Robust Q-switching based on stimulated Brillouin scattering assisted by Fabry-Perot interference

Shaodong Hou; Yang Lou; Nan Zhao; Ping Chen; Fangfang Zhang; Yang Chen; Feng Lin; Jinyan Li; Luyun Yang; Jinggang Peng; Haiqing Li; Nengli Dai

doi:10.1364/OE.27.005745

1. Introduction

SBS is the fundamental nonlinearity with lowest threshold occurring in all states of matter due to wave interference and diffraction of acoustic grating. This nonlinearity has been investigated for numerous purposes such as Brillouin scattering induced transparency and slow light control [1–4], the pulse compression based on Brillouin backscattering [5–10], microscopic optical imaging [11–16], high performance photonic filter [17–22] and the passive Q-switch operation and self-pulsing [23–31].

For applications like pulses generation, the natural advantages of low cost, simple configuration, high peak power and all-fiber setup facilitate the prosperity of researches of the SBS-based pulsed laser. As early as 1997, S.V. Chernikov realized the self-starting SBS-based Q-switched fiber laser (SBSQFL) for the first time in rare-earth ion doped fiber lasers [30]. Despite of the simple structure and high peak power, the output pulse train showed random pulse amplitude and repetition rate which was induced by the stochastic nature of SBS and Rayleigh scattering (RS). Afterwards, the SBSQFL was widely investigated in different wavelengths and materials. Simulations [8,32,33] have been done to explore the dynamics in the Q-switching process. In experiments, the SBS-based Q-switching is often used for supercontinuum generation [26,30,34], rogue waves study [25] and random lasers [23] due to the high pulse peak power. However, unstable output pulses seriously limit the applications of this kind of Q-switched laser. For decades, great efforts have been made to explore efficient ways to stabilize the SBSQFLs. In 1998, Chen et al. proposed to stabilize the pulse repetition frequency by adding an acousto-optic modulator into the cavity to actively modulate the pulse [35]. In 2009, Pan et al. demonstrated that one can control the gain by injecting modulated pump to stabilize the repetition rate [36]. In 2010, Pan et al. suggested that experimenting in low temperature or isolated system may help stabilize the pulse [37]. These proposed methods, although effective, would complicate the system and weaken the advantages of passive SBSQFL in terms of low cost and convenience, therefore not fundamentally solving the problem.

The instability of the Q-switched output pulses is derived from the random thermal noise and random RS in the system. The former one acts to initiate the nonlinear Brillouin scattering process [38,39] which will lead to Q-switching process. The latter one provides random feedback which constitutes the resonant cavity of the Q-switched laser. Due to the non-feedback cavity end, the random thermal noise and RS causes exceedingly unstable Q-switching process. The amplitude and repetition frequency of the Q-switched pulse usually fluctuate within the range of 10%-40%. Therefore, the instability and uncontrollability of SBS passive Q-switching are observed. Although this characteristic can produce occasional pulses with great peak power-average power ratio, accidentally generated super-pulse will cause damage to the fiber and device [37,40]. Moreover, the Q-switched pulse is usually accompanied by parasitic pulses with multi-peaks structure, also greatly limiting the application of passive Q-switching based on SBS.

In this paper, we adapted a classic model firstly proposed by A. A. Fotiadi to simulate SBS-based Q-switching process [28]. Gain process was added to this model. Numerical results show that sub-nanoscale spectrum modulation effect such as FP interference is efficient for SBS-based Q-switching stabilization. Then we introduced FP interference by two un-contact ends of fiber patch cords into cavity in experiments to stabilize the Q-switching process. For the first time, we present an all-fiber robust SBSQFL without any external measures. This fiber laser has a simpler and cheaper configuration than most Q-switched fiber lasers. Such a simple configuration shows great stability. The measured SNR is as high as 62.96 dB under 600 mW pump. The laser configuration proposed in this paper provides a new, simple, integrated, low cost, all-fiber and wavelength-independent solution for generating stable and controllable passive Q-switched pulses.

