Fig. 1: Concept of parametric dispersion modeling.

a For wave propagation through an isotropic medium such as glass, dispersion due to frequency difference \(\Delta \omega\) amounts to a scalar phase term, ψ. In single mode fiber (SMF), the polarization-dependence of residual waveguide anisotropy leads to wavelength-dependent polarization states and polarization mode dispersion (PMD), where \(\vec \tau\) is the PMD vector, and the \({{{\mathbf{\sigma }}}}_n\) are the Pauli spin matrices²⁷. In MMF, a change in wavelength impacts both the polarization and the spatial modes. b All these manifestations of dispersion can be modeled by an exponential of a polynomial in the frequency difference \(\Delta \omega\). Specifically, we measure the MMF TM at several discrete optical frequencies and fit these measurements to the corresponding dispersion model with matrix series \({{{\mathbf{X}}}}_k\), referenced at \(\omega _0\). We then reconstruct the TM \({{{\bar{\mathbf M}}}}\left( \omega \right)\) at continuous ω to predict the full spatio-spectral TM