dorsal/arxiv
View SchemaField Theory for Coherent Optical Pulse Propagation
| Authors | Q-Han Park, H. J. Shin |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9709002 |
| URL | https://arxiv.org/abs/solv-int/9709002 |
| DOI | 10.1103/PhysRevA.57.4621 |
Abstract
We introduce a new notion of "matrix potential" to nonlinear optical systems. In terms of a matrix potential $g$, we present a gauge field theoretic formulation of the Maxwell-Bloch equation that provides a semiclassical description of the propagation of optical pulses through resonant multi-level media. We show that the Bloch part of the equation can solved identically through $g$ and the remaining Maxwell equation becomes a second order differential equation with reduced set of variables due to the gauge invariance of the system. Our formulation clarifies the (nonabelian) symmetry structure of the Maxwell-Bloch equations for various multi-level media in association with symmetric spaces $G/H$. In particular, we associate nondegenerate two-level system for self-induced transparency with $G/H=SU(2)/U(1)$ and three-level $\L $- or V-systems with $G/H = SU(3)/U(2)$. We give a detailed analysis for the two-level case in the matrix potential formalism, and address various new properties of the system including soliton numbers, effective potential energy, gauge and discrete symmetries, modified pulse area, conserved topological and nontopological charges. The nontopological charge measures the amount of self-detuning of each pulse. Its conservation law leads to a new type of pulse stability analysis which explains nicely earlier numerical results.
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"abstract": "We introduce a new notion of \"matrix potential\" to nonlinear optical systems.\nIn terms of a matrix potential $g$, we present a gauge field theoretic\nformulation of the Maxwell-Bloch equation that provides a semiclassical\ndescription of the propagation of optical pulses through resonant multi-level\nmedia. We show that the Bloch part of the equation can solved identically\nthrough $g$ and the remaining Maxwell equation becomes a second order\ndifferential equation with reduced set of variables due to the gauge invariance\nof the system. Our formulation clarifies the (nonabelian) symmetry structure of\nthe Maxwell-Bloch equations for various multi-level media in association with\nsymmetric spaces $G/H$. In particular, we associate nondegenerate two-level\nsystem for self-induced transparency with $G/H=SU(2)/U(1)$ and three-level $\\L\n$- or V-systems with $G/H = SU(3)/U(2)$. We give a detailed analysis for the\ntwo-level case in the matrix potential formalism, and address various new\nproperties of the system including soliton numbers, effective potential energy,\ngauge and discrete symmetries, modified pulse area, conserved topological and\nnontopological charges. The nontopological charge measures the amount of\nself-detuning of each pulse. Its conservation law leads to a new type of pulse\nstability analysis which explains nicely earlier numerical results.",
"arxiv_id": "solv-int/9709002",
"authors": [
"Q-Han Park",
"H. J. Shin"
],
"categories": [
"solv-int",
"nlin.SI"
],
"doi": "10.1103/PhysRevA.57.4621",
"title": "Field Theory for Coherent Optical Pulse Propagation",
"url": "https://arxiv.org/abs/solv-int/9709002"
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