Topology-optimized distributed 3d anisotropic Raman emission

Abstract

Topology optimization (TO) of 3D surface-enhanced Raman scattering (SERS) substrates faces challenges in managing field singularities and modeling orientation-averaged anisotropic molecules. We present 3D TO for manufacturable SERS substrates that maximize spatially averaged signals from randomly oriented, anisotropic molecules in both elastic and inelastic scattering. A new trace formulation provides a closed-form rotational average of anisotropic Raman tensors, which are not equivalent to isotropic molecules because of tensor nonlinearity. Optimized silver and Si3N4 devices show that lengthscale constraints are sufficient to suppress designs that rely on unphysical mathematical field divergences at sharp corners. Metallic designs deliver broadband enhancement and remain robust to typical Raman shifts, whereas dielectric designs yield narrower, quality-factor-limited gains that are inferior to metallic designs for quality factors below about 500. Our approach readily incorporates additional physics, such as a nonlinear damage model. Together, these results provide a practical route to improved manufacturable SERS substrates and extend naturally to other distributed-emitter design problems.

Figures (5)

• Figure 1: An overview of the 3d SERS setup illustrates the substrate, design layer, and fluid layer containing Raman-active molecules. An incident pump wave (frequency $\omega_\text{p}$, angle $\theta_\text{p}$) excites the molecules, leading to emitted Raman light (frequency $\omega_\text{e}$, angle $\theta_\text{e}$).
• Figure 2: Performance and polarization for 2d metallic SERS TO. (a) Enhancement factor for designs optimized for monopolarized (y-output) and bipolarized (x- and y-output) emission, compared to optimized sphere arrays with 20 nm gaps. (b) Contributions to enhancement ($g_x, g_y$) for the bipolarized 3d design, illustrating the dominance of one polarization.
• Figure 3: 3d dielectric SERS TO with 2d-DOFs. (a) Objective $g$ vs. iteration, showing $\beta$ and $\kappa$ epochs for the 2d metal (blue), 3d dielectric (orange), and 2d dielectric (red) optimizations in this work. (b) Spectral response $g$ vs. wavelength for the optimized 3d dielectric design compared to the 2d dielectric design. Insets: (b, top right) 3d and 2d optimized dielectric geometries compared against 2d metallic; (c) $|\mathbf{E}|^4$ (yellow) and material (gray) cross sections for the 2d optimized metal, highlighting the concentration near the surface of the device; (d) $|\mathbf{E}|^4$ cross-section for the 3d optimized dielectric, illustrating field concentration in air.
• Figure 4: Impact of (a) material/molecular anisotropy and (b) inelastic Raman scattering on 3d optimized SERS structures (2d-DOFs). All plots show emission wavelength swept, and panel (a) evaluates every spectrum with the anisotropic figure of merit to mimic real molecules while contrasting different design assumptions, revealing that isotropically optimized devices remain within $\sim$20% of their anisotropic counterparts across the spectrum. Panel (a) compares Isotropic TO (purple/red for metal/dielectric respectively) and Anisotropic TO (brown/orange for metal/dielectric respectively). Panel (b) compares Elastic TO (purple/red for metal/dielectric) and Inelastic TO (green/pink for metal/dielectric). All configurations begin elastic and isotropic for the first two epochs to generate comparable local optima. The geometries for all cases are displayed on the right; arrows indicate the final result after the last two epochs under different configurations.
• Figure 5: Effect of nonlinear damage regularization on 3d optimized metallic structures (2d-DOFs). (a) Optimized geometries for different design thresholds $E_{\mathrm{th}}$ used during optimization. (b) Raman enhancement for structures optimized with $E_{\mathrm{th}}=10$ (red) and without any damage threshold during their optimization (purple), plotted against a varying evaluation threshold $E_{\mathrm{th}}$. Sphere array performance is shown for reference (dashed green). Markers correspond to the designs in (a) evaluated at their respective optimization $E_{\mathrm{th}}$. $G_{nl}$ is the nonlinear-damage-regularized objective (Raman enhancement penalized by quenching).