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Abstract
We investigate an all-fiber all-polarization-maintaining dispersion-managed ultrafast fiber laser mode-locked by nonlinear polarization evolution in polarization-maintaining fibers both numerically and experimentally. We find that the laser can operate in different regions among a wide net dispersion, including dispersion-managed solitons, dispersion-managed dissipative solitons, bound state solitons and noise-like pulses. The laser generates the dispersion-managed soliton pulses with a maximum 3 dB bandwidth of 37.84 nm, which can be further compressed to 161.37 fs. Moreover, pulses generation simulation under different net dispersion condition has been carried out. Nonlinear pulse evolution dynamics in laser cavity has been analyzed through numerical simulation as well. The results are basically consistent with the experimental ones.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Ultrafast mode-locked fiber lasers have drawn considerable attention due to a range of scientific studies and commercial applications. Environmental stability and reliability are the key issues for fiber lasers used in various conditions. In order to further reduce the impact of environmental instability, all-fiber all-polarization-maintaining (PM) construction is considered to be an optimal solution. Saturable absorbers (SA) play important roles in mode-locked ultrafast fiber laser, classified into the intrinsic saturable absorbers (semiconductor saturable absorber mirror [1], graphene [2] and carbon nanotubes [3]), and the artificial saturable absorber (nonlinear optical loop mirror [4], nonlinear amplifying loop mirror [5], nonlinear polarization evolution (NPE) [6]). Compared to the intrinsic SAs, NPE is most commonly used mode-locking technology with advantages of high damage threshold and fast response time. Nevertheless, traditional NPE mode-locking technique is incapable of achieving all-fiber all-PM construction, which suffers from environmental disturbance.
For the last few years, all-fiber all-PM NPE mode-locked fiber lasers [7–14] have gradually attracted significant interest in the field. Such NPE mode-locked fiber lasers with all-fiber and all-PM design have avoided the employment of free-space components and mechanical devices, maximizing the benefits of fiber lasers and providing better environmental stability, which are promising for further mass market application. Recent experiments with all-normal-dispersion PM-NPE mode-locked lasers both can achieve dissipative soliton (DS) pulses and noise-like (NL) pulses. Nielsen et al. demonstrated an all-PM mode-locked Yb-doped fiber laser where NPE process occurred between a FM and a polarizer [7], which delivered NL pulses. Zhou et al. presented DS laser mode-locked with PM NPE in a semi ring cavity [8], generating DS pulses with 2.9 nJ single pulse energy and 5.9 ps pulse width. The application of Faraday mirror (FM) compensates the birefringence effect in fibers. Szczepanek et al. presented a new method, using three PM-fiber segments by setting proper splicing angle, to achieve NPE process [9]. When increasing the number of fiber segments, more symmetrical output pulse spectrum and time profile could be obtained [9–12]. But this scheme has strict requirements on the length of the optical fiber. Later, the group reported a multi-segment all-PM-fiber NPE reflective artificial SA [13]. The oscillator emitted 1 nJ pulses with duration of 230 fs after compression at a repetition rate of 13.4 MHz. In terms of optimizing the self-starting performance of PM-NPE mode-locked fiber lasers, Peng et al. demonstrated an improved PM-NPE structure which is consisted of a piece of PM gain fiber and a FM in combination with angle splicing [14]. The slope of nonlinear transmission curve of SA is steepened thanks to the gain fiber, which contributes to the self-starting of mode locking.
In the aforementioned works, all-PM fiber lasers mode-locked by PM-NPE worked in all normal or anomalous dispersion regime, however, no accomplishment of other net cavity dispersion situation was yet reported by this SA configuration. The dispersion management (DM) technique can improve the operation of fiber lasers by controlling the excess nonlinearity effect. The DM cavity can provide relatively wide spectrum, which support shorter pulse and will be very suitable for further amplification and compression system [15–17].
