can only produce spherical focused spots along the optical axis, we propose a method to generate spherical focused spots in any arbitrary spatial direction in a 4Pi focusing system, which consists of two opposing high numerical aperture objective lenses with the same focus. Spherical focused spots with equivalent three-dimensional spatial resolution have important applications in optical microscopy and metal particle capture. In particular, these spots can trap metal particles at resonant wavelengths, which is because the enhanced axial gradient force and the symmetry of the 4Pi focusing system can offset the axial scattering and absorption forces, making it possible to stabilize the trapping of resonant metal particles and precisely control the motion trajectory of metal particles. Spherical focused spots should be generated at any spatial position to capture resonant metal particles at arbitrary spatial positions. To our knowledge, this is the first time that controllable spherical focused spots can be obtained at an arbitrary spatial position. The proposed method features greater flexibility than traditional approaches, making it highly valuable for applications involving nanoparticle capture at arbitrary spatial locations.MethodsWe present a method to generate spherical focused spots with the specified spatial direction and spacing in a 4Pi focusing system using dipole antenna radiation fields generated by de-focusing. The method involves placing the spatial dipole antenna with predefined lengths and polarization direction at the focal point of the 4Pi focusing system and solving the inverse problem to determine the input field on the objective pupil plane that generates spherical focused spots. By utilizing the field on the pupil plane and selecting the appropriate length of the dipole antenna, spatial spherical focused spots can be obtained.Results and DiscussionsFirstly, the number of generated spatial spherical focused spots is related to odd or even multiple of half wavelength (Fig. 2). When the length of the dipole antenna L is an odd multiple of half wavelength, two same intensity spherical spots symmetrical at the center of the focus are formed in the set spatial direction. When L is an even multiple of half wavelength, three spherical focused spots with the equal size are formed, with one high-intensity spot at the focus and two lower-intensity spots symmetrically arranged. Since the distance between spatial spherical focused spots is calculated to be equal to L, the distance of spatial spherical focused spots can be easily adjusted by changing the parameter L. Meanwhile, arbitrary spatial directions of spherical focused spots are created to demonstrate the flexibility of the proposed method (Figs. 4 and 5). It is observed that the direction of the spherical focused spots is consistent with the polarization direction of the dipole antenna. Finally, we investigate the normalized input field Eiρ,φ required to create the spatial spherical focused spots (Figs. 6 and 7). It is evident that the polarization direction of the input field is determined by the dipole antenna parameter φ0, and the dipole antenna parameter θ0 determines the spatial rotation angle of the input field.ConclusionsWe present a simple and flexible method for generating spherical focused spots of prescribed length and controllable spatial orientation. By focusing the electromagnetic field radiated by a virtual dipole antenna in reverse at the focal point of a 4Pi focusing system, spherical focused spots with specified characteristics can be conveniently obtained. The simulation results show that the number of spherical focused spots is related to odd or even multiple of half a wavelength, and the distance between spherical focused spots is adjustable and only depends on the antenna length L, while the spatial direction of spherical focused spots is controllable and depends on the antenna parameters θ0,φ0. Furthermore, all spherical focused spots generated by the optical antennas are of the same size, with a full width at half maximum (FWHM) of 0.459λ. The generated spatial spherical focused spots have potential applications in precise multi-point trapping of spatial nanoparticles with full degrees of freedom, showing broad prospect in optical micro-manipulation. ObjectiveTo solve the problem that the traditional method can only produce spherical focused spots along the optical axis, we propose a method to generate spherical focused spots in any arbitrary spatial direction in a 4Pi focusing system, which consists of two opposing high numerical aperture objective lenses with the same focus. Spherical focused spots with equivalent three-dimensional spatial resolution have important applications in optical microscopy and metal particle capture. In particular, these spots can trap metal particles at resonant wavelengths, which is because the enhanced axial gradient force and the symmetry of the 4Pi focusing system can offset the axial scattering and absorption forces, making it possible to stabilize the trapping of resonant metal particles and precisely control the motion trajectory of metal particles. Spherical focused spots should be generated at any spatial position to capture resonant metal particles at arbitrary spatial positions. To our knowledge, this is the first time that controllable spherical focused spots can be obtained at an arbitrary spatial position. The proposed method features greater flexibility than traditional approaches, making it highly valuable for applications involving nanoparticle capture at arbitrary spatial locations.MethodsWe present a method to generate spherical focused spots with the specified spatial direction and spacing in a 4Pi focusing system using dipole antenna radiation fields generated by de-focusing. The method involves placing the spatial dipole antenna with predefined lengths and polarization direction at the focal point of the 4Pi focusing system and solving the inverse