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Abstract
Dissipative solitons (DSs), which are pulses with high pulse energy and a broad rectangular output spectrum, have several applications. In a fiber system, the generation of higher-order DS requires a mode converter with a high and flat conversion efficiency that can cover the working waveband. The requirements on high and flat conversion efficiency as well as broadband working waveband is a great challenge for a traditional mode converter. This study presents an L-band mode-locked fiber laser with a 3-dB bandwidth of more than 47 nm and a first-order cylindrical vector (CV) mode DS output based on an ultra-broadband long-period fiber grating (LPFG). The fabricated mode converter is a novel cascading LPFG with an ultra-broadband working bandwidth and flat conversion efficiency which could meet the demand of DS mode conversion. The 15-dB bandwidth is 149.76 nm, from 1515.36 nm to 1665.12 nm. Furthermore, the conversion efficiency in the range of the output spectrum is 98.60 ± 0.23%. The single-, double-, and triple-soliton output characteristics and their real-time spectra are observed using time-stretched dispersion Fourier transformation (TS-DFT) technology. Experimental results demonstrate that the first-order CV mode DS laser can maintain its dynamics after mode conversion under the accuracy of detection system, implying that the LPFG works only as a mode converter. The broadband DS laser with CV mode output in the L-band has been presented for the first time in study, to the best of our knowledge. This study is also the first to detect real-time characteristics for a higher-order mode-locked fiber laser using the TS-DFT technology. The proposed type of LPFG is s good candidate for generating higher-order mode lasers with an all-fiber structure.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Cylindrical vector (CV) mode, which is the eigensolution of Helmholtz equation in fiber systems, has been extensively analyzed in recent years owing to its donut-shaped intensity and vector electric distribution [1,2]. CV beams present various applications, such as particle manipulation [3], high-resolution imaging and measurement [4], surface plasmon excitation [5], material processing [6], and optical communication [7]. They are also an important base for generating the orbital angular momentum (OAM) mode [8]. Higher-order modes, especially CV and OAM modes, have been used for a long time for sensing and large-capacity communications in all-fiber systems [9,10]. The traditional methods of generating a CV beam, such as q-plate [11], computer-generated holograms created by a programmed spatial light modulator (SLM) [12] and metastructure [13], are accurate but present a considerable insertion loss when coupled with fiber. Consequently, the all-fiber methods used to generate CV mode, such as mode selective coupler (MSC) [14], fiber grating [15] and photonics lantern [16], have gained widespread interest. Notably, long-period fiber grating (LPFG) is well-suited for all-fiber mode converters owing to its higher conversion efficiency and a simpler fabrication approach.
High-energy conventional solitons (CS) typically split due to the accumulation of a strong nonlinear phase shift when circulating in an anomalous cavity [17]. This is an adverse limitation in the application of CS mode-locked fiber lasers. When performing dispersion management in cavity, the pulse width is extended and the peak power is reduced owing to the introduction of chirp, which is able to avoid pulse splitting and achieve a higher pulse energy output [18–20]. Dissipative solitons (DSs) are high-energy pulses produced by all-normal or large-normal-dispersion fiber lasers; they usually have a wider output spectrum and are more convenient to get a higher peak power in cavity, which makes them scalable in oscillator and external amplifier [21]. In order to obtain a DS with a higher-order mode output, high and uniform conversion efficiency is required for the mode converter in the range of mode-locked output spectrum, which is a considerable challenge in all-fiber systems. Wang et al. first developed an all-fiber mode-locked fiber laser by using an MSC and achieved a higher-order DS soliton output at C-band [22]. However, the introduction of MSC produced strong interference at the higher-order mode port. Cai et al. obtained the bound state of first-order CV mode DS in a dispersion-managed cavity by using the MSC at C-band [23]. Chen et al. introduced a Tm/Ho-co-doped DS fiber laser with CV mode output using a MSC at 2 µm waveband [24]. However, these lasers did not present a higher-order mode output spectrum, due to which it cannot be determined whether the output status is destroyed. Although MSC can get a broad working bandwidth to cover the output spectrum of the fiber laser, the conversion efficiency is not sufficiently high to get a high-purity higher-order mode; the influence of uneven conversion efficiency also adversely affects the output characteristics at the working waveband. Tao et al. experimentally demonstrated an all-fiber mode-locked laser emitting broadband-spectrum cylindrical vector mode pulse based on a LPFG [25]. The LPFG as a mode converter has a 125 nm working bandwidth from 940 nm to 1065 nm with a conversion efficiency of 93.7% (12 dB). The LPFG using the dual-resonant effect can achieve a broad working bandwidth as well as a high and flat conversion efficiency; this type of mode converter has also been reportedly applied for higher-order mode-locked fiber laser operation in communication waveband [26]. However, the working waveband is still limited by the dispersion characteristics of the fiber used. Once the fiber structure is determined, the working waveband of LPFG mode converter using the dual-resonant effect is fixed, which makes this fabrication method lack of flexibility. This indicates that a new type of fiber must be specially designed when the working waveband of mode converter is to be changed, which is very problematic. Lastly, to the best of our knowledge, there have been no studies conducted on DS with higher-order mode output at L-band.
