Route to stable dispersion-managed mode-locked Yb-doped fiber lasers with near-zero net cavity dispersion

Dongyu Yan; Bowen Liu; Jie Guo; Meng Zhang; Yuxi Chu; Youjian Song; Minglie Hu

doi:10.1364/OE.403456

1. Introduction

Mode-locked Yb-doped fiber lasers are becoming increasingly important in different scientific fields such as, frequency comb spectroscopy [1,2], optical metrology [3], and biomedical imaging [4]. These lasers have attracted extensive applications due to their short pulse duration and high pulse energy. Meanwhile, various pulse shaping mechanisms such as solitons [5], dispersion-managed solitons [6], similaritons [7], and dissipative solitons [8], have been explored to improve the laser performance. Specifically, the dispersion-managed mode-locked fiber lasers with pulse breathing process guarantee a short pulse duration [9] and low timing jitter [10].

For dispersion management in Yb-doped fiber lasers, chirped fiber Bragg gratings (CFBGs) have been exploited in cavities to provide anomalous dispersion. The CFBG offers attractive advantages including all-fiber configuration, compactness, and low insertion loss compared with other dispersion-compensating components like grating pairs [11] and photonic crystal fibers [12]. However, the CFBG reflection bandwidth is limited by fabrication technique, and is much narrower than the gain bandwidth of the Yb-doped fibers [13]. Consequently, the CFBG induces an obvious spectral filtering effect, affecting the operation of mode-locked fiber lasers. And some theoretical studies have demonstrated that spectral filtering plays a decisive role in pulse breaking [14,15] and soliton regimes transition [16] of dispersion-managed mode-locked fiber lasers. However, studies of the spectral filtering effect on mode-locking stability of mode-locked Yb-doped fiber lasers have not been reported yet.

Simulation studies on dispersion-managed mode-locked fiber lasers have demonstrated that the properties of the output pulses are significantly affected by the net cavity dispersion (NCD) [17,18]. The dechirped pulse duration is predicted to be minimum at near-zero NCD [18]. However, simulation studies have revealed an unstable region near zero NCD where stable mode-locking cannot be attained [19]. The unstable region near zero NCD has been experimentally observed in Er-doped fiber lasers and it is attributed to the effect of gain filtering [20,21]. As the pulse spectral bandwidth increases, the filter effect becomes more apparent and the loss from the gain filtering rises. Subsequently, the peak power of the pulse is reduced by this extra loss, leading to insufficient nonlinear effect to support stable mode-locking. In dispersion-managed mode-locked Yb-doped fiber lasers, the CFBG utilized for dispersion compensation induces a strong filtering effect potentially causing instability [13,22]. To resolve this near-zero NCD instability, saturable absorbers (SAs) with high modulation depths can be used [18,23]. Therefore, it is important to investigate the stability of mode-locking as affected by spectral filtering of different modulation depths.

In this paper, we numerically investigate the stability of a dispersion-managed mode-locked Yb-doped fiber laser with a strong filtering effect near zero NCD. According to the simulations, the size of the unstable region depends on the modulation depth of the SA. When the modulation depth is deep enough to compensate for the spectral filtering loss, stable mode-locking can operate throughout the dispersion regime. Experimentally, the stable mode-locking is obtained at near-zero NCD by using a semiconductor saturable absorber mirror (SESAM) with a modulation depth of 34%. The results of output spectral bandwidth against the NCD are found to be consistent with the numerical simulation. By optimizing the NCD, the oscillator generates pulses with a 17-nm bandwidth and a 1032-nm central wavelength. The dechirped pulse duration is 139 fs. Finally, a compact all-fiber amplifier is constructed to further increase the pulse energy, making it as a useful tool for scientific research.

2. Numerical simulation and results

Numerical simulation is performed to analyze the stability of dispersion-managed mode-locked Yb-doped fiber lasers with near-zero NCD. The numerical simulation model is based on a linear cavity configuration, as shown in Fig. 1. It consists of: a piece of Yb-doped fiber (YDF), a piece of single-mode fiber (SMF), a saturable absorber (SA), and a chirped fiber Bragg grating (CFBG). To separately analyze various effects of the CFBG, the model is split into three components: a short dispersion compensating fiber (DCF), a filter, and an optical coupler (OC).

