Rigorous theory of the diffraction of Gaussian beams by finite gratings: TM polarization

Diffraction of TM-polarized Gaussian beams by N equally spaced slits (finite grating) in a planar perfectly conducting thick screen is treated. We extend to the TM polarization case the results of a previous paper where the TE polarization was considered [J. Opt. Soc. Am. A 20, 827 (2003).]. The far-field diffraction patterns, the transmission coefficient τ, and the normally diffracted energy E as a function of several optogeometrical parameters are analyzed within the so-called vectorial region. The existence of constant-intensity angles in the far field when the incident beam wave is scanned along the N slits is shown. In addition, the property E =Nτ/λ, valid in the scalar region, is extended to the TM polarization case in the vectorial region, λ being the wavelength. The coupling between slits is analyzed, giving an oscillating amplitude-decreasing function as the separation between slits increases, where the period for these oscillations is the wavelength λ. Finally, the extraordinary optical transmission phenomena that appear when the wavelength is larger than the slit width (subwavelength regime) are analyzed.