Multipole expansion of acoustical Bessel beams with arbitrary order and location

Zhixiong Gong (1) , Philip L Marston (2) , Wei Li (1) , Yingbin Chai (1)

1 HUST - Huazhong University of Science and Technology [Wuhan]
2 WSU - Washington State University

An exact solution of expansion coefficients for a T-matrix method interacting with acoustic scattering of arbitrary order Bessel beams from an obstacle of arbitrary location is derived analytically. Because of the failure of the addition theorem for spherical harmonics for expansion coefficients of helicoidal Bessel beams, an addition theorem for cylindrical Bessel functions is introduced. Meanwhile, an analytical expression for the integral of products including Bessel and associated Legendre functions is applied to eliminate the integration over the polar angle. Note that this multipole expansion may also benefit other scattering methods and expansions of incident waves, for instance, partial-wave series solutions.

Domaines: Acoustique [physics.class-ph]

Zhixiong Gong, Philip L Marston, Wei Li, Yingbin Chai. Multipole expansion of acoustical Bessel beams with arbitrary order and location. Journal of the Acoustical Society of America, 2017, 141 (6), pp.EL574-EL578. ⟨10.1121/1.4985586⟩. ⟨hal-03330010⟩