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Abstract
High-repetition-rate (up to GHz) femtosecond mode-locked lasers have attracted significant attention in many applications, such as broadband spectroscopy, high-speed optical sampling, and so on. In this paper, the characteristics of dispersion-managed, polarization-maintaining (PM) 1-GHz mode-locked fiber lasers were investigated both experimentally and numerically. Three compact and robust 1-GHz fiber lasers operating at anomalous, normal, and near-zero dispersion regimes were demonstrated, respectively. The net dispersion of the linear cavity is adjusted by changing types of PM erbium-doped fibers (EDFs) and semiconductor saturable absorber mirrors (SESAMs) in the cavity. Moreover, the long-term stability of the three mode-locked fiber lasers is proved without external control. In order to better understand the mode-locking dynamics of lasers, a numerical model was constructed for analysis of the 1-GHz fiber laser. Pulse evolution simulations have been carried out for soliton, dissipative-soliton, and stretched-pulse mode-locking regimes under different net dispersion conditions. Experimental results are basically in agreement with the numerical simulations.
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1. Introduction
Femtosecond mode-locked lasers [1,2] play a pivotal role in many applications, most of which may benefit from a higher repetition-rate, such as a higher maximum interferogram acquisition rate in ultrafast and broadband spectroscopy [3,4], an improved signal-to-noise ratio (SNR) and a wider disambiguating frequency range in high-speed optical sampling [5], a purer signal extraction in microwave signal generation [6,7], a greater transmission capacity in coherent optical communications [8,9], an improved bioimaging quality in nonlinear bioimaging [10], a larger instantaneous bandwidth in photonic radars [11], and so on. In addition, it is worth mentioning that the cavity length is inversely proportional to the repetition-rate, which will make the system more compact.
The fiber-based laser, is considered an attractive choice for generating high repetition-rate femtosecond pulses, and stands out for its compactness, robust performance metrics, high reliability, high spatial beam quality, low maintenance and cost-efficiency, and is widely favored by researchers [12–29]. Conventional non-polarization maintaining fibers are sensitive to environmental perturbations, which may lead to vector solitons [30,31]. In order to avoid the perturbations from the variation of temperature, humidity, and air pressure, PM fibers have to be used. By using PM fibers, the linear polarization state can remain invariable during propagation, which is conducive to the realization of stable and reliable fiber laser [15,32–36].
Generally speaking, researchers use real saturable absorbers (SAs) to implement high repetition-rate mode-locked fiber lasers. So far, high repetition rate mode-locked fiber lasers have been obtained with different real SAs, such as semiconductor saturable absorber mirror (SESAM), carbon nanotubes (CNTs), graphene, and other two-dimensional materials [1,21,37–39]. Among those SAs mentioned above, the SESAM has been widely adopted in mode-locked fiber lasers for its reliability, flexibility, and commercial availability.
Moreover, with the dynamic balance among different factors such as dispersion, nonlinearity, gain and loss, the outputs of the stable mode-locked lasers can be in different soliton states. The net dispersion of the laser resonator can be designed to operate in the anomalous dispersion regime, normal dispersion regime, and near-zero dispersion regime, resulting in soliton mode-locking, dissipative soliton mode-locking and stretched pulse mode-locking respectively. Furthermore, the dispersion plays a key role in the noise of the resonator. Through proper dispersion management, it is expected that mode-locked laser source with lower noise can be obtained. And a lower noise laser will promote the development of the above applications [2].
However, compared with conventional MHz repetition rate, it takes more efforts to develop a stable GHz repetition-rate fiber laser. For instance, the trend of Q-switched mode-locking in GHz repetition-rate fiber lasers will inevitably increase [40–43]. Additionally, it is more difficult to realize dispersion management and suppress instability. in an ultrashort cavity with only10 cm-long fiber. Thus, for stable operation of high repetition-rate mode-locked fiber lasers, it is crucial to understand the internal mode-locking mechanism of fiber lasers and choose appropriate parameters. Numerical analysis is an important approach for understanding the physical mechanisms of mode-locked fiber lasers and for improving the laser performance. Previously, researchers have done a lot of theoretical simulation works on the dynamics of mode-locked lasers from different aspects [13,42–53].
