Jun Shibayama

Improved finite-difference beam-propagation method based on the generalized Douglas scheme and its application to semivectorial analysis

The generalized Douglas scheme for variable coefficients is applied to the propagating beam analysis. Once the alternating direction implicit method is used, the truncation error is reduced in the transverse directions compared with the conventional Crank-Nicholson scheme, maintaining a tridiagonal system of linear equations. Substantial improvement in the accuracy is achieved even in the TM mode propagation. As an example of the semivectorial analysis, the propagating field and the attenuation constant of a bent embedded waveguide with a trench section are calculated and discussed.

Performance evaluation of several implicit FDTD methods for optical waveguide analyses

The performance of the recently developed implicit finite-difference time-domain methods (FDTDs) is compared with that of the traditional explicit FDTD. For the implicit methods, the alternating-direction implicit (ADI) FDTD and the envelope ADI-FDTD are investigated. In addition, the locally one-dimensional (LOD) scheme is newly introduced into implicit FDTDs, i.e., LOD- and envelope LOD-FDTDs are developed for simple implementation of the algorithm and reduced CPU time. Numerical dispersion analysis is performed, demonstrating the improved dispersion properties of the envelope FDTD. Numerical results of a waveguide grating reveal that the wavelength responses obtained from the ADI/LOD-FDTD gradually shift toward a longer wavelength as the time step (/spl Delta/t) is increased. For the envelope ADI/LOD-FDTD with /spl Delta/t=8/spl Delta/t/sub CFL/, in which /spl Delta/t/sub CFL/ is determined by the stability criterion, the responses are in good agreement with the response of the explicit FDTD, showing the comparable CPU time to that of the explicit FDTD. Further calculations of a waveguide with high-reflection coatings reveal that the CPU time of the envelope LOD-FDTD with /spl Delta/t=32/spl Delta/t/sub CFL/ is reduced to 25% of that of the explicit FDTD.

Modified finite-difference formula for the analysis of semivectorial modes in step-index optical waveguides

The modified finite-difference formula is presented for the second derivative of a semivectorial field in a step-index optical waveguide. The present formula achieves a truncation error of O(/spl Delta/x/sup 2/) provided the discontinuity coincides with a mesh point or lies midway between two mesh points. Furthermore, the formula allows a general position of the interface, when used with the beam-propagation method (BPM). To demonstrate the effectiveness of the formula, asymmetric step-index waveguides are analyzed using the imaginary-distance BPM.

Simple Trapezoidal Recursive Convolution Technique for the Frequency-Dependent FDTD Analysis of a Drude–Lorentz Model

A concise formulation of the frequency-dependent finite-difference time-domain (FDTD) method is presented using the trapezoidal recursive convolution (TRC) technique for the analysis of a Drude-Lorentz model. The TRC technique requires single convolution integral in the formulation as in the recursive convolution (RC) technique, while maintaining the accuracy comparable to the piecewise linear RC (PLRC) technique with two convolution integrals. The TRC technique is introduced not only to the traditional explicit FDTD, but also to the unconditionally stable implicit FDTD based on the locally one-dimensional (LOD) scheme. Through the analysis of a surface plasmon waveguide, the effectiveness of the TRC technique is investigated for both explicit FDTD and LOD-FDTD, along with the existing RC and PLRC techniques.

A Frequency-Dependent LOD-FDTD Method and Its Application to the Analyses of Plasmonic Waveguide Devices

Detailed frequency-dependent formulations are presented for several efficient locally one-dimensional finite-difference time-domain methods (LOD-FDTDs) based on the recursive convolution (RC), piecewise linear RC (PLRC), trapezoidal RC (TRC), auxiliary differential equation, and \mmb Z transform techniques. The performance of each technique is investigated through the analyses of surface plasmon waveguides, the dispersions of which are expressed by the Drude and Drude-Lorentz models. The simple TRC technique requiring a single convolution integral is found to offer the comparable accuracy to the PLRC technique with two convolution integrals. As an application, a plasmonic grating filter is studied using the TRC-LOD-FDTD. The use of an apodized and a chirped grating is found quite effective in reducing sidelobes in the transmission spectrum, maintaining a large bandgap. Furthermore, a plasmonic microcavity is analyzed, in which a defect section is introduced into a grating filter. Varying the air core width is shown to exhibit tunable properties of the resonance wavelength.

