Unveiling Modal Optical Properties: Physical Regularities, Correlations, and Extremal Bounds in Ring-Core Fibers

Currently, optical fiber design and optimization rely on empirical trial-and-error methods to achieve the target optical properties. However, these exploratory approaches cannot directly determine optimal structures, predict extremal bounds of optical properties, or reveal physical regularities and correlations between modal properties. This study investigates the statistical relationships and extremal bounds of optical properties in ring-core fibers using a neural network-based data generation and analysis approach. The proposed fast and accurate method uses neural networks to generate large-scale fiber optic property data, including dispersion and effective refractive index differences ($\Delta n_{\mathit {eff}}$). Systematic statistical analysis of the generated data reveals significant intermodal correlations, demonstrating that these properties are constrained within well-defined boundaries under specific conditions. Furthermore, neural network validation confirms inherent constraint relationships between low-order and high-order mode properties, as well as between dispersion and$\Delta n_{\mathit {eff}}$. This work bridges data-driven modeling with physical interpretation, provides new insights into fundamental intermodal relationships, and offers practical guidance for the design of specialty fibers with tailored or extreme optical performance.