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• Abstract

SECTION I

## INTRODUCTION

The 2 $\mu\hbox{m}$ fiber laser has attracted intense attention for its various applications in remote sensing, nonlinear frequency conversion, spectroscopy, LIDAR, and medicine. For some of these applications, pulses of short duration are needed. Mode-locking and Q-switching are two common methods to generate pulse laser [1], [2], [3], [4], [5], [6], [7], [8]. Most of the reported mode-locked Tm-doped pulse lasers are realized by passive mode-locking, using semiconductor saturable absorber mirror (SESAM) [1], [2], [3], [4] or graphene saturable absorber (GSA) [5], [6]. As for active mode-locking, Eckerle et al. reported an actively mode-locked Tm-doped fiber laser based on bulk optics component using acousto-optic modulator (AOM) [8]. However, all-fiber configuration laser has advantages such as compactness and robustness in practical application. Heretofore, there were no demonstrations (to our knowledge) on 2 $\mu\hbox{m}$ all-fiber pulse laser by active mode-locking and phase-modulating.

This letter presents two Tm-doped actively mode-locked and relaxation oscillation modulated 2 $\mu\hbox{m}$ pulse lasers, with all-fiber intracavity modulation using an electronic optical phase modulator (EOPM).

SECTION II

## EXPERIMENTAL DETAILS

Fig. 1 depicts the setup of the linear-cavity fiber laser. The pump laser generates 1.57 $\mu\hbox{m}$ continuous wave laser as pump source. The 2 $\mu\hbox{m}$ fiber laser cavity is formed by two fiber Bragg gratings (FBGs), a piece of 4 m long Tm-doped fiber, and an EOPM. The high reflectivity (HR) FBG has reflectivity of 99% at 1.95 $\mu\hbox{m}$; the other FBG, the output coupler (OC), has a low reflectivity of 30% at 1.95 $\mu\hbox{m}$. The bandwidths of the FBGs are 0.5 nm and 1.0 nm for the OC FBG and HR FBG, respectively. The Tm-doped fiber is single-cladding fiber with core diameter of 9 $\mu\hbox{m}$ and cladding diameter of 125 $\mu\hbox{m}$, and the absorption coefficient at 1.57 $\mu\hbox{m}$ is about 7 dB/m. The EOPM works at $1.90\ \mu\hbox{m} \sim 2.20\ \mu\hbox{m}$ with a tested insertion loss of 4.2 dB. The whole laser cavity is $\sim$8.22 m long. The function generator can generate arbitrary wave electronic signal with bandwidth of 100 MHz.

Fig. 1. Setup of the actively mode-locked and relaxation oscillation modulated linear-cavity fiber laser. TDF: Tm-doped fiber; PM: phase modulator; FG: function generator.
SECTION III

## RESULTS

The home-made 1.57 $\mu\hbox{m}$ pump laser generated output power of 336.0 mW, and the average output power of the Tm-doped laser reached 14.3 mW. The high insertion loss of the EOPM resulted in a low slope efficiency of 15%. The fiber laser's wavelength was centered at 1.95 $\mu\hbox{m}$ with a spectral linewidth of less than 0.078 nm, as Fig. 2 shows. The optical spectral analyzer employed in the experiment has a resolution of 0.05 nm.

Fig. 2. Output power and spectrum (inset) of the linear-cavity fiber laser.

The calculated fiber laser's longitudinal mode frequency interval, $\Delta u_{q} = c/2nL$, was around 12.580 MHz. $L$ ($\sim$8.22 m) is the length of laser cavity, $n$ ($\sim$1.45) is the refractive index of the medium, and $c$ is the light speed in vacuum space. When applying proper signal on the EOPM according to $\Delta u_{q}$, mode-locked pulse trains were generated. The pulse shape was measured by a high speed commercial InGaAs PIN detector with bandwidth of 10 GHz and a digital phosphor oscilloscope with bandwidth of 1.5 GHz.

