### Abstract

Complex order parameter descriptions of large aspect ratio, single longitudinal mode, two-level lasers with flat end reflectors, valid near onset of lasing and for small detunings of the laser from the peak gain, are given in terms of a complex Swift-Hohenberg equation for Class A and C lasers and by a complex Swift-Hohenberg equation coupled to a mean flow for the case of a Class B laser. The latter coupled system is a physically consistent generalized rate equation model for wide aperture stiff laser systems. These universal order parameter equations provide a connection between spatially homogeneous oscillating states of the complex Ginzburg-Landau equation description of the laser system valid for finite negative detunings, and traveling wave states, described by coupled Newell-Whitehead-Segel equations valid for finite positive detunings. One of the main conclusions of the present paper is that the usual Eckhaus instability boundary associated with a long wavelength phase instability, and which delineates the region of the stable traveling wave solutions for Class A and C lasers, no longer defines the stability boundary for the mathematically stiff Class B laser. Instead a short wavelength phase instability appears causing the stability domain to shrink as a function of increasing stiffness of the system. This prediction is consistent with the strong spatiotemporal filamentation instabilities experimentally observed in a borad area semiconductor laser, a Class B system.

Original language | English (US) |
---|---|

Pages (from-to) | 478-498 |

Number of pages | 21 |

Journal | Physica D: Nonlinear Phenomena |

Volume | 83 |

Issue number | 4 |

DOIs | |

State | Published - Jun 1 1995 |

### Fingerprint

### ASJC Scopus subject areas

- Condensed Matter Physics
- Statistical and Nonlinear Physics

### Cite this

**Universal description of laser dynamics near threshold.** / Lega, Joceline C; Moloney, Jerome V; Newell, Alan C.

Research output: Contribution to journal › Article

*Physica D: Nonlinear Phenomena*, vol. 83, no. 4, pp. 478-498. https://doi.org/10.1016/0167-2789(95)00046-7

}

TY - JOUR

T1 - Universal description of laser dynamics near threshold

AU - Lega, Joceline C

AU - Moloney, Jerome V

AU - Newell, Alan C

PY - 1995/6/1

Y1 - 1995/6/1

N2 - Complex order parameter descriptions of large aspect ratio, single longitudinal mode, two-level lasers with flat end reflectors, valid near onset of lasing and for small detunings of the laser from the peak gain, are given in terms of a complex Swift-Hohenberg equation for Class A and C lasers and by a complex Swift-Hohenberg equation coupled to a mean flow for the case of a Class B laser. The latter coupled system is a physically consistent generalized rate equation model for wide aperture stiff laser systems. These universal order parameter equations provide a connection between spatially homogeneous oscillating states of the complex Ginzburg-Landau equation description of the laser system valid for finite negative detunings, and traveling wave states, described by coupled Newell-Whitehead-Segel equations valid for finite positive detunings. One of the main conclusions of the present paper is that the usual Eckhaus instability boundary associated with a long wavelength phase instability, and which delineates the region of the stable traveling wave solutions for Class A and C lasers, no longer defines the stability boundary for the mathematically stiff Class B laser. Instead a short wavelength phase instability appears causing the stability domain to shrink as a function of increasing stiffness of the system. This prediction is consistent with the strong spatiotemporal filamentation instabilities experimentally observed in a borad area semiconductor laser, a Class B system.

AB - Complex order parameter descriptions of large aspect ratio, single longitudinal mode, two-level lasers with flat end reflectors, valid near onset of lasing and for small detunings of the laser from the peak gain, are given in terms of a complex Swift-Hohenberg equation for Class A and C lasers and by a complex Swift-Hohenberg equation coupled to a mean flow for the case of a Class B laser. The latter coupled system is a physically consistent generalized rate equation model for wide aperture stiff laser systems. These universal order parameter equations provide a connection between spatially homogeneous oscillating states of the complex Ginzburg-Landau equation description of the laser system valid for finite negative detunings, and traveling wave states, described by coupled Newell-Whitehead-Segel equations valid for finite positive detunings. One of the main conclusions of the present paper is that the usual Eckhaus instability boundary associated with a long wavelength phase instability, and which delineates the region of the stable traveling wave solutions for Class A and C lasers, no longer defines the stability boundary for the mathematically stiff Class B laser. Instead a short wavelength phase instability appears causing the stability domain to shrink as a function of increasing stiffness of the system. This prediction is consistent with the strong spatiotemporal filamentation instabilities experimentally observed in a borad area semiconductor laser, a Class B system.

UR - http://www.scopus.com/inward/record.url?scp=0001258631&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0001258631&partnerID=8YFLogxK

U2 - 10.1016/0167-2789(95)00046-7

DO - 10.1016/0167-2789(95)00046-7

M3 - Article

VL - 83

SP - 478

EP - 498

JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

SN - 0167-2789

IS - 4

ER -