Investigation on acoustic modes induced by backward stimulated Brillouin scattering in acoustic wave-guided single mode optical fibers

Abstract

The acoustic Helmholtz equation was derived, its analytical solution and the characteristic equation of the uniform guide mode in single mode fibers were obtained by the method of separation of variables. The normalized frequency of the acoustic mode is defined, the eigenvalue range of the acoustic mode is analyzed by magnitude approximation of the Bessel function, and the cut-off frequency，far from the cut-off state of the acoustic mode induced by backward stimulated Brillouin scattering, the dispersion and the multi-peak Brillouin gain spectrum were investigated. The research results indicate that the longitudinal acoustic fundamental mode L₀₁can’t be cut-off and is mainly confined in the fiber core, which is coupled with the optical fundamental mode LP₀₁ to form the main peak of the Brillouin gain spectrum. The other higher-order acoustic modes all have low cut-off frequency and are distributed more in the fiber cladding than L₀₁ which couple with the optical fundamental mode LP₀₁ to form the sub speaks of the Brillouin gain spectrum. The transverse normalized phase constant and effective refractive index of the acoustic mode increase with the increase of the normalized frequency. Only longitudinal acoustic modes L_0<i>n</i> contribute to backward Brillouin gain spectrum in single mode fibers. When the GeO₂ concentration is less than 4% and core radius of 4.5 μm, the single mode characteristics of the fiber are maintained, but the maximum number of acoustic L_0<i>n</i> modes are 4. With the increase of GeO₂ concentration in the fiber core, the Brillouin gain spectrum is red-shifted and the number of acoustic modes increase, the Brillouin gain peak value of L₀₁ mode gradually increases, and the contribution of higher-order modes decrease. The single-mode fiber with germanium doped core concentration of 3.65% and core radius of 4.3 μm has 4 L_0<i>n</i> modes and 16 L<i>_mn</i>(<i>m</i>>0) modes at the wavelength of 1.55 μm, and one main peak and two subpeaks in the Brillouin gain spectrum are arised due to the acousto-optic coupling of the acoustic L₀₁, L₀₃, and L₀₄ modes with the optical LP₀₁mode. The single-mode fiber with core germanium doped concentration of 15% and core radius of 1.3 μm has 3 L_0<i>n</i> modes and 7 L<i>_mn</i>(<i>m</i>>0) modes, the Brillouin gain spectrum is presented with 3 main peak due to the acousto-optic coupling of the L₀₁, L₀₂, and L₀₃ modes with the LP₀₁ mode. These conclusions are well satisfied with the reported experimental phenomena and provide theoretical references for the research and application of SBS acoustic waveguide in optical fibers.