Evaluation of the impact of weak end feedback on the SBS threshold in high-power narrow-linewidth fiber amplifiers

Wei Li; Yu Deng; Chen Qi; Yisha Chen; Yisha Chen; Pengfei Ma; Pengfei Ma; Pengfei Ma; Pengfei Ma; Wei Liu; Wei Liu; Wei Liu; Wei Liu; Zhou Pu; Lei Si; Lei Si; Lei Si

doi:10.1364/OE.522400

1. Introduction

High-power narrow-linewidth fiber amplifiers have been highly desired in numerous applications such as coherent and spectral beam combinations [1–3], nonlinear frequency conversion [4], remote communication [5], and so forth. Nevertheless, the power scaling of high-power narrow-linewidth fiber amplifiers is restricted by stimulated Brillouin scattering (SBS) [6,7], stimulated Raman scattering (SRS) [8,9], and transverse mode instability (TMI) [10–12] effects, especially for those with linewidth below 50 GHz or narrower, SBS effect will be the main limitation [13–15]. In high-power fiber laser systems, pure phase modulation is a traditional spectral broadening technique that could provide excellent SBS suppression for the system [16–23]. Based on the pure phase modulation technique, the output power of narrow-linewidth fiber lasers has been developed to muti-kilowatts [19–23]. However, recent studies have pointed out that weak end feedback would degrade the performance of the pure phase modulation technique qualitatively [24–26]. Specifically, a weak end reflection of spectral component down to the Brillouin frequency shift in the output signal light could act as a seed laser and contribute to the amplification of Brillouin Stokes light. In this case, weak end feedback would lead to a quick decrease of the SBS threshold and break the desired tradeoff between SBS and spectral linewidth in high-power narrow-linewidth fiber amplifiers [27–30].

Although, the reported research have proved that the end feedback will decrease the SBS threshold of the system, it should be noted that the spectral linewidth considered in those above-mentioned studies is below 10 GHz, while the spectral linewidth of the reported multi-kilowatt narrow-linewidth fiber amplifiers is commonly tens or hundreds of GHz [19–23]. Correspondingly, it is still unclear how weak end feedback would impact the SBS effect when the spectral linewidth is over 10 GHz, which is of vital importance for achieving better tradeoff between SBS suppression and spectral linewidth narrowing in a multi-kilowatt narrow-linewidth fiber amplifier.

This work aims to investigate the impact of weak end feedback on the SBS threshold of practical high-power narrow-linewidth fiber amplifiers quantitatively when the spectral linewidth ranges from several to tens of GHz. Experimentally, we calibrate the reflectivity of weak end reflections and measure the SBS threshold of high-power narrow-linewidth fiber amplifiers when the spectral linewidth and reflectivity are different. Theoretically, we propose a new spectral evolution model to describe the SBS effect in high-power narrow-linewidth fiber amplifiers in the presence of weak end feedback, which is capable of analyzing SBS effects over a spectral width of several hundred GHz.

2. Experiment demonstrations and result analysis

2.1 Experiment setup

The schematic diagram of the experiment is illustrated in Fig. 1 which is based on a classical master oscillator power amplifier (MOPA) structure. The single-frequency source (SFS) is a linearly polarized fiber laser with a central wavelength of 1063.98 nm. After the seed, a LiNbO3 electro-optical modulator (EOM) with a half-wave voltage of 10 V and a bandwidth of 10 GHz is used for linewidth broadening. Then, the modulated seed is injected into two pre-amplifiers and the seed power is amplified to ∼10 W. Afterwards, a circulator is inserted to separate the backward propagating laser for power and spectrum measurement, at where a power meter (Power meter 1 with the maximum operating power and resolution of 500 mW and 10 nW) and an optical spectrum analyzer (OSA with resolution of 0.02 nm) are applied. Before the main amplifier, a band past filter (BPF) with a bandwidth of 1064 ± 1 nm is utilized to remove the sideband noise in the spectrum. To avoid other effects at high power, the main amplifier is built on a foreword pumping scheme, and 915 nm LDs are used. A 42 m Yb-dopped fiber (YDF) with a core/cladding diameter of 20/400 µm is used in the main amplifier, which has a pump absorption ratio of 0.5 dB/m at 915 nm. Near the end of the amplifier, a cladding power stripper (CPS) is directly manufactured on the active fiber to strip out the residual pump power. The amplified laser is then output through a quartz block holder (QBH) or an angle, which is eventually transported into the power meter 2 for power recording.

