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Mid-infrared ultrashort pulses generated from a hybrid mode-locked Er:ZBLAN fiber laser

Linpeng Yu, Qinghui Zeng, Shuai Wang, Jinhui Liang, Jinzhang Wang, Jiachen Wang, Xing Luo, Peiguang Yan, Fanlong Dong, Xing Liu, Qitao Lue, Chunyu Guo, and Shuangchen Ruan

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Abstract

By combining nonlinear polarization rotation (NPR) and semiconductor saturable absorber, we report a hybrid mode-locked Er:ZBLAN fiber oscillator at 2.8 µm. Stable 325-fs mode-locked pulses with an average power of 131 mW and a record signal-to-noise ratio of 79 dB at the fundamental frequency of 55.4 MHz are generated. Numerical simulations are carried out based on the modified coupled nonlinear Schrödinger equations, and offer new insights into the underlying dynamics of pulse generation. The simulations indicate that compared with Er:ZBLAN fiber lasers mode-locked by NPR alone, the hybrid mode-locked Er:ZBLAN fiber oscillator allows a wider range and a lower threshold of the pump power while maintaining the ultrashort pulse width. Moreover, we numerically demonstrate that the hybrid mode-locked oscillator is less sensitive to the variation of polarization states, which will increase its robustness against environmental disturbance. This is the first time that the hybrid mode-locking technique is applied in the mid-infrared, opening up new opportunities for the development of stable ultrafast mid-infrared laser sources and practical applications outside the laboratory.

© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement

1. Introduction

3 µm-class mid-infrared (MIR) mode-locked fluoride fiber lasers (MLFFLs) operating in the molecule “fingerprint” region have attracted great attention for their various applications such as molecule detection, material processing, and medical surgery [1,2]. A variety of passively mode-locking mechanisms, relying on real or artificial saturable absorbers (SAs), have been developed for generating ultrashort pulses at 2.8 µm in Er-doped fluoride fiber lasers. The first reported mode-locked Er:ZBLAN fiber oscillator operating at 2.8 µm used a Fe:ZnSe crystal as a real SA, from which continuous-wave mode-locked pulses with an estimated pulse duration of 19 ps and an average power of 51 mW were generated [3]. In addition to Fe:ZnSe crystals, significant efforts have been made to develop new SAs for MIR MLFFLs, including semiconductor saturable absorber mirrors (SESAMs) [4,5] and novel low-dimensional materials (graphene [6], black phosphorus [7,8], gold nanowires [9], etc.). However, due to the slow recovery time, mode-locked pulses based on real SAs are usually characterized by a long pulse width (picosecond level). To obtain femtosecond mode-locked pulses, employment of artificial SAs is required, which possess a high modulation depth and a nearly instantaneous response time. Nonlinear polarization rotation (NPR), as a representative of artificial SAs, has become a major method to develop femtosecond mode-locked Er-doped fluoride fiber lasers since the first demonstration by Hu et al. in 2015 [10]. Based on the NPR technique, a series of studies have been conducted in MLFFLs at 2.8 µm concerning the dispersion management [11,12], wavelength tunability [13,14] and nonlinear amplification [15,16]. Nevertheless, NPR mode-locked lasers are relatively unstable due to the variation of polarization states caused by environmental disturbance.

To solve this problem, an improved approach named hybrid mode-locking technique has been developed, which takes advantage of the co-action of real SA and NPR. In hybrid mode-locking, the real SA facilitates pulse initiation process and stabilizes the mode-locked operation by suppressing multiple pulses or continuous wave (CW) while the NPR acts as a pulse shaper and pushes the pulse width towards femtoseconds [17]. Cooperation of the two mode-locking mechanisms permits a self-starting stable laser system with ultrashort pulse generation. Up till now, this kind of hybrid mode-locking technique has been reported in ytterbium [17–19], erbium [20,21], thulium [22] and holmium [23] -doped silica fiber lasers. However, hybrid mode-locking has not been realized in MIR Er:ZBLAN fiber lasers.

