Abstract
Planar dielectric waveguides are key to silicon photonics but suffer from scattering losses due to sidewall roughness. This work revisits the classical analysis of Lacey and Payne for TE modes, providing a complete derivation of radiation loss using Green's functions, Fourier analysis, and the Wiener-Khinchin theorem. Exponential and Gaussian autocorrelation models are examined, yielding closed-form expressions that link roughness statistics to attenuation. Results show Gaussian models predict higher peak loss and faster decay, while exponential models offer simpler, experimentally validated approximations. These findings provide scaling laws and practical design guidance for minimizing scattering and enabling ultralow-loss integrated waveguides.