Single-mode–multimode–single-mode (SMS) fiber structures are widely used in optical engineering as compact and low-complexity platforms for refractive-index (RI), temperature, and strain sensing, where spectral features arise from multimode interference (MMI) within the multimode fiber (MMF) section. Despite their practical relevance, predictive modeling remains challenging for large-diameter MMF segments because the number of guided modes can be very large, making the choice of a sufficient modal basis unclear and often computationally prohibitive.

This work presents a numerical framework to quantify how MMF diameter and length govern modal excitation and the resulting transmission spectrum, while enabling a justified reduction in the modal space. For each geometric configuration, MMF eigenmodes and propagation constants are computed, and the propagated field is sampled on transverse planes along the device length. A power-normalized modal decomposition is then performed using overlap integrals between the propagated transverse fields (Ep, Hp) and the MMF eigenmode fields (Em, Hm). This yields complex modal coefficients am(z) and the modal power distribution Pm(z), which are used to rank modes by contribution and to determine a minimal subset that ensures spectral convergence.

The approach provides a physically grounded criterion to select the required number of modes and to assess the impact of higher-order modes on dominant spectral features. The transmission spectrum is interpreted as the accumulated differential phase among the excited modes and their recapture at the output single-mode fiber, offering a practical route toward accurate and computationally efficient simulation of SMS devices for optical sensing and related photonic engineering applications.