In this letter, we demonstrate an all-fiber all-PM dispersion-managed ultrafast Yb-doped laser mode-locked by PM-NPE, for the first time to our knowledge. The dispersion-managed PM-NPE fiber laser was investigated both numerically and experimentally for a wide net cavity dispersion region. The output pulses for dispersion-managed soliton, dispersion-managed dissipative soliton, bound state soliton and noise-like regime were achieved respectively in different net cavity dispersion conditions under different pump power and the characteristics for each region were investigated by numerical analysis, so it is with the dynamics of DM soliton inside the cavity. Numerical simulations mostly confirm the experimental results.
2. Experimental setup
The schematic diagram of the proposed all-PM-NPE mode-locked fiber laser is illustrated in Fig. 1. The linear cavity is composed of entirely PM fibers (PM980, Nufern) and PM optical components. The gain is provided by a 90 cm PM Yb-doped fiber (PM-YSF-HI-6/125, Nufern) with small pump absorption of ∼250 dB/m @ 976nm. The active medium is pumped via wavelength division multiplexer (WDM) with a laser diode (LD) that operates at 976 nm with an maximum output power of 500 mW. The chirped fiber Bragg grating (CFBG) is employed for intra-cavity dispersion compensation. The dispersion of the CFBG has been measured to be -0.79 ps2 at 1030 nm. Simultaneously, the CFBG serves as both Gaussian shaped bandpass filter and output coupler of the linear cavity. It possesses a measured peak reflectivity of about 30% centered at 1030 nm with spectral bandwidth of 16 nm.
Fig. 1. Schematic diagram of all-PM-NPE ultrafast fiber laser. PM, polarization maintaining; CFBG, chirped fiber Bragg grating; LD, laser diode; ISO, isolator; WDM, wavelength division multiplexer; PM-YSF, polarization maintaining Yb-doped fiber; FM, Faraday mirror.
The pivotal part of the laser cavity is the artificial saturable absorber composed of a fast axis blocked WDM, PM-YSF, PM fiber and FM. The WDM transmits only light polarized along the slow axis, which acts as a polarizer in the NPE structure so that the low power pulse without proper polarization rotation would be attenuated. In order to change the polarization, the opportune splicing angle is acquired between the slow axes of two PM fibers. Furthermore, the NPE takes place in the gain fiber and the PM980 regarded as Kerr medium, as shown in red arrow line in Fig. 1, where the pulse polarization state is affected by the Kerr nonlinearity. According to theoretical analysis and previous experiments [7–14], we find that the gain fiber is beneficial to increase the slope of transmittance curve of SA at low power, which facilitates its self-starting and mode locking. Using a FM is a simple solution for effectual compensation of group velocity mismatch (GVM) between two orthogonal polarizations induced by fiber birefringence.
In our experiment, the output power was measured with thermal power meters (Gentec-EO). The optical spectra of the laser were recorded by an optical spectrum analyzer (Yokogawa) with a resolution of 0.02 nm. The RF spectra were recorded by a RF spectrum analyzer (Agilent, Model: N9320B) and the autocorrelation traces of the pulses were measured with a commercial autocorrelator (Femtochrome, Model: FR 103-XL).
3. Experimental results and analysis
Once the optimum conditions of splicing angle and length of PM980 were captured, self-started mode-locking could be achieved simply by increasing the power of the pump LD. By carefully adjusting the splicing angle to 32° between slow axes of two PM fiber and setting the length of PM980 to 9 m, self-starting and stable picosecond mode-locked pulses were obtained. Experimentally, the net cavity dispersion (ND) is altered through slightly changing the fiber length (L1) of PM980 between CFBG and WDM.
