The differential theory of diffraction of light by an arbitrary object described in spherical coordinates is developed. Expanding the fields on the basis of vector spherical harmonics, we reduce the Maxwell equations to an infinite first-order differential set. In view of the truncation required for numerical integration, correct factorization rules are derived to express the components of D in terms of the components of E, a process that extends the fast Fourier factorization to the basis of vector spherical harmonics. Numerical overflows and instabilities are avoided through the use of the S-matrix propagation algorithm for carrying out the numerical integration. The method can analyze any shape and/or material, dielectric or conducting. It is particularly simple when applied to rotationally symmetric objects.
© 2005 Optical Society of America
(000.3860) General : Mathematical methods in physics
(000.4430) General : Numerical approximation and analysis
(050.1940) Diffraction and gratings : Diffraction
(290.5850) Scattering : Scattering, particles
Diffraction and Gratings
Brian Stout, Michel Nevière, and Evgeny Popov, "Light diffraction by a three-dimensional object: differential theory," J. Opt. Soc. Am. A 22, 2385-2404 (2005)