Simulation of scattering from layered spheres with known surface electric field distributions using Mie theory and modified angular spectrum method: Applications to corneal sensing

Abstract

Mie theory is a powerful method to evaluate the scattered fields from the multilayered sphere, where the incident field is expanded to the vector spherical harmonic (VSH) presentation. Then scattered fields are obtained by the T-matrix method. However, obtaining the VSH coefficients for arbitrarily shaped incident fields is difficult and time-consuming. This paper proposes a novel 3D angular spectrum method (3D ASM) for evaluating the VSH coefficients for the incident field, which is defined from the required electric field distribution positioned on the spherical surface. This allows the VSH expansion and evaluation of the scattered fields from a multilayered sphere illuminated with an arbitrary incident wavefront in the Mie Scattering range. This has been computationally challenging with previous methods. First, the advantage of the beam created with the proposed method compared to the nominal Gaussian beam illumination is addressed with the spherical bandstop filter simulation. Then the incident field computed by the proposed method is compared to the physical-optics simulations showing precise agreement. As an example of the proposed methodology, the cornea is modeled as a multilayered spherical structure, and the scattered fields are computed from the cornea illuminated by the incident field with spherical top-hat and tapered top-hat wavefronts. Also, the coupling coefficients of the incident and scattered fields from the cornea model are computed in the 200 - 400 GHz frequency range. The results are compared with coupling coefficients obtained with Gaussian beam illumination and referenced to the reflectivity obtained from plane wave illumination on an analog planar structure. The top-hat beams show increased agreement with the planar stratified medium theory compared to the plane wave and Gaussian beam illumination