Fig. 1. Schematic diagram of the high-power narrow-linewidth fiber amplifier.

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Compared to other phase modulation signals, the white-noise signal is superior in adjusting the spectral linewidth of phase-modulated single-frequency lasers over a wide range. Thus, we choose the white-noise signal to construct the phase-modulated single-frequency seed lasers for the signal light broadening in the experiment. By adjusting the intensity of the WNS-driven signal, seed lasers with different linewidths could be obtained. The specific linewidths of the modulated seeds are measured by a Fabry–Perot interferometer (FPI, with a free spectral range (FSR) of 10 GHz) or an OSA (with a resolution of 0.02 nm). Here, the choice of the FPI or OSA depends on whether the linewidths of the seeds exceed the resolution of the OSA. The measured results are shared in Fig. 2, in which the inserted figure is measured by the FPI while others are measured by the OSA. As shown in the figure, the full-width at half-maximum (FWHM) linewidths of these seeds are measured to be 0.95 Hz, 7.8 GHz, 10.5 GHz, 16.8 GHz, and 22.5 GHz. With such seeds injected, the SBS effect in the main amplifier is further investigated while different strengths of end reflection are imported.

Fig. 2. The linewidths of the modulated seeds.

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2.2 Measurement of the end reflectivity

Except for the linewidth control, another important issue we focus on in the experiment is how to import and accurately characterize different end reflections. In detail, we introduce different end reflections by changing the angle of the fiber output port, as shown in the typical diagram Fig. 3(a). Theoretically, the greater angle of the output port we introduce, the lower power will be reflected to the fiber core [31]. However, due to the difference in the flatness of the output surface at different angles, as well as the endcap being plated with anti-reflection film, the reflectivity can’t be directly characterized by the output angles. For scientifically characterizing the reflectivity, we did the following analysis based on the backward power and output power measured in the experiment.

Fig. 3. (a) The typical diagram of the output port; (b)- (h) represent to the second-order nonlinear fitting of the backward power and the output power at different output angles.

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When a fiber amplifier operates well below the SBS and SRS threshold, it is reasonable to attribute the backward power to the contribution of weak end reflections. In this case, the practical end reflectivity could be estimated by measuring the backward and forward output powers experimentally. In detail, the backward light could be divided into two parts. The first part of the backward light is transmitted into the fiber cladding. For this part, its power will not be amplified and its interaction with the signal light in the fiber core could be negligible. For the second part that propagates in the cladding, its power will be amplified again and the amplification factor of backward light is approximately equal to that of the foreword signal. Thus, the practical end reflectivity of the fiber core or cladding could be estimated through the following formula:

(1)$${P_{back}} = a \times {P_0} \times \Omega + b \times {P_0} \times {\Omega ^2}$$

where the P_back denotes the total power of the backward light, P₀ is the injected signal power and Ω is the amplification factor while a and b represent to the reflectivity of the fiber cladding and core, respectively. In the experiment, the direct data that we could obtain is the output power and the backward power, so the following substitution is made:

(2)$$\left\{ \begin{array}{l} {P_{signal}} = {P_0} \times \Omega \\ {P_{back}} = c \times {P_{signal}} + d \times P_{signal}^2\\ a = c\\ b = d \times {P_0} \end{array} \right.$$

where P_signsl is the output power. c and d are the second-order nonlinear fitting coefficients which is the analysis result of the nonlinear fitting between output power and backward power. Therefore, the connection between backward power and cladding/core reflectivity could be described as:

(3)$${P_{back}} = a \times {P_{signal}} + b \div {P_0} \times P_{signal}^2$$

Next, power amplification experiments are carried out and the backward power at different angles is recorded for reflectivity estimations. To avoid the influence of the SBS effect on the analysis of the reflectivity, the linewidth of the seed laser is adjusted to the widest one (22.5 GHz) while the output power is kept below 150 W for all different angles. The nonlinear fitting results at different angles are illustrated in Fig. 3(b)-(h).