2. Simulation method

To better understand SBS-based Q-switching dynamics, a rigorous simulation of this system is necessary. The schematic diagram of the theoretical model simulated in this work is shown in Fig. 1. Due to low feedback of the signal, pump light causes highly accumulated inverted population in erbium-doped fiber. Cascaded Stokes waves begin to occur and induce corresponding acoustic waves. Then these Stokes waves are enhanced by the acoustic waves in turn, thus Q-switching process starts. The energy transfer between Stokes waves and acoustic waves is shown in Fig. 1 below.

Fig. 1 The diagrammatic sketch of the simulations and the energy transfer between different orders of the Stokes waves and the acoustic waves. The left end (painted in purple) represents spectrum modulation device in this paper, which indicates fiber ring resonator in conventional cases.

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In simulations, the light is reflected by the random RS (unconditionally) and nonlinear SBS (while threshold is reached) at each point along the cavity. One cavity end is FBG with 99% reflection. The another end provides no feedback as reported in previous publications [23–30] (usually is a fiber ring resonator). But in the method we propose, additional weak feedback is contributed by an imaginary device whose reflectivity varies with wavelength. This device causes spectrum modulation effect at sub-nanoscale. These additional feedbacks change random cavity to a fixed length, performing different feedbacks on different orders of Stokes waves. Stokes waves with relatively low feedback help to accumulate inverse population while the others with high feedback resonate in the cavity and initiate Q-switching process. This additional feedback weakens the effect of the random SBS and RS, further regulating the pulse train.

The following is a series of coupled equations for simulating the SBS based system:

\frac{n}{c} \frac{\partial A_{0}^{\pm}}{\partial t} \pm \frac{\partial A_{0}^{\pm}}{\partial z} = \frac{g_{S B S}}{2 A_{e f f} (λ_{0})} (- ρ_{0}^{\pm} A_{1}^{\mp}) + Γ_{0} \frac{1}{2} (σ_{e} (λ_{0}) N_{2} - σ_{a} (λ_{0}) N_{1}) A_{0}^{\pm} - \frac{1}{2} α (λ_{0}) A_{0}^{\pm} + 2 Γ_{0} σ_{e} (λ_{0}) N_{2} \frac{h c^{2} Δ λ}{λ_{0}^{3} | A_{0}^{\pm} |}

\frac{n}{c} \frac{\partial A_{k}^{\pm}}{\partial t} \pm \frac{\partial A_{k}^{\pm}}{\partial z} = \frac{g_{S B S}}{2 A_{e f f} (λ_{k})} (ρ_{k - 1}^{\mp}^{*} A_{k - 1}^{\mp} - ρ_{k}^{\pm} A_{k + 1}^{\mp}) + Γ_{k} \frac{1}{2} (σ_{e} (λ_{k}) N_{2} - σ_{a} (λ_{k}) N_{1}) A_{k}^{\pm} - \frac{1}{2} α (λ_{k}) A_{k}^{\pm} + η_{k}^{\pm} A_{k}^{\mp}

T_{2} \frac{\partial ρ_{k}^{\pm}}{\partial t} + ρ_{k}^{\pm} = A_{k}^{\pm} A_{k + 1}^{\mp}^{*} + f_{k}^{\pm} (z, t)

\frac{n}{c} \frac{\partial P_{p}}{\partial t} + \frac{\partial P_{p}}{\partial z} = Γ_{p} P_{p} (σ_{e} (λ_{p}) N_{2} - σ_{a} (λ_{p}) N_{1}) - a (λ_{p}) P_{p}

\frac{d N_{2}}{d t} = \frac{Γ_{p} λ_{p} P_{p}}{h c A_{e f f} (λ_{p})} (σ_{a} (λ_{p}) N_{1} - σ_{e} (λ_{p}) N_{2}) + \sum_{i = 1}^{k} \frac{Γ_{i} λ_{i}}{h c A_{e f f} (λ_{i})} (A_{i}^{+} A_{i}^{+}^{*} + A_{i}^{-} A_{i}^{-}^{*}) (σ_{a} (λ_{i}) N_{1} - σ_{e} (λ_{i}) N_{2}) - \frac{N_{2}}{τ_{2}}

Where

A_{0}^{\pm}

is amplitude of the

k_{t h}

order Stokes light (k = 0,1,2,3,4,5),

ρ_{k}^{\pm}

represents

k_{t h}

order photon induced sound wave.

g_{S B S}

is the Brillouin gain.

