Efficient numerical method for analyzing optical bistability in photonic crystal microcavities

Abstract

Nonlinear optical effects can be enhanced by photonic crystal microcavities and be used to develop practical ultra-compact optical devices with low power requirements. The finite-difference time-domain method is the standard numerical method for simulating nonlinear optical devices, but it has limitations in terms of accuracy and efficiency. In this paper, a rigorous and efficient frequency-domain numerical method is developed for analyzing nonlinear optical devices where the nonlinear effect is concentrated in the microcavities. The method replaces the linear problem outside the microcavities by a rigorous and numerically computed boundary condition, then solves the nonlinear problem iteratively in a small region around the microcavities. Convergence of the iterative method is much easier to achieve since the size of the problem is significantly reduced. The method is presented for a specific two-dimensional photonic crystal waveguide-cavity system with a Kerr nonlinearity, using numerical methods that can take advantage of the geometric features of the structure. The method is able to calculate multiple solutions exhibiting the optical bistability phenomenon in the strongly nonlinear regime.

Nonlinear response from optical bound states in the continuum

“…are non-positive. Finally, we verified our findings by comparing the solution of equation ( 14) against exact numerical solutions of equation ( 3) obtained with Fourier-Chebyshev pseudospectral method [45]. For our numerical simulations we took n 2 = 5 × 10 −18 m 2 /W which corresponds to silicon at 1.8µm [46].…”

Optical bistability with bound states in the continuum in dielectric gratings

“…To obtain the nonlinear scattering spectra Eq. ( 1) was solved numerically with the pseudospectral method 51 . In our simulations we took n 2 = 5 • 10 −18 m 2 /W which corresponds to silicon at 1.8 µm 52 .…”

Efficient method for lasing eigenvalue problems of periodic structures

“…Like the multipole method, the DtN-map method uses the fast converging cylindrical wave expansion, but it works in one period and does not require lattice sums. The DtN-map method has found many applications for analyzing PhC structures and devices [16][17][18][19][20]. In particular, it has been used to study passive PhC microcavities [21].…”