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 × 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 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.
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BibTeX
@misc{mauser2026optical,
title = {{Optical Fourier Architecture for Universal Nonlinear Functions}},
author = {Martin F. X. Mauser and Joshua Morris and Sara Galatro and Philip Walther and Borivoje Dakic},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.37746},
eprint = {2609.37746},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.37746},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Optical Fourier Architecture for Universal Nonlinear Functions
AU - Martin F. X. Mauser
AU - Joshua Morris
AU - Sara Galatro
AU - Philip Walther
AU - Borivoje Dakic
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.37746
UR - https://arxiv.org/abs/2609.37746
AB - We introduce an exact algebraic architecture that evaluates an arbitrary finite Fourier series using a two-mode (2 × 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 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.
ER -