problem to determine the input field on the objective pupil plane that generates spherical focused spots. By utilizing the field on the pupil plane and selecting the appropriate length of the dipole antenna, spatial spherical focused spots can be obtained.Results and DiscussionsFirstly, the number of generated spatial spherical focused spots is related to odd or even multiple of half wavelength (Fig. 2). When the length of the dipole antenna L is an odd multiple of half wavelength, two same intensity spherical spots symmetrical at the center of the focus are formed in the set spatial direction. When L is an even multiple of half wavelength, three spherical focused spots with the equal size are formed, with one high-intensity spot at the focus and two lower-intensity spots symmetrically arranged. Since the distance between spatial spherical focused spots is calculated to be equal to L, the distance of spatial spherical focused spots can be easily adjusted by changing the parameter L. Meanwhile, arbitrary spatial directions of spherical focused spots are created to demonstrate the flexibility of the proposed method (Figs. 4 and 5). It is observed that the direction of the spherical focused spots is consistent with the polarization direction of the dipole antenna. Finally, we investigate the normalized input field Eiρ,φ required to create the spatial spherical focused spots (Figs. 6 and 7). It is evident that the polarization direction of the input field is determined by the dipole antenna parameter φ0, and the dipole antenna parameter θ0 determines the spatial rotation angle of the input field.ConclusionsWe present a simple and flexible method for generating spherical focused spots of prescribed length and controllable spatial orientation. By focusing the electromagnetic field radiated by a virtual dipole antenna in reverse at the focal point of a 4Pi focusing system, spherical focused spots with specified characteristics can be conveniently obtained. The simulation results show that the number of spherical focused spots is related to odd or even multiple of half a wavelength, and the distance between spherical focused spots is adjustable and only depends on the antenna length L, while the spatial direction of spherical focused spots is controllable and depends on the antenna parameters θ0,φ0. Furthermore, all spherical focused spots generated by the optical antennas are of the same size, with a full width at half maximum (FWHM) of 0.459λ. The generated spatial spherical focused spots have potential applications in precise multi-point trapping of spatial nanoparticles with full degrees of freedom, showing broad prospect in optical micro-manipulation.
Acta Optica Sinica
- Publication Date: May. 25, 2024
- Vol. 44, Issue 10, 1026033 (2024)
Study of High-Efficiency Metasurfaces Based on Optical Thin Films
Ke Jin, Yongqiang Liu, Jun Han, Huina Wang, and Yinghui Wang
ObjectiveThe problem of low optical efficiency commonly exists on metasurfaces, which restricts their application and development. Although the efficiency of metasurfaces designed based on dielectric nanobricks structures is greatly improved compared to metal metasurfaces, the scattering and reflection losses of the unit structure are still relatively large. Metasurfaces are generally composed of high refractive index nanobricks to reduce their thickness and preparation process difficulty. Due to the high refractive index of the equivalent film layer on a high refractive index metasurfaces, it leads to significant interface reflection loss. In terms of improving the efficiency of metasurface devices, current research mainly focuses on improving the diffraction efficiency of metasurfaces and reducing scattering losses. However, there is no research focus on the reflection loss of metasurfaces currently, so it is necessary to study reducing the reflection loss of metasurfaces.MethodsWe propose an efficient design scheme for metasurfaces based on optical thin film theory to solve the problem of interface reflection loss caused by the mismatch between the equivalent refractive index of the metasurfaces and the substrate, as well as the mismatch between the equivalent optical thickness of the metasurfaces and the wavelength. First, we design the metasurface lens. Then, based on the equivalent medium theory, the metasurfaces are equivalent to a layer of dielectric thin films and serve as the outermost layer of the multi-layer antireflection coating system, with the equivalent layer thickness being the height of the metasurfaces. Finally, the optical thin film theory is adopted to design the antireflection coating that matches the substrate and incident medium.Results and DiscussionsWe simulate the near-infrared broadband silicon nanobrick metasurface lens on the quartz substrate and compare it with the metasurfaces designed with optical thin films. The transmittance of the antireflection coating designed by the equivalent medium theory is much higher than that of the equivalent film layer on the metasurfaces, with an average transmittance of 12.4% higher (Fig. 4). Comparison is made between the light field distribution patterns of a metasurface lens without optical thin films and with optical thin films (the antireflection coating structure of optical thin films combined with a metasurface) at different wavelengths (1460, 1530, 1600 nm). It can be seen that the focal spot size and focal length of the two types of structured metasurfaces at the same wavelength are basically the same. In the case of optical thin films, the light intensity at the focal point is significantly higher than that without optical thin films, whereas the focal point position is not affected by the antireflection coating and remains unchanged. This indicates that optical thin films only increase the transmittance of the metasurfaces and have little effect on their focusing performance (Figs. 5-7). The transmittance curves in the 1450-1600 nm wavelength range and the