Programable photonic meshes provide a promising platform for analog matrix-vector multiplication, but their scalability is often limited by the large phase-shift ranges required in universal interferometer circuits. We introduce a perturbative programing method that operates the circuit near a fixed reference configuration and realizes the target transformation through interferometric subtraction, thereby reducing the required programable phase excursion. We develop this approach for photonic matrix-vector multiplication architectures based on universal unitary meshes and for low-depth nonunitary constructions based on sums of unitaries. We identify favorable reference configurations through a local conditioning criterion, analyze the phase statistics obtained for random target matrices, and show that perturbative programing produces phase distribution shrinking as the matrix size increases. Identified reference point allows for the subtraction to be carried out electronically after detection, avoiding the interferometric subtraction loss. We further quantify the trade-off between the reduced phase range and the intrinsic overhead introduced by the subtraction architecture and show that for sufficiently lossy phase shifters the reduced phase range can compensate for this penalty. These results identify perturbative programing as a conditional but potentially useful route toward more scalable programable photonic matrix processors.

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• Integrated optics
• Photonics