Summary
Optical devices that process waves usually face limits because light can only bend and spread so much, which restricts how detailed their outputs can be. The authors show a way to create complicated functions with light that have details finer than those physical limits, by cleverly encoding input information in the light's wavefront and then using special patterns to get outputs that behave like 'superoscillations.' Unlike traditional methods that focus on shaping the light field itself, this approach works on the relationship between input and output, letting the device do more complex calculations. Their experiments with visible light prove this concept, opening up new ways to design optical computers that process more complex information than previously thought possible.
What this means in practice
- •For optical engineers: Build wave-based processors that compute complex functions beyond diffraction limits using superoscillatory input-output designs.
- •For photonic device designers: Develop multiplexed optical systems to evaluate multiple intricate light-based functions simultaneously beyond conventional bandwidth constraints.
Authors
Yuntian Wang, Md Sadman Sakib Rahman, Aydogan Ozcan
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.