When ND is close to zero but still positive, which equals to 0.039 ps2, the mode-locked output pulse with the widest spectrum was achieved. By increasing pump power to 270 mW, the laser was mode-locked with multi-pulsing delivery, as shown in Fig. 2(a). The bound state operation (Fig. 2(b)) was observed through appropriately reducing the pump to 79 mW. When gradually decreasing the pump power to 50 mW, stable single mode-locking pulses were exported from CFBG with average powers of 2.265 mW at a repetition rate of 6.17 MHz. A broad smooth pulse spectrum with 3-dB bandwidth of 37.84 nm centered at 1030.15 nm was obtained at the output port, which is shown in Fig. 2(c). The RF spectra around the fundamental and harmonic repetition rates are shown in Fig. 2(f) and its inset, measured at a resolution of 10 Hz and 1 kHz, respectively. The RF spectrum centered at 6.17 MHz, presented in Fig. 2(f), shows a signal-to-noise ratio of about 65 dB of the generated pulses. Additionally, the laser directly produced pulses with pulse duration of 10.35 ps, which were compressed down to 161.37 fs under the assumption of a sech2 shape by grating pairs (600 line/mm), as shown in Fig. 2(d) and Fig. 2(e). The corresponding time bandwidth product of compressed pulses is larger than the Fourier Transform limit. This may be due to uncompensated high order dispersion [18]. The power stability test of the laser over 2 hours is shown in Fig. 2(g). A mean output power of 2.365 mW with ∼0.0005 mW rms instabilities over 2 hours represents a 0.02% relative rms noise with respect to the average signal power.
Fig. 2. (a) Optical spectrum of multi-pulsing operation; inset, autocorrelation trace of multiple pulses; (b) optical spectrum of bound state; (c) optical spectrum of single pulse mode-locking operation; (d) autocorrelation trace of output pulse; (e) autocorrelation trace of the compressed pulse; (f) the radio-frequency spectrum at the fundamental frequency; inset, RF spectrum at harmonic frequency; (g) output power stability test in a duration of 2 hours.
Then we examined the dependence of the laser operation on the net cavity dispersion. Figure 3 shows the characteristics of output pulses as a function of the ND values, which range from relatively large negative dispersion to considerably large positive dispersion. The cavity produced pulses with individual characteristics working in different ND regions. When the ND was anomalous, the laser generated NL pulses. Note that average power of the NL pulse given in Fig. 3(a) was the output power when NL operation self-starting. Passive mode-locked dispersion-managed soliton pulses were achieved at the dispersion conditions ranging from 0.023 ps2 to 0.064 ps2 at mode-locking threshold of 210∼270 mW. At the dispersion conditions ranging from 0.080 ps2 to 0.197 ps2, self-starting DS pulses were achieved, whose mode-locking thresholds were about 260∼340 mW. When the ND was positive and more than 0.25 ps2, the laser generated NL pulses at mode-locking threshold of about 430 mW. By contrast, self-starting threshold of pulse generation became higher when ND was lager. It might be related to the higher requirement of the modulation depth of SA when the laser propagate in the normal dispersion region [19].
Fig. 3. (a)Output pulse characteristics of different net cavity dispersions (MP: multi-pulsing); (b) output pulse characteristics of different ND.
When the ND was from 0.038 ps2 to 0.197 ps2, the stable mode-locked single-pulse operations were obtained at relatively low pump power even when the pump power is decreased below the continuous wave (CW) threshold. It is worth mentioning that the cavity operation will generally transform from NL pulses to bound state and then to single mode-locked pulses with the same repetition rate by appropriately reducing the pump power. The spectra of the mode-locked laser under different dispersion working regions are presented in Fig. 3(b). We set ND parameters as 0.197 ps2, 0.152ps2, 0.0797 ps2 and 0.039 ps2, corresponding to repetition rate of 5.18 MHz, 5.43 MHz, 5.88 MHz and 6.17 MHz. Steep rising and falling edges could be observed in the spectrum of blue curve in Fig. 3(b) under the pump power of 54 mW, which is attributed to the DS feature. But when the ND was scaled up to 0.251 ps2, as shown in Fig. 4, the laser worked in NL regime, and produced pulses with 39.38 mW of average power at 271 mW of pump power and 4.91 MHz repetition rate as shown in Fig. 4.
