Abstract
ABSTRACT We present a new analytical method for solution of 1-D quantum and optical systems, based on the differential transfer matrices. This approach can be used for exact calculation of various functions including reflection and transmission coefficients, band structures as well as bound states. We show the consistency of WKB method with out approach and discuss improvements for even symmetry and infinite periodic structures. Moreover a general variational representation of bound states is introduced. As application examples, we consider several test cases including the reflection and band structure of gratings as well as bounded states of inhomogeneous waveguides. An excellent agreement between the results from our differential transfer matrix method with other methods is observed where possible. Keywords: Integrated optics, Mathematical methods in physics, Electromagnetic theory, Inhomogeneous media 1. INTRODUCTION The analytical solution of 1-D wave propagation problems in arbitrary non-homogeneous quantum and optical systems has been studied in numerous reports. The existing known approaches include the Transfer Matrix Function (TMF)
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