In this work, by combining NPR and semiconductor SA, we demonstrate a hybrid mode-locked Er:ZBLAN fiber laser in the MIR for the first time. Stable 325-fs mode-locked pulses at 2.8 µm with a record signal-to-noise ratio of 79 dB at the fundamental frequency of 55.4 MHz are generated. Numerical simulations show that the hybrid mode-locked Er:ZBLAN fiber oscillator allows a wider range and a lower threshold of the pump power, and a higher tolerance of polarization states over traditional Er:ZBLAN fiber lasers mode-locked by NPR alone, which can explain its easily self-starting feature and high stability. Our work paves the way for the development of stable ultrafast MIR laser sources, enabling a wide range of practical applications.

2. Experimental setup and results

The schematic of the experimental setup is presented in Fig. 1. A 3.1-m-length 7 mol.% Er-doped double-clad ZBLAN fiber (Le Verre Fluoré) is used as the gain medium which has a core diameter of 15 µm (NA = 0.12) and a double-D shaped inner cladding diameter of 260 µm (NA = 0.45). Both fiber ends are cleaved at an angle of 8° to prevent parasitic lasing caused by the Fresnel reflection. The pump beam, from a 976-nm LD with a pigtailed output fiber with a core diameter of 105 µm (NA = 0.22), is coupled into the active fiber by employing a plano–convex BK7 lens L1 (f = 10 mm) and a plano–convex CaF2 lens L2 (f = 20 mm). Dichroic mirrors are placed at 45° to guide the 2.8-µm laser beam. Before being output by an output coupler with a 50% reflection at 2.8 µm, the signal beam collimated by another plano–convex CaF2 lens L3 (f = 20 mm) is modulated by a semiconductor saturable absorber (BATOP GmbH) which is placed between a pair of plano–convex CaF2 lens (L4 and L5, f = 20 mm). The NPR unit consists of a half-wave plate (HWP), polarization-dependent isolator and quarter-wave plate (QWP).

 figure: Fig. 1.

Fig. 1. Schematic of the hybrid mode-locked Er-doped fluoride fiber laser. LD, laser diode; DM, dichroic mirror; L, lens; PD-ISO, polarization-dependent isolator; HWP, half-wave plate; QWP, quarter-wave plate; OC, 50/50 output coupler; SA, saturable absorber.

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By adjusting the orientations of waveplates in the laser, self-starting mode-locking is easily achieved under a pump power of 2.56 W. The temporal pulse train measured by a photodetector (VIGO System, PCI-9, bandwidth: 250 MHz) in 10 ms time scale is depicted in Fig. 2(a), of which the remarkable regularity highlights the high temporal stability. Figure 2(b) presents the radio-frequency (RF) spectrum measured by an RF spectrum analyzer (Rohde & Schwarz FSWP), which exhibits a high signal-to-noise ratio of 79 dB at the fundamental frequency. The repetition rate of 55.4 MHz matches well with the total cavity length including the fiber length and free-space length of 3.1 m and 0.8 m, respectively. The smooth decline of the harmonics with no modulations, caused by the limited bandwidth (250 MHz) of the detector, indicates that the laser operates in a single-pulse state. The spectrum, as shown in Fig. 2(c), is centered at the wavelength of 2790 nm with a 3-dB bandwidth of 17 nm, which is measured by an optical spectrum analyzer covering from 1.5 to 3.4 µm (Yokogawa, AQ6376). The typical Kelly sidebands imply the fundamental mode-locking in the soliton regime, while the absorption lines in the spectrum are due to water vapor in atmosphere. The experimental absorption background has also been measured by utilizing a homemade flat MIR supercontinuum source, which is presented in Fig. 2(c) and agrees well with the experimental absorption lines in the spectrum. Figure 2(d) displays the autocorrelation trace obtained by utilizing a commercial intensity autocorrelator (Femtochrome, FR-103 XL). The measured pulse duration is 376 fs assuming a sech2 pulse shape.

 figure: Fig. 2.

