Computing fields in a cyclindrically curved dielectric layered media

The matrix method provides a rapid method of analyzing propagation through layered media in integrated optics, fiber Bragg filters, thin film layers and geophysical oil exploration. In this paper we investigate an extension to analyze a planar layered dielectric media that is bent around a cylinder, causing leaky waves to propagate out radially from the layered waveguide. The intensity of the leaking light is determined by first converting the cylindrical configuration into a Cartesian coordinate system. In the process the dielectric media is altered to provide an equivalent plane layer model. This model is solved using the matrix method to determine how the strength of the radiation depends on the curvature of the waveguide. This problem can arise when determining losses due to the bends in integrated optic circuits mounted on cylindrical forms.