focusing efficiency at 1450, 1490, 1530, 1565, 1600 nm wavelengths are simulated and calculated. From the transmittance curves, it can be seen that in the 1450-1600 nm wavelength range, the transmittance of the metasurface lens designed with optical thin films remains around 94.0%, with the highest peak reaching 95.5%, which is much higher than that of metasurface without optical thin films, with an average increase of more than 10.5% (Fig. 8 and Fig. 9). The results of simulation calculations indicate that our proposed idea of combining optical thin films with metasurfaces is reasonable and has the potential to be applied to the actual production of metasurfaces.ConclusionsWe propose the concept of using optical thin films to improve the efficiency of metasurfaces. The characteristics of metasurface lens are studied in the near-infrared, and based on the properties of additional functional optical thin films on metasurfaces, the influence of the antireflection coating on the transmittance and focusing performance of metasurfaces are studied. Research has shown that combining the structure of optical thin films with the metasurfaces can significantly improve the optical efficiency of metasurfaces without affecting their optical properties. The idea of combining metasurfaces with the proposed optical thin films is expected to solve the problem of low efficiency of metasurfaces, bringing new ideas for the design of metasurface devices. ObjectiveThe problem of low optical efficiency commonly exists on metasurfaces, which restricts their application and development. Although the efficiency of metasurfaces designed based on dielectric nanobricks structures is greatly improved compared to metal metasurfaces, the scattering and reflection losses of the unit structure are still relatively large. Metasurfaces are generally composed of high refractive index nanobricks to reduce their thickness and preparation process difficulty. Due to the high refractive index of the equivalent film layer on a high refractive index metasurfaces, it leads to significant interface reflection loss. In terms of improving the efficiency of metasurface devices, current research mainly focuses on improving the diffraction efficiency of metasurfaces and reducing scattering losses. However, there is no research focus on the reflection loss of metasurfaces currently, so it is necessary to study reducing the reflection loss of metasurfaces.MethodsWe propose an efficient design scheme for metasurfaces based on optical thin film theory to solve the problem of interface reflection loss caused by the mismatch between the equivalent refractive index of the metasurfaces and the substrate, as well as the mismatch between the equivalent optical thickness of the metasurfaces and the wavelength. First, we design the metasurface lens. Then, based on the equivalent medium theory, the metasurfaces are equivalent to a layer of dielectric thin films and serve as the outermost layer of the multi-layer antireflection coating system, with the equivalent layer thickness being the height of the metasurfaces. Finally, the optical thin film theory is adopted to design the antireflection coating that matches the substrate and incident medium.Results and DiscussionsWe simulate the near-infrared broadband silicon nanobrick metasurface lens on the quartz substrate and compare it with the metasurfaces designed with optical thin films. The transmittance of the antireflection coating designed by the equivalent medium theory is much higher than that of the equivalent film layer on the metasurfaces, with an average transmittance of 12.4% higher (Fig. 4). Comparison is made between the light field distribution patterns of a metasurface lens without optical thin films and with optical thin films (the antireflection coating structure of optical thin films combined with a metasurface) at different wavelengths (1460, 1530, 1600 nm). It can be seen that the focal spot size and focal length of the two types of structured metasurfaces at the same wavelength are basically the same. In the case of optical thin films, the light intensity at the focal point is significantly higher than that without optical thin films, whereas the focal point position is not affected by the antireflection coating and remains unchanged. This indicates that optical thin films only increase the transmittance of the metasurfaces and have little effect on their focusing performance (Figs. 5-7). The transmittance curves in the 1450-1600 nm wavelength range and the focusing efficiency at 1450, 1490, 1530, 1565, 1600 nm wavelengths are simulated and calculated. From the transmittance curves, it can be seen that in the 1450-1600 nm wavelength range, the transmittance of the metasurface lens designed with optical thin films remains around 94.0%, with the highest peak reaching 95.5%, which is much higher than that of metasurface without optical thin films, with an average increase of more than 10.5% (Fig. 8 and Fig. 9). The results of simulation calculations indicate that our proposed idea of combining optical thin films with metasurfaces is reasonable and has the potential to be applied to the actual production of metasurfaces.ConclusionsWe propose the concept of using optical thin films to improve the efficiency of metasurfaces. The characteristics of metasurface lens are studied in the near-infrared, and based on the properties of additional functional optical thin films on metasurfaces, the influence of the antireflection coating on the transmittance and focusing performance of metasurfaces are studied. Research has shown that combining the structure of optical thin films with the metasurfaces can significantly improve the optical efficiency of metasurfaces without affecting their optical properties. The idea of combining metasurfaces with the proposed optical thin films is expected to solve the problem of low efficiency of metasurfaces, bringing new ideas for the design of metasurface devices.