Fig. 2. Output characteristics of the hybrid mode-locked Er-doped fluoride fiber laser. (a) Pulse train. (b) RF spectrum at the fundamental frequency. Inset: RF spectrum in an 800-MHz span. (c) Optical spectrum (blue) and atmospheric transmission (black) inside the OSA. (d) Autocorrelation trace fitted by a sech2 profile.

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The evolution of the pulse width and pulse energy with the pump power for the soliton operation mode is depicted in Fig. 3. As the pump power is increased, the output pulse energy is accordingly enlarged, reaching a maximum value of 2.4 nJ and a maximum average power of 131 mW. A slope efficiency of 8% is obtained by linear fitting, which is relatively low due to the large cavity loss. The pulse width decreases with the pump power, reaching a minimum value of 325 fs under the pump power of 2.93 W. Further increasing the pump power will render the pulsation state unstable, resulting in a Q-switching mode-locking state. The soliton order is calculated according to N = (γP0τ2/|β2|)1/2, where γ is the nonlinear coefficient, P0 is the peak power, τ is the pulse width, and β2 is the second-order dispersion [24]. The result shows that during the pulse energy scaling process, the output pulses have a nearly constant soliton order of ∼1.14, maintaining the fundamental soliton state.

 figure: Fig. 3.

Fig. 3. Experimental results for the pulse width and pulse energy under different pump power from the hybrid mode-locked Er:ZBLAN fiber laser.

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3. Numerical simulations and discussion

A numerical model is developed for a further investigation on the hybrid mode-locking in Er:ZBLAN fiber lasers, as shown in Fig. 4. The simulation parameters are kept the same as the experimental parameters. The HWP, polarizer and QWP, constituting the NPR unit, are represented by their Jones matrix in the simulation. The angles of the fast axis of the HWP and QWP relative to the horizontal polarization component are denoted as θHWP and θQWP, respectively. As demonstrated in Ref. [25], the presence of molecular gas absorption in the free-space sections will affect the mode-locked performances. Accordingly, we have considered the absorption of atmospheric water vapor within the 0.8-m free space section. The total cavity loss is estimated to be 65%, in which the 12.5% insertion loss of the SA has been taken into account.

 figure: Fig. 4.

Fig. 4. Numerical model of hybrid mode-locking. SA, saturable absorber; OC, 50/50 output coupler; HWP, half-wave plate; POL, polarizer; QWP, quarter-wave plate.

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The nonlinear Schrödinger equation, solved by the split-step Fourier method [24], has been widely employed in simulating fiber lasers. To describe the light propagation in the 3.1-m gain fiber, we use modified coupled nonlinear Schrödinger equations of the form:

$$\frac{{\partial u}}{{\partial z}} = - \frac{i}{2}{\beta _2}\frac{{{\partial ^2}u}}{{\partial {t^2}}} + \frac{1}{6}{\beta _3}\frac{{{\partial ^3}u}}{{\partial {t^3}}} + \frac{g}{2} + i\gamma \left( {{{\left| u \right|}^2} + \frac{2}{3}{{\left| v \right|}^2}} \right)u$$
$$\frac{{\partial v}}{{\partial z}} ={-} \frac{i}{2}{\beta _2}\frac{{{\partial ^2}v}}{{\partial {t^2}}} + \frac{1}{6}{\beta _3}\frac{{{\partial ^3}v}}{{\partial {t^3}}} + \frac{g}{2} + i\gamma \left( {{{|v |}^2} + \frac{2}{3}{{|u |}^2}} \right)v$$
where u and v denote the slowly varying electric field envelopes of the optical pulses along the two orthogonal polarization components, z is the propagation distance along the fiber axis, t is the time-delay of pulses. β2 of -83 fs2/mm and β3 of 476 fs3/mm represent the second-order and third-order dispersion of the Er:ZBLAN fiber, respectively [26]. γ of 0.145 W-1km-1 is the nonlinear coefficient of the Er:ZBLAN fiber [27]. For an active fiber, g symbolizes the saturation gain, which has a spectral dependence g(ω). Considering the gain profile as a Lorentzian line shape, the gain is therefore given by
$$g(\omega ) = \frac{{{g_0}}}{{1 + \frac{{{E_p}}}{{{E_s}}}}} \cdot \frac{1}{{1 + {{(\frac{{\omega - {\omega _0}}}{{0.5\mathrm{\Delta }\omega }})}^2}}}$$
where g0 of 4 m-1 and Δω represent the small signal gain coefficient and gain bandwidth of gain medium, respectively. The gain bandwidth is set to 120 nm [11]. Ep stands for the single pulse energy and the gain saturation energy Es has a positive correlation with the pump power. In the case of forward pumping, the pump power is attenuated along the propagation distance, which is embodied by a function Es = Es0·exp(-αz) [28]. α is numerically set to be 3 dB/m, corresponding to the absorption coefficient of the gain fiber at the pump wavelength.

