Diffraction of Gaussian and Hermite-Gaussian beams by finite gratings

The diffraction of Hermite-Gaussian beams by N equally spaced slits in a planar screen (a lamellar finite grating) at the scalar diffraction regime is analyzed. We start from the Rayleigh-Sommerfeld theory for two-dimensional problems with Dirichlet conditions and Kirchhoffs approximation. The theory is presented for beams at oblique incidence; however, in the numerical simulation mainly normal incidence is considered. For Gaussian beams the ratio of the intensity diffracted at normal direction E at minimum and maximum transmitted power is studied in this paper as a function of the beam width L. Also, far Gaussian beams, the angular positions theta (min), of the first minimum of the diffraction patterns as a function of the L-spat diameter is analyzed. Two methods to determine L for Gaussian beams are proposed. For Hermite-Gaussian beams an interesting diffraction property previously presented for one slit [J. Opt. Sec. Am. A 12, 2440 (1995)] is generalized to finite gratings, namely, tau = lambda (E/N), where tau is the transmission coefficient and lambda is the wavelength of the incident radiation. We study this property in detail and analyze its validity conditions in terms of the optogeometrical parameters of the system. This property might be useful in determining the total energy transmitted by a lamellar grating from knowledge of the intensity diffracted in the normal direction. (C) 2001 Optical Society of America.