### Abstract

We introduce a 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 multilevel media. We show that the Bloch part of the equation can be solved identically through g and the remaining Maxwell equation becomes a second-order differential equation with a reduced set of variables due to the gauge invariance of the system. Our formulation clarifies the (non-Abelian) symmetry structure of the Maxwell-Bloch equations for various multilevel media in association with symmetric spaces G/H. In particular, we associate the nondegenerate two-level system for self-induced transparency with G/H = SU(2)/U(1) and three-level A 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 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 different type of pulse stability analysis that explains earlier numerical results.

Original language | English |
---|---|

Pages (from-to) | 4621-4642 |

Number of pages | 22 |

Journal | Physical Review A - Atomic, Molecular, and Optical Physics |

Volume | 57 |

Issue number | 6 |

Publication status | Published - 1998 Dec 1 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Atomic and Molecular Physics, and Optics

### Cite this

*Physical Review A - Atomic, Molecular, and Optical Physics*,

*57*(6), 4621-4642.

**Field theory for coherent optical pulse propagation.** / Park, Q Han; Shin, H. J.

Research output: Contribution to journal › Article

*Physical Review A - Atomic, Molecular, and Optical Physics*, vol. 57, no. 6, pp. 4621-4642.

}

TY - JOUR

T1 - Field theory for coherent optical pulse propagation

AU - Park, Q Han

AU - Shin, H. J.

PY - 1998/12/1

Y1 - 1998/12/1

N2 - We introduce a 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 multilevel media. We show that the Bloch part of the equation can be solved identically through g and the remaining Maxwell equation becomes a second-order differential equation with a reduced set of variables due to the gauge invariance of the system. Our formulation clarifies the (non-Abelian) symmetry structure of the Maxwell-Bloch equations for various multilevel media in association with symmetric spaces G/H. In particular, we associate the nondegenerate two-level system for self-induced transparency with G/H = SU(2)/U(1) and three-level A 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 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 different type of pulse stability analysis that explains earlier numerical results.

AB - We introduce a 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 multilevel media. We show that the Bloch part of the equation can be solved identically through g and the remaining Maxwell equation becomes a second-order differential equation with a reduced set of variables due to the gauge invariance of the system. Our formulation clarifies the (non-Abelian) symmetry structure of the Maxwell-Bloch equations for various multilevel media in association with symmetric spaces G/H. In particular, we associate the nondegenerate two-level system for self-induced transparency with G/H = SU(2)/U(1) and three-level A 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 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 different type of pulse stability analysis that explains earlier numerical results.

UR - http://www.scopus.com/inward/record.url?scp=0032099236&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0032099236&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0032099236

VL - 57

SP - 4621

EP - 4642

JO - Physical Review A - Atomic, Molecular, and Optical Physics

JF - Physical Review A - Atomic, Molecular, and Optical Physics

SN - 1050-2947

IS - 6

ER -