Analysis on acoustic modes and Brillouin gain spectra of backward stimulated Brillouin scattering in W-type acoustic waveguide optical fibers

The acoustic Helmholtz equations of W-type acoustic waveguide fibers, including WI- and WII-type acoustic velocity of vl_,2 < vl_,3 < vl_,1 and vl_,2 < vl_,1 < vl_,3, separately are solved by using the method of separation of variables, and their characteristic equations are derived according to the boundary condition and the acoustic Helmholtz equations. The distribution and cut-off of acoustic modes are analyzed by introducing acoustic normalized frequencies. The dependence of the acoustic inner core radius, the acoustic velocities in the acoustic inner and acoustic outer core on acoustic modes, and Brillouin gain spectra (BGS) is investigated. The results indicate that two significant peaks of the BGS are induced by acousto-optic coupling of L₀₁ and L₀₂ acoustic modes with LP₀₁ optical mode. The acousto-optic overlap factor of the L₀₁ acoustic mode decreases first and then increases, and that of the L₀₂ acoustic mode increases first and then decreases with the rise of acoustic inner core radius. Due to the difference of the acoustic mode field distribution, the gain peak induced by L₀₁ mode is sensitive to the acoustic velocity of the acoustic inner core, and that of the L₀₂ mode is sensitive to the acoustic velocity of the acoustic outer core. These conclusions agree well with the reported experimental results, and provide theoretical references for research and application of backward stimulated Brillouin scattering of acoustic waveguide optical fibers.