Diffraction of hermite–gaussian beams by a slit

Diffraction of Hermite–Gaussian beams of arbitrary order by a slit is treated. We start from the Rayleigh integral equation for two-dimensional diffraction problems with Dirichlet conditions and the Kirchhoff approximation. We analyze the transmission coefficient t, the intensity diffracted at normal direction E, and the ratio of the minimum transmitted power to the maximum transmitted power, k. New analytical expressions for t and k are given in simple form as a function of the position of the incident beam wave (with respect to the slit) and the spot size. Also, an interesting diffraction property of E and t given by E ­ tyl is presented, where l is the wavelength of the incident beam wave. We have found that the diffraction patterns at minimum transmitted power have an unusual shape: At vertical incidence the diffracted energy at normal direction is always null.