Matrix symmetry and normality in multimode fiber transport

Multimode fibers (MMFs) support high-dimensional optical transport within a compact form factor, with growing applications in biomedical imaging, telecommunications, and quantum engineering. Realizing this potential requires accurate knowledge of the fiber transmission matrix (TM); yet experimentally measured TMs are often corrupted by system-level distortions that obscure the underlying modal physics and limit wavefront control. Here, we show that the reciprocity of optical waves imposes symmetry constraints that provide self-consistency conditions for identifying and correcting such distortions. Enforcing these constraints enables improved recovery of the transported fields and allows the computational synthesis of confocal images from reflection measurements through the fiber. We further introduce matrix normality as a physically meaningful metric that quantifies the orthogonality of the propagating modes encoded in the TM. Using controlled static compression of the fiber, we demonstrate experimentally that departures from normality at a single wavelength predict a monotonic reduction in the spectral bandwidth of the principal mode basis. These results reveal a direct connection between spatial modal structure and spectral stability in MMF transport. More broadly, they establish a unified framework for understanding and controlling broadband light propagation in MMFs and complex waveguides.