A finite-difference time-domain beam-propagation method for TE- and TM-wave analyses

The application of the existing time-domain beam-propagation method (TD-BPM) based on the finite-difference (FD) formula has been limited to the TE-mode analysis. To treat the TM mode as well as the TE mode, an improved TD-BPM is developed using a low-truncation-error FD formula with the aid of the alternating-direction implicit scheme. To improve the accuracy in time, a Pade (2,2) approximant is applied to the time axis. Although the truncation error in time is found to be O(/spl Delta/t/sup 2/), as in the case of the Pade (1,1) approximant, this method allows us to use a large time step. A substantial reduction in CPU time is found when compared to the conventional method in which a broadly banded matrix is solved by the Bi-CGSTAB. The effectiveness in evaluating the TE- and TM-mode waves is shown through the analysis of the power reflectivity from a waveguide facet. This method is also applied to the analysis of a waveguide grating. The accuracy and efficiency of the TD-BPM are assessed in comparison with the finite-difference time-domain method.

Eigenmode analysis of a light-guiding metal line loaded on a dielectric substrate using the imaginary-distance beam-propagation method

Fundamental characteristics of a light-guiding metal line are revealed and discussed through the eigenmode analysis using the three-dimensional (3-D) imaginary-distance beam-propagation method (ID-BPM) based on the alternating-direction implicit scheme. For the present ID-BPM, the multiplication factor of the eigenmode is derived and the paper described how the present method works in the ID procedure. An efficient absorbing boundary condition is described, which is suitable for the eigenmode analysis using the ID-BPM. After confirming the effectiveness of the present method, the characteristics of the light-guiding line composed of a metal (Au) with a finite width and thickness on a substrate (SiO/sub 2/) are investigated. Numerical results for a metal thickness of 0.2 /spl mu/m show that the effective index and the propagation loss decrease as the metal width is reduced. It is shown that not only the higher order modes but also the first mode has a cutoff metal width. Near the cutoff width, the propagation loss of the first mode (/spl sime/10dB/mm at a wavelength of 1.55 /spl mu/m) is less than those of the higher order modes. Finally, in order to reduce the propagation loss, a dielectric core was added under the metal line.

Modified finite-difference beam propagation method based on the generalized Douglas scheme for variable coefficients

The accuracy of the implicit finite-difference beam propagation method (FD-BPM), in which the phase term is not split, is improved using the generalized Douglas scheme. The propagation error of the fundamental mode in two- and three-dimensional waveguides is evaluated by the mode-mismatch loss calculation. It Is demonstrated that the truncation error is reduced to O(/spl Delta/x)/sup 4/ in the transverse direction, even when the parabolic wave equation contains variable coefficients, The computational time is almost identical to the conventional FD-BPM based on the Crank-Nicholson scheme.<<ETX>>

Efficient time-domain finite-difference beam propagation methods for the analysis of slab and circularly symmetric waveguides

The generalized Douglas scheme is applied to the time-domain finite difference beam propagation methods (TD-BPMs) in rectangular and cylindrical coordinates. High accuracy and efficiency are demonstrated through the analysis of optical pulse propagation in slab and circularly symmetric waveguides. As an example of a reflection problem, the TD-BPM in cylindrical coordinates is applied to the analysis of a fiber Bragg grating with a sinusoidal index change. Effectiveness of the present scheme is discussed in comparison with the conventional TD-BPM and the finite-difference time-domain method.

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

The performance of the recently developed time-domain beam-propagation methods (TD-BPMs) is compared with that of the finite-difference time-domain (FDTD) method. For the TD-BPMs, we investigate full-band (FB), wide-band (WB), and narrow-band (NB) methods based on the implicit finite-difference (FD) schemes. Owing to the use of the slowly varying envelope, a time step of the TD-BPM can be chosen to be larger than that of the FDTD. Although the numerical results of a waveguide grating obtained from the FB- and WB-TD-BPMs agree well with that from the FDTD, the CPU times are longer than that of the FDTD due to the solution of broadly banded matrices. Introducing the alternating-direction implicit method (ADIM) into the WB- and NB-TD-BPMs contributes to a reduction in the CPU time. To make the methods more efficient, a fourth-order accurate FD formula is applied to the ADIM-based WBand NB-TD-BPMs, leading to reduced CPU times to 40% and 6% of that of the FDTD, respectively.