A reformulation of geometrical optics using ray time and ray energy as canonical coordinates, with an Airy transform connecting the two phase spaces, yields nonsingular envelope equations near reflection points.
Ponderomotive forces on waves in modulated media
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abstract
Nonlinear interactions of waves via instantaneous cross-phase modulation can be cast in the same way as ponderomotive wave-particle interactions in high-frequency electromagnetic field. The ponderomotive effect arises when rays of a probe wave scatter off perturbations of the underlying medium produced by a second, modulation wave, much like charged particles scatter off a quasiperiodic field. Parallels with the point-particle dynamics, which itself is generalized by this theory, lead to new methods of wave manipulation, including asymmetric barriers for light.
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Geometrical optics in phase space
A reformulation of geometrical optics using ray time and ray energy as canonical coordinates, with an Airy transform connecting the two phase spaces, yields nonsingular envelope equations near reflection points.