Fig. 1. The numerical simulation model. YDF: Yb-doped fiber; SMF: single-mode fiber; SA: saturable absorber; DCF: dispersion compensating fiber; OC: optical coupler. The dispersion compensating fiber, the filter, and the optical coupler constitute a chirped fiber Bragg grating.

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In this simulation, the pulse evolution of fiber laser is modeled via the modified nonlinear Schördinger equation [24]:

(1)$$\begin{array}{l} \frac{{\partial A({z,\tau } )}}{{\partial z}} + \frac{i}{2}\left( {{\beta^{(2 )}} + ig\frac{1}{{\Omega _g^2}}} \right)\frac{{{\partial ^2}A({z,\tau } )}}{{\partial {\tau ^2}}}\\ = \frac{g}{2}A({z,\tau } )+ \frac{{{\beta ^{(3 )}}}}{6}\frac{{{\partial ^3}A({z,\tau } )}}{{\partial {\tau ^3}}} + i\gamma {|{A({z,\tau } )} |^2}A({z,\tau } ), \end{array}$$

where A(z,τ) is the field envelope, z is the propagation coordinate, τ is the time-delay parameter, β⁽²⁾ and β⁽³⁾ are the corresponding second-order and third-order dispersion parameters, γ is the nonlinear parameter, and Ω_g is the gain bandwidth. The gain g is modeled by:

(2)$$g = \frac{{{g_0}}}{{1 + {{{P_{\textrm{ave}}}(z )} / {{P_{\textrm{sat}}}}}}},$$

where g₀ is the small-signal gain, P_sat is the saturation power and P_ave is the average power of pulses. When the signal pulse enters the gain fiber from both sides in linear cavities, the average power is calculated as:

(3)$${P_{\textrm{ave}}}(z )= {f_{\textrm{rep}}}\int_{ - {{{T_R}} / 2}}^{{{{T_R}} / 2}} {{{|{A({z,t} )} |}^2}} dt + P_{\textrm{ave}}^ \leftarrow (z),$$

where f_rep is the repetition rate and T_R is the roundtrip time. $P_{\textrm{ave}}^ \leftarrow (z)$ is the average power of the incoming signal from the opposite direction of the gain fiber. The time-dependent absorption q(t) of a slow saturable absorber is modeled by:

(4)$$\frac{{\partial q(t )}}{{\partial t}} ={-} \frac{{q(t )- {A_0}}}{{{\tau _{\textrm{SA}}}}} - \frac{{{{|{A(t )} |}^2}}}{{{E_{\textrm{SA}}}}}q(t ),$$

where A₀ is the non-saturated loss of an unexcited absorber, τ_SA is the recovery time and E_SA is the absorber saturation energy. The reflection R(t) of the saturable absorber is calculated by:

(5)$$R(t) = 1 - q(t )- {\alpha _{\textrm{ns}}},$$

where α_ns is the nonsaturable loss. The modulation depth ΔT of a saturable absorber is defined as the difference between the non-saturated loss and the nonsaturable loss:

(6)$$\Delta T = {A_0} - {\alpha _{\textrm{ns}}},$$

The parameters of the simulation are similar to the experimental values. The gain fiber is a piece of 56 cm YDF. The gain bandwidth of the YDF is set at 40 nm and centered at 1030 nm. The small-signal gain is 30 dB and the gain saturation energy is 0.1 nJ [25]. The SA is modeled with a recovery time of 0.7 ps, a saturation energy of 50 pJ and non-saturable loss of 22%. The group delay dispersion of the CFBG is −0.1 ps² at 1030 nm. The CFBG reflection bandwidth is 17.5 nm and the peak reflectivity is 11.3% centered at 1030 nm. The CFBG is modeled as a 10-cm dispersion compensating fiber (DCF) with a −1 ps²/m group velocity dispersion (GVD) at 1030 nm and a Gaussian bandpass filter with a 17.5-nm bandwidth, a 1030-nm central wavelength, and a 89% coupling ratio. In the simulation, the length of the SMF is adjusted to vary the NCD from −0.03 ps² to +0.03 ps².