Acta Optica Sinica
- Publication Date: May. 10, 2024
- Vol. 44, Issue 10, 1026032 (2024)
1.1-1.5 μm Waveband High Power Random Vortex Beams Based on Acoustically-Induced Fiber Grating
Yang Li, Tianfu Yao, Chenchen Fan, Xiulu Hao, Xiaoya Ma, Jiangming Xu, Qingsong Zhang, Xianglong Zeng, and Pu Zhou
ObjectiveIn recent years, vortex beams carrying orbital angular momentum (OAM) have caught much attention due to their research significance and application prospects. With the applications of vortex beams in sensing, measurement, and high-capacity optical communication, the output bandwidth and wavelength tunability of vortex beams have become a research focus. Breaking through the emission wavelength limitation of rare-earth doped fiber, and the device of broadband mode conversion is the basis for realizing the output of special band/broadband vortex light. Currently, many devices can realize vortex beam output in a fiber laser. However, most devices are designed and manufactured according to the target wavelength. The acoustically-induced fiber grating (AIFG) achieves mode conversion by acousto-optic coupling in passive fibers. When the operating wavelength changes, it only needs to change the frequency of the loaded electric signal, without re-designing and replacing the parameters of the mode conversion device. Theoretically, it has an extremely wide operating bandwidth. Considering the above requirements, the structure of random Raman fiber laser (RRFL) based on distributed Rayleigh backscattering is adopted to realize broadband vortex beams by combining the AIFG.MethodsBy combining the AIFG and RRFL, when the output wavelength is converted by Raman frequency shift, there is no need to redesign and replace the mode conversion device. The transmission spectrum of the LP01 mode is tested in Fig. 1(b), which indicates that there is a high efficiency of mode conversion from 1000 to 1700 nm. The RRFL is built as shown in Fig. 2. An amplified spontaneous emission (ASE) source including two amplification stages is utilized as the pump source which is then coupled into the half-open cavity of RRFL by wavelength division multiplexing (WDM). The half-open cavity is formed by a high-reflective (HR) optical fiber mirror which is attached to the WDM, a piece of gain fiber, and a homemade fiber endcap. The reflectance of the HR mirror is more than 99.5% at 1-2 μm, and anti-reflection coating is conducted on the endcap to evade unwanted end feedback. The gain fiber is the commercial CS980 fiber with a length of 500 m. Once the suitable electrical signal is loaded on the AIFG, the output mode is converted to LP11 mode, and the ring-shaped radially polarized light and vortex beam with topological charge l=±1 output can be realized by precise polarization control.Results and DiscussionsWhen the pump power reaches the Raman threshold, the pump energy begins to transfer to the Raman Stokes. By integrating the output spectrum, the variation curves of the Raman optical power of each order are calculated, as shown in Fig. 3(a). When the pump power reaches 76 W, the output wavelength reaches 1513.7 nm by the six-stage Raman shift, with a power of 23.6 W and a total efficiency of 31.1%. With the cascaded wavelength conversion, the purity and efficiency of high-order Raman light decrease, which is shown in Figs. 3(c) and 3(d). With the increasing output wavelength, the loss of gain fiber rises with the incomplete conversion of each stage, which results in a gradual efficiency decrease. Once there is a π/2 phase difference between the eigenmodes by controlling the polarization controller (PC), the vortex beam can be realized via the superposition of the two modes, and the “Y-shaped” interference fringe can be detected by the self-interference experiment (Fig. 5), which proves that the vortex beam with topological charge l=±1 is generated.ConclusionsWe propose an all-fiber high-power RRFL with vortex beam output in the 1.1-1.5 μm band. Based on the cascaded Raman shift and broadband AIFG, the output of vortex beams with topological charges l=±1 at 1133.9, 1197.6, 1260.5, 1331.8, 1414.5, and 1513.7 nm wavelengths is realized, and the topological charge is verified by self-interference experiments. After the six-stage conversion, the power at 1513.7 nm wavelength is 23.6 W, with an efficiency of 31.1%. The ultra-wide wavelength tuning capability of the AIFG is expected to make it a key device to fill the spectral gap of vortex beams and can provide a reliable light source for the application of special wavelength vortex beams. By replacing the pump source, gain fiber, and related devices, the wavelength coverage of the vortex beam can be further expanded in other wavebands, and