Hisamatsu Nakano

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 Short Polarization Converter Using a Triangular Waveguide

A novel polarization converter using a triangular waveguide is proposed and analyzed by the imaginary-distance beam-propagation method based on Yees mesh and the finite-difference time-domain method. The polarization conversion length is investigated as a function of relative refractive index difference. It is found, for a silicon core embedded in a silica cladding, that the conversion length is 2 mum, while the insertion loss is 0.5 dB at a wavelength of 1.55 mum. The extinction ratio is more than 20 dB over a wide wavelength range of 1.25 to 1.65 mum. Using a geometrically expanded model, the polarization conversion behavior is verified in the experiment at a microwave frequency of 15 GHz. Finally, reasonable polarization conversion is obtained with a modified structure, in which the two corners of the triangular waveguide are cut and the cut plane is aligned with a square input (output) waveguide.

Coupled Waveguide Polarization Splitter With Slightly Different Core Widths

A coupler-type transverse electric/transverse magnetic (TE/TM) polarization splitter, in which a metal-loaded core is slightly widened, is analyzed using the three-dimensional beam-propagation method. Before analyzing the splitter with the slightly different core widths, the performance of a splitter with two identical cores is evaluated. The use of the two identical cores results in a high crosstalk and a low extinction ratio due to the phase mismatch between the waveguides with and without the metal for the TE mode. Therefore, the core width in the metal-loaded waveguide is slightly widened so as to restore the phase-matching condition. In contrast to the conventional splitter with the two identical cores, the present splitter is found to offer a low crosstalk of less than -30 dB and a high extinction ratio of more than 30 dB with a coupling efficiency of more than 97% at a wavelength of 1.55 mum. In addition, the wideband operation is demonstrated over a wavelength range of 1.50 to 1.61 mum.

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.

Frequency-Dependent Locally One-Dimensional FDTD Implementation With a Combined Dispersion Model for the Analysis of Surface Plasmon Waveguides

The implicit finite-difference time-domain (FDTD) method based on the locally one-dimensional scheme is extended to the frequency-dependent version for the analysis of the Drude-Lorentz model. The piecewise linear recursive convolution method is introduced, in which a large time step can be utilized. Analyses of a metal-cladding optical waveguide supporting a surface plasmon polariton reveal that the present method provides wavelength responses comparable to those of the explicit FDTD, while reducing the computational time to less than 50%.

A Branch-Type TE/TM Wave Splitter Using a Light-Guiding Metal Line

The three-dimensional (3-D) beam-propagation method is applied to the analysis of a novel transverse electric/transverse magnetic (TE/TM) wave splitter using a light-guiding metal (Ag) line with an embedded dielectric (SiO2) waveguide. Before analyzing the splitter, a mode converter with a tapered metal is designed to smoothly convert the guided mode of an embedded waveguide into the surface plasmon-polariton (SPP) mode, and vice versa. After demonstrating the effectiveness of a converter consisting of a two-step linear taper, the performance of the splitter is evaluated. To obtain a high coupling efficiency, the wavefront mismatch of the SPP mode is compensated for. In addition, a TE-pass polarizer is added to the TE output waveguide, reducing the undesirable TM wave. In contrast to the long device length of a conventional branch-type splitter (>1000 mum), the present splitter is found to have a noticeably short device length of less than 200 mum, although a loss of about 3 dB is observed for the TM wave. The crosstalk and the extinction ratio are, respectively, evaluated to be less than -15 dB and more than 15 dB for a branching angle of 16plusmn2deg at wavelengths of 1.31 and 1.55 mum

LOD-BOR-FDTD Algorithm for Efficient Analysis of Circularly Symmetric Structures

The unconditionally stable locally 1-D (LOD) scheme is used to develop an efficient implicit body-of-revolution (BOR) finite-difference time-domain (FDTD) method. In the LOD-BOR-FDTD, the number of arithmetic operations of the resultant finite-difference equations is significantly reduced, when compared with the alternating-direction implicit (ADI) BOR-FDTD. Numerical results of circular cavity resonators reveal that the LOD-BOR-FDTD provides resonance frequencies identical to the ADI counterparts, with the computational time being reduced to 70%.

Numerical Investigation of a Kretschmann-Type Surface Plasmon Resonance Waveguide Sensor

A Kretschmann-type surface plasmon resonance waveguide sensor is analyzed using the wide-angle beam- propagation method (BPM) with the complex Pade approximant and the finite-difference time-domain (FDTD) methods based on the recursive convolution (RC) and piecewise linear RC (PLRC) techniques. The wavelength responses of the sensor are calculated, and a detailed comparison of the numerical results is made. The BPM results are validated through a comparison with the FDTD results, in which the PLRC technique is required in terms of accuracy. The waveguide sensor shows a maximum absorption wavelength shift from 0.609 to 0.623 mum, as the refractive index of an analyte is increased from 1.330 to 1.334, which is comparable to the sensitivity of the conventional Kretschmann configuration.

Polarization Coupling Between Strongly Guiding Waveguides Stacked Laterally

The full-vectorial beam-propagation method is applied to the assessment of the coupling characteristics between strongly guiding waveguides stacked laterally. The polarization crosstalk behavior of square waveguides stacked laterally is demonstrated by the eigenmode and beam-propagation analyses. In order to make use of the polarization crosstalk constructively, we determine the vertical spacing between the two square waveguides. Almost complete conversion can be obtained, when the two waveguides are stacked diagonally. Another coupler composed of two rectangular waveguides is studied to realize the polarization conversion without exchanging the power with the same polarization. A crossing-waveguide-type polarization converter is also developed, with a short device length of less than 80 mum at a wavelength of 1.55 mum.