Optical electromagnetic vector-field modeling for the accurate analysis of finite diffractive structures of high complexity

Abstract

An electromagnetic vector-field model for design of optical components based on the finite-difference time-domain method and radiation integrals is presented. Its ability to predict the optical electromagnetic dynamics in structures with complex material distributions is demonstrated. Theoretical and numerical investigations of finite-length surface-relief structures embedded in polymer dielectric waveguiding materials are presented. The importance of several geometric parameter dependencies is indicated as far-field power distributions are rearranged between diffraction orders. The influences of the variation in grating period, modulation depth, length, and profile are investigated.

Energy flow in photonic crystal waveguides

“…The analyses in this paper rely on two numerical models based on the FDTD method 12 and Bloch theory, respectively, for the TM polarization ͑the electric vector field is oriented along the axis of the rods͒. The Bloch theory model is based on plane-wave expansions and a variational principle.…”

“…Figure 1 shows the energy flow ͑Poyn-ting vector͒ in a conventional dielectric slab waveguide and in a waveguide with a photonic crystal cladding with a triangular lattice of GaAs rods in air, computed with the use of the finite-difference time-domain ͑FDTD͒ method. 12 In conventional planar slab waveguides, light is guided in the high index film layer in which plane-wave components propagate via the mechanism of total internal reflection at planar material interfaces. In these waveguides, a Gaussian distribution of energy is present with a tail continuing in the cladding, and there is a net effective energy flow with the Poynting vector directed in the direction along the guide.…”

Simulations of nanograting-assisted light coupling in GaN planar waveguide

“…A possible approach to reduce time and effort is an accurate computer simulation of a desired structure. One of the commonly used methods for a simulation of the periodic structures of a finite extent is a finite difference time-domain (FDTD) method (Cryan et al 2005;Dridi and Bjarklev 1999). The FDTD method can be used to tackle a large class of the problems and precisely solves the equations governing the device behavior, but at the cost of computational resources.…”

Staircase-free finite-difference time-domain formulation for general materials in complex geometries

“…In the following analysis we use a total-field/scattered-field formulation with a perfectly matched layer [15] terminated with a PEC wall for the new formulation and the FDTD model based on the Yee scheme developed in [5]. …”