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

Abstract

We analytically study roughness-induced scattering loss in a photonic crystal waveguide ͑PCW͒. A crosssectional eigenmode orthogonality relation is derived for a one-dimensional ͑1D͒-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 ␣ 1 and ␣ 2 such that the loss coefficient ␣ can be written as ␣ = ␣ 1 n g + ␣ 2 n g 2 ͑n g is the group index͒. By finding analytic formulas for ␣ 1 and ␣ 2 , and examining their ratio, we show why the backscattering loss generally dominates the radiation loss for n g Ͼ 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.

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“…Several numerical approaches have been proposed: initial works have relied on a perturbation model [4][5][6][7][8]. More recent approaches rely on complex frequency-pole analysis [9], combination of coupled-wave and perturbation methods [10], or coupled-Bloch-mode methods [11][12][13]; all require an accurate modeling of the complex and barely known disorder by a statistical geometrical deformation. For experiments performed with periodic waveguides with lengths of several hundreds of micrometers or millimeters, it is conceivable that several deformations, not only the inevitable hole roughness, but also size-hole variation and hole displacements, have to be taken into account.…”