Coupled dielectric waveguides: variational estimations

Abstract

Two dielectric waveguides coupled through small windows are considered. In the case of single coupling window we prove the existence of an eigenvalue below the threshold. It’s estimation is obtained. If there is the periodic set of coupling windows a band below the threshold exists. Using variational estimations of the band edges we prove that there exists a gap between the band and the threshold. This result shows that the system has a property of photonic band gap material (photonic crystal). It can be used for construction of optical fiber systems.