## Abstract

Pseudo random phase modulation signals have been shown to provide considerable stimulated Brillouin scattering (SBS) suppression in narrow linewidth Yb-doped all-fiber amplifiers. In terms of coherent beam combining, however, pseudo random signals display a linear drop in visibility; leading to pronounced drops in combining efficiencies for small path length deviations. To that end, we report a novel filtered pseudo random modulation approach for enhanced combining efficiency and coherence length performance. Here a low pass radio frequency (RF) filter is used to mitigate the PRBS high frequency components, thereby suppressing the sidelobes in the optical spectrum. This leads to an approximate Gaussian visibility function and improved coherence lengths of up to 27% in a kW class fiber amplifier (954 W). In addition, the spectral sidelobe suppression leads to concurrent SBS threshold enhancement due to a reduction in the spectral overlap between the Rayleigh reflected light and the Stokes shifted light. This reduction in the SBS seeding phenomena leads to ~10% SBS threshold improvements in a kW class fiber amplifier. Theoretical and experimental data is presented to substantiate the improved coherence length and SBS suppression. More importantly, the simultaneous nonlinear SBS suppression and coherence length benefits of the filtered PRBS approach can have a significant impact for high power, narrow linewidth, all-fiber amplifiers.

© 2017 Optical Society of America

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### Equations (11)

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(1)
$$\begin{array}{c}\tilde{E}\text{}={A}_{LF}(z,t){e}^{i({k}_{L}z-{\omega}_{L}t)}\\ +{A}_{LB}(z,t){e}^{i(-{k}_{S}z-{\omega}_{S}t)}{e}^{-i{\Omega}_{B}(zn/c+t)}\\ +{A}_{S}(z,t){e}^{i(-{k}_{S}z-{\omega}_{S}t)}+\text{}c.c.\end{array}$$
(2)
$${\nabla}^{2}\tilde{E}-\frac{{n}^{2}}{{c}^{2}}\frac{{\partial}^{2}\tilde{E}}{\partial {t}^{2}}=\frac{1}{{\epsilon}_{0}{c}^{2}}\frac{{\partial}^{2}\tilde{P}}{\partial {t}^{2}}$$
(3)
$$\tilde{P}={\epsilon}_{0}{\gamma}_{e}\tilde{\rho}\tilde{E}$$
(4)
$$\frac{c}{n}\frac{\partial {A}_{LF}}{\partial z}+\frac{\partial {A}_{LF}}{\partial t}=\frac{\omega {\gamma}_{e}}{2{n}^{2}{\rho}_{0}}\rho \left({A}_{S}+{A}_{LB}{e}^{-i{\Omega}_{B}(zn/c+t)}\right)$$
(5)
$$-\frac{c}{n}\frac{\partial {A}_{LB}}{\partial z}+\frac{\partial {A}_{LB}}{\partial t}=\frac{\omega {\gamma}_{e}}{2{n}^{2}{\rho}_{0}}{\rho}^{*}{A}_{LF}{e}^{i{\Omega}_{B}(zn/c+t)}$$
(6)
$$-\frac{c}{n}\frac{\partial {A}_{S}}{\partial z}+\frac{\partial {A}_{S}}{\partial t}=\frac{\omega {\gamma}_{e}}{2{n}^{2}{\rho}_{0}}{\rho}^{*}{A}_{LF}$$
(7)
$$\frac{{\partial}^{2}\tilde{\rho}}{\partial {t}^{2}}-\frac{{\Gamma}_{B}}{{q}^{2}}{\nabla}^{2}\frac{\partial \tilde{\rho}}{\partial t}-{\nu}_{S}^{2}{\nabla}^{2}\tilde{\rho}=-\frac{1}{2}{\epsilon}_{0}{\gamma}_{e}{\nabla}^{2}\u3008{\tilde{E}}^{2}\u3009+\tilde{f}$$
(8)
$$\begin{array}{l}\frac{{\partial}^{2}\rho}{\partial {t}^{2}}+\left({\Gamma}_{B}-2i{\Omega}_{B}\right)\frac{\partial \rho}{\partial t}-i{\Omega}_{B}{\Gamma}_{B}\rho \\ ={\epsilon}_{0}{\gamma}_{e}{q}^{2}{A}_{LF}\left({A}_{S}^{*}+{A}_{LB}^{*}{e}^{i{\Omega}_{B}(zn/c+t)}\right)-2i{\Omega}_{B}f\end{array}$$
(9)
$${A}_{LB}(z=L,t)=\sqrt{R}{A}_{LF}(z=L,t)$$
(10)
$$\left|V\left(\tau \right)\right|=\left|{{\displaystyle \int}}_{-\infty}^{+\infty}PSD\left(\omega \right){e}^{-i\omega \tau}d\omega \right|=\frac{{I}_{max}-{I}_{min}}{{I}_{max}+{I}_{min}}$$
(11)
$$PSD\left(\nu \right)={\left|{\displaystyle {\int}_{-\infty}^{+\infty}{A}_{LF}}(z=0,t){e}^{i\omega t}dt\right|}^{2}$$