Analysis of near field characteristics of a diffractive optical laser beam profile shaper using a high accuracy finite difference time domain method

Abstract

The finite-difference time-domain (FDTD) method as realized in the Yee algorithm is very useful for solving the analytically intractable diffraction problems that arise in the design of diffractive optical elements (DOE). The error, e, of the Yee algorithm is rather large. We introduce a new high accuracy version of the Yee algorithm based on nonstandard finite differences. We have verified its performance by comparing with known analytical solutions. We have used this algorithm to study the near field (0 - 10 wavelengths) diffraction patterns of three binary phase gratings. Grating (1) has a constant period, while grating (2) has a variable one. Grating (3) is generated by interlacing grating (1) with (2). The period of grating (1) is on the order of a wavelength. Some of these computed fields display interesting and possibly useful Fourier spectra.