Abstract
1. Introduction
Cylindrical vector beams (CVBs) are optical beams that carry polarization singularities. Due to the unique polarization and amplitude characteristics of the optical fields of CVBs, many applications have been explored in the field of optical communication[
Ultrafast CVBs are generally obtained by mode excitation and selection of solitons from the mode-locked laser platform, where the soliton presented in the vector or scalar state[
In recent years, researches on ultrafast CVBs have focused on how to excite and select high-order modes to improve the conversion efficiency of to or the purity of ultrafast CVBs. In this context, the offset coupling spot (OSS), fiber grating, and mode selective coupler (MSC) have been employed to obtain ultrafast CVBs[
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However, CVBs, as vector modes, are sensitive to the vector properties of solitons, but the influence of soliton vector dynamics on the realization of ultrafast CVBs has attracted little attention in previous research. In this Letter, we explore the role of soliton vector properties in realizing ultrafast CVBs and pay attention to the conversion efficiency of solitons to CVBs, rather than that of to . In the experiment, we innovatively demonstrate ultrafast CVBs based on vector-locked solitons (group-velocity-locked vector solitons, GVLVSs) fiber laser platform. Compared with the ultrafast CVBs based on vector change periodic solitons and scalar solitons, the high polarization stability of vector-locked solitons not only greatly improves the efficiency of solitons converting into ultrafast CVBs, but also extends the ultrafast CVBs operation from the fundamental frequency to the harmonic regime for the first time, to the best of our knowledge. The output power and conversion efficiency of ultrafast CVBs based on vector-locked solitons are more than 2.4 times that based on scalar solitons and 4.1 times that based on vector change periodic solitons. Moreover, the superior vector stability of vector-locked solitons guarantees ultrafast CVBs operation at the repetition rate from 25 MHz to 198 MHz, with the pulse of .
2. Experiment Section
The configuration of the proposed all-fiber passively mode-locked GVLVSs laser setup is illustrated in Fig. 1(a). A 976 nm laser diode (LD) pumps a 35 cm long erbium-doped fiber (EDF) (Er80-8/125, Liekki) by a wavelength division multiplexer (WDM). A graded-index multimode fiber (GIMF) is inserted into the ring cavity and combined with the single fiber to form a single-mode fiber–graded-index multimode fiber–single-mode fiber (SMS) ultrafast switch. The set-up includes a polarization-independent isolator to ensure unidirectional propagation in the cavity, and a polarization controller (PC) to continuously adjust the in-cavity birefringence. A 90:10 coupler is utilized to extract the laser pulses through the 10% port. The output soliton train can be polarization-resolved along two birefringence axes with a polarization beam splitter (PBS) and PC2 external to the cavity.
Figure 1.(a) Experimental configuration of all-fiber GVLVSs fiber laser; (b) oscilloscope traces of these GVLVSs along the two orthogonal polarization axes; (c) polarization-resolved spectrum of GVLVSs; (d) pulse duration of GVLVSs.
Self-started mode-locking can be easily obtained as the lasing threshold is reached with the fundamental repetition rate of 25 MHz. Figure 1(b) depicts the oscilloscope trace after the polarization-resolved measurement. The pulse intensity of the two orthogonally polarized solitons (red and blue pulse trains) is uniform. Moreover, the central wavelengths of the vertical and horizontal components after being polarization-resolved are located on both sides of the total spectrum, which is a typical feature of the GVLVSs spectrum[
By increasing the pump power above 35 mW, noisy pulsations are observed, corresponding to unstable multipulse mode-locking states. Upon increasing the pump power to 69 mW, stable harmonic mode-locking (HML) can be obtained, and the repetition rate reaches 75 MHz, corresponding to the third harmonic order. Figure 2 shows the oscilloscope traces of the typical mode-locked and HML operation evaluation at different pump powers. With proper adjustment of PC1, multiple pulses from the third up to the eighth HML are generated within the laser round trip at the pump power from 35 mW to 130 mW, corresponding to 75 MHz, 175 MHz, and 198 MHz, as shown in Figs. 2(b)–2(d). The RF spectrum of GVLVSs from fundamental to HML regimes is shown in Fig. 2(e)–2(h). The RF spectrum at the fundamental repetition rate is 25 MHz at 35 mW, and the signal-to-noise ratio (SNR) exceeds 44 dB. With the maximum pump power, the SNR for the eighth harmonic solitons is 49.1 dB. In the whole process, there is no satellite peak emerging in the RF spectrum, which indicates that there is no vector resonance modulation instability (VRMI) in the harmonic mode-locked state.
Figure 2.(a)–(d) Oscilloscope trace and (e)–(h) RF spectrum of the output pulses at different pump power.
In order to obtain the ultrafast CVBs, an LPFG, inscribed on a graded-index two-mode fiber (FM GI-2, YOFC) by a -laser source (CO2-H10, Han’s Laser), is connected to the output port and demonstrated as a mode converter. The intensity profiles of the radially and azimuthally polarized beams are captured by the CCD camera (CinCam CMOS-1201). The transmission spectrum of the TM-LPFG is shown in the red curve in Fig. 3(a). The transmission spectrum bandwidth of the LPFG is 5 nm, from 1563 nm to 1568 nm, which covers the central wavelength of the vector mode-locked fiber laser. The surface morphology of TM-LPFG is shown in Fig. 3(b), the period is 700 µm, and the illustration is the details of the TM-LPFG. In the experiment, the GVLVSs based on SMS can operate at both radially and azimuthally polarized modes throughout the fundamental repetition rate and HML, and the doughnut shape intensity profiles are shown in Figs. 4(a1) and 4(f1), respectively. The ultrafast CVBs emission has high mode purity that is calculated to be 97.2% by calculating the percentage bending loss[
Figure 3.(a) Transmission spectrum of LP01 mode of the TM-LPFG; (b) the surface morphology of TM-LPFG (inset: enlarged part).