Γ_{k}

is the overlap factor of effective mode of fiber core and Stokes.

Γ_{P}

means overlap of core and pump.

σ_{a} (λ)

and

σ_{e} (λ)

is the absorption cross section and emission cross section of

{Er}^{3 +}

ions at wavelength

λ

, respectively.

N_{1}

and

N_{2}

is ground state population and excited state population of

{Er}^{3 +}

ions respectively.

Δ λ

is 3-dB ASE bandwidth.

η_{k}^{\pm}

is the stochastic RS of

k_{t h}

order Stokes.

f_{k}^{\pm} (z, t)

is the Langevin noise sources of the

k_{t h}

order Stokes.

T_{2}

is relaxation time of the acoustic wave.

τ_{2}

is lifetime of the

{Er}^{3 +}

ions at upper state

These equations are solved by finite difference method. In the simulations, k = 5, up to 5 orders of Stokes are considered; $g_{SBS} = 5 \times 10^{- 11}$ m/W; reflectivity of FBG $R_{F B G} = 0.9998$ ; initial pump power $P = 1 W$ ; $Δ λ = 6 nm$ , $τ_{2} = 10 m s$ , $T_{2} = 22 n s$ . The stochastic RS and the Langevin noise sources term are Gaussian stochastic processes with zero mean. As for the boundary conditions, in the conventional cases, $R_{l} = 0, R_{1 - 5} = 0$ are employed at output 2, where $R_{l}$ represents the reflectivity of the fundamental light lasing in the cavity and $R_{1 - 5}$ denotes the reflectivity of the Stokes from the first order to the fifth order. In modified case, boundary conditions are in a saddle shape: $R_{l} = 0.04, R_{1} = 0.01, R_{2 - 3} = 0, R_{4} = 0.01, R_{5} = 0.04$ .

3. Simulation results

Figure 2(a) and Fig. 2(b) show the simulated pulse trains under the conventional and modified boundary condition, respectively. It is shown that conventional output pulses possess parasitic pulses and high instabilities in terms of repetition rate and pulse amplitude. While the saddle-shape boundary condition presents a rather steady and orderly pulse sequence without parasitic pulses. For the simulated pulse in the time window, the RMS instability of repetition rate drops from 8.24% to 0.86% and pulse amplitude instability is weakened from 43.42% to 1.36%.

Fig. 2 (a) The pulse sequence in a 2 ms span of the conventional boundary condition and insert: detail of a typical pulse. (b) The pulse sequence of the saddle-shape boundary condition. (c) The difference map of pulse-pulse interval and peak power of two simulated pulse sequence shown by olive and orange dots. Insert graph shows the enlarged view of the difference map of saddle-shape boundary condition.

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Figure 2(c) shows the difference map of pulse-pulse interval and the peak power. The ordinate represents the peak power difference and the abscissa corresponds to peak-to-peak span difference of adjacent pulses. The olive dots are the simulation results of traditional boundary condition while the orange dots denote the result of saddle-shaped boundary condition. In conventional conditions, peak power difference ranges from −120 W to 70 W and pulse-pulse interval difference varies from −38 µs to 40 µs. But in saddle shape conditions, absolute value of peak power difference and pulse-pulse interval difference is controlled below 0.2 W and 2 µs respectively. Simulation results clearly show that saddle shape conditions greatly improve the stability of SBSQFLs.