1-GHz repetition rate is sufficient to adequately sample narrow gas absorption features at atmospheric pressure [4], while it also maintains flexibility when it refers to electronic interfaces and digital sampling (compared to a repetition rate up to 10 GHz and higher). However, there have been no detailed reports of investigation of dispersion managed polarization-maintaining 1-GHz fiber lasers both experimentally and theoretically.
In this paper, dispersion-managed polarization-maintaining 1-GHz mode-locked fiber lasers are investigated experimentally and theoretically based on commercial components. Numerical simulations based on the generalized nonlinear Schrödinger equation were constructed for three different dispersion regimes. The initial process of passive mode-locking and the characteristics of the output pulses were investigated. In experiment, three compact and robust 1-GHz fiber lasers operating at three different dispersion regimes were demonstrated, resulting in soliton mode-locking, dissipative soliton mode-locking and stretched pulse mode-locking respectively. The net dispersion of the linear cavity is adjusted by changing types of the erbium-doped fiber (EDF) and SESAM in the cavity. The experimental results are in very good agreement with numerical results. In section 2, we introduce the basic experimental structure of the 1-GHz mode-locked fiber laser. Section 3 introduces the numerical model used in this work. In section 4, we present the experimental and numerical results for the three mode-locked fiber lasers operated in different mode-locking regimes. In section 5, we discuss the results and give conclusions.
2. Experimental setup
Figure 1 illustrates the basic configurations of the polarization-maintaining 1-GHz mode-locked fiber laser using a SESAM. The laser cavity is simple and compact, consisting of a ∼10 cm PM EDF, two ceramic ferrules and a piece of SESAM. As a gain medium, both ends of the PM EDF were inserted and glued in a ceramic ferrule, and were flat-polished. In order to increase the pump efficiency, the dielectric films (DFs) were coated on both ends of the PM EDF. On the left side of the PM EDF, the DF exhibits a high transmittance of ∼98% at the pump wavelength of 980 nm, as well as a high reflectivity of ∼98% at 1550 nm. In contrast, on the right end of the PM EDF, the DF exhibits a high transmittance of ∼98% at 1550 nm, as well as a high reflectivity of ∼98% at 980 nm. The coated right end is then butt-coupled to a SESAM, which is the key device to realize mode-locking. The PM EDF was pumped by a 980 nm laser diode (LD) through a PM wavelength division multiplexer (WDM). The mode-locked optical pulses are then outputted through a PM isolator (ISO), which can prevent unwanted reflections into the laser cavity.
Fig. 1. Experimental setup of the all-PM 1-GHz mode-locked fiber laser. LD: laser diode; PM WDM: polarization-maintaining wavelength division multiplexer; PM ISO: polarization-maintaining isolator; DF: dielectric films; PM EDF: polarization-maintaining Er-doped fiber.
To realize dispersion management, two types of PM EDFs and two different SESAMs were used in this work. Both the PM EDFs and the SESAMs are commercially available. The first PM EDF (EDF-1) has an anomalous dispersion of -21 fs2/mm and a gain coefficient of 0.55 dB/cm at 1550 nm. The other PM EDF (EDF-2) has a normal dispersion of 30 fs2/mm at 1550 nm and a gain coefficient of 0.8 dB/cm at 1550 nm. And the two SESAMs: SESAM-1 and SESAM-2, both have a chip area of 4.0 mm × 4.0 mm and a thickness of 450 µm, were used as mode-locker. The main parameters of the SESAMs are listed in Table 1.
