Abstract

We present a complete electromagnetic study, which includes electric, magnetic, and Poynting vector fields of diffracted convergent spherical waves under all possible polarization states compatible with Maxwell’s equations. Exit pupil boundary conditions for these polarizations were obtained by means of Hertz potentials. Using these boundary conditions, two-dimensional Luneburg diffraction integrals for the three components of electric and magnetic fields were formulated, and after some approximations, we showed that the complete electromagnetic description of the inhomogeneous polarization states of spherical waves is reduced to the knowledge of seven one-dimensional integrals. The consistency of the method was tested by comparison with other previously reported methods for linearly polarized (LP), TE, and TM polarizations, while the versatility of the method was showed with the study of nonstandard polarization states, for example, that resulting from the superposition of TE and TM dephased spherical waves, which shows a helicoidal behavior of the Poynting vector at the focalization region, or the inhomogeneous LP state that exhibits a ring structure for the Poynting vector at the focal plane.

© 2013 Optical Society of America

Diffraction of converging electromagnetic waves

Taco D. Visser and Sjoerd H. Wiersma
J. Opt. Soc. Am. A 9(11) 2034-2047 (1992)

Analysis of the focal shift of converging spherical waves using the convolution method

R. M. Simonds
J. Opt. Soc. Am. A 2(6) 830-832 (1985)

Electromagnetic diffraction of light focused through a planar interface between materials of mismatched refractive indices: an integral representation

P. Török, P. Varga, Z. Laczik, and G. R. Booker
J. Opt. Soc. Am. A 12(2) 325-332 (1995)

Scattering by a radially stratified infinite cylinder buried in an absorbing half-space

Siu-Chun Lee
J. Opt. Soc. Am. A 30(4) 565-572 (2013)

Rigorous analytical modeling of high-aperture focusing through a spherical interface

Thanh Xuan Hoang, Xudong Chen, and Colin J. R. Sheppard
J. Opt. Soc. Am. A 30(7) 1426-1440 (2013)