One can notice that the peak power of the conventional boundary condition is much higher than that of the saddle shape boundary condition. The pulse width of the conventional and saddle-shape boundary conditions is of nanoseconds and microseconds, respectively. The situation happens because in the conventional cases with weaker feedback, the inverse population must be accumulated to a higher level to stimulate the SBS. The formed pulse doesn’t resonate in the cavity since there is no feedback at one end. The pulse consumes the inverse population and emits out. In comparison, the inverse population in saddle shape condition is accumulated to a lower level and the formed pulse resonates in the cavity.

Figure 3 shows the evolution of the fundamental lasing light and 1st to 5th orders of Stokes waves with the saddle boundary condition employed when Q-switching process was stable. From the figure, we can see that 1st to 5th orders of Stokes waves were not emitted synchronously because they didn’t have maximum power at the same time. It seems that the fundamental lasing light emitted a pulse firstly and then the Stokes waves emitted their own pulses in order. This is because the normally growth of the fundamental lasing light was interrupted by the growing SBS gain. As the intensity of Stokes waves grew, SBS gain from lower order Stoke wave and loss to gain upper order Stokes wave was changing. Stokes waves has a higher intensity near the FP element end. The overall output is shown in Fig. 1. The overlap of these unsynchronized lights and intense SBS gain cause a peak pioneer at every pulse.

Fig. 3 (a) The evolution of the fundamental lasing light. (b)-(f) The evolution of the stimulated Stokes waves of the order 1-5. A time duration of 280 µs in vertical direction and a cavity length of 29 m in lateral direction is displayed respectively. Different parts of the cavity are separated by gray dashed lines.

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For a spectrum modulation device inserted cavity, the detailed process can be expounded as follow: the inverse population accumulates in the cavity and fundamental lasing light slowly grows due to the gain and loss competition. At the point the SBS threshold of a certain order of Stokes wave with high enough feedback is reached, this order begins to resonate, expending inverse population and growing at exponential rate because of high gain provided by the SBS and the reflection given by the FP interferometer. Thereupon each Stokes wave forms a pulse and outputs. Finally, a giant pulse composed of different orders of Stoke waves is obtained. The inverse population is consumed and a new cycle begins. Weak resonating signal acts as original signal and get amplified. The Q-switching progress becomes non-random and stable Q-switched output is formed.

4. Experiments and analysis

The experimental setup is shown in Fig. 4. A 980 nm pump source with a maximum output power of 600 mW was pumped into the 9 m Er-doped fiber through a WDM. Three ports of the WDM all had pigtails of 1.5 meters. Then the Er-doped fiber was spliced with 20 m single mode fiber. The FBG used in setup showed a high reflectivity of 99.86%, the center wavelength at 1550.85 nm and the 3dB bandwidth of 1.67 nm. A FP interferometer was applied at one end of WDM to introduce sub-nanoscale spectrum modulation effect into cavity. The FP interferometer acts not only as cavity mirror to provide feedback for cascaded Stokes waves but also as the spectrum modulation device to modulate them. Its diagrammatic sketch is shown in the insert of Fig. 4. This FP interferometer was made of two end faces of two fiber patch cords. Each end face provides around 4% Fresnel reflection. It causes spectrum modulation effect and enhances the light intensity by multi-beam interference. Enhanced light near FP interferometer is conducive to the SBS process initiation. The FBG with 1.67 nm bandwidth can provide feedbacks for multi-orders of Stokes. The feedback of these Stokes waves can be tuned by the FP interferometer. Generally, every adjacent order of Stokes is spacing around 0.1 nm near 1550 nm and the FP interferometer is capable of modulating feedbacks of different orders of Stokes at that scale.

Fig. 4 The experimental setup. The pump source has a maximum output of 600mW, 20m SMF is used to lower down the SBS threshold. Insert: The detailed composition of the FP interferometer. Common commercial and pre-cleaned FC/PC connectors are used in the experiments.