The transmission of the SA can be estimated by T(t) = 1−quns−q(t), where quns of 4% and q(t) are the unsaturated loss and response of the SA, respectively. The slow SA is modeled by the following equation [29], which is solved using the 4th-order Runge-Kutta method:

$$\frac{{\textrm{d}q(t)}}{{\textrm{d}t}} ={-} \frac{{q(t) - \mathrm{\Delta }T}}{{{\tau _{rec}}}} - \frac{{q(t){{|{A(t)} |}^2}}}{{{E_{sa}}}}$$
where ΔT = 6% is the modulation depth and τrec = 10 ps is the recovery time. The saturation energy Esa is calculated according to the saturation fluence (300 µJ/cm2) of the SA provided by the manufacturer.

A stable single-soliton state based on hybrid mode-locking is realized with Es0 of 2.3 nJ, θHWP of 17π/24 and θQWP of 11π/24. The evolutions of output temporal profiles and spectra originated from a random noise within 1000 roundtrips are shown in Fig. 5(a) and 5(b). Stable mode-locked pulses with a pulse energy of 4.1 nJ are obtained after ∼100 roundtrips, while the typical Kelly sidebands in Fig. 5(b) confirm the soliton operation. A slight frequency shift relative to the center wavelength of 2790 nm is observed for the mode-locked pulses, which causes the temporal drift in Fig. 5(a). Figure 5(c) and 5(d) depict the evolutions of the output pulse profiles and spectra with the gain saturation energy Es0. Note that adjusting the Es0 is equivalent to changing the pump power. As Es0 increases to 1.4 nJ, 1.7 nJ, 2.0 nJ, 2.3 nJ and 2.6 nJ, the output pulse energy increases up to 2.5 nJ, 3.0 nJ, 3.6 nJ, 4.1 nJ, and 4.6 nJ, respectively. The spectrum is symmetrically broadened due to the enhanced self-phase modulation effect, while the corresponding pulse profile is gradually compressed. The simulation results qualitatively agree well with the experimental results, which demonstrates the validity of our numerical model.

 figure: Fig. 5.

Fig. 5. Simulation results for hybrid mode-locking when θHWP = 17π/24 and θQWP = 11π/24. Evolutions of (a) output temporal profiles and (b) spectra versus roundtrips. (c) Output spectra and (d) temporal profiles under different initial gain saturation energy Es0.

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Furthermore, we have compared the hybrid mode-locked pulses with the pulses mode-locked by NPR alone in terms of pulse width and pulse energy, and present the results in Fig. 6. The waveplate orientations θHWP and θQWP are fixed at 17π/24 and 11π/24, respectively. The NPR MLFFL can only run at a relatively high gain saturation energy Es0 ranging from 1.4 nJ to 2.5 nJ. Unstable mode-locking will occur once Es0 exceeds 2.5 nJ in the simulation. Within the range of stable mode-locking, femtosecond pulses with several-nanojoules pulse energy are generated. As a comparison, the hybrid MLFFL can be initiated at a low Es0 while maintaining a similar ultrashort pulse width, as shown by the triangles in Fig. 6. Moreover, the hybrid MLFFL supports a higher pump power, allowing the gain saturation energy Es0 to reach 2.7 nJ. Therefore, incorporation of the SA can decrease the mode-locking threshold and extend the mode-locking range of the pump power without affecting the pulse shaping effect caused by the NPR. The relatively lower output pulse energy of the hybrid MLFFL under the same Es0 is caused by the additional insertion loss of the SA.

 figure: Fig. 6.