According to the estimation formula above shared, the reflectivity of the fiber core and cladding (a and b) could be obtained, as shared in Table 1. As above mentioned, only the backward light that propagates in the fiber core will overlap with the SBS gain spectrum and affect the SBS threshold of the system. So, in the following analysis, we will focus on these measured b to investigate their specific influence on the SBS threshold. Besides, for all the analysis results, the values of a and b only vary within one order of magnitude, which means that when the output power is amplified beyond 10 W, the core reflectivity b will take the domain in the backward power. Consequently, setting the power at 150 W can accurately reveal the small difference among parameter b. From the results shown in Table 1, we can see that the core reflectivity b of the endcap is measured to be -62.0 dB. As for the angled output conditions, the value of b decreased from -51.7 dB to -62.8 dB with the increase of output angle, except for the 10.3° angled one (presumably due to the end surface damage). In the following analysis, we will base on these measured b to investigate its specific influence on the SBS threshold.

Table 1. The analysis results

View Table

2.3 SBS threshold analysis

Based on the above designs, we further investigated the SBS threshold of the system at different linewidths and core reflectivity. In the experiment, the SBS threshold is defined as the output power when the power ratio of the backward propagating power reaches 0.3‰ of the output power. Figure 4 demonstrates the total result of the measured SBS thresholds when the core reflectivity and linewidths are different. This figure demonstrates that the SBS threshold decreases with the growth of core reflectivity when the linewidth is wider than 7.8 GHz. For example, when the linewidth of the seed laser is broadened to 22.5 GHz, the SBS threshold of the system decreases from 546 W to 205 W when the core reflectivity increases from -62.8 dB to -51.7 dB. But when the linewidth of the seed laser is narrower than 7.8 GHz, the SBS threshold will barely change with the increase of core reflectivity. To give a specific description of this phenomenon, we import a SBS threshold changing ratio (ξ) which is defined as:

(4)$$\xi = \frac{{{P_{\max }} - {P_{\min }}}}{{{P_{ave}}}}$$

where P_max, P_min, and P_ave are the maximum, minimum, and average SBS thresholds measured at the same linewidth when core reflectivity changes from -51.7 dB to -62.8 dB. As a result, the SBS threshold changing ratio is calculated to be 5.8%, 7.2%, 57.6%, 85.3%, and 81.6% for the linewidth of 0.95 GHz, 7.8 GHz, 10.5 GHz, 16.8 GHz, and 22.5 GHz, respectively. The results quantitively confirm that when the linewidth of the seed laser is controlled below 7.8 GHz, the value of ξ is less than 10% indicating that the core reflectivity has little impact on the SBS threshold of the system. Otherwise, when the linewidth of the seed laser is broadened beyond 7.8 GHz, the value of ξ will exceed over 50% indicating that even a weak change in core reflectivity will provide a significant impact on the SBS threshold of the system.

Fig. 4. The SBS threshold of the system at different end feedback.

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Further, we calculated the SBS threshold enhancement factor by taking the SBS threshold measured at the core reflectivity of -51.7 dB as the standard, and the result has been demonstrated in Fig. 5. When the linewidth of the seed laser is broadened beyond 7.8 GHz, lower core reflectivity can obtain a significant higher SBS threshold enhancement factor. Besides, with the growth of linewidth, the SBS threshold enhancement factor will gradually elevate from 1 to 2.85 when the linewidth is below 16.8 GHz. However, when the linewidth is broadened beyond 16.8 GHz, the SBS threshold enhancement factor performs a downward trend, indicating that the core reflectivity has the greatest effect on the SBS threshold around 16 GHz (near the SBS frequency shift). Namely, when the linewidth is broadened beyond 16 GHz, the increase of the SBS threshold caused by spectral broadening will be greater than the decrease of the SBS threshold caused by core reflectivity.

