## Abstract

The threshold for second-order stimulated Brillouin scattering (SBS) in a fiber has been investigated; the study was motivated, in part, by the need to determine the operational dynamic range of SBS fiber beam combiners. Theoretical analysis showed that the second-order Stokes threshold is approximately 130 times the first-order threshold. Experimentally, however, the threshold was found to be only 15 times greater. This dramatic reduction in threshold was determined to be due to the generation of second-order Stokes photons through four-wave mixing, which in turn seeds the second-order SBS process. Suppression of internal Fresnel reflection at the front fiber facet can help to restore the threshold to the higher value.

© 2002 Optical Society of America

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### Equations (10)

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(1)
$$\frac{\partial}{\partial z}{A}_{p}=-{g}_{B}{\epsilon}_{0}{\mathit{cnA}}_{p}|{A}_{s}{|}^{2}+i2{\epsilon}_{0}{n}_{2}\omega {\mathit{nA}}_{\mathrm{sf}}^{2}{A}_{s2}^{*}\times exp[i(2{k}_{\mathrm{sf}}-{k}_{s2})z]-\frac{\alpha}{2}{A}_{p},$$
(2)
$$\frac{\partial}{\partial z}{A}_{s}=-{g}_{B}{\epsilon}_{0}{\mathit{cnA}}_{s}|{A}_{p}{|}^{2}+{g}_{B}{\epsilon}_{0}{\mathit{cnA}}_{s2}|{A}_{s}{|}^{2}+\frac{\alpha}{2}{A}_{s},$$
(3)
$$\frac{\partial}{\partial z}{A}_{\mathit{sf}}=i4{\epsilon}_{0}{n}_{2}\omega {\mathit{nA}}_{\mathrm{sf}}^{*}{A}_{p}{A}_{s2}\times exp[i({k}_{p}+{k}_{s2}-{k}_{\mathrm{sf}})z]-\frac{\alpha}{2}{A}_{\mathrm{sf}},$$
(4)
$$\frac{\partial}{\partial z}{A}_{s2}={g}_{B}{\epsilon}_{0}{\mathit{cnA}}_{s2}|{A}_{s}{|}^{2}+i2{\epsilon}_{0}{n}_{2}\omega {\mathit{nA}}_{\mathrm{sf}}^{2}{A}_{p}^{*}\times exp[i(2{k}_{\mathrm{sf}}-{k}_{p})z]-\frac{\alpha}{2}{A}_{s2}.$$
(5)
$$\frac{\partial}{\partial z}{A}_{p}=-{\eta}_{\mathrm{SBS}p}{g}_{B}{\epsilon}_{0}{\mathit{cnA}}_{p}|{A}_{s}{|}^{2}+i{\eta}_{\mathrm{FWM}}2{\epsilon}_{0}{n}_{2}\omega {\mathit{nA}}_{\mathrm{sf}}^{2}{A}_{s2}^{*}-\frac{\alpha}{2}{A}_{p},$$
(6)
$$\frac{\partial}{\partial z}{A}_{s}=-{\eta}_{\mathrm{SBS}s}{g}_{B}{\epsilon}_{0}{\mathit{cnA}}_{s}|{A}_{p}{|}^{2}+\frac{\alpha}{2}{A}_{s},$$
(7)
$$\frac{\partial}{\partial z}{A}_{\mathit{sf}}=i{\eta}_{\mathrm{FWM}}4{\epsilon}_{0}{n}_{2}\omega {\mathit{nA}}_{\mathrm{sf}}^{*}{A}_{p}{A}_{s2}-\frac{\alpha}{2}{A}_{\mathrm{sf}},$$
(8)
$$\frac{\partial}{\partial z}{A}_{s2}={\eta}_{\mathrm{SBS}2}{g}_{B}{\epsilon}_{0}{\mathit{cnA}}_{s2}|{A}_{s}{|}^{2}+i{\eta}_{\mathrm{FWM}}2{\epsilon}_{0}{n}_{2}\omega {\mathit{nA}}_{\mathrm{sf}}^{2}{A}_{p}^{*}-\frac{\alpha}{2}{A}_{s2},$$
(9)
$${P}_{\mathrm{sth}2}=21\frac{{A}_{\mathrm{eff}}}{{g}_{B2}{L}_{\mathrm{eff}}},$$
(10)
$${L}_{\mathrm{eff}}=\frac{1}{{I}_{s}(0)}{\int}_{0}^{L}{I}_{s}(z)\mathrm{d}z.$$