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Optical Computing of Mathematical Derivatives using Dispersion and Coherent Detection

Early attempts in the field of optical computing were futile because they aimed to construct an all-optical equivalent of the digital computer [1]. However, photonics does have potential for performing certain computing functions in the analog domain [1]. These analog photonic hardware accelerators precede an optical-to-electrical conversion and alleviate bandwidth, dynamic range and power consumption bottlenecks on the subsequent electronics [2]. Far from a general purpose computer, photonic hardware accelerators are custom designed to perform specific signal transformations in real time and in analog domain. The computational operations that have already been realized by these analog optical computing primitives include integration [3], data compression [4], time-bandwidth engineering [5], logarithm [6] and optical dynamic range compression [7]. Optical implementation of temporal differentiation has been demonstrated in two ways: field differentiators realized using a micro-ring resonator [8] and intensity differentiators implemented using phase modulation [9].