the application of vortex light in multi-dimensional optical communication and interaction between light field and matter can be further expanded. ObjectiveIn recent years, vortex beams carrying orbital angular momentum (OAM) have caught much attention due to their research significance and application prospects. With the applications of vortex beams in sensing, measurement, and high-capacity optical communication, the output bandwidth and wavelength tunability of vortex beams have become a research focus. Breaking through the emission wavelength limitation of rare-earth doped fiber, and the device of broadband mode conversion is the basis for realizing the output of special band/broadband vortex light. Currently, many devices can realize vortex beam output in a fiber laser. However, most devices are designed and manufactured according to the target wavelength. The acoustically-induced fiber grating (AIFG) achieves mode conversion by acousto-optic coupling in passive fibers. When the operating wavelength changes, it only needs to change the frequency of the loaded electric signal, without re-designing and replacing the parameters of the mode conversion device. Theoretically, it has an extremely wide operating bandwidth. Considering the above requirements, the structure of random Raman fiber laser (RRFL) based on distributed Rayleigh backscattering is adopted to realize broadband vortex beams by combining the AIFG.MethodsBy combining the AIFG and RRFL, when the output wavelength is converted by Raman frequency shift, there is no need to redesign and replace the mode conversion device. The transmission spectrum of the LP01 mode is tested in Fig. 1(b), which indicates that there is a high efficiency of mode conversion from 1000 to 1700 nm. The RRFL is built as shown in Fig. 2. An amplified spontaneous emission (ASE) source including two amplification stages is utilized as the pump source which is then coupled into the half-open cavity of RRFL by wavelength division multiplexing (WDM). The half-open cavity is formed by a high-reflective (HR) optical fiber mirror which is attached to the WDM, a piece of gain fiber, and a homemade fiber endcap. The reflectance of the HR mirror is more than 99.5% at 1-2 μm, and anti-reflection coating is conducted on the endcap to evade unwanted end feedback. The gain fiber is the commercial CS980 fiber with a length of 500 m. Once the suitable electrical signal is loaded on the AIFG, the output mode is converted to LP11 mode, and the ring-shaped radially polarized light and vortex beam with topological charge l=±1 output can be realized by precise polarization control.Results and DiscussionsWhen the pump power reaches the Raman threshold, the pump energy begins to transfer to the Raman Stokes. By integrating the output spectrum, the variation curves of the Raman optical power of each order are calculated, as shown in Fig. 3(a). When the pump power reaches 76 W, the output wavelength reaches 1513.7 nm by the six-stage Raman shift, with a power of 23.6 W and a total efficiency of 31.1%. With the cascaded wavelength conversion, the purity and efficiency of high-order Raman light decrease, which is shown in Figs. 3(c) and 3(d). With the increasing output wavelength, the loss of gain fiber rises with the incomplete conversion of each stage, which results in a gradual efficiency decrease. Once there is a π/2 phase difference between the eigenmodes by controlling the polarization controller (PC), the vortex beam can be realized via the superposition of the two modes, and the “Y-shaped” interference fringe can be detected by the self-interference experiment (Fig. 5), which proves that the vortex beam with topological charge l=±1 is generated.ConclusionsWe propose an all-fiber high-power RRFL with vortex beam output in the 1.1-1.5 μm band. Based on the cascaded Raman shift and broadband AIFG, the output of vortex beams with topological charges l=±1 at 1133.9, 1197.6, 1260.5, 1331.8, 1414.5, and 1513.7 nm wavelengths is realized, and the topological charge is verified by self-interference experiments. After the six-stage conversion, the power at 1513.7 nm wavelength is 23.6 W, with an efficiency of 31.1%. The ultra-wide wavelength tuning capability of the AIFG is expected to make it a key device to fill the spectral gap of vortex beams and can provide a reliable light source for the application of special wavelength vortex beams. By replacing the pump source, gain fiber, and related devices, the wavelength coverage of the vortex beam can be further expanded in other wavebands, and the application of vortex light in multi-dimensional optical communication and interaction between light field and matter can be further expanded.
