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Observation of Eisenbud–Wigner–Smith states as principal modes in multimode fibre



Generally, light becomes scattered in space and time as it is coupled among multiple spatial paths during propagation through disordered media or multimode waveguides. This limits the pulse duration and spatial coherence that can be obtained after light exits such a medium. Eisenbud–Wigner–Smith eigenstates, originally proposed in nuclear scattering, are a unique set of input/output states that, despite spatiotemporal scattering during propagation, arrive at the output temporally unscattered. In fibre optics, these states manifest as principal modes that allow pulses and spatial coherence to be maintained despite propagation through a medium that would otherwise have destroyed these properties. These states generalize the phenomena of orthogonal fast/slow axes in a birefringent object to a basis with N axes, where N is the total number of spatial/polarization modes in the scattering medium. We experimentally demonstrate the existence of principal modes using a 100 m length of multimode fibre as the propagation medium.

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Figure 1: Propagation of an arbitrary spatial state and a principal mode through a scattering medium.
Figure 2: System for measurement of the optical transfer matrices, U(ω), and observation of the principal modes.
Figure 3: Calculation of the principal modes.
Figure 4: Wavelength response of each mode basis.
Figure 5: Observation of a principal mode (PM5) and comparison with a Laguerre-Gaussian mode (LG0,1H) in a six-mode fibre.
Figure 6: Second-order mode dispersion of principal modes.


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The authors thank Corning for providing the six-mode fibre used in these experiments. The authors also acknowledge the Linkage (LP120100661) with Finisar Australia, Laureate Fellowship (FL120100029), Centre of Excellence (CUDOS, CE110001018) and DECRA (DE120101329) programmes of the Australian Research Council.

Author information




J.C. designed and performed the experiments, analysed the data and wrote the document. J.S. led the project, helped with data analysis and article writing and provided funding. B.E. provided mentoring and guidance regarding the general direction of the project and provided funding.

Corresponding author

Correspondence to Joel Carpenter.

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The authors declare no competing financial interests.

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Carpenter, J., Eggleton, B. & Schröder, J. Observation of Eisenbud–Wigner–Smith states as principal modes in multimode fibre. Nature Photon 9, 751–757 (2015).

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