This paper proposes and demonstrates an L-band DS mode-locked fiber laser with first-order CV mode output based on a broadband LPFG mode converter. Single-, double-, and triple-soliton output characteristics and their real-time spectra are analyzed by using the time-stretched dispersion Fourier transformation (TS-DFT) technology. Experimental results indicate that the first-order CV DS laser can maintain its dynamics after mode conversion under the accuracy of the detection system, implying that the LPFG works only as a mode converter and does not further affect the time-domain characteristics. This study is the first to realize such a broadband DS laser with CV mode output using LPFG as a mode converter in 1600 nm waveband, to the best of our knowledge. It also presents the novel detection of real-time characteristics for a higher-order mode-locked fiber laser using the TS-DFT technology. The mode converter fabricated in this study is a novel cascading LPFG which could achieve an ultra-broadband working bandwidth and flat conversion efficiency in any waveband. The 15 dB bandwidth is 149.76 nm, from 1515.36 nm to 1665.12 nm. Furthermore, the conversion efficiency in the range of the output spectrum is 98.60 ± 0.23%. This type of LPFG mode converter provides an ideal method to achieve higher-order mode lasers with high-quality using all-fiber structures.
2. Experimental set-up and LPFG fabrication
2.1 Dissipative soliton fiber laser diagram
Figure 1 presents a schematic diagram of the proposed L-band DS fiber laser. A 9.5 m normal dispersion Er-doped fiber (EDF, Fibercore, I-25(980/125)) is used as the gain medium to simplify the fiber laser structure and ensure the operation in the DS regime. The EDF has a group velocity dispersion of 40 ps2/km at 1550 nm, and its signal absorption coefficients are 23.9 dB/m at 980 nm and 41.14 dB/m at 1530 nm, respectively. This EDF is co-directionally pumped by a 976 nm LD using a 980/1550 wavelength-division multiplexer. Two polarization controllers (PCs) combined with a polarization-dependent isolator (PD-ISO) form an artificial saturable absorber, while the PD-ISO ensures unidirectional operation. The remaining fibers, including device pigtails (∼8.3 m in total), are single-mode fibers (SMFs) with a group velocity dispersion of -23 ps2/km at 1550 nm. The net dispersion of the cavity is 0.19 ps2. An output coupler (OC) with a coupling ratio of 21:79 at 1.6 µm is selected and an output efficiency of 79% is extracted, which helps in decreasing intra-cavity nonlinearity, increasing output power, and enabling L-band mode-locked operation.
Fig. 1. Diagram of the proposed L-band mode-locked fiber laser. PD-ISO: Polarization dependent isolator. OC: output coupler. WDM: Wavelength division multiplexer. PC: polarization controller. LD: laser diode. OSA: Optical spectrum ana lyzer. DCF: dispersion compensation fiber. PD: Photodetector. pol: Polarizer.
An optical spectrum analyzer (OSA, Yokogawa, AQ6370D) is used in the experiment to detect the output spectrum of the laser, two high-speed photodetectors (45-GHz bandwidth, DiscoverySemi, DSC10H; 50-GHz bandwidth, Finisar, XPDV2320R) and a real-time oscilloscope (33-GHz bandwidth, 100Gsamples/s, Tektronix DPO75902SX) are used to record the real-time pulse trace of the laser. In the meantime, autocorrelation (AC) trace is measured by an FR-103XL and radio frequency (RF) is measured by a RF spectrum analyzer (Agilent CSA N1996A). Furthermore, a dispersion compensation fiber (DCF, Yangtze Optical Fibre and Cable) is used to perform TS-DFT and to observe the real-time spectrum evolution. The total length of DCF1 (used in detection point A) and DCF2 (used at detection point B) are 1.5 km and 1.0 km with total dispersion of 236.99 ps/nm and 195.07 ps/nm at 1600 nm, respectively. The original output characteristics are obtained at detection point A and the converted first-order CV mode output characteristics are obtained at detection point B. It should be noted that because of the ∼0.5 m single-mode fiber (SMF) pigtails in front of two high-speed photodetectors and the single-mode operation of DCF, we need to couple first-order pulses in few-mode fiber (FMF) into fundamental mode by dislocating the FMF and SMF when detecting the pulse trace and real-time spectrum. Lastly, a CCD camera (Find-r-scope, 85700) is used to detect the mode-field distribution of the generated first-order CV mode.