Acta Optica Sinica
- Publication Date: May. 25, 2024
- Vol. 44, Issue 10, 1026031 (2024)
Mid-Infrared Polarized Beam Combiner Based on Anomalous Reflective Metasurface
Lulu Yang, Xin Wang, Meng Zhang, Suhui Yang, and Jinying Zhang
ObjectiveHigh-power mid-infrared lasers extensively apply in explosive monitoring, medical diagnosis, environmental monitoring, infrared countermeasures, and industrial control. However, limited by the upper-level electron injection efficiency and the energy level structure, the output power of the mid-infrared laser quantum cascade operating under fundamental transverse mode cannot exceed 3 W. Beam combining technology has been proven to be an effective way to further expand output power and brightness. Taking full advantage of good linear polarization characteristics of semiconductor lasers, polarization beam combining offers simple structure and high efficiency. Moreover, it can be synergistically combined with other beam combining technologies to further enhance output power and laser brightness. Traditional polarization beam combiners are Brewster plate, metal grating polarizer, and birefringent prism. For the Brewster plate, broadband (approximate 100 nm), high transmission coating for P-polarization is required. It is a big challenge to mid-infrared. Due to the presence of metal lines, the transmission of the metal grating polarizer is usually lower than 80%, which results in a low beam combing efficiency. Commonly used birefringent MgF2 prism in mid-infrared has a small separation angle of 1.2°, which makes the optical path arrangement difficult. Metasurfaces offer a high degree of freedom in optical wave amplitude, phase, and polarization state regulations. It has already been applied in polarization beam splitters, which inspires the design of a beam combiner. By anomalous reflection, two light beams with orthogonal polarizations and different incident angles can be reflected in the same direction. We propose a polarization beam combiner based on anomalous reflection metasurface, which shows a high efficiency and broad working spectral band.MethodsThe proposed metasurface consists of periodic supercells. Each supercell contains 10 discrete single cells, which comprise a metal substrate, a dielectric middle layer, and a top rectangular column. By changing the two side lengths of the rectangular column of single cells, desired phase responses can be achieved for two orthogonal polarized incident beams. When ten optimized single cells are arranged spatially, the X-direction linear polarization (X-LP) incident beams experience a positive linear phase response. Meanwhile, the Y-direction linear polarization (Y-LP) incident beam experiences a negative linear phase response. Therefore, both beams are reflected perpendicularly to the metasurface when the incident angles of X-LP and Y-LP beams are 11.54° and -11.54° respectively.Results and DiscussionsAccording to the purpose and methodology of this study, we design a metasurface polarization beam splitter optical path operating in the middle-wave infrared range [Fig. 1(a)] and a three-layer metasurface structure [Fig. 1(b)]. By modeling the individual unit cell of the metasurface [Fig. 1(c)], we calculate the phase and amplitude responses of X-LP and Y-LP incident beams as we vary the length and width of the rectangular antenna column from 0.2 to 1.6 μm [Fig. 2(a)-(b)]. The particle swarm optimization algorithm is employed to determine the dimensions of the rectangular antenna that satisfy our desired phase requirements (Table 1). The phase introduced by the designed single cell aligns well with expectations for both incident polarizations while maintaining consistently high reflectivity levels throughout [Fig. 2(c)]. When the collimated X-LP and Y-LP beams with a central wavelength of 4.0 μm and incident angles of 11.54° and -11.54° reach the metasurface, both beams are reflected anomalously in the normal direction of the metasurface [Fig. 3(a)-(b)]. Reversely, when the collimated X-LP and Y-LP beams incident perpendicularly on the metasurface beam combiner, the X-LP beam is reflected in 11.54° direction and the Y-LP beam is reflected in -11.54° direction [Fig. 3(c)-(d)]. When the incident beam has a divergence angle of 50 mrad, the reflected beam has a divergence angle of 48 mrad [Fig. 3(e)]. To study the anomalous reflection of the metasurface for a light source with broad spectral bandwidth, we scan the incident light central wavelength from 3.9 to 4.1 μm. The resulting combined beam exhibits a divergent angle of 10 mrad while the