Numerical Analysis of Leaky Modes in Two-Dimensional Photonic Crystal Waveguides Using Fourier Series Expansion Method with Perfectly Matched Layer

Numerical Modeling of Photonic Crystal Circuits Using Fourier Series Expansion Method Based on Floquet-Modes

“…However, the method is also applied to the photonic crystals consisting of circular cylinders by introducing the staircase approximation or using a numerical integration to derive the transfer matrix for one periodicity cell. Also, when the number of rows of cylinders on each side of the waveguide is not enough, the radiation loss can be taken into account by introducing the perfectly matched layer near the artificial boundaries (Li & Ho, 2004;Yasumoto et al, 2002;Zhang & Jia, 2007).…”

Numerical Analysis of Microcavities on Two-dimensional Photonic Crystals

“…Where H x y ð Þ ¼ h 0 H y denotes the normalized magnetic field, η 0 ¼ ffiffiffiffiffiffiffiffiffiffiffi ffi μ 0 =" 0 p , and v y ð Þ ¼ 1 þ is y ð Þ ½ À1 denotes the stretched coordinate variable [1] characterizing the assumed PMLs. Under the fictitious periodicity of the system, the electric and magnetic fields are approximated by the truncated Fourier series as follows:…”

“…The lattice parameters were chosen as r=0.2h, ɛ r = 11.56, r 0 =0, and L x =L y where a single rod located at the centre of 2L x þ 1 ð ÞÂ 2L y þ 1 À Á sized crystal is removed. The PML parameters in σ(y) [1] are assumed to be w=h, σ M =8.0, and q=2.1. The values of Q are shown in Figs.…”

“…During the past decay, the mode resonance or mode guidance in photonic crystals with point or line defects have been extensively investigated using various analytical or numerical approaches. In this paper, we shall analyze the resonant modes of microcavities formed by a point defect on a two-dimensional photonic crystal, using a Fourier series expansion method [1] combined with perfectly matched layers (PMLs). The numerical examples are compared with those [2] computed by the FDTD method based on a supercell approximation.…”

Accuracy Improvement of the Fourier Series Expansion Method for Floquet-Mode Analysis of Photonic Crystal Waveguides

“…Miyamoto et al [9] proposed a formulation of grating waveguides based on the Fourier series expansion method, and the Floquet-modes were obtained by the eigenvalue calculation of the transfer matrix for one periodicity cell. Their formulation was applied to Floquet-mode analysis of photonic crystal waveguides [10,11], and provided sufficiently accurate results in many applications. Recently, we found there is a limitation of the truncation order when increasing the accuracy.…”