On leaky mode approximations for modal expansion in multilayer open waveguides

We propose an analytic method to calculate the leaky mode functions to enable modal expansion without encountering the normalization and orthogonality problems of the unphysical mode shape. The wave functions of leaky modes are derived from the explicit formulas of normalized radiation modes. Using leaky modes to approximate a continuum of radiation modes greatly simplifies the analysis of excitation, transitions, propagation, and radiation of light waves in multilayer waveguide structures. Upon comparison with the beam propagation method and modal propagation method, we show that the leaky mode approximation while requiring a much simpler computation is as accurate. This method can also provide better physical insight to device operations