In the simulation, if the relative change of pulse energy is lower than 10⁻⁹ in two consecutive round trips, the solution is assumed to be converged. If the solution does not converge after 2000 roundtrips, the laser is assumed to be operating in an unstable state. Figure 2(a) shows the number of roundtrips until the solution has converged near zero NCD with different modulation depths of SAs. At 10% modulation depth, stable laser pulses cannot be obtained between +0.008 ps² and +0.02 ps² (Fig. 2(a), white area)). When the modulation depth is increased to 20%, the unstable region reduces by 50%. When the modulation depth is larger than 30%, the stable mode-locking operates throughout the dispersion regime. When the NCD is +0.01 ps², the maximum output spectral bandwidth can be obtained, as it will be described in detail below. But it is difficult to achieve stable mode locking close to +0.01-ps² NCD when modulation depth is lower than 30%. Figures 2(b) and (c) show the intra-cavity pulse evolution in the time and frequency domains at +0.01-ps² NCD when using a SA with a 30% modulation depth. The simulation predicts the maximum pulse duration of 3.43 ps at the entrance of CFBG. After the CFBG, the pulse is rapidly compressed to 150 fs, corresponding to a temporal breathing ratio of 23. The temporal compression leads to a high peak power, thus the spectrum shows a fast broadening from the nonlinear effect in the gain fiber. Meanwhile, the spectral filter effect of CFBG is much obvious, and the asymmetric spectral effect of slow saturable absorbor is also shown.

Fig. 2. (a) Number of roundtrips until convergence against NCD with different modulation depths. Linear scale: 0 oe-28-20-29766-i001 2000 (white area: unstable region). (b) Time-domain and (b) frequency-domain evolution at +0.01-ps² NCD using a SA with a 30% modulation depth. Linear scale: 0 oe-28-20-29766-i002 1.

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Numerical simulation is also performed to analyze the effect of spectral filtering on the stability of dispersion-managed mode-locked fiber lasers. Figure 3 shows the spectral bandwidth at different modulation depths as the CFBG filter bandwidth varies from 30 nm to 10 nm. For a deep modulation depth of 40%, stable operation can be obtained throughout the dispersion regime with different filter bandwidths. The filtering effect only restricts the maximum spectral bandwidth in the dispersion-managed mode-locked fiber laser. At a 30-nm filter bandwidth, the output spectral bandwidth suddenly jumps to 17.2 nm at +0.01-ps² NCD. By contrast, there is no obvious jump at a 10-nm filter bandwidth. When the modulation depth is 30%, unstable region (Fig. 3(d), white area) begins to appear around +0.015-ps² NCD at a 10-nm filter bandwidth. When the modulation depth is 20%, the range of the unstable region increases as the filter bandwidth of the CFBG gets narrower. However, stable operation can still be attained throughout the dispersion regime at a 30-nm filter bandwidth (Fig. 3(a)). As the modulation depth reduces to 10%, the range of the unstable region further increases. When the filtering bandwidth is lower than 10 nm, the output pulses are unstable in the entire dispersion regime. As the modulation depth decreases, the pulse energy slightly increases, enhancing the nonlinear effect and broadening the spectrum. But on the other hand, sufficient modulation depth is required to overcome the instability from the spectral filtering effect.

Fig. 3. Plots of spectral bandwidth (FWHM) against NCD at different modulation depths when using CFBGs with filter bandwidths of (a) 30 nm, (b) 17.5 nm, (c)12 nm, and (d) 10 nm. Linear scale: 5 nm oe-28-20-29766-i003 18 nm (white area: unstable region).

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3. Experimental setup and results

