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Geometry and control of threewave interactions
 in The Arnoldfest
, 1997
"... The integrable structure of the threewave equations is discussed in the setting of geometric mechanics. LiePoisson structures with quadratic Hamiltonian are associated with the threewave equations through the Lie algebras su(3) and su(2, 1). A second structure having cubic Hamiltonian is shown to ..."
Abstract

Cited by 4 (1 self)
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The integrable structure of the threewave equations is discussed in the setting of geometric mechanics. LiePoisson structures with quadratic Hamiltonian are associated with the threewave equations through the Lie algebras su(3) and su(2, 1). A second structure having cubic Hamiltonian is shown to be compatible. The analogy between this system and the rigidbody or Euler equations is discussed. Poisson reduction is performed using the method of invariants and geometric phases associated with the reconstruction are calculated. We show that using piecewise continuous controls, the transfer of energy among three 1 waves can be controlled. The so called quasiphasematching control strategy, which is used in a host of nonlinear optical devices to convert laser light from one frequency to another, is described in this context. Finally, we discuss the connection between piecewise constant controls and billiards.
Light propagation through a coiled optical fiber and
, 705
"... The nature of changes in the interference pattern caused by the presence of polarizationchanging elements in one or both beams of an interferometer, in particular those caused by an effective optical activity due to passage of a polarized beam through a coiled optical fiber are clarified. It is poi ..."
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The nature of changes in the interference pattern caused by the presence of polarizationchanging elements in one or both beams of an interferometer, in particular those caused by an effective optical activity due to passage of a polarized beam through a coiled optical fiber are clarified. It is pointed out that for an incident state that is not circularly polarized so that the two interfering beams go to different polarization states, there is an observable nonzero Pancharatnam phase shift between them which depends on the incident polarization state and on the solid angle subtended by the track of the ⃗kvector at the centre of the sphere of ⃗kvectors. The behaviour of this phase shift is singular when the two interfering states are nearly orthogonal. It is shown that for zero path difference between the two beams, the amplitude of intensity modulation as a function of optical activity is independent
unknown title
, 2003
"... Nonachromaticity and reversals of topological phase as a function of wavelength ..."
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Nonachromaticity and reversals of topological phase as a function of wavelength