Fig. 3 shows the actively mode-locked pulse train; the modulating signal of EOPM was sine wave with frequency of 11.884 MHz and voltage of 10 V. The difference between the calculated $\Delta u_{q}$ and the practical one was mainly caused by the error of $L$. The energy fluctuation was less than 4%, and the pulse duration was about 816 ps. It is found that the change of the signal's shape and voltage did not directly influence the pulse train. Moreover, the modulation frequency with integer multiple of 11.884 MHz could also generate stable mode-locked pulse train. In addition, the stable mode-locked pulse can be generated when the modulation frequency of the EOPM is in the range of $\Delta u_{q}$ (or integer multiple of $\Delta u_{q}$) ± 0.005 MHz. If the modulation frequency is out of the range, the mode-locked pulse is not stable and even cannot be generated.

Fig. 3. Stable pulse train of actively mode-locked Tm-doped linear-cavity fiber laser and the pulse shape (inset).

Stable and kilohertz-level pulse train was obtained in experiment when applying phase modulation signal with frequency of several kilohertz. The reasonable explanation is to connect the cause of this pulse train with the modulation on the fiber laser's relaxation oscillation phase [9], [10], [11]. Generally, the relaxation oscillation frequency $u_{R}$ is determined by the fractional cavity loss per pass $\delta$, actual pump power $P$, threshold of laser pump power $P_{th}$, the roundtrip time of light in the cavity $\tau_{c}$, and the decay time of upper lasing level $\tau_{f}$, as Formula 1 depicts [9] TeX Source $$\upsilon_{R} = {1 \over 2\pi}\sqrt{\delta(P/P_{th} - 1) \over \tau_{c} \tau_{f}}.\eqno{\hbox{(1)}}$$

In the linear cavity, $\delta$ was 0.964, $P_{th}$ was 150 mW, $\tau_{c}$ was 83.8 ns, and $\tau_{f}$ was 1.8 ms [12], [13]. If the pump power $P$ was 324 mW, $u_{R}$ was 7.9 kHz. Making the modulating frequency of EOPM to be around 8 kHz when the pump power was 324 mW, the stable pulse train was generated. Fig. 4 shows the pulse train; the pulse repetition rate was 10 kHz, and the pulse duration was 5.885 $\mu\hbox{s}$. The modulating signal was sine wave with frequency of 10 kHz and voltage of 10 V, and the pump power was 330 mW. It is found that the stable pulse train's frequency changes along with the modulating frequency in a certain range (around $u_{R}$) at different pump power levels. When the modulating frequency is about twice of $u_{R}$, the stable pulse train's frequency is half of the modulating frequency at low pump power. However, if the pump power increases, stable pulse train with higher frequency can be generated. The energy fluctuation of the pulse train was less than 7%.

Fig. 4. Stable pulse train of actively relaxation oscillation modulated Tm-doped linear-cavity fiber laser and the pulse shape (inset).

We consider that this pulse train is mainly realized by modulating the phase of relaxation oscillation, which stimulates and controls the stable pulse train. As the pump power increased, the range of laser pulse covered higher frequency. Fig. 5 depicts the curves of the pulse train's frequency and the relaxation oscillation frequency with different pump powers. The pulse train's repetition rate was in the range of 4 kHz $\sim$ 18 kHz. One can see that the pulse's frequency changes along with $u_{R}$ generally, which conforms to our explanation. However, thorough theoretical analysis of this experiment's result is needed, but rather complicated, and which is not the item of this paper.

Fig. 5. Frequency ranges of stable pulse train by relaxation oscillation modulating with different pump powers of linear-cavity fiber laser. Blue star: frequency ranges of pulse train; red circle: frequency of relaxation oscillation.

The all-fiber ring-cavity laser was set up to generate actively mode-locked and relaxation oscillation modulated pulse train. Fig. 6 shows the sketch of the system. Continuous wave pump laser of 1.57 $\mu\hbox{m}$ was identical with the linear-cavity fiber laser. The gain media here was 2 m long single-cladding Tm-Ho co-doped fiber with 9 $\mu\hbox{m}$ core diameter and 125 $\mu\hbox{m}$ cladding diameter. A circulator ensured unidirectional light propagation in the cavity, meanwhile it made the HR FBG a part of the laser cavity. The HR FBG was the same as the one in linear-cavity. The 1.95 $\mu\hbox{m}$ laser output was provided by the 50% port of a fiber coupler. The length of the cavity was about 17.34 m, and the calculated $\Delta u_{qr}$ was 11.932 MHz.