Table 1. Main parameters of SESAMs
As shown in Table 1, the dispersion of the SESAM-1 is positive while the dispersion of the SESAM-2 is negative. Generally speaking, the dispersion of SAs can be ignored since it is much smaller than that of the fiber. However, the fiber dispersion becomes very small because of the ultrashort cavity in 1-GHz mode-locked fiber lasers, so the dispersion of the SA must be taken into account. In this paper, we use the mutual compensation of SA dispersion and optical fiber dispersion to realize simple dispersion management. By properly matching the PM EDF and the SA, three different dispersion states can be obtained, leading to soliton mode-locking, dissipative soliton mode-locking and stretched pulse mode-locking respectively.
The optical spectrum of the output laser was measured by an optical spectrum analyzer at a spectral resolution of 0.02 nm. The pulse train was detected by a high-speed 50 GHz bandwidth photodetector, and monitored by an oscilloscope. The radio-frequency (RF) spectrum was detected by the same high-speed photodetector and measured by a RF signal analyzer. The pulse duration was measured by a commercial autocorrelator.
3. Numerical model
In order to further understand the pulse dynamics and mode-locking properties, we carried out numerical analysis of the 1-GHz mode-locked fiber lasers using the extended nonlinear Schrödinger equation:
The SA is simply modeled by a transmission function [54]:
where ΔT and αns are the MD and the nonsaturable loss respectively. I(t) is the instantaneous pulse energy and Isat is the saturation intensity. The transmission function indicates that the transmission of the material increases with the increasing of the incident beam intensity.In this work, the evolution starts from an initial noise pulse which was obtained by using a random function. The similar parameters used in the experiment were assumed as the simulation model. Different mode-locking states can be achieved by changing the dispersion parameters. Pulses evolution simulation has also been carried out for soliton, dissipative-soliton, and stretched-pulse mode-locking regimes.
4. Results and discussion
4.1 Soliton mode-locking regime
By using the EDF-1 and SESAM-1, the net dispersion of the cavity is estimated to be ∼-1500 fs2, leading to soliton mode-locking.
Firstly, in order to provide guidance for the experiment, we carried out a numerical analysis for the soliton mode-locking regime. Figure 2(a) shows the variation of the pulse width and spectrum width for the initial process of the 1-GHz fiber laser in the soliton mode-locking regime. Similarly, the evolutions of the peak power and the pulse energy are demonstrated in Fig. 2(b). To begin with, the noise circulated in the linear cavity and is amplified on each roundtrip by the gain fiber EDF. Due to the saturable absorption characteristics of the SA, the absorption loss of the part with strong light intensity is very small when passing through the SESAM. Thus, the stronger intensity components survive and continue to be amplified in the cycle. When the threshold is reached, the amplified pulse component realizes pulse shaping and pulse compression because of the soliton effect. At this time, the pulse width decreases rapidly, the spectrum width increases rapidly, and the peak power and pulse energy also increase rapidly. Stability of all above parameters is reached after about ∼100 roundtrips, when the initial random noise input is mode-locked into a stable pulse. A pulse width of ∼0.11 ps and a spectral width of ∼30.7 nm were obtained. The peaks arose in the temporal width are caused by the soliton effect. The output characteristics showed similar behavior to the previous work [44].
Fig. 2. Simulation results. (a) Variation of pulse width and spectrum width over 1000 roundtrips. (b) Variation of pulse peak power and pulse energy over 1000 roundtrips. (c) Evolution of the spectral profile for the pulse over 1000 roundtrips. (d) Evolution of the temporal profile for the pulse over 1000 roundtrips. (e) Spectral shapes of output pulse for soliton mode-locking regime. (f) Temporal shape of output pulse for soliton mode-locking regime.
