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Abstract
We experimentally and numerically demonstrate the all-normal dispersion (ANDi) ytterbium (Yb)-doped fiber laser based on nonlinear amplifying loop mirror (NALM) mode-locked, which allows tunable single-wavelength and dual-wavelength outputs. The pulses tuning ranges of the dual-wavelength are from 1032.24 nm to 1053.13 nm and from 1047.94 nm to 1069.05 nm, and the repetition frequency difference varies from 1766Hz to 1834Hz. To our knowledge, this is the widest dual-wavelength tuning range of Yb-doped fiber lasers based on NALM mode-locked. We test for 90 minutes and have high stability in both single-wavelength and dual-wavelength. In addition, the pulsed collision dynamics between two solitons at different wavelengths are numerically studied. Numerical results show that during the pulse collision, the two solitons pass through each other and maintain their properties, which also confirms the particle nature of the isolated wave. Our research contributes to the dynamics of dual-wavelength solitons collision in NALM mode-locked fiber laser and provides what we believe to be is a new idea for tunable Yb-doped dual-comb sources.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
High-precision, flexible, and stable wavelength-tunable fiber lasers have a wide range of applications in the fields of fiber sensing, spectrum measurement, optical communication, biomedicine [1–4], and so on. At present, saturable absorbers are one of the core devices for multi-wavelength tunable mode-locked, for example, real saturable absorbers including carbon nanotube (CNT) [5], semiconductor saturable absorber mirror (SESAM) [6], and 2D materials [7], as well as quasi-saturable absorbers including nonlinear optical loop mirror (NOLM) [8,9], nonlinear polarization evolution (NPE) [10–13], and nonlinear amplifying loop mirror (NALM) [14–17]. Among them, NALM features not only good environmental stability and high efficiency but also the asymmetric amplification structure inside the cavity enabling it to generate high repetition frequency. A pulse output with a repetition frequency of up to 700 MHz was realized based on this structure by Liu et al. [18]. However, the experiment and theory of dual-wavelength tunable ytterbium-doped fiber (YDF) laser based on NALM mode-locked have not been reported.
In recent years, dual-comb technology has been widely applied in fiber optic sensing and optical communication due to its advantages of ultra-high resolution, high sensitivity, and high sampling rate. Dual-wavelength lasers have also received special attention as dual-comb sources. Ti: sapphire [19] and Nd: CNGG [20] used to generate dual-wavelength in solid-state lasers have been studied earlier, and fiber lasers are considered to be the best choice to produce single-cavity dual-wavelength due to their high efficiency and flexibility. Single-cavity dual-wavelength spotlighted the intercoherence of asynchronous pulse trains without a complex phase-locked loop system. Several single-cavity dual-wavelength generation methods have been reported, including polarization multiplexing [21–23], directional multiplexing [24,25], and wavelength multiplexing [26,27]. Wavelength multiplexing introduces a periodic filter inside the cavity, and dual-wavelength or even multi-wavelength mode-locked can be achieved by adjusting the cavity parameters. This also leads to the fact that the generation of dual-wavelength is random and difficult to tune [28–33]. Some scholars have used birefringent filters to achieve dual-wavelength tuning [34–36], but the tuning range is limited to 17 nm, and there is still room for improvement.
In this paper, we report the all-normal dispersion (ANDi) fiber laser based on NALM mode-locked, which can achieve stable and tunable flexible outputs of single-wavelength and dual-wavelength, and the experimental results are in agreement with the simulated Sagnac filter transmission curve. The tuning of single-wavelength ranges from 1034.53 nm to 1069.81 nm. And dual-wavelength pulses from 1032.24 nm to 1053.13 nm and from 1047.94 nm to 1069.05 nm with about 21 nm tuning amount, which indicates that our work will provide a new idea for tunable YDF dual-comb sources. In addition, we numerically investigated the dynamics of pulse collisions between two solitons of different wavelengths adopting a bimodal contour filter formed by the superposition of two Gaussian functions as a filtering model. Numerical results show that during the pulse collision, the two solitons pass through each other and maintain their properties, which also confirms the particle nature of the isolated wave.
