2026-10-14T05:34:31Z https://api.figshare.com/v2/oai

oai:figshare.com:article/34046850 2026-10-01T16:01:06Z category_37476 portal_1023 item_type_12 month_year_10_2026

Optical Fourier Architecture for Universal Nonlinear Functions Martin F. X. Mauser (17152217) Joshua Morris (25157352) Sara Galatro (25157355) Philip Walther (13102902) Borivoje Dakic (23506543) Physics (arXiv) physics.optics (arXiv) quant-ph (arXiv) 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. 2026-09-29T00:00:00Z Text Preprint 10.48550/arXiv.2609.37746 https://figshare.com/articles/preprint/Optical_Fourier_Architecture_for_Universal_Nonlinear_Functions/34046850 CC0