Figure 2(c) and (d) shows the evolution of the spectral profile and the evolution of the temporal profile over 1000 roundtrips. We can clearly see the noise input eventually builds up as a single pulse after ∼100 roundtrips. The phenomenon of the shift of the pulse center position can be clearly observed in Fig. 2(d). After the pulse enters the steady state, the central part of the pulse shifts obviously to the right. However, as shown in Fig. 2(c), the evolution of the spectrum shows that the spectrum has no obvious shift after the steady state is achieved. This phenomenon shows that the pulse moves as a whole in the time domain, but the shape of the pulse does not change significantly.
Figure 2(e) and (f) show the characteristics of final output pulse for the soliton mode-locking regime. As shown in Fig. 2(e), a spectrum with Kelly sidebands was obtained, which is in good agreement with the experimental results in Fig. 3(b). And a sech2-shaped pulse was generated as shown in Fig. 2(f).
Fig. 3. Experimental results. (a) Typical pulse train of fundamental mode-locked fiber laser with ∼0.95 ns pulse interval. (b) Optical spectrum. (c) Measured RF spectrum. Inset: the wide-range RF output spectrum. (d) Measured autocorrelation trace (grey line) and sech2 fitting trace (red line).
In the experiment, thanks to the simple and compact structure of the laser, self-starting mode-locking could be achieved simply by increasing the pump power to the threshold power to achieve stable mode-locking. The output characterization of the laser is shown in Fig. 3.
For soliton mode-locking regime, a stable continuous wave mode-locked state is realized at a threshold pump power of 500 mW. Figure 3(a) shows the time domain characteristics of the mode-locked laser, which delivered uniform pulse trains with a temporal period of about 0.95 ns. Figure 3(b) illustrates the optical spectrum of the soliton mode-locking fiber laser with a typical Kelly sideband, which is in good agreement with the numerical results in Fig. 2(e). The optical spectrum has a central wavelength of 1567.5 nm and a 3 dB spectral bandwidth of 17.7 nm, which is equivalent to a transform-limited pulse width of ∼146 fs. As shown in Fig. 3(c), the RF spectrum indicates a 1.049 GHz fundamental pulse repetition rate with SNR of 82.9 dB, which matches with the temporal period of 0.95 ns in Fig. 3(a). The resolution bandwidth (RBW) and span are 10 Hz, and 800 kHz, respectively. The wide-range RF spectrum of the fundamental repetition rate and its harmonics in a span of 26.5 GHz (limited by the bandwidth of the RF signal analyzer) are depicted in the insert of Fig. 3(c). The considerably high SNR and the clear intensity of the wide-range RF spectrum confirm that the laser is operating at a steady continuous-wave (CW) mode-locking state. As shown in Fig. 3(d), the autocorrelation trace has a full width at half maximum (FWHM) of 467 fs, corresponding to a temporal width of 303 fs, when a sech2 pulse shape is assumed with a deconvolution factor of 1.54. The pulse width is larger than the 146-fs transform-limited pulse width, which indicates that the pulses are slightly chirped.
In order to further prove the stability of the laser, it was placed in a laboratory environment without any external control, and recorded its output power and spectra evolution for 3 hours. As a result, Fig. 4 shows the stability of the output power for 3 hours with a relative standard deviation (RSD) of 1.03%. The spectra recorded are shown in false color in the inset of Fig. 4 without any obvious collapse, indicating the stability of the 1-GHz soliton mode-locking fiber laser.
4.2 Dissipative soliton mode-locking regime
Similarly, by using EDF-2 and SESAM-1, the net dispersion of the cavity is estimated to be ∼+3600 fs2, resulting in a dissipative soliton mode-locking regime.
To make a comparison, a numerical analysis for the dissipative soliton mode-locking regime was carried out. Figure 5(a) and (b) show the initial process of the 1-GHz dissipative soliton mode-locked fiber laser. As shown in Fig. 5(a), the stability of the pulse width and spectrum width could be reached after ∼200 roundtrips. A pulse width of ∼1.65 ps and a spectral width of ∼7.51 nm were obtained. And a small periodical modulation was observed in the pulse width. Correspondingly, as shown in Fig. 5(b), the peak power and pulse energy tend to be stable as the pulse enters a stable mode-locking state. A slight overshoot was observed, especially for the peak power. Normally, it is necessary to use a spectral filter for dissipative soliton mode-locking. It is worth mentioning that we did not use any spectral filter, but dissipative soliton mode-locking was achieved successfully due to the spectral filter effect of the gain fiber EDF [51].