The experimental setup of the dispersion-managed mode-locked Yb-doped fiber laser is shown in Fig. 4. The laser cavity design is based on a Fabry-Perot (FP) cavity configuration. This laser is constructed with all polarization maintaining (PM) fibers for environmental stability. A highly Yb-doped PM fiber (Nufern, PM-YSF-6/125-HI) with a pump absorption of 250 dB/m at 975 nm and a length of 56 cm is used as a gain medium. This fiber is pumped by a single-mode 976-nm laser diode (LD), through a PM wavelength division multiplexer (WDM). Self-starting passive mode-locking is achieved via a SESAM. The SESAM is glued on a copper heat sink mounted on a mirror holder and is used as one end mirror of the FP cavity. Based on the above simulation results, a SESAM with a modulation depth of 34%, a relaxation time of 700 fs, and a saturation fluence of 70 µJ/cm² (Batop, SAM-1040-56-700fs) is chosen. To achieve the saturation threshold, a lens with a 11-mm focal length is utilized in focusing the light. A CFBG inscribed in a PM980 fiber is employed to compensate for intracavity dispersion. The dispersion of the CFBG is −0.1 ps² at 1030 nm, corresponding to ∼42 MHz repetition rate at zero NCD operation. The CFBG shows Gaussian-shaped reflection spectrum with a 17.5-nm bandwidth and 11% peak reflectivity at 1030 nm, as shown in the inset of Fig. 4. An optical spectrum analyzer (YOKOGAWA, AQ6370B) is used to measure the output optical spectrum of the laser. A radio frequency (RF) analyzer (Agilent, 8560EC) and a high-speed photodetector (Thorlabs, DET10A/M) are used to measure the RF spectrum of the pulse train. Furthermore, the temporal intensity is measured via a commercial optical autocorrelator (APE, PulseCheck).

Fig. 4. Experimental setup of the passively mode-locked all-PM fiber laser. LD: laser diode; WDM: wavelength division multiplexer; CFBG: chirped fiber Bragg grating; YDF: Yb-doped fiber; SMF: single-mode fiber; SESAM: semiconductor saturable absorber mirror. Inset: Measured reflection spectrum of the CFBG.

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The NCD can be changed from −0.015 ps² to +0.0056 ps² by altering the length of SMF between the collimator and the YDF. Figure 5(a) shows the FWHM spectral bandwidth of output pulses against the NCD at 50-mW pump power. According to the results, when the laser is operating at a net anomalous dispersion of −0.015 ps², it produces pulses with a 9.2-nm spectral bandwidth. In the anomalous dispersion regime, the spectral bandwidth gradually increases as the NCD reduces. As shown in Fig. 5(c), the laser generates pulses with Gaussian-like shape spectra. When the NCD is increased to normal dispersion, the maximum spectral bandwidth of 14.7 nm is obtained at +0.0021-ps² NCD. The output spectrum is shown in Fig. 5(d), and the typical steep edges of the spectrum indicate normal NCD. Further increasing the NCD to +0.0056 ps², the spectral bandwidth decreases to 11 nm. Notably, the spectral bandwidth decreasing rate in the normal dispersion direction is faster than the anomalous dispersion direction. Figures 5(d) and 5(e) show that the output spectra fit well in parabolic profiles, typical of a self-similar regime [16]. When the NCD is higher than +0.0056 ps², the laser keeps operating in the continuous-wave regime no matter the increase in pump power. As the NCD increases in the normal dispersion region, the pulse duration significantly increases. The longer pulses experience more loss from the absorption of the SESAM, thus stable mode-locking is not achieved. For comparison, the SESAM of the fiber laser is replaced by a low-modulation-depth (26%) one with a relaxation time of 3 ps and a saturation fluence of 50 µJ/cm² (Batop, SAM-1040-35-3ps). As shown in Fig. 5(b), stable mode-locking can be attained at a relatively large anomalous NCD at 80-mW pump power. As the dispersion approaches zero, the spectral bandwidth gradually increases. An unstable region (Fig. 5(b), grey shaded area) is observed when the NCD is higher than −0.015 ps². It is demonstrated that the SESAM with higher modulation depth can stabilize the mode-locking operation near zero NCD.

Fig. 5. (a) Spectral bandwidth of output pulses versus the NCD with 34% modulation depth of the SESAM. (b) Output spectral bandwidth versus the NCD with 26% modulation depth the SESAM. Output spectra with 34% modulation depth of the SESAM at a NCD of (c) −0.0062 ps², (d) +0.0021 ps², and (e) +0.0056 ps².

