Spatial eigenstates are a familiar part of optical waveguide theory. Such states enter and exit the waveguide as the same spatial state. As illustrated in Fig. 1. In the idealised case, a perfect waveguide, free of mode coupling, perturbations and ignoring chromatic dispersion, these spatial eigenstates also propagate with a single group-delay. However in reality, light propagation in multimode optical fibre is more complicated. Perturbations and mode coupling are such that as the length of propagation increases, it is increasingly unlikely that light can travel from one end of the waveguide to the other, maintaining its spatial state along the entire length of propagation. In this case, a change in wavelength, or fibre length will result in a different set of spatial eigenstates, as illustrated in Fig. 1. The spatial eigenstates become a coincidence of fibre length and wavelength, rather than modes with well-defined propagation constant and group-delay as for the ideal waveguide case. Eisenbud-Wigner-Smith (EWS) states, also known as principal modes [1]–[7], are the eigenstates of the group-delay operator and hence propagate through the fibre associated with a single group delay, and are wavelength independent. However unlike spatial eigenstates, EWS states do not in general have the same spatial state at input and output, as illustrated in Fig. 1. EWS states were first proposed decades ago [1], [6], but were only recently observed experimentally[2]. These states are of significance for their ability to propagate through a scattering medium, yet arrive free of first-order mode dispersion. EWS states are the basis with the least wavelength dependence, and hence also the states with the highest spatial coherence for a given spectral bandwidth at the source. EWS states also identify the maximum and minimum possible propagation delay through the waveguide.

© 2017 IEEE

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