Fig. 5. Simulation results. (a) Variation of pulse width and spectrum width over 1000 roundtrips. (b) Variation of pulse peak power and pulse energy over 1000 roundtrips. (c) Evolution of the spectral profile for the pulse over 1000 roundtrips. (d) Evolution of the temporal profile for the pulse over 1000 roundtrips. (e) Spectral shapes of output pulse for dissipative soliton mode-locking regime. (f) Temporal shape of output pulse for dissipative soliton mode-locking regime.
Figure 5(c) and (d) shows the evolution of the spectral profile and the evolution of the temporal profile over 1000 roundtrips. It clearly shows the state of the pulse proceeding from noise into stable mode-locking. After about 200 roundtrips, both the time domain and the spectrum domain become stable.
Figure 5(e) and (f) show the characteristics of final output pulse for the dissipative soliton mode-locking regime. As shown in Fig. 5(e), a rectangle-like spectrum with a smooth roof and steep edges was obtained. Then, a gaussian-like pulse was generated as shown in Fig. 5(f).
Next, we conducted an experimental study. When the pump power was set to 550 mW, the continuous wave laser oscillation was achieved. Figure 6(a) shows the time domain characteristics of the mode-locked laser, which delivered uniform pulse trains with a temporal period of about 0.95 ns exiting the cavity. Figure 6(b) illustrates the optical spectrum of the dissipative soliton mode-locking fiber laser, which shows an asymmetric shape. Compared with the symmetrical shape in the simulation in Fig. 5(e), the asymmetrical shape in the experiment may be caused by the nonlinear absorption of the SA [17]. The optical spectrum has a central wavelength of 1561.9 nm and a 3 dB spectral bandwidth of 5.11 nm. As shown in Fig. 6(c), the RF spectrum indicates a 1.059 GHz fundamental pulse repetition rate with a SNR of 73.8 dB. The RBW and span are 10 Hz, and 800 kHz, respectively. The wide-range RF spectrum of the fundamental repetition rate and its harmonics in a span of 26.5 GHz are depicted in the insert of Fig. 6(c). The considerably high SNR and the clear intensity of the wide-range RF spectrum confirm that the laser is operating at a steady CW mode-locking state. As shown in Fig. 6(d), the autocorrelation trace has a FWHM of 3.6 ps, corresponding to a temporal width of 2.55 ps, when a gaussian-like shape is assumed with a deconvolution factor of 1.414.
Fig. 6. Experimental results. (a) Typical pulse train of fundamental mode-locked fiber laser with ∼0.95 ns pulse interval. (b) Optical spectrum. (c) Measured RF spectrum. Inset: the wide-range RF output spectrum. (d) Measured autocorrelation trace (grey line) and Gauss fitting trace (red line).
Similarly, the stability of the laser was verified by placing it in a laboratory environment without any external control, and recording its output power and spectra evolution for 3 hours. As a result, Fig. 7 shows the stability of the output power for 3 hours with an RSD of 0.29%. The spectra recorded are shown in false color in the inset of Fig. 7 without any obvious collapse, indicating the stability of the 1-GHz dissipative soliton mode-locking fiber laser.
4.3 Stretched pulse mode-locking regime
Then, by using EDF-2 and SESAM-2, the net dispersion of the cavity is estimated to be ∼+500 fs2, indicating a stretched pulse mode-locking regime.
