Multimode instabilities in a homogeneously broadened ring laser

Journal Article · Sun Sep 01 04:00:00 EDT 1985 · Phys. Rev. A; (United States)

DOI:https://doi.org/10.1103/PhysRevA.32.1563· OSTI ID:5451178

Lugiato, L A; Narducci, L M; Eschenazi, E V; Bandy, D K; Abraham, N B

This paper contains a description of the behavior of a multimode unidirectional ring laser with a homogeneously broadened active medium. Our formulation is based on the conventional Maxwell-Bloch (MB) equations, but is distinguished from other treatments by the inclusion of a finite mirror reflectivity and an arbitrary value of the gain parameter. We review the steady-state behavior of the system and analyze the longitudinal profile of the field and of the atomic variables. With an appropriate transformation of variables, we transform the boundary conditions of the ring cavity into standard periodicity type, even in the presence of a finite reflectivity, and derive an infinite hierarchy of coupled mode equations. We analyze exactly the linear stability of the system, and investigate the dependence of the instability domain on the reflectivity and gain parameters. A numerical study of the full MB equations for a parameter range of the type explored in the recent experiments by Hillman et al. (Phys. Rev. Lett. 52, 1605 (1984)) reveals similarities, but also considerable differences between the results of the theory and the main experimental signatures of their instability. However, the injection of numerical noise shows the presence of numerous coexisting basins of attraction which are likely to play a significant role in the dynamics of a noisy laser.

• Research Organization: Dipartimento di Fisica dell'Universita degli Studi di Milano, via Celoria 16, I-20133 Milano, Italy
• OSTI ID: 5451178
• Journal Information: Phys. Rev. A; (United States), Journal Name: Phys. Rev. A; (United States) Vol. 32:3; ISSN PLRAA
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
420300* -- Engineering-- Lasers-- (-1989)
AMPLIFICATION
DIFFERENTIAL EQUATIONS
EQUATIONS
GAIN
INSTABILITY
LASERS
MAXWELL EQUATIONS
MIRRORS
NOISE
OPTICAL PROPERTIES
OSCILLATION MODES
PARAMETRIC ANALYSIS
PARTIAL DIFFERENTIAL EQUATIONS
PHYSICAL PROPERTIES
REFLECTIVITY
RING LASERS
SURFACE PROPERTIES