Gaussian beam sphere optics in condensed matter research

Abstract

Transparent spheres in which the radius R of the sphere is larger than or equal to the wavelength λ of light have currently become of particular interest for quite a number of physical problems (2D colloidal crystal structures composed of transparent spheres, photonic crystals and meta-materials) and applications (laser lithography, fiber-optic systems, super resolution microscopy, biomedical applications, and others). The optical properties of a “full” sphere, when the light aperture r is of order R and the sphere is a natural spherical aberration, have not been investigated in ample detail yet. Strong spherical aberration makes focusing nontrivial. Usually, the exact solution of sphere optics is obtained using the Mie theory, the generalized Lorenz–Mie theory (GLMT), DFT, DDFT codes, which do not give much of a physical insight, as it requires summation of a large number of terms in a multipole expansion even for moderate sphere sizes. In this work we present an algorithm for describing the focusing properties of a transparent sphere using the Gaussian beam approximation that gives a good description of the field in the region of lens caustic. The algorithm developed for the spherical systems was used to create a code for calculating based on standard computation systems spheres with diameters ranging from ∼λ to thousands of λ. The results obtained were compared with the data of some authors obtained earlier by more sophisticated methods.