Fig. 6. Output pulse characteristics versus initial gain saturation energy Es0 in the NPR MLFFL and hybrid MLFFL.

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NPR mode-locked lasers are sensitive to the variation of polarization states, which will limit their practical applications outside the laboratory. To further study the sensitivity of hybrid mode-locking to polarization states, we have tracked the changes of the output pulses while rotating the waveplates under a fixed gain saturation energy Es0 of 2 nJ. Figure 7(a) and 7(c) depict the simulation results of output pulse durations and pulse energies under different combinations of waveplate angles, respectively, in which the black blocks represent the non mode-locking state. For comparison, we also present the simulation results of the NPR mode-locked laser in Fig. 7(b) and 7(d). It can be observed that both the NPR mode-locking and hybrid mode-locking only support a few combinations of waveplate angles, while these combinations eventually form several separate groups. When the laser switches among these groups, the mode-locked pulses characteristics are accordingly changed, including the pulse duration and pulse energy. Compared with the NPR mode-locked laser, the hybrid mode-locked laser possesses a larger area for each mode-locking group, implying that the hybrid mode-locked laser can still achieve mode-locking even under a large continuous adjustment of polarization states. The relatively lower sensitivity to the variation of polarization states will make it more robust against environmental disturbance. Moreover, as the area differs for each mode-locking group, the tolerance to the variation of polarization states is different. It is suggested that one should find the most stable mode-locking state among all the groups in practical experiments.

 figure: Fig. 7.

Fig. 7. Simulation results of pulse durations and corresponding pulse energies obtained from (a,c) the hybrid MLFFL and (b,d) NPR MLFFL under different combinations of waveplate angles.

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To further check the stability of the hybrid mode-locked Er:ZBLAN fiber laser, we have experimentally measured the power fluctuation over two hours (acquisition rate = 1 Hz) and present the result in Fig. 8(a). For comparison, we also present the experimental result of the NPR mode-locked Er:ZBLAN fiber laser in Fig. 8(a). In the NPR mode-locked Er:ZBLAN fiber laser, the semiconductor SA and the corresponding confocal lenses (L4 and L5) are removed, while the other parameters are kept almost the same. It is seen that the hybrid mode-locked laser possesses a lower normalized root-mean-square (RMS) deviation (0.66%) than that (1.07%) of the NPR mode-locked laser, demonstrating the good stability of the hybrid mode-locking technique. Moreover, to evaluate the pulse noise features, we have also measured the single sideband (SSB) relative-intensity noise (RIN) of the hybrid mode-locked laser and the NPR mode-locked laser. Figure 8(b) shows the SSB RIN traces of the first harmonic and the corresponding integrated RMS RINs. The hybrid mode-locked laser possesses a lower SSB RIN in the almost whole frequency range. The sharp noise spikes below 1 kHz mainly arise from the acoustics and environmental vibrations. Integrating over the range of 10 Hz∼10 MHz, the RINs of the hybrid mode-locked laser and the NPR mode-locked laser are calculated to be 0.24% and 0.31%, respectively. It can be inferred that the hybrid mode-locked laser has a better suppression of noise.

 figure: Fig. 8.

Fig. 8. Experimental results of stability measurements in the hybrid mode-locked laser and the NPR mode-locked laser. (a) Output power fluctuation. (b) SSB RIN traces and integrated RMS RINs.

