Steven G. Johnson

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.

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.

We present a practical methodology for the inverse design of compact high-order/multiresonance filters in linear passive 2-port wave-scattering systems, targeting any desired transmission spectrum (such as standard pass/stop-band filters). It can deliver filters sized only a few wavelengths by incorporating overlapping resonances, in contrast to traditional designs via coupled-mode theory leading to rather large devices with spatially separated resonators. It is particularly suited for frequency spectra with sharp (passband-to-stopband) transitions, where previous “brute-force" design attempts faced severe difficulties. Our formulation allows for both large-scale topology optimization and few-variable parametrized-geometry optimization. It is an extension of a quasi-normal mode theory and analytical filter-design criteria (on the system resonances and background response) derived in our previous work. Our present optimization-oriented formulation relies solely on a scattering solver and imposes these design criteria as equality constraints with easily calculated (via the adjoint method) derivatives, so that our algorithm is numerically tractable, robust, and well-suited for large-scale inverse design. We demonstrate its effectiveness by designing 3rd- and 4th-order elliptic and Chebyshev filters for photonic metasurfaces, multilayer films, and electrical LC -ladder circuits.

This paper presents a rigorous proof that arbitrarily weak perturbations produce localized vibrational (phonon) modes in one- and two-dimensional discrete lattices, inspired by analogous results for the Schr{ö}dinger and Maxwell equations, and complementing previous explicit solutions for specific perturbations (e.g., decreasing a single mass). In particular, we study monatomic crystals with nearest-neighbor harmonic interactions, corresponding to square lattices of masses and springs, and prove that arbitrary localized perturbations that decrease the net mass lead to localized vibrating modes. The proof employs a straightforward variational method that should be extensible to other discrete lattices, interactions, and perturbations.

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.

This study formulates a volumetric inverse-design methodology to generate a pair of complementary focusing metalenses for terahertz imaging: the two lenses exhibit equal and opposite shifts in focal length with frequency. An asymmetry arises, where we find a focal length that decreases with frequency to be more challenging to achieve (without material dispersion) given fabrication constraints, but it is still possible. We employ topology optimization, coupled with manufacturing constraints, to explore fully freeform designs compatible with 3D printing. Formulating an optimization problem that quantifies the goal of maximal complementary focal shifts, while remaining differentiable and tractable, requires a carefully selected sequence of constraints and approximations.

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 ].