Optical Fourier Architecture for Universal Nonlinear Functions

Abstract:We introduce an exact algebraic architecture that evaluates an arbitrary finite Fourier series using a two-mode ($2 \times 2$) linear optical circuit, with the only tunable components being single-mode phase shifters encoding the function argument. We prove that such a circuit must exist for every Fourier series and derive an analytical method for its construction based on spectral factorisation. The resulting optical system exhibits an $\mathcal{O}(N)$ depth for an $N$-harmonic expansion, executing function evaluations in the passive optical time-of-flight. Finally, we validate our claims numerically, demonstrating that even for sequences with thousands of Fourier terms, our proposed circuit construction correctly synthesises continuous and discontinuous nonlinear functions. Our architecture thus provides a universal, deterministic foundation for single-variable nonlinear optical computing on integrated photonic platforms.

Optics (physics.optics); Quantum Physics (quant-ph)

arXiv:2609.37746 [physics.optics]

(or arXiv:2609.37746v1 [physics.optics] for this version)

https://doi.org/10.48550/arXiv.2609.37746 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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