High speed simulation methods for multimode optical devices

Abstract

Photonic crystals are periodic nanostructures that could affect the motion of photons. Many applications benefit from blending with the structure, such as waveguides, lasers, LEDs, etc. There are several numerical methods available to simulate photonic crystal structures: FDTD, PWEM, and RCWA. Finite-difference time domain (FDTD) is a general method to solve electromagnetic fields. It consumes more memory and time than the other two methods because it calculates each small difference in time and space. The plane wave expansion method (PWEM) and rigorous coupled-wave analysis (RCWA) are both frequency domain methods. PWEM is very fast. It calculates the eigensystem of a photonic crystal layer and generates the band diagram. However, PWEM cannot properly handle multilayer structures. Whereas RCWA can calculate field distribution and generate band diagrams from diffraction efficiency of multilayer devices. Because RCWA is a semi-analytical method (compute transverse plane numerically and compute longitudinal direction analytically), which is generally faster than FDTD, a full numerical method. However, to generate an accurate high-resolution band diagram, more than thousands and even millions of RCWA simulations are required, depending on the resolution. Improving the calculation efficiency of RCWA is a continuous task in this area. There have been plenty of studies improving the convergence rate of RCWA. Accurate result can be obtained with a lower number of harmonics. However, the computational efficiency of a fixed number of harmonics is not sufficiently improved. This thesis utilised multiple techniques to speed up the RCWA algorithm. First, the RCWA is parallelised on GPU hardware using GPU computing tools. The calculation efficiency is improved at least 2 times. Second, the classic symmetry RCWA method is implemented on GPU, which further speeds up simulation speed for symmetric structures. Third, a without eigensystem RCWA method is developed which replaces the computational-expensive eigensystem solution with an efficient matrix exponential method. It produces significant speedup compared with the conventional method. The symmetry method can be combined with the without eigensystem method delivering even faster calculation efficiency. Finally, a VCSEL RCWA algorithm is developed for periodic central emitting devices such as grating VCSEL, photonic crystal VCSEL and PCSEL. It accurately obtains the resonant wavelength and far-field pattern. The calculation efficiency of the method outperforms the Lumerical FDTD simulations.

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Identifiers

ORCID for Jingxiao Xu: orcid.org/0000-0001-6116-0057

ORCID for Pavlos Lagoudakis: orcid.org/0000-0002-3557-5299

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