2. Experimental setup
Figure 1 illustrates the experimental setup of a dual-wavelength tunable ANDi fiber laser based on NALM mode-locked. The 976 nm with the maximum pump power of 600 mW laser diode is injected into the cavity by a 980/1064 nm wavelength-division multiplexer (WDM). The NALM ring and unidirectional ring (UR) of a figure-eight cavity are connected by a 50:50 optical coupler 1 (OC1). The NALM ring consists of a 25 cm gain fiber (YDF: Liekki Yb 1200-6/125 DC, GVD = 24 ps2/km), a 19 cm polarization-maintaining fiber (PMF: Corning PM 980, GVD = 24 ps2/km) and a polarization controller 1 (PC1). The passive UR cavity is formed by PC2, 90:10 OC2, and a polarization-independent optical isolator (PI-ISO).
Fig. 1. Schematic setup of the mode-locked fiber laser with NALM. WDM, wavelength-division multiplexer; YDF, Yb-doped fiber; PMF, polarization-maintaining fiber; PC, polarization controller; OC, optical coupler; PI-ISO, polarization-independent optical isolator.
The rest of the fibers are single-mode fibers with a group velocity dispersion (GVD) parameter of 23 ps2/km in the cavity. The total cavity length is 13.28 m and the cavity dispersion is 0.3 ps2 at 1060 nm. Where the PMF provides enough birefringence and filter interval, which is affected by its length. The polarized state in the cavity is controlled by both PC1 and PC2. The PI-ISO guarantees the unidirectional transmission of the unidirectional ring cavity. 10% of the energy is exported to the outside of the cavity by OC2, and another 90% of the energy oscillates inside the cavity. To increase geometric asymmetry and facilitate self-started, the splicing of YDF is as close as possible to the WDM. In the experiment, 10% of the output energy was detected by the optical spectrum analyzer (OSA, AQ6370C, Yokogawa), Radio frequency (RF) spectrum analyzer (N9000B, Keysight), oscilloscope (DSO9104A, Agilent Technologies), and autocorrelator (APE PulseCheck-50).
The transmission function of the Sagnac filter could be simplified as the following equation by using the Jones matrix:
where k is defined as the coupling ratio of 50% for OC2, θ is represented as the rotation angle of the PCs, $\varphi = \pi \Delta nL/\lambda $ indicating the phase difference caused by the birefringence, Δn is the birefringence coefficient of the PMF, and L is the length of the PMF, λ represents the central wavelength of the spectrum.The free spectral region (FSR) of the Sagnac filter is indicated by $FSR = {\lambda ^2}/\Delta nL$, when k = 50%, $\theta = \pi /2$, and $\Delta n = 3.63 \times {10^{ - 4}}$. It can be seen from the equation that as the wavelength increases the filtering interval becomes wider. The filtered spectrum of Sagnac is shown in Fig. 2, where the purple curve is the simulation data and the red curve is the actually measured continuous wave (CW). The experimental data is identical to the simulation data and the two filter intervals are 15.62 nm and 16.13 nm, respectively. The PCs in the cavity are adjusted to achieve tunability of the filter spectrum so that the central wavelength of the mode-locked pulse can be adjusted.
3. Results and discussion
When the pump power is 80 mW, the single-wavelength mode-locked with pulse splitting is easily achieved. When we reduce the pump power to 63 mW, a stable single-pulse dissipative soliton can be obtained by exploiting the hysteresis properties of the laser cavity. The experimental results of dissipative solitons are shown in Fig. 3. The 3-dB bandwidth of 7.83 nm, and the central wavelength of the mode-locked pulse is 1066.28 nm, which is consistent with the central wavelength of the filter transmission spectrum in Fig. 3(a). The repetition frequency is 15.48 MHz, corresponding to the cavity length of 13.28 m. The resolution bandwidth (RBW) is 1 Hz, and the number of scan points is 40,001 with the signal-to-noise ratio is 73 dB in Fig. 3(b), which indicates that the mode-locked state is stable. Meanwhile, the RF spectrum measurement within 550 MHz is shown in Fig. 3(b). Gaussian fitting to the measured autocorrelation trace of the pulse indicates the full width at half maximum (FWHM) of the pulse duration of 12.49 ps as shown in Fig. 3(c). The trace of the oscilloscope is shown in Fig. 3(d), and the pulse in 100 ms is stationary, further indicating a stable mode-locked state of the dissipative soliton. The two pulse trains are separated by 64.5 ns, which corresponds to the reciprocal of the repetition rate.
Fig. 3. Fiber laser single-wavelength output characteristics. (a) Output spectrum of CW and DS. (b) RF spectrum. (c) Autocorrelation trace. (d) Pulse trains at different time scales (top: within 100 ms, bottom: within 1 µs).
