Transport equations for the Wigner distribution function in an inhomogeneous and dispersive medium

Martin J. Bastiaans

The Wigner distribution function of an optical signal, which can be considered as the momentary temporal and local spatial spectrum of the signal, is defined. Equations are derived which describe the transport of the Wigner distribution function in a medium, e.g. a plasma, that is weakly inhomogeneous in space and time, and exhibits weak dispersion for the temporal as well as the spatial frequency variable. The transport equations are compared with the eikonal equation in geometrical optics giving, as a geometrical-optical formulation of the transport equations, that along the path of a geometrical-optical light ray the Wigner distribution function has a constant value.

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