Efficient computation of photonic crystal waveguide modes with dispersive material

Abstract

The optimization of PhC waveguides is a key issue for successfully designing PhC devices. Since this design task is computationally expensive, efficient methods are demanded. The available codes for computing photonic bands are also applied to PhC waveguides. They are reliable but not very efficient, which is even more pronounced for dispersive material. We present a method based on higher order finite elements with curved cells, which allows to solve for the band structure taking directly into account the dispersiveness of the materials. This is accomplished by reformulating the wave equations as a linear eigenproblem in the complex wave-vectors k. For this method, we demonstrate the high efficiency for the computation of guided PhC waveguide modes by a convergence analysis.

Adaptive finite element methods for computing band gaps in photonic crystals

“…Since fabrication is simpler in 2D than in 3D and since the 2D case still includes many important applications, (e.g., [27]), considerable numerical interest has focussed on the 2D case -e.g. [4,11,14,17,32,34,39,40] -and the present paper obtains the first rigorous theory for adaptive finite element methods in this case.…”

“…There are already a number of papers about low order finite element methods for PCs [4,10,14,15,24,28] and most recently there has been considerable interest in p and hp methods, with the latter having the potential to obtain exponential accuracy [16,32,39,40] . Accurate computations based on a priori hp refinement strategies are shown in [39,40]. However, as far as we are aware, until now no one has used adaptivity based on a posteriori error estimates on these problems.…”

Theory of carrier depletion and light amplification in active slow light photonic crystal waveguides

“…Many popular numerical methods and codes, e.g., MIT Photonic Bands (MPB) based on plane wave expansion in a supercell [21], FDTD eigenmode extraction based on a proper pulsed excitation in a periodic system [22] and finite-element (FE) analysis of a superccell [23], are available to evaluate such eigenvalue problem with different computational cost and efficiency [24,25]. In this paper, we implement FE vectorial field eigenmode calculations [26] of three-dimensional passive W1 line-defect PhC membrane waveguide based on a supercell approach.…”

Optimization of a Plasmon-Assisted Waveguide Coupler Using Fem and MMP

“…In Sections 2-4, we outline the available numerical optimizers and electromagnetic field solvers. Then in Section 5, we apply the evolution strategy using two fundamentally different solvers, one is MMP based on a boundary discretization method [10], and another is CONCEPTs based on a domain discretization method [11,12]. We perform the statistical analysis of the optimizer using different solvers.…”