reflectivity is maintained as high as 95% (Fig. 4). Based on the above theoretical simulation results, the reflected beam propagation properties in the free space are investigated by Zemax’s physical optical propagation (POP) tool. Assuming both X-LP and Y-LP incident beams are fundamental Gaussian beams, the beam quality factor of the reflected X-LP beam is 1.11, and that of the reflected Y-LP beam is 1.12 (Fig. 5). Therefore, when X-LP and Y-LP beams are combined to propagate in the same direction, the beam quality factor of the combined beam is 1.12 [Fig. 6(a)]. The spectrum of the combined beam coincides well with the overlap of the two individual incident laser spectra [Fig. 6(b)]. Consequently, this study demonstrates that a polarization beam combiner based on the anomalous reflective metasurface has not only high combination efficiency but also broad operation bandwidth. It is suitable to be used for the mid-infrared QCL power combining.ConclusionsWe study a polarization beam combiner based on anomalous reflective metasurface, which is utilized to combine two incident beams with orthogonal linear polarizations. The beam combiner consists of periodic supercells with a dimension of 2 μm×20 μm. Each supercell contains 10 single cells of 2 μm×2 μm. The single cell comprises a metal substrate, a dielectric middle layer, and a top rectangular column. When the collimated X-LP and Y-LP beams with a central wavelength of 4.0 μm and incident angles of 11.54° and -11.54° reach the metasurface, both beams are reflected anomalously in the normal direction of the metasurface. The polarization beam combination is realized. Within a broad spectral band of 3.9 to 4.1 μm, high average anomalous reflectivity of 96.6% and 97.7% are obtained for X-LP and Y-LP incident beams, respectively. Based on the near field reflective intensity and phase distribution, the propagation of the combined beam in free space is simulated by the periodic field splicing method and Gaussian beam propagation law. Assuming both X-LP and Y-LP incident beams are fundamental Gaussian beams, the beam quality factor of the combined beam is 1.12. The metasurface beam combiner shows high design flexibility and can be prepared by mature MEMS technology. It has a good potential to solve the problems in mid- and long-infrared power beam combinations. ObjectiveHigh-power mid-infrared lasers extensively apply in explosive monitoring, medical diagnosis, environmental monitoring, infrared countermeasures, and industrial control. However, limited by the upper-level electron injection efficiency and the energy level structure, the output power of the mid-infrared laser quantum cascade operating under fundamental transverse mode cannot exceed 3 W. Beam combining technology has been proven to be an effective way to further expand output power and brightness. Taking full advantage of good linear polarization characteristics of semiconductor lasers, polarization beam combining offers simple structure and high efficiency. Moreover, it can be synergistically combined with other beam combining technologies to further enhance output power and laser brightness. Traditional polarization beam combiners are Brewster plate, metal grating polarizer, and birefringent prism. For the Brewster plate, broadband (approximate 100 nm), high transmission coating for P-polarization is required. It is a big challenge to mid-infrared. Due to the presence of metal lines, the transmission of the metal grating polarizer is usually lower than 80%, which results in a low beam combing efficiency. Commonly used birefringent MgF2 prism in mid-infrared has a small separation angle of 1.2°, which makes the optical path arrangement difficult. Metasurfaces offer a high degree of freedom in optical wave amplitude, phase, and polarization state regulations. It has already been applied in polarization beam splitters, which inspires the design of a beam combiner. By anomalous reflection, two light beams with orthogonal polarizations and different incident angles can be reflected in the same direction. We propose a polarization beam combiner based on anomalous reflection metasurface, which shows a high efficiency and broad working spectral band.MethodsThe proposed metasurface consists of periodic supercells. Each supercell contains 10 discrete single cells, which comprise a metal substrate, a dielectric middle layer, and a top rectangular column. By changing the two side lengths of the rectangular column of single cells, desired phase responses can be achieved for two orthogonal polarized incident beams. When