Extrinsic optical scattering loss in photonic crystal waveguides due to fabrication disorder and surface roughness

Optical scattering loss in sub-micron scale patterned waveguides is one of the most important physical mechanisms dictating the limitations and applications of optical devices containing such structures. Despite this,there has been little theoretical work describing the extrinsic scattering losses in photonic crystal waveguides due to random fabrication variations such as disorder and surface roughness. While much work has been devoted to the characterization of ideal, lossless photonic crystal devices, the role of extrinsic optical scattering loss has not yet been suitably addressed. We present explicit formulas that describe extrinsic optical scattering loss for arbitrary sub-micron patterned waveguides occuring due fabricated imperfections such as disorder and surface roughness. Using a real-space Green function formalism, we derive original expressions for the backscattered loss and the total transmission loss, including out-of-plane contributions. Numerical calculations for planar photonic crystal waveguides yield extrinsic loss values in overall agreement with experimental measurements reported in the literature. Additionally, our formulas offer physical insight, including scaling rules that indicate how waveguide losses may be reduced by improved design. In particular, we highlight that loss becomes unavoidably large for operating frequencies approaching the photonic bandedge.