Due to the filtering mechanism of the Sagnac filter, wavelength-tunable can be achieved by tuning the PCs, and the results are shown in Fig. 4. Single wavelength tuning range is from 1034.53 nm to 1069.81 nm. We also find that the 3-dB bandwidth of the tuned spectrum varies from 4.36 nm to 7.83 nm, and the pulse width ranges from 30.75 ps to 12.49 ps as shown in Fig. 5. The filter bandwidth varies slightly at different PCs states. As a result, the mode-locked pulses have different 3-dB bandwidths at different wavelengths. We measured spectrum stability for 90 minutes in 1066.28 nm, with Fig. 6(a) showing the overall change. Figure 6(b) shows the variation of central wavelength and peak power, respectively, corresponding to standard deviations (σ) of 0.034 nm and 0.035 dBm, which indicate spectrum stability.
Fig. 5. The 3-dB bandwidth and the corresponding pulse width of the optical spectrum at different wavelengths.
Fig. 6. Stability of the single-wavelength spectrum within 90 minutes. (a) Stability of spectrum in three-dimensional X-Y view. (b) The variation of central wavelength and peak power.
By increasing the pump power to 98 mW, stable dual-wavelength output is achieved. The central wavelength is 1037.98 nm and 1054.26 nm, respectively, with the FWHM of 6.03 nm and 5.14 nm, as shown in Fig. 7(a). The repetition frequency difference is 1806Hz, as shown in the RF spectrum of Fig. 7(b). The signal-to-noise ratio of 70 dB, and several small peaks symmetrically distributed on both sides correspond to the beat frequency of the two pulses. The repetition frequency of the longer band is 15.484178 MHz, while the repetition frequency of the shorter band is 15.482372 MHz, and the existence of asynchronous pulses is proven by the difference in repetition frequency, which is caused by fiber dispersion. This can be expressed by the formula [37]:
where c is the light speed in a vacuum, D represents the average GVD of the cavity, Δλ is the wavelength interval, n refers to the average refractive index of the fiber core, and L represents the length of the cavity. In the experiment, D = -34.9 ps/nm·km, n = 1.56, L = 13 m, and the calculation shows that Δf = 1814Hz, which is consistent with the experimental result.Fig. 7. Fiber laser dual-wavelength output characteristics. (a) Output spectrum of CW and DS. (b) RF spectrum. (c) Temporal interferogram of the dual-wavelength pulse trains on the oscilloscope with the range of 2 ms. (d) Interval of randomly recorded pulse trains.
The dual-wavelength pulse trains can also be detected by the oscilloscope. It can be seen that one pulse is triggered while another pulse continues to pass through the screen on the oscilloscope. The difference in repetition frequency can be mapped out in the interference pattern of the dual-wavelength pulse trains as shown in Fig. 7(c). The interval between the beat frequency signal is 554.6 µs which is consistent with the repetition frequency difference of 1806Hz. The relative motion of two pulses can also be observed on the oscilloscope. We randomly record a set of pulse trains with pulse intervals of 64.58 ns and 64.57 ns, respectively. The time difference between the corresponding asynchronous pulses is 29.43 ns, as shown in Fig. 7(d).
By adjusting the PCs, continuous dual-wavelength tuning is achieved. We present six sets of the tunable dual-wavelength and its corresponding RF spectrum, with the short-wavelength tuning range from 1032.24 nm to 1053.13 nm, the long-wavelength tuning range from 1047.94 nm to 1069.05 nm in Fig. 8(a). And the repetition frequency difference tuning range of 1766Hz-1834Hz in Fig. 8(b). The FSR of the Sagnac filter increases with the red shift of the wavelength leading to the change in the dual-wavelength spacing during the tuning process. Due to normal cavity dispersion, the repetition frequency increases with the red shift of the central wavelength. In addition, there are significant amplified spontaneous emission components at 1070 nm and 1037 nm in the short-wavelength spectrum of 1038 nm and 1052 nm, respectively, which are located in the peak transmission bands of the Sagnac filter.
Dual-wavelength stability is also significant in the application of dual-comb sources. Here, we test spectrum stability for 90 minutes without additional vibration isolation and temperature control. As shown in Fig. 9(a), there is no marked change in the overall dual-wavelength. To observe the changes in the spectrum more clearly, the changes in the peak power of the dual-wavelength are shown in Fig. 9(b). The red line indicates 1037.98 nm with the σ of 0.032 dBm and the blue refers to 1054.26 nm with the σ of 0.033 dBm. The subtle changes in the central wavelength spacing of dual-wavelength are shown in Fig. 9(c), the σ of only 0.001 nm implies superior stability of dual-wavelength. Meanwhile, the central wavelengths of both pulses have the σ of 0.035 nm.
