High-Precision Modal Analysis of Multimode Waveguides from Amplitudes via Large-Step Nonconvex Optimization

Abstract

Optimizing multimodal waveguide performance depends on modal analysis; however, existing methods focus predominantly on modal power distribution (MPD) and, limited by experimental hardware and conditions, exhibit low accuracy, poor adaptability, and high computational cost. This work presents a novel framework for comprehensive modal analysis (recovering both power and relative phase) using aperture field (AF) and far field (FF) amplitude measurements. We formulate the modal analysis as a nonconvex optimization problem under a power-normalization constraint and, inspired by recent advances in deep learning, introduce a large-step strategy to solve it. Our method retrieves both the MPD and the modal relative-phase distribution(MRPD). The effectiveness of the proposed method is validated through visualization of the nonconvex optimization process via its loss landscape. Under noiseless conditions, analysis results of $93$ electromagnetic modes indicate that the relative amplitude accuracy $\mathrm{MRE_{Modulus}}$, and the phase accuracy $\mathrm{MAE_{Phase}}$, both reach the level of machine precision. Through noise simulations of the AF and environmental background, the operational principles of the method are demonstrated under signal-to-noise ratio (SNR) conditions ranging from $10~\mathrm{dB}$ to $60~\mathrm{dB}$. Experiments further confirm that error suppression is effectively achieved by increasing the number of sampling points, thereby maintaining high accuracy and strong robustness. Within a unified evaluation framework, the absolute amplitude error $\mathrm{MAE_{Modulus}}$, and the phase error $\mathrm{MAE_{Phase}}$, are as low as $1.633\times10^{-8}$ and $0$, respectively. The accuracy is significantly superior to existing methods, while also exhibiting higher computational efficiency.