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4. Conclusion

In conclusion, we demonstrate a hybrid mode-locked Er-doped fluoride fiber laser by combining NPR and semiconductor SA. Stable 325-fs pulses at 2.8 µm with an average power of 131 mW and a record signal-to-noise ratio of 79 dB at the fundamental frequency of 55.4 MHz are generated. This is the first time for the hybrid mode-locking technique being applied in MLFFLs. A numerical model is developed for a better understanding of the pulse generation dynamics. The numerical results show that compared with NPR MLFFLs, the hybrid MLFFL supports a wider range and a lower threshold of the pump power while maintaining the ultrashort pulse width. Moreover, the relatively lower sensitivity to the variation of polarization states of the hybrid MLFFL will make it more robust against environmental disturbance, offering great potential for stable 2.8-µm ultrashort pulse sources applied in industrial fields such as material processing and medical surgery. The work reported here can also facilitate the development of stable MLFFLs at other wavelengths, such as Ho-doped MLFFLs at 2.9 µm and Dy-doped MLFFLs beyond 3 µm.

Funding

National Natural Science Foundation of China (61775146, 61905151, 61935014, 61975136, 62105222); Basic and Applied Basic Research Foundation of Guangdong Province (2019A1515010699); Shenzhen Science and Technology Innovation Program (CJGJZD20200617103003009, GJHZ20210705141801006, JCYJ20210324094400001); Beijing Municipal Natural Science Foundation (JQ21019).

Disclosures

The authors declare no conflicts of interest.

Data availability

Data underlying the results presented in this paper are available from the corresponding authors upon reasonable request.

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Data availability

Data underlying the results presented in this paper are available from the corresponding authors upon reasonable request.

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Figures (8)
Fig. 1.
Fig. 1. Schematic of the hybrid mode-locked Er-doped fluoride fiber laser. LD, laser diode; DM, dichroic mirror; L, lens; PD-ISO, polarization-dependent isolator; HWP, half-wave plate; QWP, quarter-wave plate; OC, 50/50 output coupler; SA, saturable absorber.

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Fig. 2.
Fig. 2. Output characteristics of the hybrid mode-locked Er-doped fluoride fiber laser. (a) Pulse train. (b) RF spectrum at the fundamental frequency. Inset: RF spectrum in an 800-MHz span. (c) Optical spectrum (blue) and atmospheric transmission (black) inside the OSA. (d) Autocorrelation trace fitted by a sech2 profile.

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Fig. 3.
Fig. 3. Experimental results for the pulse width and pulse energy under different pump power from the hybrid mode-locked Er:ZBLAN fiber laser.

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Fig. 4.
Fig. 4. Numerical model of hybrid mode-locking. SA, saturable absorber; OC, 50/50 output coupler; HWP, half-wave plate; POL, polarizer; QWP, quarter-wave plate.

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Fig. 5.
Fig. 5. Simulation results for hybrid mode-locking when θHWP = 17π/24 and θQWP = 11π/24. Evolutions of (a) output temporal profiles and (b) spectra versus roundtrips. (c) Output spectra and (d) temporal profiles under different initial gain saturation energy Es0.

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Fig. 6.
Fig. 6. Output pulse characteristics versus initial gain saturation energy Es0 in the NPR MLFFL and hybrid MLFFL.

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Fig. 7.
Fig. 7. Simulation results of pulse durations and corresponding pulse energies obtained from (a,c) the hybrid MLFFL and (b,d) NPR MLFFL under different combinations of waveplate angles.

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Fig. 8.
Fig. 8. Experimental results of stability measurements in the hybrid mode-locked laser and the NPR mode-locked laser. (a) Output power fluctuation. (b) SSB RIN traces and integrated RMS RINs.

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Equations (4)

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∂ u ∂ z = − i 2 β 2 ∂ 2 u ∂ t 2 + 1 6 β 3 ∂ 3 u ∂ t 3 + g 2 + i γ ( | u | 2 + 2 3 | v | 2 ) u
∂ v ∂ z = − i 2 β 2 ∂ 2 v ∂ t 2 + 1 6 β 3 ∂ 3 v ∂ t 3 + g 2 + i γ ( | v | 2 + 2 3 | u | 2 ) v
g ( ω ) = g 0 1 + E p E s ⋅ 1 1 + ( ω − ω 0 0.5 Δ ω ) 2
d q ( t ) d t = − q ( t ) − Δ T τ r e c − q ( t ) | A ( t ) | 2 E s a
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