Figure 4.Intensity profiles of ultrafast CVBs based on vector-locked and non-vector-locked solitons. (a) and (f) are radially and azimuthally polarization beams without a polarizer; (b)–(e) and (g)–(j) show the profiles of the output beam after passing through a linear polarizer. Arrow indicates the orientation of the linear polarizer.
Figure 5.Output power of ultrafast CVBs depends on the incident power of vector and non-vector-locked solitons.
Since the CVBs are vector modes, the polarization dynamics of solitons should be investigated to explain the role of solitons vector properties in the process of ultrafast CVBs formation. We used a polarimeter (PAX1000IR2/M, Thorlabs) to record the state of polarization (SOP) based on SMS, CNT, and NPR mode-locking operation. The polarization evolution for fundamental and HML regimes based on SMS mode-locking is shown in Figs. 6(a) and 6(b). The GVLVSs can be observed on the surface of a Poincaré sphere at the fundamental frequency and HML regime, as shown in Fig. 6(a). GVLVSs based on SMS mode-locking are associated with a fixed points polarization attractor on a Poincaré sphere. The observed phase difference of GVLVSs indicates that GVLVSs are polarization-fixed left-handed and right-handed vector-locked solitons. The degree of polarization (DOP) corresponding to the fundamental repetition rate and harmonic regime is higher than 75% and achieves the maximum value of at the fundamental repetition rate, as shown in Fig. 6(b), where the DOP and phase difference of vector-locked solitons are fixed as constants. Figures 6(c) and 6(d) are the measured polarization dynamic states based on CNT mode-locking. Figure 6(c) shows that the polarization attractor generated by the rapid jump of phase difference is a line on the Poincaré sphere. The trajectory of rapid oscillation can be seen from the evolution of phase difference shown in Fig. 6(d). The oscillation trajectory in the fixed orientation indicates that the solitons have vector properties and change periodically. Therefore, the solitons obtained by CNT mode-locking are vector-periodically-changed solitons. Figures 6(e) and 6(f) are the measured polarization dynamic states based on NPR mode-locking. The polarization attractor on the Poincaré sphere contains a circular region close to the pole of the Poincaré sphere, and the randomness of oscillation orientation of the polarization attractor indicates that the solitons based on NPR mode-locking are scalar solitons. Therefore, the vector properties of solitons determine the conversion efficiency of solitons into ultrafast CVBs and the output characteristics of ultrafast CVBs.
Figure 6.Time evolution of solitons based on SMS, CNT, and NPR mode-locking in terms of (a), (c), (e) Stokes parameters at the Poincaré sphere and (b), (d), (f) intensities of orthogonally polarized modes.
To explain the relationship between soliton vector properties and CVBs, we need to establish the vector distribution of CVBs. Figure 7 illustrates the polarization and intensity profiles of CVBs. The expression of CVBs in cylindrical coordinates is as follows:
Figure 7.Polarization and intensity profiles of ultrafast CVBs: (a) radial polarization TM01, (b) angular polarization TE01.
is the angle between the positive half axis of the Y axis and the electric field line, and the orthogonal mode and mode correspond to Eq. (1) at and 90°, respectively. For vector-locked solitons, the vector-locked characteristics and high DOP guarantee the polarization components of vector-locked solitons are partially consistent with those of the mode and mode, which is beneficial to improving the coupling efficiency of the solitons to the mode and mode. On the contrary, the periodical or irregular change of the vector properties of solitons makes it impossible to find the identical vector state in CVBs, so the conversion efficiency of scalar solitons and vector solitons with vectors changing periodically into CVBs will not be improved. However, the improved coupling efficiency of vector-locked solitons leads to nonuniform intensity profiles of CVBs, as shown in Figs. 4(a1) and 4(f1).
3. Conclusion
In conclusion, we investigate the effect of vector dynamics on ultrafast CVBs implementation and innovatively propose a novel technical method to realize femtosecond CVBs based on vector-locked solitons (GVLVSs). The vector-locked solitons are obtained by an all-fiber passively mode-locked laser. Compared with vector-periodically-changed solitons and scalar solitons, the excellent vector-locked characteristics of GVLVSs not only increase the conversion efficiency of solitons to CVBs and the output power of CVBs by 4.1 times and 2.4 times, respectively, but also expand the ultrafast CVBs from the fundamental frequency to harmonic regime for the first time, to the best of our knowledge. The femtosecond CVBs at 1564.72 nm can be tuned from 25 MHz to 198 MHz, corresponding to the fundamental repetition rate to the eighth harmonic order, with the calculated purity of 97.2%. This is the highest repetition rate reported for ultrafast CVBs based on passive mode-locking. This ultrafast CVB based on vector-locked solitons not only opens up their applications in high-repetition rate fields, but also provides a new idea for generation of high-order ultrafast optical vortices.
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