Extrinsic Optical Scattering Loss in Photonic Crystal Waveguides: Role of Fabrication Disorder and Photon Group Velocity

Formulas are presented that provide clear physical insight into the phenomenon of extrinsic optical scattering loss in photonic crystal waveguides due to random fabrication imperfections such as surface roughness and disorder. Using a photon Green-function-tensor formalism, we derive explicit expressions for the backscattered and total transmission losses. Detailed calculations for planar photonic crystals yield extrinsic loss values in overall agreement with experimental measurements, including the full dispersion characteristics. We also report that loss in photonic crystal waveguides scales inversely with group velocity, at least, thereby raising serious questions about future low-loss applications based on operating frequencies that approach the photonic band edge.

Figure 1

Example contour plots of the lowest-lying TE-like propagating waveguide mode with normalized wave vector $\overline{k}=0.32$ and $\overline{k}=0.4$; the corresponding (normalized) mode frequencies are $\overline{\omega }=0.276$ ($n_g=4.7$) and $\overline{\omega }=0.265$ ($n_g=11$), respectively.

Figure 2

(a) $xx$ (solid curve) and $xy$ components (dashed curve) of $\mathrm{I}\mathrm{m}[{\overleftrightarrow{\mathbf{G}}}^B]$ plotted as a function of frequency, for both $\mathbf{r}$ and ${\mathbf{r}}^{\prime }$ fixed at the location indicated by the marked “x” in (c). (b) $yy$ (solid curve) and $yx$ (dashed curve) components at x in (d). The GFT elements are normalized by the free-space Green function. (c) $|\mathrm{I}\mathrm{m}[{\overleftrightarrow{\mathbf{G}}}_{xx}]|$ as a function of ${\mathbf{r}}^{\prime }$ for $\mathbf{r}$ located at the x, and for $\overline{\omega }=0.265$. (d) $|\mathrm{I}\mathrm{m}[{\overleftrightarrow{\mathbf{G}}}_{yx}]|$, located at x, for $\overline{\omega }=0.281$.

Figure 3

(a) Total loss as a function of frequency, for $\sigma =4\mathrm{n}\mathrm{m}$ and $l_p=40\mathrm{n}\mathrm{m}$. (b) Loss versus the rms roughness $\sigma$, corresponding to backscatter loss (solid curve) and total loss (dotted curve), for $l_p=40\mathrm{n}\mathrm{m}$. (c) Loss versus correlation length $l_p$, for $\sigma =4\mathrm{n}\mathrm{m}$.