Coupled-mode analysis of contra-directional coupling between two asymmetric photonic crystal waveguides

Abstract

A self-contained coupled-mode theory for the coupled two asymmetric photonic crystal waveguides (PCWs) is presented. The first-order coupled-mode equations are derived under a weak coupling assumption. The coupling coefficients are obtained systematically by a matrix calculus using the modal solutions of each PCW in isolation. The coupled-mode equations are solved for contra-directional coupling between two asymmetric PCWs formed by a hexagonal lattice of circular air holes in a dielectric medium. The power transmission spectra at different output ports of the coupled PCWs are investigated. It is shown that the self-contained coupled-mode analysis is useful to characterize a peculiar feature of the contra-directionally coupled PCWs as a drop filter.

Realization of All-Optical Digital Amplification in Coupled Nonlinear Photonic Crystal Waveguides

“…The dispersion diagrams of the coupled PCWs (Fig. 1) are studied based on the coupled-mode formulation [29,30], which we have recently proposed using the first-order perturbation theory while taking into account a weak coupling effect (mutual coupling coefficient is much smaller than the propagation constant in the single isolated PCW). Based on the derived coupled-mode equations the propagation constant βh/2π of the weakly coupled PCWs (Fig.…”

“…Recently, Yasumoto and Jandieri have developed a self-consistent coupled-mode formulation for the coupled PCWs using perturbation theory (assuming small perturbations in the mode propagation constant) [29,30]. It provides both a useful analytical technique for the approximation of the coupling between adjacent PCWs and a good physical insight of the underlying coupling mechanisms.…”

“…It provides both a useful analytical technique for the approximation of the coupling between adjacent PCWs and a good physical insight of the underlying coupling mechanisms. In the first-order coupled-mode analysis, the guided field supported by the two-parallel waveguide system is approximated using the Floquet theorem as follows [29,30]:…”

“…properties with respect to the x-axis and having a periodicity in z with a period 2π/h [29,30]. The function F (t, z − vt) depicts the slowlyvarying amplitude and v S,A denotes a group velocity for symmetric and antisymmetric (super-) modes, respectively.…”

Linear Amplification of Optical Signal in Coupled Photonic Crystal Waveguides

“…The dispersion diagrams of the coupled PCWs ( Fig. 1) are studied based on the coupled-mode formulation [8], [9], which we have recently proposed using the firstorder perturbation theory taking into account a weak coupling effect. Based on the derived coupled-mode equations [8], [9] normalized propagation constant βh/2π of the pillar type coupled PCWs (Fig.1) for the even mode and odd mode versus the normalized frequency h/λ 0 is calculated and it is plotted in Fig.…”