Fig. 5. The SBS threshold enhancement factor.

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Moreover, from the results shared in Fig. 4 and Fig. 5, we also find that even if the end reflectivity decreases from -61.5 dB to -62.8 dB (within 1.5 dB), the SBS threshold enhancement will increase over 184 W, when the linewidth is wider than 16 GHz. At this time, taking the SBS threshold measured at the end reflectivity of -61.5 dB as the standard, the SBS threshold will enhance 1.63 and 1.56 times at the linewidth of 16.8 GHz and 22.5 GHz as the end reflectivity reduces to -62.8 dB.

Limited by the maximum spectrum broadening level of the EOM phase modulator as well as the influence of the potential SRS effect, further investigation of the effect of the core reflectivity on the SBS threshold would be hard to accomplish in the experiment. To study this phenomenon in a wider spectral range and propose a more general conclusion, more comprehensive theoretical researches have been carried out.

3. Theoretical investigation

3.1 Numerical model

To analyze the impact of weak end feedback on the SBS threshold in optical fibers theoretically, a wide frequency range over the Brillouin frequency shift is required in numerical modeling. The SBS effect in optical fibers is generally described through the three coupled amplitude equations, which involve the interactions between the pump and Brillouin Stokes fields through an acoustic wave [32]. The pump and Brillouin Stokes fields propagate in opposite directions, and the bidirectional approach is commonly applied to simulate the SBS effect in passive fibers or fiber amplifiers seeded with phase-modulated single-frequency lasers [16,33]. In a bidirectional approach, the computation iterates the counter-propagating optical fields at all positions along the fiber simultaneously. Correspondingly, more abundant transient properties of the Brillouin Stokes light could be described, while the frequency ranges considered in those simulations are limited to several GHz to tens of GHz.

Apart from the bidirectional approach, the iterative unidirectional approach could also be applied to deal with the interactions between two counter-propagating optical fields. In a unidirectional approach, the computation iterates the optical field envelope along the fiber in each direction alternately and applies the optical field envelope in the opposite direction obtained from a previous iteration [34]. Compared to the bidirectional approach, the iterative unidirectional approach is superior in the situation when the frequency range over hundreds of GHz should be considered [35]. Accordingly, we apply the iterative unidirectional approach to build the numerical modeling here.

The iterative unidirectional approach deals with the evolution of an optical field through spectral evolution, and the three coupled amplitude equations are transformed into the frequency domain:

(5)$$\frac{{\partial {{\tilde{A}}_s}}}{{\partial z}} ={-} \frac{{{\alpha _s}}}{2}{\tilde{A}_s} - \frac{{i\omega }}{{{\nu _s}}}{\tilde{A}_s}\textrm{ + }F\{{i\gamma ({{{|{{A_s}} |}^2} + 2{{|{{A_B}} |}^2}} ){A_s} + i{\kappa_1}{A_B}Q} \}$$

(6)$$- \frac{{\partial {{\tilde{A}}_B}}}{{\partial z}} ={-} \frac{{{\alpha _s}}}{2}{\tilde{A}_B} - \frac{{i\omega }}{{{\nu _s}}}{\tilde{A}_B}\textrm{ + }F\{{i\gamma ({{{|{{A_B}} |}^2} + 2{{|{{A_s}} |}^2}} ){A_B} + i{\kappa_1}{A_s}{Q^\ast }} \}$$

