Fast mode decomposition in few-mode fibers

Egor S Manuylovich,Vladislav V Dvoyrin,Sergei K Turitsyn

doi:10.1038/s41467-020-19323-6

Abstract

Retrieval of the optical phase information from measurement of intensity is of a high interest because this would facilitate simple and cost-efficient techniques and devices. In scientific and industrial applications that exploit multi-mode fibers, a prior knowledge of spatial mode structure of the fiber, in principle, makes it possible to recover phases using measured intensity distribution. However, current mode decomposition algorithms based on the analysis of the intensity distribution at the output of a few-mode fiber, such as optimization methods or neural networks, still have high computational costs and high latency that is a serious impediment for applications, such as telecommunications. Speed of signal processing is one of the key challenges in this approach. We present a high-performance mode decomposition algorithm with a processing time of tens of microseconds. The proposed mathematical algorithm that does not use any machine learning techniques, is several orders of magnitude faster than the state-of-the-art deep-learning-based methods. We anticipate that our results can stimulate further research on algorithms beyond popular machine learning methods and they can lead to the development of low-cost phase retrieval receivers for various applications of few-mode fibers ranging from imaging to telecommunications.

Highlights

Retrieval of the optical phase information from measurement of intensity is of a high interest because this would facilitate simple and cost-efficient techniques and devices
The resurgence of interest in multi-mode fibers and in fewmode fibers (FMFs), in particular, in telecommunications is mainly due to the recognition of the fact that only the application of parallel channels can cope with the fast-growing demand on capacity of communication systems
FMFs are widely believed to provide the optimal practical balance between the highly important possibility to increase the communication capacity compared to single-mode fibers and the growing complexity of signal processing when dealing with many transversal modes[1]

Summary

Results

Transverse distribution of an electric field in a fiber can be represented as a linear combination of eigenmodes Ψk: X. The problem of MD is to determine the coefficients Ck using the intensity distribution at the output of the fiber. For a fiber that supports N eigenmodes, it is necessary to determine N amplitudes and N−1 phases (as we assume φ1 = 0), a total of 2N−1 coefficients. If the intensity distribution is captured by a camera or an array of photodiodes, the obtained image can be used to recover the coefficients Ck. Consider an input image consisting of M × M pixels. We numerate the vector z along the main diagonal first, and along the columns of the lower triangular matrix Z:. We use pseudoinverse Moore–Penrose matrix and find the vector z using Eq (8)

A21 À Á A2A1 cos φ2

Discussion

Methods

Code availability