Propagation Characteristics of Dielectric Waveguides with Arbitrary Inhomogeneous Media along the Middle Layer

Distribution of energy flow by dielectric waveguide with rhombic dielectric structure along a middle layer

“…r n and t n are unknown coefficients to be determined from boundary conditions. The sign of k (n) are given by the radiation condition in guiding problem [6]. In the region S 2 (−D < x < 0), the first layer (−d < x < 0) is divided into M thin layers and the profile in each layer (d Δ d/M ) is approximated by step index profile ε(z) as shown in Fig.…”

“…Using the boundary conditions at x = −ld Δ (l = 1 ∼ M − 1), we can be obtained the matrix relation between A (1) , B (1) and A (M ) , B (M ) [6].…”

“…For the first layers to the middle layer, we can get the matrix relation between A (1) , B (1) and A (3M ) , B (3M ) as following equation [6]:…”

“…However, though it is not analyzed the propagation constants in detailed in Bragg region, many numerical results are shown only the distribution of the electromagnetic fields by using the FDTD method or another numerical techniques [3,4,5]. In previous paper [6], we analyzed the propagation characteristics of dielectric waveguide composed of dielectric circular cylinders array loaded with dielectric circular cylinders or dielectric triangular cylinders along a middle layer. In addition, we also investigated the distribution of energy flow at the guided area for the case of dielectric circular cylinders and dielectric triangular cylinders along a middle layer for both TE 0 and TM 0 modes.…”

“…Consequently, we considered that the energy is carried outside by the influence of asymmetric structure [6].…”