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Physical Review Letters

Origin of periodic, chaotic, and bistable emission from Raman lasers

Robert G. Harrison, Weiping Lu, Pradeep Kumar Gupta

Published Sep 25, 1989• 32 citations
Publisher

Abstract

Single mode homogeneously broadened Raman laser emission is shown to be mathematically reducible to a simple description similar to that of the Haken-Lorenz model. However, the physically distinct lasing mechanism involving a two-photon interaction with an equivalent two-level system in a noninverted state allows for considerably relaxed operating conditions where periodic, chaotic, and bistable behavior are identified. Results are in good accord with earlier experiments.

DOI
10.1103/physrevlett.63.1372

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Physical Review A•Jun 1, 1994•0 citations
Single mode homogeneously broadened Raman laser emission is shown to be mathematically reducible to a simple description similar to that of the Haken-Lorenz model. However, the physically distinct lasing mechanism involving a two-photon interaction with an equivalent two-level system in a noninverted state allows for considerably relaxed operating conditions where periodic, chaotic, and bistable behavior are identified. Results are in good accord with earlier experiments.
Detailed analysis of the steady-state and dynamical unstable behavior of single-mode, homogeneously broadened Raman lasers is presented. Bistable features of the Raman emission and its operating conditions are determined from steady-state analysis. Parametrization of the dynamical behavior shows instabilities to exist over a broad range of operation conditions and for broad cavity detuning to the low-frequency side of the gain center where the bistable emission also prevails. Notably, period-doubling routes to chaos and sustained oscillatory behavior in both intensity and phase are found to occur for both good and bad cavity conditions, the dynamics of the phase revealing additional temporal features to that of intensity.
In 1966 Haken and Risken, Schmid and Weidlich(1) showed that under proper conditions the stationary state of a homogenously broadened, single mode ring laser can become unstable. The instability requires a "bad cavity" situation, i.e. the cavity damping constant must be larger than the atomic decay rates. Later, Haken(2) proved that such an instability coincides with the well known Lorenz instability, which leads to chaotic behaviour. On the other hand, Risken and Nummedal and independently Graham and Haken(3) analyzed the homogeneously broadened ring laser taking into account all the longitudinal cavity modes. They showed that under appropriate conditions in the good cavity case some cavity modes, different from the one resonant with the atomic system, can become unstable. In this case, one has the formation of a pulse that travels in the cavity. In 1978, Bonifacio and Lugiato(4) showed that a similar self-pulsing behaviour in good cavity conditions occurs in optical bistability in a ring cavity filled with a homogeneously broadened atomic sample.
The behavior of a cascade laser in which two fields are simultaneously amplified is theoretically investigated. Each field is coupled with one of the transitions of a ladder three- level atomic or molecular system in conditions of homogeneous broadening. Steady-state as well as dynamic solutions are considered. Cooperative emission of both fields is found in steady state regime. Single-field solutions can loose stability through two different types of Hopf bifurcations. One of them can appear below the Lorenz-Haken second laser threshold, and the `bad cavity' condition is not necessarily required. In the unstable regimes transitions to chaos via the quasiperiodicity road are found. The influence of cavity detuning and the passage from cascade to two-photon laser are considered.