When the ND was from 0.023 ps2 to 0.032 ps2, the laser maintained exporting mode-locked pulses, nevertheless, they are multi-pulsing states. If the pump was decreased further, the laser was incapable of generating ultrashort pulses and delivered NL pulses.
Different from typical pulse operation achieved in the normal dispersion region, the output pulses here exhibit characteristics of NL operation in the anomalous dispersion region, showing representative autocorrelation (AC) trace with a double-scale structure with a narrow coherence peak riding on a broad pedestal. Figure 5 exhibits the specifics of NL pulses working at a repetition rate of 8.13 MHz equivalent to the ND of -0.160 ps2. The output power of 64.96 mW was limited by the maximum pump power of LD. The output performance of NL pulses matches well with the simulation results (as shown in Part 4).
In NL regime, whatever in the normal dispersion region or in the anomalous dispersion region, the laser realized self-starting at high power. As the pump power gradually decreased, the laser still exhibited features of pulses in NL regime, and the output power decreased. When the pump power reduced to low enough, the laser was unable to be mode-locked.
According to PM-NPE architecture, both the splicing angle and PM980 fiber length can change the saturable absorption characteristics. The splicing angle can not only change the transmission curve period but also effect the modulation depth of the SA [7–11,14]. In previous experiments, the output property of the laser at about 6 MHz repetition rate was relatively stable. In order to judge the impact of the splicing angle between slow axes of two PM fiber on output performance, we tried to change it from 18° to 40° with fixed repetition rate around 5.99 MHz which corresponding to ND of 0.064 ps2. In this situation, the larger angle of splice was, the easier it was to obtain single pulse mode locking. When the splicing angle was from 30° to 18°, the single mode-locking pulses could be obtained although it was unstable. However, when the angle was more than 40° or less than 18°, the stable mode locking pulses failed to be acquired. Figure 6 shows typical AC traces and the corresponding spectra of output pulses emitted directly from the laser. As shown in Fig. 6, nonlinear effects accumulate distinctly with increasing the angle resulted in widening spectra.
Fig. 6. (a) Spectra and (b) autocorrelation traces of output pulses for different cross-splicing angle when ND=0.064 ps2.
4. Simulation results and analysis
To confirm the experimental observations, we numerically simulated the pulse formation in the laser cavity under different cavity dispersion. We used the coupled nonlinear Schrodinger equations, written as below [20].
Table 1. Simulation Fiber Parameters of Laser
As the saturation energy is increased, the output pulses exhibit different characteristics at different ND. Primarily, we set L1=4 m corresponding to ND=-0.075 ps2. We choose four different values of ${E_{sat}}$ as 0.02 nJ, 0.03 nJ, 0.04 nJ and 0.045 nJ. Figure 7 shows the simulation results of output directly from CFBG. Note that other simulation results in this letter are from this location as well. The pulse width broadens as the pump power increasing, up to 1.822 ps, 2.01 ps, 2.306 ps and 2.541 ps respectively. In addition, the spectral width widens with ${E_{sat}}$ increasing to 0.04 nJ and then narrows as ${E_{sat}}$ continues to raise, which is dominated by the self-phase modulation (SPM) effect. Figure 7(c) also provides the pulse energy evolution in the anomalous dispersion region. It can be seen in Fig. 7(c) that the light propagation in the cavity over 150 roundtrips evolve into the stable mode locking state. Compared with the simulation results of ND parameters as -0.17 ps2, as shown in Fig. 7(d)-(f), the laser can emit pulses with higher power, which achieve mode-locking states in a larger range of ${E_{sat}}$. And it works in NL regime when pump continues to increase.
Fig. 7. (a) Spectra; (b) autocorrelation traces; (c) pulse energy evolution of output pulses when ND=-0.075 ps2. (d) Spectra; (e) autocorrelation traces; (f) pulse energy evolution of output pulses when ND=-0.17 ps2.
