All-optical differential equation solver with constant-coefficient tunable based on a single microring resonator

Abstract

Photonic integrated circuits for photonic computing open up the possibility for the realization of ultrahigh-speed and ultra wide-band signal processing with compact size and low power consumption. Differential equations model and govern fundamental physical phenomena and engineering systems in virtually any field of science and engineering, such as temperature diffusion processes, physical problems of motion subject to acceleration inputs and frictional forces, and the response of different resistor-capacitor circuits, etc. In this study, we experimentally demonstrate a feasible integrated scheme to solve first-order linear ordinary differential equation with constant-coefficient tunable based on a single silicon microring resonator. Besides, we analyze the impact of the chirp and pulse-width of input signals on the computing deviation. This device can be compatible with the electronic technology (typically complementary metal-oxide semiconductor technology), which may motivate the development of integrated photonic circuits for optical computing.

On-Chip Tunable Second-Order Differential-Equation Solver Based on a Silicon Photonic Mode-Split Microresonator

“…Amongst them, the ODE solvers based on silicon PICs are very attractive since they could offer competitive advantages of micro-scale footprint, low power consumption, capability of large-scale integration, and compatibility with well-developed silicon fabrication technologies. In previous reports, first-order ODE solvers implemented by on-chip silicon micro-ring resonators (MRRs) were demonstrated [16,17]. On the other hand, high-order ODE solvers performing more powerful computing and processing functionalities are also of great significance in characterization of more complicated high-order systems.…”

Parallel integro-differential equation solving via multi-channel reciprocal bianisotropic metasurface augmented by normal susceptibilities

“…36 susceptibilities. Considering all of them during the metasurface design causes the problem to be practically difficult to solve, especially in the presence of spatial derivatives in equations (6), (7). Consequently, the normal susceptibilities are typically not taken into account for simplicity, as justified by the fact that it is generally possible to find an equivalent metasurface with purely tangential polarizations [56].…”

“…The first one requires an optical feedback loop [4,5], while the second one relies on an engineered temporal impulse response [6]. Fiber gratings [5], silicon micro-ring resonator [7], and all-optical differentiator [6] have been proposed as some candidates for implementation of these solutions. However, in addition to involving either a redundant loop [8] or an additional optical pump [9], the configuration of these schemes suffer from microelectronic limitations regarding operational speed, power consumption and significantly larger size, which is inappropriate in the new generation of optical systems [3,10].…”

“…'metamaterial-assisted optical signal processing' or 'computational metamaterials' pioneered by Silva et al [11], has offered the third solution through providing a new venue for executing the signal processing functions in optics. The prominent wave-matter-interacting capabilities of metamaterial family suggest a variety of intriguing wave-based phenomena such as all-optical logics [12], all-optical differentiators and integrators [13][14][15] and some more sophisticated computing operators, such as differential and integro-differential equation solvers or/and image processing tools at the miniaturized hardware level [4,6,7,9]. The design of these freshly germinated meta-computing devices are still ongoing within two distinct frameworks of Fourier method and Green's function (GF) approach [16].…”

Temporal analog optical computing using an on-chip fully reconfigurable photonic signal processor

“…It is more convenient for an integrated photonic structure to perform any mathematical operations, such as convolution with an arbitrary function and pulse shaping, in time domain [1,2,3,4,5,6,7]. Therefore, analog optical computing has gained widespread applications in optical communication and real-time spectroscopy for processing optical signals in time domain.…”