Beyond the effective index method: improved accuracy for 2D simulations of photonic crystal waveguides

Abstract

Simulation of photonic structures is a necessary step in the design of devices with tailored optical properties. As 3D simulations are time-intensive, the effective index method (EIM) is widely used to reduce systems to 2D models, including in the design of photonic crystal devices. We show that the EIM is poorly suited to model photonic crystal waveguides, giving inaccurate approximations of group velocity and propagation loss. The proposed effective period method provides significantly more accurate estimations of device behaviour without any increase of computation time.

Multi-objective constrained design of nickel-base superalloys using data mining- and thermodynamics-driven genetic algorithms

“…Performing 3D simulations of designs generated by the SPEARS algorithm (in 2D) shows that the 2D results generally underestimate the group index. This is consistent with the results in [27]. It is worth reiterating here that other 2D approximation methods, for example the effective index method, also underestimate the group index and have in fact a bigger discrepancy to the 3D results [27].…”

“…This is consistent with the results in [27]. It is worth reiterating here that other 2D approximation methods, for example the effective index method, also underestimate the group index and have in fact a bigger discrepancy to the 3D results [27]. The effect of the underestimation of the group index on the results of optimised waveguides depends on the FOMs used for optimisation.…”

“…We use the MIT photonics band plane wave solver (MPB) [26] to solve the PhC waveguides. As 3D simulations would be too resource-consuming for an optimisation algorithm without migrating to large scale computing systems, we use the effective period approximation [27] to solve a 2D equivalent of each waveguide (a reduction in the computation time by a factor of 100-1000). Our MPB base code [27,28] not only solves for the PhC band structure, but also for the propagation loss [11,27].…”

“…As 3D simulations would be too resource-consuming for an optimisation algorithm without migrating to large scale computing systems, we use the effective period approximation [27] to solve a 2D equivalent of each waveguide (a reduction in the computation time by a factor of 100-1000). Our MPB base code [27,28] not only solves for the PhC band structure, but also for the propagation loss [11,27]. All results presented within this paper are obtained through simulation runs on a laptop computer equiped with a 2.2 GHz Intel Core i7 processor, running 6 threads in parallel.…”

“…As mentioned earlier, the optimisation routine is implemented using 2D simulations, with the effective period method [27], as 3D simulations are too time consuming for a full optimisation run. In this section we assess the accuracy of the optimisation results when compared to 3D simulations of the structure with the same design parameters.…”