Compressed T-Matrix for Arbitrarily Shaped Objects

This paper proposes a novel numerical method for computing the T-matrix of arbitrarily shaped scatterers. Initially, a reference surface is chosen to enclose the object. The rotational tangential component of the scattered field on the reference surface is directly computed from the rotational tangential component of the incident field using the generalized transition matrix (GTM). Then the incident spherical harmonic modes are projected onto the reference surface. The corresponding scattered fields on the reference surface are calculated with GTM and their far fields are expressed in terms of the outgoing spherical harmonic modes. The orthogonality of the spherical vector basis functions is employed to derive the two transformation matrices. The T-matrix for the scatterer is obtained by multiplying them with the GTM. A compressed T-matrix (CT-Matrix) is introduced to collect the response of the significant modes, the size of which is much smaller than that of the T-matrix. Numerical examples are provided to validate the accuracy of the proposed method.