Simple boundary condition for terminating photonic crystal waveguides

Abstract

Many photonic crystal (PhC) devices are non-periodic structures due to the introduced defects in an otherwise perfectly periodic PhC, and they are often connected by PhC waveguides that serve as input and output ports. Numerical simulation of a PhC device requires boundary conditions to terminate PhC waveguides that extend to infinity. The rigorous boundary condition for terminating a PhC waveguide is a non-local condition that connects the wave field on the entire surface (or line in two-dimensional problems) transverse to the waveguide axis, and it is relatively difficult to use, especially for realistic devices, such as those in PhC slabs. In this paper, a simple approximate boundary condition involving a few points in the waveguide axis direction is introduced. The new boundary condition is used with the Dirichlet-to-Neumann map method to take advantage of the lattice structures and identical unit cells in PhC devices. Comparisons with the rigorous non-local boundary condition indicate that the simple boundary condition gives accurate solutions if the computational domain is enlarged by a few lattice constants in each direction.

Second-order sensitivity analysis for a photonic crystal waveguide bend

“…The boundary conditions on the top and left sides are rigorous nonlocal conditions established based on expanding the transmitted and reflected waves in Bloch modes of the PhC waveguides [13]. It is also possible to use approximate and simpler boundary conditions on the top and left sides [15], but the truncated domain must be slightly increased. The boundary condition on the left side is inhomogeneous, since there is an incident wave in the horizontal waveguide, and it gives rise to the vector f in Eq.…”

Compact wavelength demultiplexer via photonic crystal multimode resonators

“…The problem is solved by the BFGS quasi-Newton method [22]. In each iteration, the Dirichletto-Neumann (DtN) map method developed in our earlier works [23][24][25] is used to calculate the transmission coefficients for the three frequencies. That method can take advantage of the many identical unit cells and the circular geometry of the rods, and it includes a rigorous boundary condition for terminating PhC waveguides [23].…”

Circuit model for efficient analysis and design of photonic crystal devices

“…It is seen that the transmission remains more than 48% for ω n = 0.352-0.412 and is almost complete at ω n = 0.378. Although this simple design leads to relatively high transmission in a large bandwidth, better performances can be obtained by numerical optimization [30].…”