Extraction of bend-resolved modal basis in deformed multimode fiber

Mode mixing in optical fibers caused by mechanical bending induces perturbations that distort the spatial field profile of coherent beams as they propagate through few-mode or multimode fibers. The observed output from a bent fiber commonly appears as complex speckle, which is challenging to relate directly to the underlying deformation, particularly in continuously varying systems such as aerially deployed fibers or fiber-integrated sensors in mechanical structures. We introduce a novel method for constructing a complete deformation-resolved orthonormal modal basis that captures the optical response of a multimode fiber across a range of controlled mechanical deformations. The basis is derived via a two-stage singular value decomposition framework that initially constructs deformation-specific orthonormal mode sets from speckle pattern correlation matrices and subsequently decomposes the aggregated sets to produce a unified functional basis that comprehensively spans the deformation-induced modal subspace supported by the fiber. This hierarchical framework yields an energy-balanced representation that isolates statistically dominant field components across all deformation states, approximates superpositions of the fiber’s propagation-invariant modes, systematically encodes deformation-induced perturbations, and supports robust decomposition of output fields across varying mechanical conditions. Such a basis enables tracking of mechanically induced modal evolution in deployed fibers, supporting distributed sensing, network resilience, and predictive fault diagnostics, with potential for integration into mode-division multiplexing systems.