Interference and diffraction analysis of holographic gratings using the Finite-Difference Time-Domain method

Abstract

The Finite-Difference Time-Domain method (FDTD) is based on a time-marching algorithm that has proven accurate in predicting microwave scattering from complicated objects. In this work the method is applied at optical wavelengths, more concretely the method is applied to rigorously analyze holographic gratings for the near-field distribution. It is well known that diffraction gratings with feature sizes comparable to the wavelength of light must be treated electromagnetically, because the scalar diffraction theories, including Fourier and Fresnel approximations, no longer apply. The FDTD method permits to analyze the electromagnetic field distribution in function of time and space. In optical wavelenghts the simulation of wide areas implies more memory and time processing. For that reason, some add-ons are included in order to correctly calculate the far field distribution obtained from the numerical near-field values computed in the simulation region. As a consequence the total grid simulation size can be reduced improving the performance of the simulation, in terms of memory usage and time processing. Values in the near-field region are computed due to the illumination of the grating by means of a plane wave with different angle of incidence. In addition, we compare the results obtained by the FDTD method to those obtained using the Kogelnik's theoretical expressions applied to diffraction gratings. As it will be seen in this work there is good agreement between numerical and analytical values, thus validating our FDTD implementation.