Wavelength Diversity Expands the Expressive Power of Optical Computing

Abstract

Universal function approximation underpins neural networks' capacity to represent nonlinear relationships, but realizing this capability in optical hardware requires engineering the computational features encoded in light. Here, we show that wavelength diversity enhances optical function-approximation expressivity through wavelength-scaled Fourier features generated by a shared phase encoder, without increasing the number of input-encoded harmonics. Multiple wavelengths contribute to the representation of each output function rather than merely serving as independent computational channels. We establish theoretical scaling laws and approximation-error bounds, revealing that, for nondispersive encoders, the spectral endpoints determine the accessible computational bandwidth, while intermediate illumination wavelengths enrich the available harmonics within that bandwidth. Numerical studies demonstrate improved approximation of real- and complex-valued nonlinear functions, with a representative design achieving more than a 100-fold reduction in mean-squared error relative to tested monochromatic optical processors with the same number of trainable phase features. Experimentally, we validate enhanced approximation accuracy and demonstrate the simultaneous approximation of 4,136 distinct nonlinear functions using a compact, single-layer diffractive processor under five-wavelength illumination. These results establish wavelength diversity as an additional physical resource for scaling the expressive power of optical computing and enhancing the accuracy of parallel nonlinear function approximation.