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The change of the spectral bandwidth is less obvious when the NCD varies in the anomalous dispersion region, so it is practically important for mode-locked lasers to operate at slightly negative dispersion. In our experimental setup, the NCD is −0.004 ps², where the mode-locking remains in the stretched-pulse regime. A continuous wave appears at 34-mW pump power. By increasing pump power to 45 mW, the laser delivers self-started mode-locking and stable single-pulse trains. When the pump power is 60 mW, the average output power is 6 mW, corresponding to 0.14 nJ pulse energy. According to Fig. 6(a), the output spectrum is centered at 1032 nm with a 17-nm bandwidth. The spectral profile fits well with a theoretical Gaussian profile (red dashed line). The repetition rate is 43.15 MHz, and the RF spectrum of the first harmonic of the pulse train is shown in the inset of Fig. 6(a). The signal-to-noise ratio is 80 dB, showing that this all-PM fiber laser has remarkable mode-locking stability. In Fig. 6(b), there is an autocorrelation trace of output pulses with a 3.8-ps pulse duration. With a 1000 lines/mm grating pair, pulses can be dechirped to 139 fs. The inset of Fig. 6(b) reveals that the autocorrelation trace fits well with a Gaussian function, indicating a high temporal quality.

Fig. 6. (a) Optical spectrum of output pulses (solid line) and Gaussian fitting (red dashed line) plots. Inset: The radio frequency spectrum of the first harmonic of the pulse train. (b) Autocorrelation trace of output pulses (solid line) and Gaussian fitting (red dashed line). Inset: Autocorrelation trace of the dechirped pulses (solid line) and Gaussian fitting (red dashed line).

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To scale up the output power, a compact two-stage Yb-doped fiber amplifier is constructed. The schematic of this all-PM fiber amplifier is shown in Fig. 7(a). A PM isolator is used after the fiber oscillator to avoid reverse reflections from the amplifier. In the first stage, a Yb-doped PM fiber (Nufern, PM-YSF-6/125-HI) with a length of 50 cm is used to amplify the seed pulse output from the oscillator. The first amplifier generates pulses of 22-mW average power at 200-mW pump power. In the second stage, a PM CFBG with +3.36-ps² GVD and −0.03-ps³ third-order dispersion (TOD) at 1035 nm is used as a stretcher. This CFBG is designed to compensate for the TOD of the grating compressor with 1600 lines/mm groove density. The gain fiber is a 1.5-m Yb-doped PM fiber. The second stage amplifier outputs 380-mW laser pulses with a 14-nm spectral bandwidth and a 1032-nm central wavelength (as shown in Fig. 7(b)). The output pulse is compressed to 168 fs by a 1600 lines/mm grating pair (as shown in Fig. 7(b)). This output power and dechirped pulse duration is suitable for biophotonics applications.

Fig. 7. (a) Experimental setup of the all-PM fiber amplifier. ISO: isolator; LD: laser diode; CFBG: chirped fiber Bragg grating; YDF: Yb-doped fiber; WDM: wavelength division multiplexer. (b) The spectrum and autocorrelation trace of the dechirped pulses (solid line) and gaussian fitting (red dashed line).

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4. Conclusion

In this study, we numerically investigate the effects of modulation depth and spectral filter bandwidth on the stability of a dispersion-managed mode-locked Yb-doped fiber laser near-zero NCD. It is observed that the unstable mode-locking region is significantly enlarged as the spectral filter bandwidth gets narrower. This instability is induced by the strong filtering effect of CFBG in the laser cavity, and can be overcome by increasing the modulation depth of SA. Based on this simulation, we demonstrate a route to obtain stable mode-locking operation of fiber lasers near zero NCD, via using a SA with high modulation depth. Accroding to this route, we develop a mode-locking fiber laser with CFBG for dispersion compensation. With the help of a SESAM of 34% modulation depth, the laser can keep stable mode locking at −0.004-ps² NCD, and output laser pulses with a 17-nm spectral bandwidth and a 139-fs dechirped pulse duration. Subsequently, a compact all-fiber amplification system is constructed to further increase the pulse energy to 9 nJ, making it desirable for nonlinear microscopy, frequency comb spectroscopy and precision metrology.

Funding

National Natural Science Foundation of China (U1730115, 11527808, 61535009, 61805174).

Acknowledgments

We thank Dr. Wei Chen at Nanjing University for his valuable advice on this work.

Disclosures

The authors declare no conflicts of interest.

References

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Route to stable dispersion-managed mode-locked Yb-doped fiber lasers with near-zero net cavity dispersion

Abstract

1. Introduction

2. Numerical simulation and results

3. Experimental setup and results

4. Conclusion

Funding

Acknowledgments

Disclosures

References

Cited By

Figures (7)

Equations (6)

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