Field Theory for Coherent Optical Pulse Propagation

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 $Ł$- 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.

43 pages, Latex, some comments and references are added. postscript file containing 10 figures can be obtained at http://photon.kyunghee.ac.kr/~qhpark/

References in corpus (2)

• Matched Pulse Propagation in a Three-Level System
• The Maxwell-Bloch Theory in Quantum Optics and the Kondo Model

Cited by in corpus (8)

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• Matched Pulse Propagation in a Three-Level System
• Completely integrable models of non-linear optics
• The complex sine-Gordon model on a half line
• Vector-soliton storage and three-pulse-area theorem
• Vortex Strings and Nonabelian sine-Gordon Theories
• On the Generalized Maxwell-Bloch Equations