Abstract
A finite-difference frequency-domain (FDFD) method is applied for photonic band gap calculations. The Maxwell's equations under generalized coordinates are solved for both orthogonal and non-orthogonal lattice geometries. Complete and accurate band gap information is obtained by using this FDFD approach. Numerical results for 2D TE/TM modes in square and triangular lattices are in excellent agreements with results from plane wave method (PWM). The accuracy, convergence and computation time of this method are also discussed.
Highlights
Photonic band gap materials and devices have been under intense research for over a decade following the seminal papers [1,2]
The finite-difference frequency-domain (FDFD) method has been proposed for optical waveguide analysis [10,11,12], which is accurate and stable
We show that this technique can be applied in photonic band gap analysis and we note that an FDFD approach using Helmholtz equation has been shown in [13]
Summary
Photonic band gap materials and devices have been under intense research for over a decade following the seminal papers [1,2]. The order-N method based on FDTD can effectively reduce computation It solves the Maxwell’s equations within the unit cell in timedomain by applying an initial field that covers all the possible symmetries; the eigen-modes are identified as the spectral peaks from the Fourier transform of the time-variant fields. The drawback of this method is that the accuracy depends on the number of iterations in time. We show that this technique can be applied in photonic band gap analysis and we note that an FDFD approach using Helmholtz equation has been shown in [13]. The accuracy, convergence, and computation time in the FDFD method are compared with those of PWM
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