Roughness losses and volume-current methods in photonic-crystal waveguides

We present predicted relative scattering losses from sidewall roughness in a strip waveguide compared to an identical waveguide surrounded by a photonic crystal with a complete or incomplete gap in both 2d and 3d. To do so, we develop a new semi-analytical extension of the classic "volume-current method" (Green's functions with a Born approximation), correcting a longstanding limitation of such methods to low-index contrast systems (the classic method may be off by an order of magnitude in high-contrast systems). The resulting loss predictions show that even incomplete gap structures such as photonic-crystal slabs should, with proper design, be able to reduce losses by a factor of two compared to an identical strip waveguide; however, incautious design can lead to increased losses in the photonic-crystal system, a phenomena that we explain in terms of the band structure of the unperturbed crystal.