Pengning Chao

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 Si ₃ N ₄ 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.

Information transfer through electromagnetic waves is vital to computing, imaging, telecommunications, and power management. A central figure of merit is the Shannon capacity, the maximum error-free bit-rate over a noisy channel achievable via encoding. Prior works on optical information transfer have treated waves propagating through fixed photonic structures such as vacuum, where the communication channels are predetermined and the Shannon capacity can be evaluated via a convex “water-filling” procedure, or relied on simplifications of relevant physics via circuit theory and far-field assumptions. In this article, we present limits on the significantly more difficult problem of maximizing Shannon capacity given the freedom to structure the photonic environment, allowing for the optimization of optical communication channels subject to wave propagation constraints. By combining information theory, wave scattering, and convex relaxations, we formalize the relationship between electromagnetic and information-theoretic quantities, showing how device considerations such as material choice, system size, and geometry impact optimal channel power allocations and maximum bit-rates. Our results generalize prior attempts to interpret optical communication using the spectral decomposition of the electromagnetic Green’s function, and provide a foundation for furthering understanding of how to optimally engineer information-processing photonic devices such as antennas, MIMO space-division multiplexers, and metasurface imaging kernels.

We demonstrate what is believed to be a new method that yields orders-of-magnitude acceleration in inverse design (e.g. topology optimization) of high- Q resonant cavities to maximize the local density of states (LDOS), and which is also applicable to other resonant-response metrics. The key idea is that, once conventional LDOS optimization has identified a strong resonance, subsequent optimizations can exploit a fast shift-invert eigensolver to ensure that the LDOS remains centered at the resonance peak. We show that this eliminates ill-conditioning at sharp resonances that otherwise dramatically slows LDOS (and similar) optimization for Q ≫ 100. Our method is demonstrated by design of Q > 10 ⁶ resonant cavities in 1d and 2d dielectric systems.

Our ability to structure materials at the nanoscale has, and continues to, enable key advances in optical control. In pursuit of optimal photonic designs, substantial progress has been made on two complementary fronts: bottom-up structural optimizations (inverse design) discover complex high-performing structures but offer no guarantees of optimality; top-down field optimizations (convex relaxations) reveal fundamental performance limits but offer no guarantees that structures meeting the limits exist. We bridge the gap between these two parallel paradigms by introducing a “verlan” initialization method that exploits the encoded local and global wave information in duality-based convex relaxations to guide inverse design towards better-performing structures. We first illustrate this technique via the challenging problem of Purcell enhancement, maximizing the power extracted from a small emitter in the vicinity of a photonic structure, where ill-conditioning and the presence of competing local maxima lead to sub-optimal designs for adjoint optimization. Structures discovered by our verlan method outperform standard (random) initializations by close to an order of magnitude and approach fundamental performance limits within a factor of two, highlighting the possibility of accessing significant untapped performance improvements. We further validate this method using a planewave absorption example with a lossy dielectric, showcasing how verlan initializations can mitigate getting trapped by sub-optimal local minima in photonic inverse design problems.

Surface-enhanced Raman scattering (SERS) is a critical tool for chemical sensing and spectroscopy, and a key question is how to optimally design nanostructures for maximizing SERS. We present fundamental limits on spatially averaged SERS via periodic metasurfaces, derived using sum-of-squares (SOS) programming. This work represents the use of SOS techniques in optics, overcoming difficulties that prior bounding techniques have with regard to non-linear photonic processes with higher-order figures of merit. Our bounds on the ∫∥E∥⁴dr SERS enhancement factor for 2D examples demonstrate remarkable tightness when compared with inverse-designed dielectric and metallic structures for both electrical field out-of-plane (E _z ) and in-plane (H _z ) polarizations. We show that delocalized high-Q guided modes can achieve significant, theoretically diverging SERS enhancement even in the presence of material loss. For metallic structures, we demonstrate a fundamental performance limitation for E _z -polarized drive fields due to surface plasmon excitation restrictions. By varying the separation between Raman-active molecules and the metasurface design region, we also find material-dependent bounds on the maximum strength of field singularities. Our results offer insights into optimal metasurface design strategies for enhancing light–matter interactions, and our methodology may be adapted to the study of other nonlinear photonics design problems.

Our ability to structure materials at the nanoscale has, and continues to, enable key advances in optical control. In pursuit of optimal photonic designs, substantial progress has been made on two complementary fronts: bottom-up structural optimizations (inverse design) discover complex high-performing structures but offer no guarantees of optimality; top-down field optimizations (convex relaxations) reveal fundamental performance limits but offer no guarantees that structures meeting the limits exist. We bridge the gap between these two parallel paradigms by introducing a ``verlan'' initialization method that exploits the encoded local and global wave information in duality-based convex relaxations to guide inverse design towards better-performing structures. We illustrate this technique via the challenging problem of Purcell enhancement, maximizing the power extracted from a small emitter in the vicinity of a photonic structure, where ill-conditioning and the presence of competing local maxima lead to sub-optimal designs for adjoint optimization. Structures discovered by our verlan method outperform standard (random) initializations by close to an order of magnitude and approach fundamental performance limits within a factor of two, highlighting the possibility of accessing significant untapped performance improvements.

We use sum-of-squares programming to compute bounds on surface-enhanced Raman scattering via nanostructuring, demonstrating a general technique for bounding non-linear photonics processes and elucidating fundamental scaling laws to large area field enhancement.

This erratum corrects a misstatement regarding the absence of non-integrable singularities in 2d distributed Raman sensing applications and a formula [Eq. (9)] for one case of Raman enhancement. These changes do not impact the other results presented in the original manuscript [ Opt. Express 31, 4964 (2023)10.1364/OE.472646 ].