Explicit formulas of normalized radiation modes in multilayer waveguides

A new formulation for the normalization of radiation modes in one-dimensional lossless multilayer waveguide structures is derived using the transmission matrix method. In this formulation, an individual radiation mode is excited by two sources located at opposite ends of the two outermost regions of the waveguide. Proper choice of the absolute phase of one of the sources results in simple expressions for the normalized radiation modes. Calculation of radiation loss of grating-assisted directional couplers is used as an example to show the simplicity and usefulness of this method.<
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