Rigorous Analysis of Superconducting Multilayer Optical Waveguides

In this paper, we present the transfer matrix method (TMM) as a general formulation to find the TE and TM dispersion equations of general multilayer structures consisting superconductors, semiconductors and dielectrics. We then introduce Cauchy integration method (CIM) as an efficient and general numerical method in order to solve the previously found dispersion equations. In the next step we apply both TMM and CIM to a superconductor-dielectric-superconductor multilayer structure consisting of YBCO thin films grown on the glass substrate. In this example we will find the optical propagation characteristics of the waveguide such as the propagation and attenuation constants and power distribution of the optical signal through out the structure as a function of the substrate thickness for several thicknesses of the superconducting layers. We briefly show that how these results can be employed in the design of the optoelectronic devices such as traveling-wave superconducting photodetectors.