Reducing Disorder-Induced Backscattering in Photonic Crystal Waveguides through Inverse Design

TL;DR

This work tackles disorder-induced backscattering in photonic crystal waveguides (PCWs), a major obstacle to practical slow-light applications. It introduces a gradient-based inverse-design framework built on a fast 3D guided-mode expansion (GME) and a physics-based backscattering formula to minimize losses while preserving a target group index $n_g$. Numerical demonstrations on conventional W1-like and topological ZIW PCWs show approximately a 6x reduction in backscattering at selected $k$-points, with maintained single-mode operation and manageable bandwidth. The approach is fully 3D, computationally efficient, and generalizable to tune additional metrics such as effective mode volume and Purcell enhancement, offering a practical path to deploying PCWs in nonlinear optics and quantum photonics.

Abstract

Photonic crystal waveguides (PCWs) allow for the engineering of photonic modes and band structures to control the flow of light and light-matter interactions within the waveguide. They have shown potential for enhancing optical nonlinearities, quantum dot single photon emissions, as well as optical buffers due to their ability to confine fields on-chip and produce slow-light modes. While these features are promising for applications in nanophotonics, PCWs are prone to high scattering losses due to disorder-induced backscattering, which has remained a significant problem for decades, across various waveguide designs. By combining a fast mode solving approach with physics-based scattering formulas and inverse design, we show how backscattering losses can be significantly reduced, even when working at the same group index. We demonstrate substantial improvements for both W1-like waveguide modes as well topological waveguide modes. Our general methodology is fully three dimensional and can be used to introduce new PCWs for a variety of design metrics.

Figures (7)

• Figure 1: (a) A 3D view and (b) a unit cell of the W1 and ZIW waveguides on the top and bottom, respectively. In this paper, $a=266$ nm, $r=79.8$ nm, $r_0=27.9$ nm, $r_1=62.5$ nm, and $h=170$ nm, where $h$ is the thickness of the slab. The slab material has a permittivity of $\epsilon_2=3.4638$, and the surrounding material is air with a permittivity of $\epsilon_1=1$. The dashed vertical lines indicate the direction of propagation. (c) A representation of the type of fabrication noise assumed in this paper. The statistical parameters are the standard deviation, $\sigma$, and the correlation length, $l_p$. In this paper, we use $l_p=40$ nm and $\sigma=3$ nm.
• Figure 2: Backscatter loss figures-of-merit versus iteration number in the inverse design process, for W1 and ZIW structures, normalized by the original design value. Panels (a) and (c) show the evolution of the loss figure-of-merit calculations during the inverse design processes, for the W1 and ZIW waveguides, respectively. In addition, the pink curve shows the maximum value that a constraint is violated by. This is primarily at the beginning of the optimization process, where the constraints are not strictly enforced. Panels (b) and (d) show the hole positions of the original, middle and optimized designs in purple, blue, and orange respectively. The light propagates along the $x$ direction in the center of the plot. The darker gray regions indicate the holes that were allowed to move during optimization.
• Figure 3: Band structure and selected modes for original and improved designs, as well as an example of one falling outside our constraints. Panel (a) shows the overlaid band structures of the W1 waveguide before (purple), in the middle of (blue), and after (orange) optimization. The gray region is the light line, the darker regions below are the respective bulk modes (the midpoint not shown), solid lines are the bands of interest, and dashed horizontal lines are additional, higher-order bands within the band gap. The pink dashed vertical line is the $\tilde{k}=0.33$ point that optimizations were preformed. The points $a$, $b$, $a'$ and $b'$ mark the edges of the single moded region for the original and final design, respectively. Panel (b) shows the electric field in the middle of the slab before, in the middle of, and after optimization (left to right). Panels (c) and (d) are corresponding plots, but for the ZIW waveguide designs.
• Figure 4: Backscatter loss figures-of-merit (loss with the group index component removed) versus group index values, for the original and optimized W1 (a) and ZIW (b) waveguides. The annotated points correspond to the edges of the single moded region shown in Fig. \ref{['fig:results']}, and the pink points correspond to the $k$-point being optimized.
• Figure 5: Example inverse designs for a contained group index of ten and twenty, for the W1 PCW. Panel (a) shows the band structure for a W1 PCW before (purple) and after an optimization targeting a group index of ten (blue) and twenty (magenta) at the $\tilde{k}=0.36$ and $\tilde{k}=0.39$ points, respectfully. The solid lines are the bands of interest, the gray region is the area above the light line, the solid region is the bulk modes outside the band gap, and the dashed lines are higher order modes within the band gap. The markers highlight the previously mentioned $\tilde{k}$ points. Panel (b) shows the Bloch-mode electric field and hole locations for the original and optimized structures at the $\tilde{k}=0.36$ and $\tilde{k}$ points previously stated, respectively.