optical engineers

Abstract: Can a material learn what deserves its attention? We show that it can in a model optical network, in which action outcomes train a persistent record in each link. The record biases whether a source is consulted and sets how strongly it changes a stored answer, so useful sources gain attention and influence without being identified in advance. The network's experience thus shapes the information available for its future learning. Resonant readouts make this learning fragile: reinforcement can carry a record past resonance, where it persists but its influence weakens. We derive bounds within which relevant signals guide the answer, irrelevant signals are rejected and stored answers remain open to revision. These bounds guide a learning rule that limits reinforcement as records form; in simulations, it acquires useful records and keeps them functional. When relevance changes, an obsolete record can block its own replacement. A local state that strengthens negative writing after unsuccessful actions releases obsolete records and completes the learning sequence more often. How a memory is read should decide how it is written.

Abstract: Physical wave processors are constrained by diffraction, but the bandwidth of the mathematical functions they implement need not be set by it. Here, we demonstrate continuous and multiplexed optical processing of superoscillatory functions, in which a scalar argument is encoded onto a wavefront and a fixed diffractive wave processor synthesizes optical responses that approximate the corresponding function outputs in parallel. Unlike conventional superoscillatory optics that generates predetermined fields, superoscillation here is expressed in the input-output dependence on the encoded argument. Its frequencies are therefore distinct from the transverse spatial frequencies of propagating light and are not subject to the same diffraction-imposed cutoff. We demonstrate complex-valued superoscillatory function synthesis and introduce a multiplexed architecture that simultaneously evaluates distinct target superoscillatory functions whose harmonic content exceeds that of the optical input encoding. Visible-light experiments further validate this beyond-encoding superoscillatory regime. Together, these results establish functional superoscillation as a design principle for wave-based computation and show how interference, diffractive depth and spatial channel allocation extend the functional reach of passive wave processors. More broadly, these analyses establish a separation between functional bandwidth and physical wave bandwidth in analog optical computation.

Abstract: We study the minimum-norm Gauss--Newton method for phase retrieval from random coded diffraction patterns with additive intensity noise. For bounded symmetric masks satisfying the standard complex moment conditions, we establish convergence guarantees with quadratic error recursions in both the resampled and fixed-data settings. In the resampled setting, $O(\log^2 n)$ masks per independent block suffice to obtain a spectral initializer within a constant-relative-radius neighborhood and to establish a local quadratic error recursion with an additive noise term. Consequently, in the noiseless case, the method achieves relative accuracy $ε$ using $O(\log\log(1/ε)\log^2 n)$ masks. In the fixed-data setting, $O(\log^6(en))$ masks suffice for spectral initialization within a neighborhood whose relative radius is proportional to $\log^{-5/2}(nL)$. Within this neighborhood, the method satisfies a linear contraction bound and eventually a quadratic error recursion. In particular, in the noiseless case, the method initially converges linearly and enters a quadratic convergence phase after $O(\log n)$ iterations, without acquiring additional masks. Numerical experiments on synthetic signals and a natural image demonstrate the method's efficiency relative to state-of-the-art algorithms.

Abstract: Vision-language models (VLMs) are increasingly being used in scientific workflows, but their ability as agents to directly control laboratory experiments from visual feedback remains underexplored. This capability is important because many laboratory tasks do not naturally provide dense, pre-defined numerical objectives: informative signals can be sparse, intermittent, or visually ambiguous. A more general laboratory agent should instead be able to interpret visual observations, take actions to acquire useful feedback, and adapt its behavior based on the consequences of those actions. We study whether general-purpose VLMs can perform this kind of closed-loop scientific control using experimental optics as a testbed. We evaluate agents on three experimental systems that isolate distinct capabilities: a Michelson interferometer, a two-mirror cavity, and a four-mirror optical relay. The agents observe camera images, directly issue actuator and measurement commands, and retain their interaction history without receiving an engineered scalar objective during control. Across these experiments and matched simulations, we find that, given task-specific natural-language guidance, VLMs can estimate actuator-response relationships, resolve ambiguous observations through intervention, and actively create informative visual feedback when signals are sparse. These results suggest that pretrained multimodal models can serve as important decision-making agents within the experimental loop. Our work also establishes optics as a physically grounded testbed for visual reasoning and active perception in scientific agents.

Abstract: The Fresnel wave surface governs the propagation of light in a transparent biaxial crystal. It is a special Kummer quartic, and we identify it exactly. Over the complex numbers the wave surface of a crystal is the Kummer surface of the Jacobian of an explicit genus-two curve branched at the signed square roots of the three principal permittivities. This Jacobian is isogenous, by an isogeny with kernel of order four, to a product of two elliptic curves. One elliptic curve carries the three permittivities, and the other carries the optic-axis angle. The physical family is Zariski dense in the locus of genus-two curves with an extra involution, and its automorphism strata are explicit. The identification instantiates a task-aware quotient, which identifies parameters that differ by a nuisance transformation and carries invariant coordinates and explicit strata. For biaxial crystals, two ratios of the permittivities form a complete invariant of the wave surface up to rotation and rescaling, and the four real nodes are given in closed form. At an interface the candidate transmitted waves are the roots of a quartic of exact degree four. Its real-root count, root order, and repeated-root events are decided by exact algebraic predicates, and along the generic single-node encounters of the paper its discriminant vanishes to second order. Floating-point solvers drop forward transmitted modes near the optic axes, and the certified solver does not. On exact equivalence classes, learned models on quotient coordinates are invariant and more accurate than models on raw tensors, while learned root-count predicates fail near the optic axes.

Abstract: We derive a novel diffuse-like BRDF based on microfacet theory. Its main novelty lies in the fact that it admits an elementary expression for both evaluation and importance sampling, while accounting exactly for all scattering orders under the Smith shadowing assumption. As such, it is the first to settle the question of whether such a construction was possible. In practice, the BRDF produces Lambertian reflectance at normal incidence and progressively concentrates reflected light around the mirror direction as incidence approaches grazing. We showcase this effect by comparing rendering results against Lambertian and state-of-the-art stochastic microfacet BRDFs.

Abstract: Current deep optics simulations struggle to balance high fidelity with computational efficiency, particularly for complex polarized and diffractive systems. To address this, we introduce a fully differentiable Shooting and Bouncing Ray (SBR) algorithm that simultaneously models geometric and physical optics fields. Unlike standard wave optics methods, our approach enables accurate, gradient-based optimization of polarized compound refractive-diffractive systems without the computational cost of full-wave simulations. We validate our method against analytical Fraunhofer diffraction patterns and state-of-the-art Fourier optics and wave optics methods. We showcase the practical utility of our differentiable engine through one application: designing a wide field-of-view achromatic lens with multiple Diffractive Optical Elements (DOEs).

Abstract: We introduce Complex-Valued Quadratic Phase Gaussian (CVQPG), a novel hologram representation method that replaces standard 2D Gaussian representations used in 2D Gaussian Splatting with 2D quadratic phase functions. CVQPG incorporates additional learnable parameters to control the curvature of these bases. We evaluate our approach against state-of-the-art methods, exceeding the visual quality by +0.19 dB (RGB) and +0.33 dB (grayscale) on average in holographic reconstructions. Specifically, our equal parameter count evaluations show that modulating the primitive's wavefront is an effective and lightweight enhancement for hologram representations. In addition, our frequency domain analysis illustrates that CVQPG has successfully preserved the mid-to-high frequency band of natural images.