Lenslet analysis by rigorous vector diffraction theory

Abstract

The accurate analysis of the electromagnetic field scattered by lenslets of dimensions of the order of the wavelength is considered. Assuming plane-wave illumination of the lenslet, a pair of coupled integral equations is derived, starting from the Stratton–Chu solution of Maxwell’s time-harmonic equations. These equations are solved rigorously (in a numerical sense) to obtain the lenslet-scattered field. For comparison, an approximate vector formula based on the aperture field is also derived and is related to the ubiquitous Fres-nel–Kirchhoff scalar diffraction formula. These analytical techniques are then applied to representative lenslets with diameters in the 2–100-wavelength range. The results demonstrate useful focusing characteristics even at 2–wavelength diameters and confirm that, depending on the accuracy required, the approximate vector formula based on the aperture field can be successfully employed for determining the lenslet-scattering characteristics.