Topology-optimized distributed 3d anisotropic Raman emission

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 maximizing spatially averaged signals from randomly oriented, anisotropic molecules, for 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 due to the tensor nonlinearity. Optimized Ag and Si₃N₄ devices show that lengthscale constraints are sufficient to suppress designs that rely on unphysical mathematical field divergences at sharp corners. Metal designs deliver broadband enhancement and remain robust to typical Raman shifts, whereas dielectric designs yield narrower, Q-limited gains that are inferior to the metallic designs for Q≲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.