2.2 Broadband LPFG with high and flat conversion efficiency fabrication
This section proposes and demonstrates a novel cascading LPFG mode converter to achieve a higher-order broadband DS output. An ultra-broadband LPFG mode converter with high and flat conversion efficiency in communication waveband is achieved by designing an appropriate pitch number and cascading parameters.
Traditional uniform working bandwidth of the LPFG is related to its pitch number [27]. The LPFG typically has a broader working bandwidth for a low pitch number, whereas the working bandwidth becomes narrower with the increase in the pitch number. A stronger refractive index (RI) modulation is required to achieve an equal conversion efficiency when cutting the pitch number of the LPFG. However, a stronger RI modulation results in a higher insertion loss in the LPFG, which is harmful for all-fiber systems. Therefore, the pitch number cannot be reduced indefinitely. According to [28], there is no effective mode conversion when the pitch number is less than 8. Conversely, over-coupling can be caused more easily due to a large pitch number [27]. Therefore, the pitch number must be set to an appropriate value.
A broadband LPFG is achieved by cascading three parts of uniform LPFGs. Pitch number of every part of the LPFG is set to 10 in order to balance the working bandwidth and requirement for RI modulation depth, according to [28]. A two-mode step index fiber (OFS), with a 19 µm core diameter and a 125 µm cladding diameter, is used as the fabrication platform. The fabrication is performed with a CO2 laser marking machine (Han’s Laser). A uniform-period LPFG is first fabricated to identify the correlation between period and resonant wavelength. Figure 2(a) illustrates the transmission spectra of LPFG for different periods. The changing trend of the transmission spectra indicates that the central resonant wavelength shifts to a shorter value when the LPFG period increases. Figure 2(b) presents the fitting curve, which is an important reference in determining the parameters of the cascading LPFG.
Fig. 2. (a) Transmission spectra versus different periods for grating pitch of 10. (b) Correlation between period and resonant wavelength.
Figure 3 presents a diagram of the cascading LPFG. Three uniform LPFGs are cascaded under different periods without any phase shift. Each LPFG has a pitch number of 10, ensuring the total pitch number of 30. The parameter, δd, is used to describe the period increment from the first part of the cascading LPFG to the third part. For example, when δd is set to 0.05 mm and the first LPFG period is set to 1.10 mm, the periods of the three parts of the LPFG are 1.10 mm, 1.15 mm, and 1.20 mm, respectively. An appropriate start period, Λ, and period increment, δd, must be selected to realize a balance between the working waveband and conversion efficiency.
Fig. 3. Profile of the cascading LPFG. Three uniform LPFGs with a period increment of δd are fabricated in order.
The first LPFG period is first set to 1.12 mm, with a corresponding resonant wavelength of 1643.98 nm. Subsequently, several cascading LPFGs with different δd values are fabricated to search the correct value. Figure 4 shows the transmission spectra at different δd when the first period is set to 1.12 mm. The start δd is 0.02 mm and the end δd is 0.045 mm with an increment of 0.005 mm. It can be observed from these transmission spectra, that when δd is 0.020 mm (black curve), there is no significant improvement in the working bandwidth of the cascading LPFG when compared to the uniform LPFG. Conversely, when δd is 0.045 mm (yellow curve), the conversion efficiency at the center waveband decreases significantly, resulting in a decrease in the efficient working bandwidth. The conversion efficiency decline at center waveband is mainly caused by the superposition of coupling by the three part of uniform LPFGs, which means the value of δd over 0.045 mm is not suitable. Therefore, setting the value of δd to 0.040 mm (bold purple curve) is the best choice to achieve a broad working bandwidth along with a high conversion efficiency. The 15-dB bandwidth is 148.46 nm from 1461.98 nm to 1610.46 nm, when δd is 0.04 mm and when the start period is 1.12 mm. However, the working bandwidth cannot completely cover the L band, which is a significant limitation. Therefore, the start period is lowered to redshift the working waveband in the next step. Additionally, the parameter, δd, must also be adjusted due to the correlation between period resonant wavelength.
