Photonic Band Characteristics in a Metallic Waveguide

Abstract

We study the transmission coefficient and photonic band characteristics in an inhomogeneous metallic circular waveguide with perfect conducting walls and having periodic variation of dielectric constant along the axial direction by the transfer matrix method. The propagation ceases below the waveguide cutoff and above that band characteristics are found to set in for different waveguide modes. In order to avoid multiple waveguide mode scattering by the superlattice, the dimension of the guide is chosen in such a manner that at the operating frequency, only the lowest mode can occur. We investigate the number of unit cells (N) dependent transmission coefficient of the structure and also when acting as single or double electromagnetic barrier. Specifically, we demonstrate the existence of super narrow transmission band and a gap region for experimentally realizable structures. Photonic crystals have important applications in optical filtering with super narrow transmission band. For the guiding structure of infinite transverse extent, the analysis is found to agree well with that of wave propagation normal to the superlattice planes. Bloch's theorem which dramatically simplifies the periodic problem does not apply. The finitely periodic case can be solved analytically for arbitrary N using the transfer matrix approach. This paper is concerned with a theory of PBS in an inhomogeneous metallic waveguide with perfect conducting walls and having periodic variation of dielectric constant along the axial direction only. In fact, the behaviour of the electromagnetic field in the optical waveguide with a stratified medium inside is analyzed. The 1D stratified medium of infinite transverse extent has been studied extensively. Here, we consider 1D finite PC which is of finite transverse extent. We develop the general theory for the guiding structure. The formulation of the problem is done so that we get scalar wave equation for the longitudinal component of the electric and magnetic fields. The component Hz satisfies the Helmholtz equation whose solution has been obtained through the transfer matrix formulation. mn mn mn m n m z     