In this paper, we propose a new technique for the transient scattering problem of periodically arrayed dispersion media for the TE case by using a combination of the Fourier series expansion method (FSEM) and the fast inversion Laplace transform (FILT) method, and analyze the pulse response for various widths of the dispersion media. As a result, we clarified the influence of the dispersion media with an air region on the resulting waveform.

In this paper, we apply an improved method for the guiding problem of dielectric waveguide with arbitrary inhomogeneous media along the middle layer introduced the defect layers, and analyzed the propagation characteristics of dielectric waveguide composed of dielectric circular cylinders and the arbitrary inhomogeneous media in the middle layer by using a combination of the improved Fourier series expansion method and multilayer method. Numerical results are given for the propagation constants in the first stop band regions, and the distribution of energy flow for both TE0 and TM0 modes. The influence of permittivity and the shape variation of arbitrary inhomogeneous media are discussed in the first stop band regions.

This paper presents a formulation of two-dimensional photonic crystal waveguide devices formed by circular cylinders. The device structures are considered as cascade connections of straight waveguides. Decomposing the structure into layers of the cylinder arrays, the input/output properties of the devices are obtained using an analysis method of multilayer structure. We introduce periodic boundary conditions in the direction perpendicular to the wave propagation, and the Floquet-modes of each layer are calculated by the Fourier series expansion method with the help of the recursive transition-matrix algorithm. Then, the input/output properties of the devices are obtained by recursive calculation of scattering matrix with each layer. The presented formulation is validated by numerical experiments by comparing with the previous works.

The Fourier series expansion method is a useful tool to approach the problems of discontinuities in optical waveguides, and it can apply to analyze the Floquet-modes of photonic crystal waveguides. However, it has known that the Floquet-mode calculation with large truncation order is limited because of the roundoff errors. This paper proposes a novel formulation of the Floquet-modes propagating in two-dimensional photonic crystal waveguides formed by circular cylinders. We introduce a periodic boundary condition as same with the conventional method, and the fields are expressed in the Fourier series expansions. The present formulation also introduces the cylindrical-wave expansions and uses the recursive transition-matrix algorithm, which is used to analyze the scattering from cylinder array. This makes us possible to obtain very high accuracy without the use of large truncation order for Fourier series expansion. The presented formulation is validated by numerical experiments.

In this paper, we propose a new technique for the scattering problems of multilayered inhomogeneous columnar dielectric gratings loaded rectangular dielectric constant both TM and TE waves using the combination of improved Fourier series expansion method, the multilayer method, and the eigenvalue matrix method. Numerical results are given for the power transmission coefficients in the parameters ε 3 /ε 0 , c/p, and b/d of rectangular cylinders to obtain the basic characteristic of the power transmission coefficients and reflection coefficients switching or frequency selective devices for both TM and TE waves. The influence of the incident angle and frequency of the transmitted power are also discussed in the connection with the propagation constant β in the free mode.

In this paper, we propose a new method for the electromagnetic fields with inhomogeneous media mixed a positive and negative regions by the combination of improved Fourier series expansion method using the extrapolation method which obtains the correct value of the eigenvalue and eigenvectors for the case of TM wave. Numerical results are given for the power reflection and transmission coefficient, the energy absorption, the electromagnetic fields, and the power flow in the inhomogeneous medium mixed the positive and negative regions including the case when the permittivity profiles touches zero for the TM wave. The results of our method are in good agreement with exact solution which is obtained the modified multilayer approximation method.

The blazing effects of dielectric grating consisting of two adjacent sinusoidally modulated layers which lead to the asymmetric profiles on a substrate are analyzed by using improved Fourier series expansion method. This method can be applied to the wide range of grating structure and gave high accurate results by comparing with those obtained by previous method. In this paper, the efficient blazing effects can be achieved by varying normalized distance (w/p) and the normalized thickness (d1/D), where D is kept fixed. The results are greater than those of trapezoidal profiles and triangular profiles. The influences of the second order of modulation index on the radiation efficiencies and normalized leakage factor are also discussed.

The propagation characteristics of dielectric waveguides with slanted grating structure are analyzed by using the combination of the improved Fourier series expansion method and the approximated multilayer method. The slanted grating region is appoximated by a structure with stratified thin modulated index layers. This method is effective to the guiding problems of the planar slanted grating, because the electromagnetic fields in each layer can be expressed by shifting the phase of the solution in the first layer. In this paper, numerical results are given for the grating with the rectangular and the sinusoidal profile for arbitrary slant angle. The radiation efficiencies for the grating with negative and positive slant angle are also discussed.

The scattering of electromagnetic waves by a dielectric grating with planar slanted-fringe is analyzed using the improved Fourier series expansion method. In the analysis, the slanted grating region is divided into layers to make an assembly of stratified thin modulated index layers. This method can be applied to a wide range of periodic structures and is especially effective in the case of planar slanted grating, because the electromagnetic fields in the each layer can easily be obtained by shifting the solution in the first layer. In this paper, the numerical results are given for grating with rectangular and sinusoidal dielectric profiles, and for TM and TE cases of arbitrary incident angle. The diffraction efficiencies obtained by the presented method are compared with the results by the coupled-wave approach; the influences of the slant angle on the diffraction efficiencies at the Wood's anomaly and at the coupling resonance frequency are also discussed.