(7)$$Q = {F^{ - 1}}\left\{ {\frac{{F\{{i{\kappa_2}{A_s}A_B^\ast } \}}}{{{{{\Gamma _B}} / {2 + i({\omega + {\Omega _B}} )}}}}} \right\} + {Q_n}$$

where the subscript s and B stand for signal light and Brillouin stokes light respectively, Ã and A are the complex amplitudes of the optical field envelope in the frequency domain and time domain respectively, ω is the reference angular frequency, ν is the group velocity of optical field envelope, α is the loss coefficient of fiber, γ is the nonlinear Kerr coefficient, Q is the complex amplitude of acoustic field in the time domain, ν_A is the acoustic velocity in fiber, Γ_B is the acoustic damping rate, Ω_B is the acoustic angular frequency, F and F^-1 denote the operation of Fourier transform and inverse Fourier transform respectively, and Q_n is the noise initiation of SBS effect [36]. Moreover, the two coupling coefficients κ₁ and κ₂ could be expressed as:

(8)$$\begin{array}{{cc}} {{\kappa _1} = \frac{{{\omega _s}{\gamma _e}}}{{2{n_s}c{\rho _0}}},}&{{\kappa _2} = \frac{{{\omega _s}{\gamma _e}}}{{2{c^2}{\nu _A}{A_{eff}}}}} \end{array}$$

where ω_s is the angular frequency of signal light, γ_e is the electrostrictive constant of silica, n is the refractive index of the fiber core, c is the light velocity in the vacuum, ρ₀ is the fiber density, and A_eff is the effective mode area of the fiber.

In a rare-earth-doped fiber amplifier, the rare-earth gain and spontaneous emission noise could also contribute to the amplification of Brillouin Stokes light. As for the rare-earth gain, it could be obtained through the steady-state rate equations [37]:

(9)$${g_s} = {\Gamma _s}({{N_2}{\sigma_e} - {N_1}{\sigma_a}} )$$

where Γ_s is the power overlap factor of signal light, σ_e, and σ_a are the absorption and emission cross sections of the doped ion at signal wavelength respectively, and N₁/N₂ is the total number of doped ion per unit volume in a ground state or excited state respectively, N₁+ N₂= N₀, and N₀ is the dopant density in fiber core.

As for the spontaneous emission noise, both its amplitude and phase satisfy the Gaussian stochastic process with zero mean value [38]:

(10)$$\begin{array}{{cc}} {\left\langle {{f_{SE}}} \right\rangle = 0}&{\left\langle {{f_{SE}} \cdot f_{SE}^\ast } \right\rangle = 2{D_{FF}}(\omega )\delta ({\omega - \omega^{\prime}} )} \end{array}$$

where <* > denotes the operation of average, f_SE is the complex amplitude of spontaneous emission noise in the frequency domain, D_FF is the diffusion coefficient, and δ is the Dirac function.

Then the major equations describing the spectral evolution of signal and Brillouin stokes lights in a rare-earth doped fiber amplifier with boundary conditions as:

(11)$$\frac{{\partial {{\tilde{A}}_s}}}{{\partial z}} = \frac{{{g_s} - {\alpha _s}}}{2}{\tilde{A}_s} - \frac{{i\omega }}{{{\nu _s}}}{\tilde{A}_s}\textrm{ + }F\{{i\gamma ({{{|{{A_s}} |}^2} + 2{{|{{A_B}} |}^2}} ){A_s} + i{\kappa_1}{A_B}Q} \}+ {f_{SE}}$$

(12)$$- \frac{{\partial {{\tilde{A}}_B}}}{{\partial z}} = \frac{{{g_s} - {\alpha _s}}}{2}{\tilde{A}_B} - \frac{{i\omega }}{{{\nu _s}}}{\tilde{A}_B}\textrm{ + }F\{{i\gamma ({{{|{{A_B}} |}^2} + 2{{|{{A_s}} |}^2}} ){A_B} + i{\kappa_1}{A_s}{Q^\ast }} \}+ {f_{SE}}$$

(13)$${\tilde{A}_B}({z = L} )= \sqrt R {\tilde{A}_s}({z = L} )$$

where Eq. (13) describes the boundary condition at the output end, L is the fiber length, and R is the end reflectivity.

