Finite difference frequency domain method: Maxwell equation solutions for optical engineering applications

Scalar diffraction theory is not applicable to electromagnetic problems in which structural (light scattering) elements have size comparable to the incident light wavelength. Such problems are usually handled by finding rigorous solutions of Maxwell’s equations. During the last decade, the Finite Difference Time Domain (FDTD) method, which provides a time-evolving simulation of the scattered light field (by solving Maxwell’s equations), has become a popular tool for treating optical problems involving micro- and nano-structures. And, even though the FDTD is applicable to problems involving wideband optical sources, it is extensively used to obtain quiescent solutions under monochromatic illumination. In the latter case, steady state solutions to Maxwell’s equations can also be found via the Finite Difference Frequency Domain (FD²) method. FD² has some specific advantages compared to FDTD. FDTD and FD² are compared in the sequel.