Fig. 4. Transmission spectrum evolution when the cascading constant, δd, is increasing. The start period $\mathrm{\Lambda }$ are all fixed at 1.12 mm.
Finally, setting the start period to 1.105 mm and δd to 0.035 mm helps in obtaining the best result that could perfectly balance the conversion efficiency and working bandwidth. Figure 5 depicts the transmission spectra. This LPFG has a 15 dB working bandwidth of 149.76 nm from 1515.36 nm to 1665.12 nm, which covers the entire C and L band in optical communication. Additionally, it also achieves a 98% conversion efficiency from 1520.44 nm to 1659.36 nm. Insert loss of the LPFG is measured to be 1.03 dB, which is mainly caused by the exposure of CO2 laser. The conversion efficiency in the range of the output spectrum of the fiber laser (1570∼1620 nm) is 98.60 ± 0.23%, which indicates that the higher-order modes converted by the LPFG have similar purity at this waveband. The mode field distribution of the LP11 mode converted by this LPFG is measured using a tunable laser source (Keysight, 8164B) and a CCD, as shown in Fig. 6. The consistent mode field distribution demonstrates that this LPFG could generate the LP11 mode with high purity at an ultra-broadband.
Fig. 5. Transmission spectrum (a) and mode conversion efficiency (b) when starting period is 1.105 mm and δd is 0.035 mm.
It can be observed from the aforementioned fabrication process, that an ultra-broadband LPFG mode converter with high and flat conversion efficiency can be achieved at any waveband as long as the selected fiber supports the targeted higher-order mode. This type of cascading LPFG can overcome the limitation of the dispersion characteristics of the fiber and be used in any waveband by careful selecting the suitable parameters. Furthermore, its simple structure and easy fabrication are highly advantageous for application in the broadband mode convertor.
3. Experimental results and discussion
3.1 Single soliton operation
A stable single soliton pulse is obtained for the pumping power of 128 mW by carefully adjusting PC1 and PC2, as shown in Fig. 1. The original output spectrum obtained at detection point A has an approximately rectangular profile with a 3 dB bandwidth of 47.69 nm from 1574.62 nm to 1622.31 nm, centering at 1596.1 nm, indicated by the black curve in Fig. 7. The red curve in Fig. 7 represents the first-order mode spectrum converted by the LPFG obtained at detection point B. The spectral difference between the two outputs is minimal. The spectrum of generated first-order mode maintains nearly the same shape as that of the original spectrum. The small difference is primarily attributed to the unevenness of the FMF end surface caused by imperfect cutting.
Pulse traces are shown in Fig. 8 and it shows that the pulse interval is 89.2 ns operating at single-soliton state. Figure 8(a) illustrates the pulse trace contrast where the black curve represents the original pulse trace, and the red curve represents the generated first-order mode pulse trace. These two curves have the same pulse interval valve of 89.2 ns. The pulse trace is then magnified and the shape of a single pulse is observed in Fig. 8(b), where it is observed that the generated first-order mode pulse maintains the single-soliton operation without any pulse spitting. The comparison between the spectrum and time trace shows that the first-order mode laser generated by the LPFG still maintains a mode-locked state of the DS under single-soliton.
Fig. 8. Pulse traces contrast before and after LPFG at single-soliton operation. (a) Pulse traces around 1000 ns scale. (b) Pulse traces magnification in 2 ns.
The RF spectra contrast is shown in Fig. 9. The RF spectra at detection point A and B show the same repetition frequency of 11.21 MHz and perform a similar singal to noise ratio (SNR), which means the fiber laser is working at fundamental frequency and has no extra noise generated by LPFG. Figure.10 shows the AC trace before and after the LPFG. The direct output pulse at point A has a full width at half maximum (FWHM) of 2.2 ps under a Gaussian fit. Combined with the 47.69 nm spectral bandwidth, the time bandwidth product is 12.32, which indicates that the obtained DS is strong chirped. After adding a suitable length of SMF outside the cavity, the FWHM could be compressed to 125 fs. The AC trace at detection point B is shown in Fig. 10(b). The FWHM is measured to be 581 fs assumming a Gaussian fit. Output power at point B is also measured, it has an average output power of 5.06 mW.