To apply the above model, we need to construct the initial inserted phase-modulated single-frequency seed lasers for the signal light. Considering that the spectral component down to the Brillouin frequency shift could also be the background spectral noise. The background spectral noise in signal light could originate from the intensity noise induced by phase modulators [39]. So, the background spectral noise in seed lasers is added by incorporating a weak intensity noise here. Then, the complex field of seed lasers in the time domain could be expressed as:

(14)$${A_{seed}} = \sqrt {{P_0}} \left[ {\textrm{exp} ({i\varphi t} )+ \sqrt {{I_n}} ({{X_0}\textrm{ + }i{X_1}} )} \right]$$

where P₀ is the seed power, φ is the phase modulation signal, I_n is the relative strength of the intensity noise, X₀ and X₁ are two standardized random variables.

To better validate the conclusions obtained from the experiment, we also chose the white-noise signal to construct the phase-modulated single-frequency seed lasers in the analysis. Here the white-noise signal could be characterized by two main parameters, the root-mean-square (RMS) amplitude and the ratio frequency (RF) bandwidth. In the simulation, we adjust the upper limit of RF bandwidth and the RMS amplitude of the white-noise signal to construct phase-modulated single-frequency seed lasers with different spectral linewidth. The constructed spectra are shown in Fig. 6 and the corresponding RMS spectral linewidth of those signal lights are measured to be 3 GHz, 5 GHz, 8.1 GHz, 13.6 GHz, 15.4 GHz, 19.2 GHz, 24.8 GHz, 29.7 GHz, and 35.1 GHz.

Fig. 6. Spectral property of the constructed phase-modulated single-frequency lasers.

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Based on the above model, we simulate the SBS effect in a typical diode-pumped high-power Yb-doped fiber amplifier seeded with phase-modulated single-frequency lasers by applying the 4^th-order Lunger Kuta method to solve the three coupled amplitude equations. This fiber amplifier operates at 1064 nm and the seed power is 10 W. In the following numerical model, to be more realistic to the experimental system, the I_n is set to be 10⁻² in seed lasers. The core diameter and inner cladding diameter of the Yb-doped fiber (YDF) are set to be 20 µm and 400 µm, respectively. The cladding absorption coefficient of the YDF is set to be 0.5 dB/m at 915 nm, and the length of the YDF is set to be 42 m. The other major simulation parameters for the fiber amplifier are listed as follows: n_s= 1.451, α_s= 15 dB/km, γ=0.37 W^-1/km, v_A= 5.904 km/s, Ω_B= 2π×16 GHz, γ_e= 0.902, ρ₀= 2210 kg/m³, and Γ_B= 2.033 × 10⁸ /s.

3.2 Basic output property of the fiber amplifier in the presence of weak end feedback

We first demonstrate the basic output property of the fiber amplifier in the presence of weak end feedback. In the simulation, we adjust the linewidth of the seed spectrum to 3 GHz and fix the pump power at 130 W. Figures 7(a) and 7(b) illustrate the normalized output spectral properties of signal and Brillouin Stokes lights when the end reflectivity R is set to be -80 dB and -40 dB. The spectral intensity is normalized through its maximum value here. As shown in Fig. 7, the spectral intensity of signal light is almost identical to the seed laser shown in Fig. 6, and the peak value of Brillouin Stokes light is at the reference frequency of about -16 GHz. Comparing Fig. 7(b) to the results shown in Fig. 7(a), an additional frequency peak appears in the spectral intensity of Brillouin Stokes light, indicating a stronger SBS effect. In addition, the average powers of the Brillouin Stokes lights are about 6 mW and 15.2 W, respectively. Therefore, the enhancement of end reflection leads to the enhancement of the SBS effect in the fiber amplifier.

Fig. 7. Normalized spectrum property of the signal and Brillouin Stokes lights when the end reflectivity R is - 80 dB (a) and - 40 dB (b).

