The extended boundary condition method, also called the null-field method, provides a semianalytic solution to the problem of electromagnetic scattering by a particle by constructing a transition matrix (T-matrix) that links the scattered field to the incident field. This approach requires the computation of specific integrals over the particle surface, which are typically evaluated numerically. We introduce here a new set of simplified expressions for these integrals in the commonly studied case of axisymmetric particles. Simplifications are obtained using the differentiation properties of the radial functions (spherical Bessel) and angular functions (associated Legendre functions) and integrations by parts. The resulting simplified expressions not only lead to faster computations, but also reduce the risks of loss of precision and provide a simpler framework for further analytical work.
© 2011 Optical Society of America
Original Manuscript: July 15, 2011
Revised Manuscript: August 10, 2011
Manuscript Accepted: August 15, 2011
Published: September 1, 2011
Walter R. C. Somerville, Baptiste Auguié, and Eric C. Le Ru, "Simplified expressions of the T-matrix integrals for electromagnetic scattering," Opt. Lett. 36, 3482-3484 (2011)