Leaky planar waveguides are critically important to the operation of present day and future integrated photonic circuits. However, to incorporate these waveguides successfully into practical photonic circuits requires an accurate knowledge of their attenuation and mode profile in operation. In contrast with previous numerical methods for obtaining leaky waveguide characteristics, which usually involve complicated algorithms to solve for the complex roots of boundary conditions, the transverse transmission/reflection (TTR) method presented here provides a straightforward and simple approach by simulating the corresponding coupled-waveguide structure. By adding a high-index layer adjacent to the cover to enable the coupling, the transmission/reflection coefficients are shown to be definitively expressed in the form of a Lorentzian that is directly related to the complex propagation constant of leaky/lossy mode. The TTR method simultaneously determines the mode profile of the leaky/lossy mode via the angle of incidence for resonant transmission/reflection. In the present work, the TTR method is applied to an antiresonant reflection optical waveguide (ARROW), a lossy waveguide structure, and a waveguide structure that is simultaneously leaky and lossy.
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