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3.3 SBS effect in the fiber amplifier when the end reflectivity is different

As we mentioned above, the theoretical SBS threshold of a fiber amplifier is generally defined as the output power of signal light when the power ratio of Brillouin Stokes light reaches a certain value. Nevertheless, the backward power contains the components of both signal and Brillouin Stokes lights in the presence of weak end feedback. To separate the contribution of the SBS effect to the backward power, we define the net power of Brillouin Stokes light as the difference between the backward powers when the SBS effect is considered or neglected in the simulations. Then, the SBS threshold is defined as the output power of signal light when the net power ratio of Brillouin Stokes light reaches 0.1‰.

Figure 8 illustrates the SBS threshold characters of the amplifier as a function of the RMS spectral linewidth of seed lasers while the end reflectivity changes from -50 dB to -70 dB. As shown in Fig. 8(a), when the RMS linewidth of the seed laser is below 5 GHz, the end reflectivity has little effect on the SBS threshold. But, once the RMS linewidth of the seed laser is broadened beyond 5 GHz, the SBS threshold of the fiber amplifier decreases with the end reflectivity in the five cases, and it decreases more quickly when the RMS spectral linewidth of seed lasers is bigger. Besides, with the broadening of linewidth, the overlap between the signal spectrum and the Brillion gain spectrum will increase at the same time. Especially for the linewidth of the seed laser ranging from 5 GHz to 16 GHz, the SBS threshold may decrease with the growth of RMS linewidth when the end reflectivity is taken into account. To give a quantitative description, we further introduce the SBS threshold enhancement factor to reveal the impact of reflectivity on the SBS threshold of the system. Here, the SBS threshold enhancement factor is defined as the SBS threshold measured at all the end reflectivity divided by the SBS threshold measured at the end reflectivity of -50 dB while the linewidth is kept the same. The result is displayed in Fig. 8(b), from which we can see that the SBS threshold enhancement factor increases with the decrease of end reflectivity, and it increases more quickly when the end reflectivity is smaller. Moreover, the SBS threshold enhancement factor increases relatively slower when the linewidth of the seed laser is broadened beyond 16 GHz, this is very close to the results of the experiment.

Fig. 8. SBS threshold characters of the amplifier when the end reflectivity changes from -50 dB to -70 dB. (a) SBS threshold of the fiber amplifier as a function of end reflectivity; (b) The corresponding enhancement factor.

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In the experiment, changes in the end reflectivity (corresponding to the core reflectivity here) only range from 51.7 dB to 62.8 dB, thus, simulation on comparing the effect of small differences in end reflectivity on the SBS threshold is of great significance to verify the experimental results. Figure 9 demonstrates the SBS threshold characters of the amplifier for the simulation and reality conditions with linewidth between 15 GHz and 25 GHz. In detail, the end reflectivity of the simulation is set at -50 dB, -60 dB, and -63 dB while the classical end reflectivity of the experiment is set at -51.7 dB, -62.0 dB, and -62.8 dB. As for the simulation results, when the linewidth is broadened to 24.8 GHz, the amplifier working at the end reflectivity of -63 dB will obtain a 136.2 W and 431.2 W SBS threshold enhancement, compared with working at the end reflectivity of -60 dB and -50 dB. As for the experiment results, when the linewidth is broadened to 22.5 GHz, the amplifier working at the end reflectivity of -62.8 dB will obtain an 89.7 W and 341 W SBS threshold enhancement, compared with working at the end reflectivity of -62.0 dB and -51.7 dB. Both the simulation and experiment results demonstrate that even small differences in end reflectivity will lead to an obvious difference in the SBS threshold. Besides, this figure also illustrates that when the linewidth is increased beyond 15 GHz, the reality results match well with the simulated results, demonstrating that our theoretical model is scientific and reliable.

Fig. 9. SBS threshold of the amplifier with a small difference in end reflectivity.

