Development of software for interference and optical diffraction analysis based on FDTD

Abstract

The Finite-Difference Time-Domain method has been applied to microwaves with successfully results. This method has not frequently been applied in optical engineering due to the disadvantages due to optical wavelengths. In this work, FDTD method has been used for simulating elemental optical systems. Interference and diffraction of light is an elementary topic in optics. The aim of this work is to develop an accurate simulation software of optical systems avoiding the problems in laboratories and the expensive price of optical instrumentation. In this work, four elementary systems have been implemented: one thin slit, two thin slit known as the Young's experiment, an array of seven thin slits and finally a circular aperture. In real laboratory, a coherent light source would illuminate these systems and diffraction pattern of bright and dark bands could be analyzed on a screen. The FDTD method solves the differential Maxwell equations, substituting the time and spatial derivates with central-difference approximation. In order to achieve successfully results with FDTD method, absorbing boundary conditions (ABC), total and scattered field (TF-SF) formulation and near-to-far field propagation have been implemented. These techniques have permitted to calculate the wave field outside the simulation grid (in a screen far away slits), reducing the simulation area to the slits plane. The numerical results calculated with FDTD method are contrasted with analytical results obtaining quite similar curves. The use of this software in practical laboratory seasons in optical degrees can provide to student the possibility of simulating many optical systems based on thin slits. Irradiance distribution can be evaluated with successfully results in different planes far away of grid simulation without performance detriment.