Benchmarking five numerical simulation techniques for computing resonance wavelengths and quality factors in photonic crystal membrane line defect cavities

Modeling electromagnetic resonators using quasinormal modes

“…The explicit correspondence between QNM calculations with an integral equation formulation and with PML truncations was illustrated in Ref. [17], and Maes et al [100], de Lasson et al [101] and Lalanne et al [102] recently compared a number of different calculation methods commonly in use in the literature. In addition to direct numerical solutions, numerous approximate methods exist, which may be used to device simple analytical descriptions of the QNM fields as well as insight to the physical mechanisms responsible for the partial trapping of the electromagnetic field.…”

Which Computational Methods Are Good for Analyzing Large Photonic Crystal Membrane Cavities?

“…We consider a finite-size semiconductor PhC membrane geometry illustrated in Fig. 1 [7]. The structure is perforated by an in-plane triangular lattice of circular air cylinders and is surrounded by free space on all sides.…”

“…Detailed structural parameters may be found in Ref. [7], and we stress that the surrounding air region is, in principle, of infinite extent.…”

“…However, the combination of the large size of the PhC Ln cavity and the full 3D nature of the geometry makes the calculation of the cavity Q factor an extremely demanding numerical challenge [7]. No matter which numerical method is used, careful convergence checks [7] with respect to the degrees of freedom must be made. In this work, we focus on two structures, a low-Q L5 cavity and a high-Q L9 cavity.…”

“…In this work, we focus on two structures, a low-Q L5 cavity and a high-Q L9 cavity. We employ the following five different computational methods [7] to compute the cavity Q factor and the resonance wavelength λ for both structures:…”