An Intensity-Only Two-Dimensional Fourier- Equation-Solving Method for Precise Mode Purity Measurement of Large-Mode-Number Few-Mode Fibers

Mode purity measurements can offer crucial opportunities for addressing the generation and transmission problems of orbital angular momentum (OAM) modes in few-mode fibers (FMFs), and driving progress across various FMF-related fields. Utilizing solely the intensity distribution at the fiber output to measure mode purity is highly attractive for numerous scientific and industrial applications. Nevertheless, due to the highly complex nonlinear inverse problem of intensity measurements, existing intensity-only methods are only applicable to a narrow range of FMFs due to their resolvable mode types (only azimuthal modes) or quantities (no more than 8 at a certain polarization). In this paper, we present a precise and robust intensity-only Fourier-Equation-Solving method for measuring the azimuthal and radial mode purity of large-mode-number FMFs, and demonstrate this method in two of the most representative and widely used FMFs, i.e., step-index FMF and graded-index FMF. Compared to the state-of-the-art intensity-only methods, when there is a known dominating mode, this method doubles the number of accurately resolvable modes (16 modes at least) in experiments, making it applicable to the vast majority of existing FMFs. We believe that this straightforward and cost-effective characterization method for FMFs and FMF-related active and passive devices can promote the development of mode-division multiplexing technology and its applications in various fields.