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When the gap between the connectors of fiber patch cables was adjusted to a proper range, the steady Q-switching conditions could be satisfied. Then the mating sleeve and connectors were fixed by UV curable adhesive. Once the pump power exceeded 72 mW, the pulses emerged, and they became more stable with the increment of pump power. The output pulses measured under different pump power are shown in Fig. 5(a). As can be seen clearly, even under low pump level, the pulse train showed steady and regular features. The orderly and stable output pulse trains indicate the feasibility of the simulations, and no parasitic pulses were observed in the whole experiments. As is depicted, the pulses under different pump levels shared the same leading peak feature which was caused by unsynchronized pulses and intense SBS gain as mentioned above.

Fig. 5 (a) Measured output pulse trains under different pump power. Right column: enlarged view of single pulse. (b) radio frequency spectrum under 600 mW.

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To characterize the stability of pulsed lasers, the signal-to-noise ratio (SNR) in radio frequency showing the contrast of the amplitude noise fluctuation and the lasing light was measured during experiments and was shown in the Fig. 5(b). The SNR was generally increasing with the increment of the pump power. And at the pump power of 600 mW which was limited by our laser source, the SNR was measured to be 62.96 dB which is the highest SNR obtained from SBS-based Q-switched fiber lasers as far as we know. Higher SNR implies greater stability of the Q-switched laser, the significantly low noise fluctuation and the steady pulse train confirm that our solution for SBS-based Q-switched lasers is valid. In the experiment, even under 600 mW pump, no degradation of output power or pulse stability was observed.

Pulse duration decreased with increment of pump power. The shortest pulse width obtained at 600mW was 8.04 µs and the corresponding repetition rate was 21.21 kHz, which were restrained by our limited pump power. The average pump power and single pulse energy both increased monotonically with pump power. The maximum output power is 57.46 mW and maximum pulse energy is 2.71 µJ (Fig. 6).

Fig. 6 (a) Pulse duration and repetition rate versus pump power. (b) Average output power and single pulse energy variation with pump power.

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To further confirm that the pulses were generated by SBS process, we investigated the intracavity spectrum near the FP interferometer. As shown in Fig. 7, a 20/80 coupling-ratio coupler was inserted in the cavity near FP interferometer. Using this configuration, the spectra of 80% and 20% output are measured simultaneously, shown in the insert figure. The spectrum of 20% output port shows multi-peaks feature and every two peaks space of 0.2 nm is exactly twice as much as the Brillouin frequency shift near 1550 nm. Shortening the length of the single mode fiber, Q-switched pulses disappeared. Considering the threshold of Brillouin scattering process is related to length of the propagating fiber and no other objects in the setup could cause multi-peaks spectrum, we can confirm that the Q-switching is indeed caused by Brillouin scattering.

Fig. 7 The experiment setup for spectrum investigation. Insert: The spectrum at 20% output port and spectrum at FP output port, the abscissa is wavelength(nm) and the ordinate is intensity(dB).

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5. Conclusions

In conclusion, we have demonstrated a highly stable SBSQFL assisted by FP interference from two un-contact fiber end faces. For the first time, steady and robust pulses without any external measures were obtained in the SBSQFL. A systemic numerical simulation and analysis is presented. Simulation results show that sub-nanoscale spectrum modulation indeed helps stabilize SBS-based Q-switched pulses. In experiments, we observed that the Q-switched fiber laser self-started at 72 mW pump power and provided SNR up to 62.96 dB with 600 mW pump power. Shortest pulse duration obtained from experiments was 8.04 µs. In addition, this kind laser has an extremely simple and cheap cavity configuration. This novel Q-switching technique we presented in this paper is promising to open up a new way to generate stable and robust Q-switched pulses in many fields. Also, it may inspire novel minds for inexpensive and widely applicable Q-switched lasers.

Funding

National Natural Science Foundation of China (11875139, 51672091).

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Robust Q-switching based on stimulated Brillouin scattering assisted by Fabry-Perot interference

Abstract

1. Introduction

2. Simulation method

3. Simulation results

4. Experiments and analysis

5. Conclusions

Funding

References

Cited By

Figures (7)

Equations (5)

Optics Express