Fig. 10. AC trace detected at (a) point A and (b) point B at single soliton operation. The insert in (a) is the compresed AC trace before LPFG.
The real-time spectra are measured before and after conversion using TS-DFT technology to further verify the stability of the generated first-order mode laser. Figure 11(a) depicts the real-time spectra before mode conversion, and Fig. 11(b) depicts the spectra after mode conversion. The spectrum after mode conversion maintains a stable shape of rectangle over 5500 round trips without broadening or compression. Interference fringes are mainly caused by the dislocation coupling between the FMF and SMF. Additionally, from the real-time spectra, we can see that the laser still performs a DS operation.
Finally, the mode-field distribution of the generated first-order single DS is detected. The first-order radial (TM01) and angular (TE01) polarized modes are detected by the CCD camera by adjusting PC3 after the LPFG. Figure 12 presents their distribution with and without a polarizer at different angles. The mode purity is also calculated using the method presented in [29]. The generated TE01 and TM01 modes present purities of 96.69% and 97.74%, respectively. The difference between the mode purity and conversion efficiency is primarily attributed to the imperfect tuning of PC3 [30].
Fig. 12. Generated TE01 and TM01 mode distribution by LPFG mode converter at single-soliton operation.
3.2 Multi-soliton operation
Multi-soliton operation can be achieved when the energy of a single soliton reaches the threshold point and splits at a higher pumping power. The multi-soliton operation can be roughly divided into the soliton bunches operation and the bound state based on the pulse interval. These are very common states in fiber lasers when the output power is high, which indicates that the analysis of the effect of LPFG on these pulses is necessary.
Double-soliton operation is achieved when the pumping power is increased to 151 mW and the two PCs are carefully adjusted in the laser cavity. In this case, the central operation wavelength and the 3-dB bandwidth of the lasing spectrum are 1592.84 nm and 37.2 nm from 1579.04 to 1616.24, respectively. The black and red curves in Fig. 13 and Fig. 14(a) represent the spectrum and pulse traces before and after the LPFG, respectively. The spectrum after the LPFG still perform a rectangular shape, indicating a DS mode-locked operation. There is no significant change of shape in the spectrum before and after the LPFG except a negligible fluctuation, which can also be explained by the uneven cutting of the FMF measuring surface.
Fig. 14. Pulse traces contrast before and after LPFG at double-soliton operation. (a) Pulse traces around 1000-ns scale. (b) Pulse traces magnification in 4 ns.
Furthermore, the pulses shown in Fig. 14(a) still maintain a time interval of 89.2 ns, indicating that the fiber laser still operates in the mode-locked state after mode conversion. Subsequently, the pulse trace is magnified to observe the time spacing between the two solitons in the same cycle. From Fig. 14(b), it can be observed that the time spacing between two solitons before and after the LPFG hold the same value of 0.3 ns, which indicates that the LPFG does not affect the loose multi-soliton operation.
The RF spectrum contrast is shown in Fig. 15. The pulses at point A and point B working at the same repetition frequancy of 11.21 MHz and perform the similar SNR, which means the LPFG does not cause additional noise on the double-soliton operation. Figure 16 shows the AC trace before and after the LPFG. The FWHM of the AC trace before and after the LPFG is measured to be 3.01 ps and 558 fs under a Gaussian fit, respectively. The compression of pulse is mainly caused by the pigtail of FMF after the LPFG. Finally, the measured output power at point B is 8.22 mW.
Figures 17(a) and 17(b) illustrate the real-time spectra. The spectrum has no significant difference and keeps the rectangular shape for more than 5500 round trips, except for the interference caused by dislocation coupling. Additionally, stability of spectrum also shows that the double-soliton operation is very stable without any disturbance over 5500 round trips, which indicates that the double-soliton operation could be maintained for a large time scale after the LPFG.
Similarly, the TE01 and TM01 modes with purities of 95.56% and 96.41% are detected on the CCD camera, as shown in Fig. 18, indicating that the radial and angular polarized light are obtained under loose two-soliton operation through mode conversion.
Fig. 18. Generated TE01 and TM01 mode distribution by LPFG mode converter at double-soliton operation.
