Accurate modeling of photonic integrated circuits (PIC) is essential for development of high performance optical components. In this work, a finite difference time domain method (FDTD), combined with a simplified uniaxial perfectly matched layer boundary condition is presented to efficiently analyze light propagation in PIC. The FDTD-SUPML formulation can be easily applied to complex optical components. Numerical examples illustrate that this combined approach gives high accuracy.
[Show abstract][Hide abstract] ABSTRACT: This chapter is a step-by-step introduction to the finite-difference time domain (FDTD) method. It begins with the simplest possible problem, the simulation of a pulse propagating in free space in one dimension. This example is used to illustrate the FDTD formulation. Then, it discusses how to determine the time step. An electromagnetic (EM) wave propagating in free space cannot go faster than the speed of light. Absorbing boundary conditions are necessary to keep outgoing E and H fields from being reflected back into the problem space. Normally, in calculating the E field, we need to know the surrounding H values; this is a fundamental assumption of the FDTD method. In order to simulate a medium with a dielectric constant other than 1, which corresponds to free space, we have to add the relative dielectric constant to Maxwell's equations. Subsequent sections lead to formulations for more complicated media. dielectric materials; Einstein-Maxwell equations; electromagnetic propagation; finite difference time-domain analysis
[Show abstract][Hide abstract] ABSTRACT: In this letter, a modification to the recently proposed unconditionally stable D-H ADI FDTD method is presented that considerably reduces the late-time error induced by the corner cells. The PML boundary is derived from the direct discretization of the modified D-H Maxwell's equations rather than the superposition of uniaxial PML boundaries. An optimal choice of the PML conductivity profile coefficients is proposed. Results show that the reflection error of the PML is limited for increased time step size beyond the Courant-Friedrichs-Lewy stability bound, and maximum reflection errors are 15 to 20 dB lower than the original formulation.
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