Similar to before, we first performed a simulation study for the stretched pulse mode-locking regime to further understand the pulse evolution. Figure 8(a) shows the variation of the pulse width and spectrum width for the initial process of the 1-GHz fiber laser in the soliton mode-locking regime. And the evolutions of the peak power and the pulse energy are demonstrated in Fig. 8(b). The stability of all the parameters above is reached after ∼180 roundtrips, when the initial random noise input is mode-locked into a stable pulse. The pulse duration increased as the number of roundtrips continually raising, and suddenly started decreasing after about 100 roundtrips. At the moment, the peak power and the pulse energy suddenly increased, and then stable mode-locking was achieved. And a small periodical modulation was observed in the pulse width. The pulse width of ∼480 fs and the spectral width of ∼24.4 nm was obtained.
Fig. 8. Simulation results. (a) Variation of pulse width and spectrum width over 1000 roundtrips. (b) Variation of pulse peak power and pulse energy over 1000 roundtrips. (c) Evolution of the spectral profile for the pulse over 1000 roundtrips. (d) Evolution of the temporal profile for the pulse over 1000 roundtrips. (e) Spectral shapes of output pulse for stretched pulse mode-locking regime. (f) Temporal shape of output pulse for stretched pulse mode-locking regime.
Figures 8(c) and (d) show the change of the spectral profile and the temporal profile over 1000 roundtrips, clearly illustrating the evolution of the pulse from noise to the stable mode-locked state after about 180 roundtrips.
As shown in Figs. 8(e) and (f), a gaussian-like spectrum and pulse were achieved, which are typical output characteristics of the final output pulse in the regime of stretched pulse mode-locking.
In the experiment, above launched pump power of 200 mW, self-started mode locking is realized. As shown in Fig. 9(a), the time domain characteristics of the mode-locked laser delivered uniform pulse trains with a temporal period of about 0.95 ns. Figure 9(b) illustrates the optical spectrum of the stretched pulse mode-locking fiber laser with a central wavelength of 1549.2 nm and a 3 dB spectral bandwidth of 12.70 nm. In contrast, the experimental spectrum in Fig. 9(b) is very similar to the simulated spectrum in Fig. 8(e). Also, the RF spectrum shown in Fig. 9(c) indicates a 1.059 GHz fundamental pulse repetition rate with a SNR of 72.9 dB, which matches the time period of 0.95 ns in Fig. 9(a). The resolution setting is the same as before. The wide-range RF spectrum of the fundamental repetition rate and its harmonics in a span of 26.5 GHz are depicted in the insert of Fig. 9(c). The high SNR and the clear intensity of the wide-range RF spectrum prove that the laser works in a stable mode-locked state. As shown in Fig. 9(d), the autocorrelation trace has a FWHM of 322 fs, corresponding to a temporal width of 228 fs, when a gaussian-like pulse shape is assumed with a deconvolution factor of 1.414.
Fig. 9. Experimental results. (a) Typical pulse train of fundamental mode-locked fiber laser with ∼0.95 ns pulse interval. (b) Optical spectrum. (c) Measured RF spectrum. Inset: the wide-range RF output spectrum. (d) Measured autocorrelation trace (grey line) and Gauss fitting trace (red line).
Finally, the stability of the stretched pulse mode-locking laser was proved by recording its output power and spectra evolution for 3 hours in a laboratory environment. Therefore, Fig. 10 shows the stability of the output power for 3 hours with an RSD of 0.78%. And the spectra recorded are shown in false color in the inset of Fig. 10 without any obvious collapse, indicating the stability of the 1-GHz stretched pulse mode-locking fiber laser.
5. Discussion and conclusion
In this paper, polarization-maintaining 1-GHz mode-locked fiber lasers with three different dispersion setups are reported. Numerical simulations based on the generalized nonlinear Schrödinger equation were constructed. The initial process of passive mode-locking and the characteristics of output pulses were investigated. The evolution of the pulse from noise to stable mode-locked state of the three regimes show similar behaviors with each other. Figure 11 shows the comparison between experimental and simulation results. As shown in Fig. 11(a), profiles of the three experimental spectra is basically consistent with the simulation ones. The experimental spectral width is determined by the pump power, so the experimental spectral width is slightly different from that obtained by simulation. Moreover, the measured pulse width is not exactly the same as the simulated pulse width, which was caused by the chirp from output tail fiber. Indeed, due to the difficulty to measure and control the parameters in the experiment precisely, there are some differences between the experimental and simulation results. However, the experimental and simulation results have similar profiles, which is already enough for us to understand the process of stable mode-locking implementation.
