TY - JOUR

T1 - Universal description of laser dynamics near threshold

AU - Lega, J.

AU - Moloney, J. V.

AU - Newell, A. C.

N1 - Funding Information:
The authors wish lo thank the Arizona Center for Mathematical Sciences (ACMS) for support. ACMS is sponsored by AFOSR contract F49620-94-I-0144DEF. The authors acknowledge support from University College Cork. J.V. Maloney and J. hga were supported in part under a European Economic Community Twinning Grant SCI-0325C( SMA), and J. Lega received support from CNRS (Centre National de la Recherche Scientifique) in the framework of a CNRS/EOJ,AS international cooperation.

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.

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

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

M3 - Article

AN - SCOPUS:0001258631

VL - 83

SP - 478

EP - 498

JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

SN - 0167-2789

IS - 4

ER -