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4. Discussion

In the experiment, we find that the SBS threshold of some angled output conditions is higher than the endcap output one, even though the endcap is plated with anti-reflection film. Especially for the 12.1° angled output one, its SBS threshold is 20.5% higher than the endcap output one at the linewidth of 16.8 GHz. This result illustrates that applying angled output conditions in the high-power narrow-linewidth fiber amplifiers could obtain lower core reflectivity than using the plane endcap. However, it should be pointed out that limited by the instability of the angle-cutting technique induced end-surface damage, the end reflectivity will be varied in a wide range. For example, the core reflectivity of the 10.3° angled output one is measured to be -61.5 dB which is higher than expected according to Ref. [22]. Besides, due to the potential end-surface damages, the systems would suffer a great risk of being destroyed when angled output conditions are applied in the high-power amplifiers. Additionally, while applying an angled output condition, the angle shouldn’t be too large, because the excessive increase in angle will do little to reduce reflectivity but induce the increase of temperature at the output port (more power leaks out from the cladding) and the degeneration of beam quality (more optical path difference). In conclusion, when considering the holistic optimization and design of high-power narrow-linewidth fiber laser systems, especially for those with linewidths around 16 GHz (SBS frequency shift), the application of properly beveled endcaps with anti-reflective coatings is a prospective option for increasing the SBS threshold.

5. Conclusion

In this work, we give out a practical method to estimate the end reflectivity of high-power fiber laser systems and we present a comparative experiment to analyze the pattern of the impact of end feedback on the SBS threshold. The experimental results show that even if the end reflectivity is reduced by 1.5 dB, the SBS threshold could be enhanced > 184 W (corresponding to 1.63 times SBS threshold enhancement) when the linewidth of the seed laser is 16.8 GHz. Then, we propose a comprehensive model to investigate the SBS threshold of high-power narrow-linewidth fiber amplifiers seeded with phase-modulated single-frequency lasers in presence of weak end feedback. This spectral evolution model is capable of calculating SBS thresholds for systems with tens of GHz linewidth. Through analyses, we demonstrate that when the end reflectivity is set to be stronger than -65 dB, the SBS threshold would perform a tendency to decline and then rise with the growth of seed linewidth. Consequently, both the experiment and simulation results demonstrate that small differences in end reflectivity will lead to an obvious difference in the SBS threshold. Our work can provide a promising reference for linewidth narrowing and in-depth system component optimization in high-power narrow linewidth fiber amplifiers.

Funding

National Key Research and Development Program of China (2022YFB3606400); National Natural Science Foundation of China (Grant No. U22A6003).

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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	Reflectivity of the fiber cladding and core
Angle	a	b
Endcap	1.73 × 10⁻⁶	6.34 × 10⁻⁷ (-62.0 dB)
2.3°	5.17 × 10⁻⁵	6.79 × 10⁻⁶ (-51.7 dB)
3.6°	1.57 × 10⁻⁷	6.37 × 10⁻⁷ (-61.9 dB)
5.6°	1.13 × 10⁻⁶	6.68 × 10⁻⁷ (-61.7 dB)
7.4°	7.85 × 10⁻⁷	6.20 × 10⁻⁷ (-62.1 dB)
10.3°	2.12 × 10⁻⁸	7.10 × 10⁻⁷ (-61.5 dB)
12.1°	9.30 × 10⁻⁷	5.29 × 10⁻⁷ (-62.8 dB)

Evaluation of the impact of weak end feedback on the SBS threshold in high-power narrow-linewidth fiber amplifiers

Abstract

1. Introduction

2. Experiment demonstrations and result analysis

2.1 Experiment setup

2.2 Measurement of the end reflectivity

2.3 SBS threshold analysis

3. Theoretical investigation

3.1 Numerical model

3.2 Basic output property of the fiber amplifier in the presence of weak end feedback

3.3 SBS effect in the fiber amplifier when the end reflectivity is different

4. Discussion

5. Conclusion

Funding

Disclosures

Data availability

References

Data availability

Cited By

Figures (9)

Tables (1)

Equations (14)

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