Fig. 11. A comparison between experimental and simulation results. (a) Experimental output spectra (solid line) and simulated spectra (dotted line) in three different states. (b) Experimental output autocorrelation traces (solid line) and simulated autocorrelation traces (dotted line) in three different states.
It is known, environmental stability and reliability are the crucial aspects of fiber lasers used in practical applications. Particularly, slight disturbance may have a great impact on the output characteristics of a high repetition-rate fiber laser for its short cavity. If non-polarization maintaining fibers are universally used in these fiber laser systems, these lasers will be sensitive to environmental perturbations. In this experiment, all the components are PM-types, thus linearly polarized output pulses are obtained. To demonstrate the superior stability of these PM fiber lasers, a long-term polarization test compared to their non-PM competitors is conducted by using soliton mode-locking regime. The degree of linear polarization (DOLP) is defined as the ratio of the power of linearly polarized light to the total optical power in an optical signal. To make a comparison, the 6-hour stability of the DOLP is measured for non-PM and the PM scheme respectively. The cavity of the non-PM competitor is built with non-PM gain fibers and passive fibers with almost same parameters. As shown in Fig. 12, the DOLP of non-PM case is between 57% and 77%, while that of the PM case is always larger than 99%, which proves that the PM laser is suitable for many polarization-related applications.
The experimental results of the three mode-locked fiber lasers in this work are summarized in Table 2. In Table 2, Laser 1,2 and 3 represent the soliton mode-locking laser, dissipative soliton mode-locking laser and stretched soliton mode-locking laser, respectively.
Table 2. The experimental results
As shown in the Table 2, the output spectral width of laser 1 is the widest of the three lasers, while that of laser 2 is the narrowest. Consistent with the theoretical results, the dissipative soliton laser has a fairly wide pulse width and the narrowest spectral width. In this case, the transform-limited pulse width of laser 1 should be the narrowest. However, the actual measured output pulse width of laser 1 is wider than that of laser 3. This is mainly due to the chirp of the output pulse caused by the output tail fiber, so that there is a difference between the measured pulse width and the theoretical pulse width. In the future, dispersion compensation techniques can be used to achieve narrower pulses.
In addition, the 3-hour long-term stability of the three mode-locked fiber lasers was proved without any external control. The RSDs of the output power of the three lasers are less than or near 1%, which are pretty good results. And the recorded 3-hour spectral evolutions of the three lasers have no obvious collapse.
In conclusion, polarization-maintaining 1-GHz mode-locked fiber lasers with three different dispersion setups are reported in this paper. The theoretical and experimental studies of the 1-GHz mode-locked fiber lasers in the three dispersion regimes were carried out separately, and the experimental results were basically in agreement with the theoretical simulations. Due to the all-PM system, all the three lasers have a high DOLP of more than 99%. And the three lasers can stably operate for more than 3 hours without any external control. Through different dispersion settings, pulse output with different pulse widths can be achieved, which could be used in applications that require different pulse widths. The three lasers reported in this paper are environmentally-stable and compact. Through further optimization, such as power amplification and frequency locking, it is expected to replace the existing commercial GHz solid-state lasers. Overall, it is believed that the results presented here could promote the development and application of high repetition-rate femtosecond mode-locked lasers.
Funding
Distinguished Young Scholar Foundation of Hunan Province (2020JJ2036); National Natural Science Foundation of China (62075240); National Key Research and Development Program of China (2020YFB2205804).
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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