Plane wave diffraction by dielectric gratings finite-difference formulation

Plane-wave diffraction by dielectric gratings of arbitrary profile (groove shape and size) is analyzed using an analytical-numerical technique. The solution method is simple, general, and numerically efficient. It involves expansion in a Fourier series of the periodic permittivity function in the inhomogeneous grating region and application of the finite differences to solve numerically the inhomogeneous vector wave equation in the region. The obliquely incident radiation is of linear polarization with either of its fields parallel to the rulings. Numerical results are presented for several gratings to demonstrate the convergence, accuracy, and reliability of the method. These also show the effect of the grating profile on its diffraction characteristics