Fast phase error calibration through radix-p optimization processing

Abstract

Optical phased arrays (OPAs) have been a popular option to manipulate the spatial behavior of the free-space optical beams. Inspired by the success of the integrated circuits (IC) industry, photonic IC (PIC) based OPAs have been actively studied in the last decade. Due to the fabrication imperfection, light passing through different paths typically results in random phase errors. The phase errors can seriously deviate the interference pattern of an OPA, and radically change the spatial distribution of the optical field. This phenomenon will significantly degrade the performance for applications like image scanning and optical wireless communication (OWC). Thermally or electrically tunable phase shifters can be applied to compensate the phase errors through dedicated calibration algorithms. However, the complexity of the calibration processes quickly increases with the number of the OPA’s elements. Hence, the whole processing can be time-consuming and this significantly pushes the overall system cost. Besides, considering the potential dynamic factors such as thermal gradient and aging effects, continuous calibration may be necessary. This results in great demand for fast and efficient calibration processing for the practical applications. In this paper, novel and efficient radix-p calibration processing is proposed which can be directly combined with most of the already reported/developed optimization algorithms as a speed-up turbo. It is shown that the computation time of the proposed radix-p processing grows linearly with the number of the OPA’s elements. In comparison to the conventional particle swarm optimization (PSO) algorithm, which exhibits exponential computation time in our numerical results, the radix-p processing shows great efficiency improvement. In the numerical results, speed with more than 12 times faster is shown for the proposed radix-p processing compared to the traditional PSO algorithms.