Then, we lengthen L1 to 5.5 m in accord with ND parameters as -0.006 ps2. ${E_{sat}}$increases to 0.02 nJ, 0.04 nJ and 0.06 nJ. The spectral width increases to 6.296 nm, 9.425 nm and 10.589 nm, and the corresponding pulse widths are 2.34 ps, 2.678 ps and 2.97 ps, respectively. Figure 8(a) depicts the spectral profiles which are smoother than those of ND=-0.075 ps2. The pulses are distorted in the time domain evolving to analogous rectangular pulses, whose shape of autocorrelation traces is similar to triangle. When the values of ${E_{sat}}$ increase slightly, the initial pulse needs to propagate so more round trips that the pulse train comes to stable mode-locking spontaneously. The comparison among Fig. 7(c), Fig. 7(f) and Fig. 8(d) turns out that the output power shares the same rising tendency with ND increasing. Additionally, it is obvious that the range of ${E_{sat}}$ is expanded to 0.06 nJ broader than that of ND=-0.075 ps2.
Fig. 8. (a) Spectra; (b) time domain; (c) autocorrelation traces; (d) pulse energy evolution of output pulses when ND=-0.006 ps2.
However, when increasing ${E_{sat}}$ to 0.08 nJ in the anomalous dispersion region, the laser no longer works in single soliton operation but in NL operation. Figure 9 shows the spectrum and the AC trace of NL operation with ND=-0.17 ps2. Note that the AC trace in Fig. 9(b) is nearly close to that in Fig. 5(b) of ND=-0.160 ps2 in preceding experiments.
Fig. 9. (a) The average linear spectrum; (b) the average autocorrelation traces of NL pulses when ND=-0.17 ps2.
Figure 10 shows the simulation characteristics with ND=0.04 ps2 which are consistent with the experimental results. In this case, a smooth spectrum is similar to that of Fig. 2(c), as presented in Fig. 10(a). When the ND rises gradually, the spectral profile shows a typical spectral characteristic of DS. The mode-locked laser is operating with bound states as adjusting${E_{sat}}$ from 0.08 nJ to 0.12 nJ in succession. We give the features of bound state operation with${E_{sat}}$=0.08 nJ in Fig. 10(d)-(g). It is mentioned that Fig. 10(d) is a transient linear spectrum operating in 400 r. Considering the speed limitation of a conventional optical spectrum analyzer, we superimpose the transient spectra from 900 r to 1000 r, and the modulation depth of the superposition spectral structure in Fig. 10(e) is much smaller than that of the transient spectrum because the output pulses in time domain are not completely stable observed from the simulation. It is obvious that the pulse needs to propagate more than 250 r in the cavity to achieve a relatively stable state. When ${E_{sat}}$ is further increased, the cavity generates NL pulses. Figure 10(h) ∼Fig. 10(k) show the NL output performances of ${E_{sat}}$ = 0.2 nJ.
Fig. 10. DS output characteristics when ND=0.04 ps2. (a) Spectra of output pulse; (b) autocorrelation traces; (c) pulse energy evolution. Output pulses characteristics when ${E_{sat}}$=0.08 nJ and ${E_{sat}}$=0.2 nJ respectively. (d)(h) Linear spectrum of 400 r; (e)(i) the average linear spectrum at 900∼1000 r; (f)(j) autocorrelation trace of pulse; (g)(k) pulse energy evolution.
When L1 is increased to 9 m corresponding to ND parameters as 0.155 ps2, the spectra are close to output spectral characteristics of all-normal dispersion semi ring cavity [8], as shown in Fig. 11. As ${E_{sat}}$ increases, the pulse appears a small pulse trail structure in the time domain, which is contribute to the basement of AC. Also the output energy of mode-locked pulses is larger than that working in the anomalous dispersion region. When increasing ${E_{sat}}$ continually to 0.2 nJ, the laser emits NL pulses.
Fig. 11. (a) Spectra; (b) time domain; (c) autocorrelation traces; (d) pulse energy evolution of output pulses when ND=0.155 ps2.
