Slow light loss due to roughness in photonic crystal waveguides: An analytic approach

We analytically study roughness-induced scattering loss in a photonic crystal waveguide (PCW). A cross-sectional eigenmode orthogonality relation is derived for a one-dimensional (1D)-periodic system, which allows us to significantly simplify the coupled mode theory in the fixed eigenmode basis. Assisted by this simplification, analytic loss formulas can be obtained with reasonable assumptions despite the complexity of PCW mode fields. We introduce the radiation and backscattering loss factors alpha(1) and alpha(2) such that the loss coefficient alpha can be written as alpha = alpha(1)n(g)+alpha(2)n(g)(2) (n(g) is the group index). By finding analytic formulas for alpha(1) and alpha(2), and examining their ratio, we show why the backscattering loss generally dominates the radiation loss for n(g) > 10. The interplay between certain mode-field characteristics, such as the spatial phase, and structure roughness is found crucial in the loss-generation process. The loss contribution from each row of holes is analyzed. The theoretical loss results agree well with experiments. Combined with systematic simulations of loss dependences on key structure parameters, the insight gained in this analytic study helps identify promising pathways to reducing the slow light loss. The cross-sectional eigenmode orthogonality may be applicable to other 1D-periodic systems such as electrons in a polymer chain or a nanowire.