Reconfigurable Integrated Optical Fractional Fourier Transform Processor by Inverse Design

Fractional Fourier Transform (FrFT) offers multi-dimensional signal processing capabilities for various applications, including synthetic aperture radar imaging, moving target detection, and optical image encryption. Recently, FrFT has also found emerging applications in neural networks and graph signal processing, enabling adaptive analysis in structured and irregular domains. However, conventional optical implementations of FrFT typically rely on bulky free-space optics (such as lens-based 4f systems) or kilometer-scale fiber arrays to achieve specific fractional orders, which are inherently non-reconfigurable and challenging to integrate. Here, we demonstrate a reconfigurable Integrated Optical Discrete Fractional Fourier Transform (IODFrFT) processor with highly transformation fidelity(average fidelity values<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\geqslant 0.948$</tex-math></inline-formula> for <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$4,6,8,10$</tex-math></inline-formula> dimensions with fractional-order precision is <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$0.01\pi$</tex-math></inline-formula>). The proposed processor employs an inverse design methodology to implement the fundamental transformation matrices derived from Discrete Fractional Fourier Transform (DFrFT) eigenvalue decomposition, integrated with programmable phase shifters for reconfiguration. This compact photonic integration approach, fabricated on a silicon platform, enables on-chip DFrFT processing with a footprint of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$2.96\,\text{mm}\times 1.44 \,\text{mm}$</tex-math></inline-formula>, representing a multiple orders of magnitude reduction compared to conventional implementations. The proposed IODFrFT processor holds significant potential for next-generation optical computing and time-frequency signal processing applications.