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A very efficient and accurate method to characterize the electromagnetic scattering from periodic arrays of two-dimensional composite cylindrical objects with internal eccentric cylindrical scatterers is presented, using the lattice sums formula and the aggregate T-matrix for cylindrical structures. The method is quite general and applies to various configurations of two-dimensional periodic arrays. The dielectric host cylinder per unit cell of the array can contain two or more eccentric cylindrical scatterers (we call them inclusions in this paper), which may be dielectric, conductor, gyrotropic medium, or their mixture with different sizes. The power reflection coefficients from one-layer or one-hundred-layered periodic arrays of composite cylinders with up to two inclusions have been numerically studied. The effect of the presence of inclusions on the properties of resonance peaks or the stopband's width will be discussed.

A wave packet reflected totally at an interface between two media may undergo the Goos–Hänchen shift and associated time delay. Two different theoretical approaches have been presented so far to evaluate this phenomenon. One is the stationary-phase method and the other is the conventional energy-flux method. In this paper, a certain deficiency existing in the conventional energy-flux method is pointed out and a new energy-flux method is derived based on an accurate argument of the conservation of energy flux. The new energy-flux method confirms the consistency of the predictions by the stationary-phase method from the point of view of the conservation of energy.

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[1] A rigorous approach for modal analysis of two-dimensional photonic crystal waveguides consisting of layered arrays of circular cylinders is presented. The mode propagation constants and the mode field profiles can be accurately obtained by a simpler matrix calculus, using the one-dimensional lattice sums, the T matrix of an isolated circular cylinder, and the generalized reflection matrices for a multilayered system. Numerical examples of the dispersion characteristics and field distributions are presented for lowest even and odd transverse electric modes of a coupled two-parallel photonic crystal waveguide with a square lattice of dielectric circular cylinders in a background free space.Citation: Yasumoto, K., H. Jia, and K. Sun (2005), Rigorous modal analysis of two-dimensional photonic crystal waveguides,

Abstract-A very efficient and accurate method to characterize the electromagnetic scattering from periodic arrays of two-dimensional composite cylindrical objects with internal eccentric cylindrical scatterers is presented, using the lattice sums formula and the aggregate T-matrix for cylindrical structures. The method is quite general and applies to various configurations of two-dimensional periodic arrays. The dielectric host cylinder per unit cell of the array can contain two or more eccentric cylindrical scatterers (we call them inclusions in this paper), which may be dielectric, conductor, gyrotropic medium, or their mixture with different sizes. The power reflection coefficients from one-layer or one-hundred-layered periodic arrays of composite cylinders with up to two inclusions have been numerically studied. The effect of the presence of inclusions on the properties of resonance peaks or the stopband's width will be discussed.

Closed form expressions for the electromagnetic fields in homogeneous anisotropic media are derived in terms of the circular cylindrical vector wave functions for isotropic media. An analytical solution is obtained for the problem of scattering by an infinite homogeneous anisotropic circular cylinder for an obliquely incident plane wave of an arbitrary linear polarization. Numerical implementation and convergence behavior of this solution is discussed. Numerical results for some special cases are compared with existing data. We also present numerical results for the more general anisotropic material case in both graphical and tabular forms. The formulation of this article can be easily generalized to the cases of more complex cases, such as other complex media cases whose eigenwave numbers and eigenwave vectors can be determined, layered structures cases, and multiscatterers cases.