A stable triple-soliton operation is achieved when the pumping power is increased to 208 mW and the positions of PC1 and PC2 are fine-tuned. These three solitons are close and form a bound state. Figure 19 demonstrates that the output spectra before and after the LPFG and both show significant interference as well as a rectangular shape. The significant interference before and after the LPFG is because the solitons in the same cavity cycle are too close. It shows that the three solitons are still very close and there is no notable separation after passing through the LPFG. But it is difficult to distinguish the difference between the original and converted spectra owing to the interference. The only thing that can be determined from this figure is that there is still a bound state in operation, but the number of pulses and the slice among them is unknown, which will be detected in this section.
Figure 20(a) shows the pulse trace contrast; they still hold the same cavity period of 89.2 ns. In the magnified Fig. 20(b), it can be observed that the three solitons are equally spaced with a spacing of 30 ps before or after the LPFG. This result illustrates that the bound state pulses can retain the same time-domain characteristics after the LPFG, and the LPFG only changes its transverse field distribution.
Fig. 20. Pulse traces contrast before and after LPFG at triple-soliton operation. (a) Pulse traces around 1000 ns scale. (b) Pulse traces magnification in 3 ns.
Since the AC trace is a time average and could not figure out the real-time soliton spacing, we do not detect AC trace at under this state. Instead, we will detect the real-time AC trace using TS-DFT technology later. RF spectrum contrast is shown in Fig. 21. The pulse before and after LPFG still hold the same repetation frequency and SNR, which means that there is no additional noise introduced by the LPFG. Lastly, the measured average output power at point B is 16.03 mW.
The real-time spectra are shown in Fig. 22, where it can be observed that interference fringes are clearly visible and stable in both the original and converted spectra over the 5500 round trips, indicating that the LPFG does not influence the bound state operation and the spectral stability in over 5500 round trips also shows that the LPFG does not cause instability on the bound state operation.
A Fourier transform is performed on the real-time spectra and the real-time AC traces are obtained in Fig. 23 to accurately measure the soliton spacing. The soliton spacing before and after mode conversion are 32.65 ps and 32.38 ps, based on the real-time autocorrelation traces. The time resolution of these two real-time autocorrelation traces are 0.13 ps and 0.15 ps before and after mode conversion, respectively. The soliton spacing difference between these two traces is 0.27 ps, which is within one to two pixels. This difference can be easily caused by the detection errors. Essentially, the LPFG has a negligible effect on the soliton spacing of the bound state at the detection resolution obtained in this study.
Finally, the TE01 and TM01 modes with purities of 97.54% and 96.34% are captured by the CCD camera in Fig. 24 by adjusting PC3 behind the LPFG, due to which a triple-soliton bound state with a CV mode distribution is generated.
Fig. 24. Generated TE01 and TM01 mode distribution by LPFG mode converter at triple-soliton operation.
Table 1. Comparison among the mode-locked fiber laser with higher-order mode output using LPFG.
At last, we make a comparison of those who also use LPFG to realize a pulsed laser with first-order mode output in Table 1. By comparing with the other works, we can see that our fiber laser has the widest 3 dB bandwidth when using a LPFG as mode converter. This is mainly due to the high and flat conversion efficiency provided by the LPFG we fabricated, which could cover the output wavelength range of fiber laser. At the same time, the flat conversion efficiency and adjustable working waveband also show that the LPFG we fabricated has better application prospects in the generation of higher-order pulsed lasers.
4. Conclusion
In conclusion, this study proposed and demonstrated an L-band DS fiber laser with first-order CV mode output based on a broadband LPFG mode converter. The mode converter fabricated in this study is a novel cascading LPFG with an ultra-broadband working bandwidth and flat conversion efficiency. The 15 dB bandwidth is 149.76 nm from 1515.36 nm to 1665.12 nm. Furthermore, the conversion efficiency in the range of the output spectrum is 98.60${\pm} $0.23%. Single-, double-, and triple-soliton operations with angular polarized and radially polarized outputs are detected. The time trace, average spectra, and real-time spectra contrast before and after mode conversion demonstrate that the introduction of LPFG only changes the transverse field distribution under the accuracy of the detection system, and has a negligible effect on the time-domain characteristics of the laser. This type of LPFG provides a candidate solution to realize broadband DS mode-locked lasers with high-quality higher-order mode output using LPFG as a mode converter.
Funding
National Natural Science Foundation of China (61775107, 61835006); National Key Research and Development Program of China (2018YFB1801802).
Disclosures
The authors declare no conflicts of interest
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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