Fig. 9. Stability of the dual-wavelength spectrum within 90 minutes. (a) Stability of spectrum in three-dimensional X-Y view. (b) Peak power variation in the output spectrum. (c) Changes in the central wavelength and its spacing of dual-wavelength.
4. Numerical simulation
Based on the theoretical model of the Ginzburg-Landau equation (GLE) [38,16], We investigate the dynamic evolution of single-wavelength and dual-wavelength mode-locked in the experimental setup shown in Fig. 1. The equation is shown below:
Table 1. Parameters in the numerical simulation of NALM mode-locked fiber laser.
In the simulation, we track the propagation of the light pulses inside the cavity, and after cycling through the cavity once, the results obtained were used as input for the next round of calculations until the light field reached a self-consistent state. The dynamic evolution of the single-wavelength soliton is shown in Figs. 10(a)-(d). Figure 10(a) and (b) show the frequency and time domain evolution of the 600 roundtrips, respectively, and the simulation results are satisfactory compared with the experimental results. The pulse offset of the pulse relative to the window in Fig. 10(b) is caused by intracavity dispersion. Zooming in on the first 30 roundtrips of data in the dotted box as shown in Fig. 10(c) and (d), we can see that the pulse stabilizes after about 15 roundtrips.
Fig. 10. Numerical simulation results of NALM mode-locked fiber laser. (a)-(d) Single-wavelength numerical simulation results. (e)-(h) Double-wavelength numerical simulation results.
The dynamic evolution of dual-wavelength solitons is shown in Figs. 10(e)-(h). Figures 10(e) and (f) are the evolution of spectrum and pulse width of the 600 roundtrips, respectively, indicating that the mode-locked is in a stable state. The nonzero cavity dispersion and different central wavelengths cause the two pulses to have different group velocities and periodically collide and separate in the cavity. After amplifying the first 50 roundtrips shown in the dotted box of Fig. 10(g), we can observe that during the pulse interaction (the 25-33 roundtrips), the corresponding spectrum shows strong fluctuations. Due to the small filter window designed in the simulation, the pulse collision period is shortened, which does not affect the observation of the pulse collision process. Subsequently, the two pulses collide and gradually separate (the 34- 44 roundtrips) and after several roundtrips, they evolve into a steady state. It is observed that the shape of the spectrum gradually stabilizes with the pulses separate, rather than the spectrum evolving into stable dissipative soliton shapes immediately upon pulse separation. The two pulses simply pass through each other in a collision without exchanging energy, which is due to the independent evolution of different wavelengths, as shown in Fig. 10(h). This numerical result is consistent with the experimental results and also provides side evidence for the credibility of the double-peak filter instead of the dual-wavelength gain spectrum theory. In the experiment, we obtained an average spectrum, so we could not observe the collision of two pulses from the experiment.
5. Conclusion
Overall, we build and perform numerical simulations of the tunable ANDi fiber laser based on NALM mode-locked. The single-wavelength tuning ranges from 1034.53 nm to 1069.81 nm, totaling 35.28 nm. A signal-to-noise ratio of up to 73 dB, and the drift of the central wavelength and peak power is only 0.034 nm and 0.035 dBm at 1066.28 nm within 90 minutes we tested. In addition, the tuning ranges of dual-wavelength pulses are from 1032.24 nm to 1053.13 nm and from 1047.94 nm to 1069.05 nm, with corresponding tuning ranges of 20.89 nm and 21.11 nm respectively. The change range of repetition frequency difference is 1766Hz-1834Hz. We also measured the stability of the dual-wavelength within 90 minutes. The changes of the central wavelength and peak power are 0.001 nm and 0.035 dBm with high stability. By simulating the collision evolution of the dual wavelength in the cavity, we find that the two pulses do not change their respective properties during the collision process, and still evolve into stable pulses after the collision. Our results confirm the Sagnac filtering effect and the important contribution of NALM mode-locked to 1 µm tunable dual-wavelength, and provide a new design idea for a wide range of tunable dual-comb sources.
Funding
National Key Scientific Instrument and Equipment Development Projects of China (51927804); Shaanxi Key Science and Technology Innovation Team Project (2023-CX-TD-06).
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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