Finite Element Method (FEM) computations in frequency domain & photonic band diagram: Applications to microcavity characterization

Photonics microcavities confine light to small volumes comparable to its wavelength, leading to enhanced nonlinear and quantum effects. It finds application in various fields, including cavity quantum electrodynamics, optoelectronics, quantum cryptography, optical parametric processes, and suppression/enhancement of spontaneous emission. It can provide confinement and directionality to an optical source and even enhance the emission process through the Purcell effect. We propose a fast and computationally efficient method for calculating the photonic bandgap of microcavity based on a hybrid Finite Element Method (FEM) and Plane Wave Expansion Method (PWEM). Band diagrams and field distributions are obtained with a considerably smaller number of nodes without sacrificing accuracy than the conventionally preferred Finite Difference Method (FDM). This computational advantage is quantified and compared. Further, we propose and demonstrate a novel technique to derive the microcavity band diagram from that of a single unit cell. This drastically reduces the computational time and complexity in deriving the cavity band structure, eigenmodes, and field distribution while being accurate and easy to implement. The technique is verified analytically and using standard simulations for both square and triangular lattices. Combining both techniques proposed above makes microcavity eigenmode and field diagram calculations straightforward, drastically faster, and much less resource-intensive.

Automated summary

Photonics microcavities confine light to small volumes, enhancing nonlinear and quantum effects, and have wide applications in various fields. This paper proposes a fast and computationally efficient method for calculating the photonic bandgap of microcavities, along with a novel technique to derive the microcavity band diagram from that of a single unit cell, reducing computational time and complexity. The combination of these techniques makes microcavity eigenmode and field diagram calculations straightforward, significantly faster, and less resource-intensive.