Ryoji Ando

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.

An LOD-FDTD Method for the Analysis of Periodic Structures at Normal Incidence

An efficient finite-difference time-domain method based on the locally one-dimensional scheme (LOD-FDTD) is developed for the analysis of periodic structures. The Sherman-Morrison formula is used to efficiently solve the cyclic matrix problem resulting from the application of the periodic boundary condition to the implicit LOD scheme. Through the analysis of a photonic band-gap (PBG) structure, numerical results are found to be identical to those of the alternating-direction implicit (ADI) counterpart. The use of dispersion control parameters enables us to use a large time-step size. As a result, the computational time is reduced to sime 50% of that of the traditional explicit FDTD while maintaining acceptable numerical results.

A 3-D LOD-FDTD Method for the Wideband Analysis of Optical Devices

An improved three-dimensional (3-D) locally one-dimensional finite-difference time-domain (LOD-FDTD) method is developed and applied to the wideband analysis of waveguide gratings. First, the formulation is presented, in which dispersion control parameters are introduced to reduce the numerical dispersion error and perfectly matched layers are simply implemented without the field components being split. Next, as a preliminary calculation, the wavelength response of the waveguide grating is analyzed in a two-dimensional problem. The dispersion control contributes to the accuracy improvement even with a large time step beyond the Courant-Friedrich-Levy limit. Finally, a 3-D waveguide grating is analyzed. The use of the dispersion control parameters only in the propagation direction enables us to employ a large time step for efficient calculations, i.e., the computation time can be reduced to about half that of the explicit counterpart. In the Appendix, maximum time step for providing a highly accurate result is also predicted using the numerical dispersion analysis.

Frequency-Dependent 3-D LOD-FDTD Method for the Analysis of Plasmonic Devices

A simple trapezoidal recursive convolution technique is utilized to develop a frequency-dependent locally one-dimensional finite-difference time-domain (FDTD) method for the three-dimensional analysis of dispersive media. A gap plasmonic waveguide is analyzed and the numerical results are compared with those of the traditional explicit FDTD. A time step ten times as large as that determined from the stability criterion can be allowed to reduce computational time by 40%, offering acceptable numerical results. A plasmonic grating is analyzed as an application.

Analysis of a photonic bandgap structure using a periodic LOD-FDTD method

The finite-difference time-domain method based on the locally one-dimensional scheme (LOD-FDTD) is extended to the analysis of periodic structures. The cyclic matrix problem resulting from the application of the periodic boundary condition to the implicit LOD scheme is efficiently solved with the Sherman-Morrison formula. The analysis of a photonic bandgap structure shows that the numerical results are identical to the alternating-direction implicit counterparts. The use of dispersion control parameters enables us to use a large time step size. As a result, the computational time is reduced to ≃ 50% of that of the traditional explicit FDTD, while maintaining acceptable numerical accuracy.

Analysis of a gap plasmonic waveguide using the frequency-dependent 3-D LOD-FDTD method

A frequency-dependent implicit locally one-dimensional finite-difference time-domain (LOD-FDTD) method is developed for the analysis of three-dimensional (3-D) plasmonic structures. A brief formulation is given with the use of the simple trapezoidal recursive convolution technique. A gap plasmonic waveguide is analyzed to validate the 3-D LOD-FDTD. The computational time is significantly reduced to 60% of that of the traditional explicit FDTD.

General formulation of an efficient implicit BOR-FDTD method based on the locally one-dimensional scheme

A complete set of equations of the LOD-BOR-FDTD has been derived for the analysis of not only fundamental but also higher-order modes with respect to the rotational direction. The number of arithmetic operation is significantly reduced in comparison with the ADI counterpart. Numerical results of a circular cavity resonator show that the resonance frequency is efficiently obtained particularly for higher-order modes, while maintaining the accuracy comparable to the ADI-BOR-FDTD. The application of the LOD scheme to cylindrical coordinates is under investigation.

Analysis of a Plasmonic Microcavity Using the Frequency-Dependent LOD-FDTD Method

A simple frequency-dependent FDTD is developed with a trapezoidal recursive convolution technique and is applied to the analysis of plasmonic microcavities. Tunable properties of the resonance wavelength are obtained with varying an air core width.