ten optimized single cells are arranged spatially, the X-direction linear polarization (X-LP) incident beams experience a positive linear phase response. Meanwhile, the Y-direction linear polarization (Y-LP) incident beam experiences a negative linear phase response. Therefore, both beams are reflected perpendicularly to the metasurface when the incident angles of X-LP and Y-LP beams are 11.54° and -11.54° respectively.Results and DiscussionsAccording to the purpose and methodology of this study, we design a metasurface polarization beam splitter optical path operating in the middle-wave infrared range [Fig. 1(a)] and a three-layer metasurface structure [Fig. 1(b)]. By modeling the individual unit cell of the metasurface [Fig. 1(c)], we calculate the phase and amplitude responses of X-LP and Y-LP incident beams as we vary the length and width of the rectangular antenna column from 0.2 to 1.6 μm [Fig. 2(a)-(b)]. The particle swarm optimization algorithm is employed to determine the dimensions of the rectangular antenna that satisfy our desired phase requirements (Table 1). The phase introduced by the designed single cell aligns well with expectations for both incident polarizations while maintaining consistently high reflectivity levels throughout [Fig. 2(c)]. When the collimated X-LP and Y-LP beams with a central wavelength of 4.0 μm and incident angles of 11.54° and -11.54° reach the metasurface, both beams are reflected anomalously in the normal direction of the metasurface [Fig. 3(a)-(b)]. Reversely, when the collimated X-LP and Y-LP beams incident perpendicularly on the metasurface beam combiner, the X-LP beam is reflected in 11.54° direction and the Y-LP beam is reflected in -11.54° direction [Fig. 3(c)-(d)]. When the incident beam has a divergence angle of 50 mrad, the reflected beam has a divergence angle of 48 mrad [Fig. 3(e)]. To study the anomalous reflection of the metasurface for a light source with broad spectral bandwidth, we scan the incident light central wavelength from 3.9 to 4.1 μm. The resulting combined beam exhibits a divergent angle of 10 mrad while the reflectivity is maintained as high as 95% (Fig. 4). Based on the above theoretical simulation results, the reflected beam propagation properties in the free space are investigated by Zemax’s physical optical propagation (POP) tool. Assuming both X-LP and Y-LP incident beams are fundamental Gaussian beams, the beam quality factor of the reflected X-LP beam is 1.11, and that of the reflected Y-LP beam is 1.12 (Fig. 5). Therefore, when X-LP and Y-LP beams are combined to propagate in the same direction, the beam quality factor of the combined beam is 1.12 [Fig. 6(a)]. The spectrum of the combined beam coincides well with the overlap of the two individual incident laser spectra [Fig. 6(b)]. Consequently, this study demonstrates that a polarization beam combiner based on the anomalous reflective metasurface has not only high combination efficiency but also broad operation bandwidth. It is suitable to be used for the mid-infrared QCL power combining.ConclusionsWe study a polarization beam combiner based on anomalous reflective metasurface, which is utilized to combine two incident beams with orthogonal linear polarizations. The beam combiner consists of periodic supercells with a dimension of 2 μm×20 μm. Each supercell contains 10 single cells of 2 μm×2 μm. The single cell comprises a metal substrate, a dielectric middle layer, and a top rectangular column. When the collimated X-LP and Y-LP beams with a central wavelength of 4.0 μm and incident angles of 11.54° and -11.54° reach the metasurface, both beams are reflected anomalously in the normal direction of the metasurface. The polarization beam combination is realized. Within a broad spectral band of 3.9 to 4.1 μm, high average anomalous reflectivity of 96.6% and 97.7% are obtained for X-LP and Y-LP incident beams, respectively. Based on the near field reflective intensity and phase distribution, the propagation of the combined beam in free space is simulated by the periodic field splicing method and Gaussian beam propagation law. Assuming both X-LP and Y-LP incident beams are fundamental Gaussian beams, the beam quality factor of the combined beam is 1.12. The metasurface beam combiner shows high design flexibility and can be prepared by mature MEMS technology. It has a good potential to solve the problems in mid- and long-infrared power beam combinations.
Acta Optica Sinica
- Publication Date: May. 25, 2024
- Vol. 44, Issue 10, 1026030 (2024)
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