To delve into the nonlinear dynamics of pulses in the fiber laser, we also simulate the evolution of DM soliton during a single roundtrip in the cavity as shown in Fig. 12. The simulation parameters are same as these of Fig. 2. The linear cavity is symmetrically expanded in the position of FM to perform a simulation conveniently. Due to the distinctive PM-NPE configuration, the pulse is divided into two beams along slow axis and fast axis of PM fiber at the first splicing point with different group velocities. Since passive fiber and gain fiber both have a normal second-order dispersion in 1 µm, two polarization lights with negative chirp are compressed through propagation in the time domain. Also the spectrum becomes narrower on account of negative chirp and SPM. At first PM gain fiber site, the rate of pulse reduction suddenly accelerates under the influence of additional gain narrowing. When arriving at FM, the distance between the two polarized pulses reaches a maximum due to the birefringence of the PM fibers. Following this, the beams on the fast and slow axes are exchanged their position in time, that is, the light previously transmitted on the fast axis begins to transmit along the slow axis, as visually shown in Fig. 13. As illustrated in insert of Fig. 12, saltation of pulse width occurs in ∼18.1 m where the two polarized pulses begin to converge, which means that the pulse with polarization along the slow axis is overtaken in time with respect to the other pulse. The value of negative chirp reduces gradually until the pulses propagating to the second PM gain fiber through interaction of dispersion and nonlinear effects on pulses. It can be seen in Fig. 12 that the pulse duration reaches the minimum value at the chirp-free point located at ∼28.6 m. After that, the pulse chirp starts to become positive so that the pulse duration and spectral width both widen simultaneously in abscissa between 29.1 m and 36.1 m. Note that the laser becomes a linearly polarized light through the second WDM. When transmitting through CFBG, the spectral width attains the maximum of 12.128 nm, and the spectrum reflected back into the cavity is narrowed down to 9.92 nm, while the transmitted pulse spectrum is changed to 19.632 nm due to reflected bandwidth of CFBG. The pulse evolves from a positive chirped pulse of 4.05 ps to a negative chirped pulse of 10.42 ps which is affected by a large negative dispersion of CFBG. As for the spatio-temporal dynamics of the dispersion-managed soliton evolution process, it can be seen from the Fig. 13.
Fig. 12. The intra-cavity evolutions of pulse duration, spectral bandwidth and energy along the cavity position.
5. Conclusion
In this paper, we demonstrated an all-polarization-maintaining dispersion-managed ultrafast fiber laser mode-locked by PM-NPE. The laser can operate in different regions among a wild net dispersion experimentally, including dispersion-managed solitons, dispersion-managed dissipative solitons, bound state solitons and noise-like pulses. The all-fiber all-PM laser directly generates stable pulses with the widest spectrum of 37.84 nm at a repetition rate of 6.17 MHz when the net cavity dispersion is 0.039 ps2. Stable mode-locked pulses with pulse duration of 10.35 ps were obtained, which were compressed to 161.37 fs. The dispersion-managed soliton pulse with a wider and smoother spectrum is a practicable candidate of seed sources for amplification and compression. We numerically investigated the characteristics and dynamics of PM-NPE dispersion-managed ultrafast fiber laser under different net cavity dispersions. The pulse propagation behaviors are unique according to the nonlinear dynamics process. As the gain saturable energy increasing, the cavity can produce dispersion-managed soliton pulses, bound state pulses and noise-like pulses when the net cavity dispersion is positive still near zero. Moreover, no bound state pulses are obtained in anomalous dispersion region and larger normal dispersion region. When the net cavity dispersion is increased, the laser can achieve mode-locking states in a larger range of gain saturable energy and produce higher output energy. The numerical indication was almost in agreement with the experimental results.
Funding
National Natural Science Foundation of China (61527822); National Key Research and Development Program of China (No. 2017YFB0405201); Beijing Municipal Commission of Education (KM201910005003).
Disclosures
The authors declare no conflicts of interest.
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