## Abstract

The stimulated Brillouin scattering (SBS) gain efficiencies were measured in the LP_{08} and LP_{01} modes of a higher-order-mode optical fiber. Gain efficiencies C_{B} of 0.0085 and 0.20 (m-W)^{-1} were measured for the LP_{08} and LP_{01} modes at 1083 nm, respectively. C_{B} is inversely proportional to the optical effective area A_{eff} and the same core-localized acoustic phonon seeds the SBS process in each case. An acoustic modal analysis and a distributed phenomenological model are presented to facilitate the data analysis and interpretation. The LP_{08} mode exhibits a threshold power-length product of 2.5 kW-m.

© 2007 Optical Society of America

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### Equations (11)

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(1)
$${A}_{\mathrm{eff}}=\frac{{\u3008{E}_{n}^{2}\left(r\right)\u3009}^{2}}{\u3008{E}_{n}^{4}\left(r\right)\u3009}$$
(2)
$${\nabla}_{\perp}^{2}\rho \left(r\right)+{\left(\frac{2\pi}{{\Lambda}_{0}}\right)}^{2}\xb7N{\left(r\right)}^{2}\xb7\rho \left(r\right)={\left(\frac{2\pi}{{\Lambda}_{0}}\right)}^{2}{N}_{\mathrm{eff}}^{2}\xb7\rho \left(r\right)$$
(3)
$$\frac{2\pi \xb7{N}_{\mathrm{eff}}}{{\Lambda}_{0}}=\frac{4\pi \xb7{n}_{\mathrm{eff}}}{{\lambda}_{0}},$$
(4)
$${f}_{m}=2\xb7{n}_{\mathrm{eff}}\xb7{V}_{{\mathrm{SiO}}_{2}}\u2044{N}_{\mathrm{eff}}^{m}\xb7{\lambda}_{0}.$$
(5)
$${\Gamma}_{m,n}=\frac{{\u3008{\rho}_{m}\left(r\right)\xb7{E}_{n}{\left(r\right)}^{2}\u3009}^{2}}{\u3008{\rho}_{m}{\left(r\right)}^{2}\u3009\xb7\u3008{E}_{n}{\left(r\right)}^{4}\u3009}\phantom{\rule{.9em}{0ex}}.$$
(6)
$$\frac{d{P}_{P}}{\mathrm{dz}}=-{C}_{B}\xb7{P}_{P}\xb7{P}_{S}-\alpha \xb7{P}_{P}-\beta \xb7{P}_{P}$$
(7)
$$\frac{d{P}_{S}}{\mathrm{dz}}=-{C}_{B}\xb7{P}_{P}\xb7{P}_{S}+\alpha \xb7{P}_{s}-\eta \xb7{\beta}_{S}\xb7{P}_{P}$$
(8)
$${R}_{\mathrm{SBS}}=\eta \xb7{\beta}_{S}\xb7L\xb7\left({e}^{G}-1\right)\u2044G.$$
(9)
$${C}_{B}\xb7\left({A}_{\mathrm{eff}}\phantom{\rule{.2em}{0ex}}\mathrm{or}\phantom{\rule{.2em}{0ex}}{A}_{m,n}^{\mathrm{ao}}\right)=\gamma \xb7{g}_{B}$$
(10)
$${g}_{B}=\frac{2\pi {n}^{7}{p}_{12}^{2}}{c{\lambda}_{0}^{2}\rho {V}_{S}\Delta {\nu}_{\mathrm{ph}}}\phantom{\rule{.9em}{0ex}},$$
(11)
$${P}_{\mathrm{th}}=\frac{\mathrm{ln}\left(\frac{{R}_{\mathrm{SBS}}}{\eta {\beta}_{S}}\xb7\frac{\gamma {g}_{B}}{{A}_{\mathrm{eff}}}{P}_{\mathrm{th}}\right)\xb7{A}_{\mathrm{eff}}}{\gamma {g}_{B}L}$$