Fig. 6. Setup of the actively mode-locked and relaxation oscillation modulated ring-cavity fiber laser. T-HDF: Tm-Ho co-doped fiber; PM: phase modulator; FG: function generator.

Fig. 7 depicts the stable pulse train of actively mode-locked ring-cavity fiber laser. The pulse's duration was 446 ps, and the repetition rate was 12.099 MHz. The modulating frequency was 12.098 MHz, and the voltage was 10 V. When the modulating frequency was integer multiple of $\Delta u_{qr}$, stable mode-locked pulse train was obtained, too. The pulse train's energy fluctuation was less than 5%. Again, the stable mode-locked pulse can only be generated when the modulation frequency of the EOPM is in the range of $\Delta u_{qr}$ (or integer multiple of $\Delta u_{qr}$) ± 0.005 MHz.

Fig. 7. Stable pulse train of actively mode-locked Tm-doped ring-cavity fiber laser and the pulse shape (inset).

The stable pulse train by relaxation oscillation modulating was generated, as Fig. 8 depicts. The pulse's duration was 1.554 $\mu\hbox{s}$ and the repetition rate was 14 kHz, while the modulation frequency is 28 kHz with voltage of 10 V. The pulse train's energy fluctuation was less than 7%.

Fig. 8. Stable pulse train of actively relaxation oscillation modulated Tm-doped ring-cavity fiber laser and the pulse shape (inset).

The repetition rate of stable pulse train covered 6 kHz $\sim$ 26 kHz and increased as the pump power scaled up, as Fig. 9 depicts. It should be noted that the actual threshold of laser pump power is affected by the cavity loss such as instruments' insertion loss and fiber fusion splicing loss, and the tested threshold may not be the exact threshold of the laser. Thus, the calculated relaxation oscillation frequency may not be exactly identical with the actual one.

Fig. 9. Frequency ranges of stable pulse train by relaxation oscillation modulating with different pump powers of ring-cavity fiber laser. Blue star: frequency ranges of pulse train; red circle: frequency of relaxation oscillation.

An interesting phenomenon is that the pulsewidth in the ring cavity is shorter than that of the linear-cavity. The actual longitudinal mode frequency intervals of the two cavities are nearly the same (11.884 MHz and 12.099 MHz). In the ring-cavity, the longitudinal laser modes can only propagate along the clockwise direction. However, in the-linear cavity, the longitudinal laser modes can oscillate in both directions. Thus, in each pulse, the number of longitudinal modes of ring-cavity is less than that of the linear-cavity, which may contribute to the shorter pulsewidth in the ring-cavity compared with that of the linear-cavity. Furthermore, the differences on the active fiber and using of FBGs may also affect the spectral linewidth of the laser, which imposes important influence on the width of the pulse [14].

SECTION IV

## CONCLUSION

In conclusion, two all-fiber actively mode-locked and relaxation oscillation modulated 2 $\mu\hbox{m}$ lasers were demonstrated experimentally, with linear-cavity and ring-cavity configurations. Stable mode-locked pulse train was obtained using an intracavity EOPM. The mode-locked pulse train's repetition rate was determined by the length of laser cavity, and the durations of the pulse were 816 ps (linear-cavity) and 446 ps (ring-cavity). Pulse train with repetition rate of several kilohertz was generated by applying proper modulating signals on the laser phase. The stable pulse train's frequency was around the lasers' relaxation oscillation frequency. We consider that it may be generated by modulating the relaxation oscillation phase and thorough theoretical analysis is needed to explain the exact cause of this stable pulse train. All the stable pulse trains' energy fluctuations were less than 7%.

## Footnotes

Corresponding author: X. Wang (e-mail: wangxiong23@gmail.com).

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