dorsal/arxiv
View SchemaSymmetries of Optical Phase Conjugation
| Authors | Predrag L. Stojkov, Milivoj R. Belic, Marko V. Jaric |
|---|---|
| Categories | |
| ArXiv ID | physics/0007019 |
| URL | https://arxiv.org/abs/physics/0007019 |
Abstract
Various algebraic structures of degenerate four-wave mixing equations of optical phase conjugation are analyzed. Two approaches (the spinorial and the Lax-pair based), complementary to each other, are utilized for a systematic derivation of conserved quantities. Symmetry groups of both the equations and the conserved quantities are determined, and the corresponding generators are written down explicitly. Relation between these two symmetry groups is found. Conserved quantities enable the introduction of new methods for integration of the equations in the cases when the coupling $\Gamma$ is either purely real or purely imaginary. These methods allow for both geometries of the process, namely the transmission and the reflection, to be treated on an equal basis. One approach to introduction of Hamiltonian and Lagrangian structures for the 4WM systems is explored, and the obstacles in successful implementation of that programe are identified. In case of real coupling these obstacles are removable, and full Hamiltonian and Lagrangian formulations of the initial system are possible.
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"abstract": "Various algebraic structures of degenerate four-wave mixing equations of\noptical phase conjugation are analyzed. Two approaches (the spinorial and the\nLax-pair based), complementary to each other, are utilized for a systematic\nderivation of conserved quantities. Symmetry groups of both the equations and\nthe conserved quantities are determined, and the corresponding generators are\nwritten down explicitly. Relation between these two symmetry groups is found.\nConserved quantities enable the introduction of new methods for integration of\nthe equations in the cases when the coupling $\\Gamma$ is either purely real or\npurely imaginary. These methods allow for both geometries of the process,\nnamely the transmission and the reflection, to be treated on an equal basis.\nOne approach to introduction of Hamiltonian and Lagrangian structures for the\n4WM systems is explored, and the obstacles in successful implementation of that\nprograme are identified. In case of real coupling these obstacles are\nremovable, and full Hamiltonian and Lagrangian formulations of the initial\nsystem are possible.",
"arxiv_id": "physics/0007019",
"authors": [
"Predrag L. Stojkov",
"Milivoj R. Belic",
"Marko V. Jaric"
],
"categories": [
"physics.optics"
],
"title": "Symmetries of Optical Phase Conjugation",
"url": "https://arxiv.org/abs/physics/0007019"
},
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