A Novel Periodic Boundary Condition Treatment in Electrodynamics Wave Interaction With Small Structures

Abstract

In the numerical study of the radiative properties of micro- and nano-structure devices, for example, the random roughness surfaces, grating surfaces, periodic photonic devices, the periodic boundary condition are frequently used to simulate device size much larger than the incident wavelength. Existing methods in handling the periodic boundary condition in the solution of the Maxwell’s equations are too limiting. A novel method is developed to efficiently treat such boundary conditions. The concept is not limited to any particular solution method of the Maxwell’s equations. The salient feature is to convert the phase difference between the corresponding boundaries from the time domain to frequency domain using a phasor diagram approach. The resulting electromagnetic field vector component equations at the boundaries are successfully tested in a finite-difference time-domain code at large angle of incidence, up to 80°, on a finite length, flat, and dielectric surface. The computed reflectivity is in good agreement with the analytical value calculated by Fresnel reflectivity.