Comparative study of several time-domain methods for optical waveguide analyses

Performance evaluation of several implicit FDTD methods for optical waveguide analyses

“…The higher order methods are also desirable for increasing the computational efficiency, since a large sampling width can be used in maintaining the accuracy of the numerical results. It should be noted, however, that a higher order ADI-FDTD has not yet been developed considering the boundary condition at a dielectric interface, which is indispensable for the optical waveguide analyses [7].…”

“…1(b) indicate that the accuracy is maintained around the center wavelength when the pulse excitation is employed, although the accurate range shrinks as ∆t is increased. It is interesting to note that the dispersion characteristics of the envelope FDTD are similar to those of the full-band TD-BPM [7], since their formulations are closely related to each other: Temporal derivatives are fully incorporated into the formulation, and only the SVE function is calculated. Fig.…”

“…Since forward and backward waves traveling in the ±z-directions predominate the properties of the waveguide, we only discuss the one-dimensional case in the z-direction [7], i.e., r x = 0. Fig.…”

“…This paper is the sequel to our previous publication [7] and investigates the performance of implicit FDTDs, such as the ADI-, LOD-FDTDs, and their envelope versions, in comparison with the traditional explicit FDTD.…”

“…It is shown that for the ADI/LOD-FDTD, the normalized phase velocity gradually degrades with an increase in ∆t, while for the envelope ADI/LOD-FDTD, the dispersion property is improved, in which the phase velocity always remains close to unity at the center wavelength. We next assess the computational accuracy and efficiency through analyzing the spectral response of the reflection coefficient for a waveguide grating [7]. Numerical results show that the responses obtained from the ADI/LOD-FDTD gradually shift towards a longer wavelength, as ∆t is increased.…”