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Springer eBooks

Effects of the Radial Variation of the Electric Field on Some Instabilities in Optical Bistability and Lasers

L. A. Lugiato, M. Milani

Published Jan 1, 1984• 3 citations
Publisher
DOI
10.1007/978-1-4684-4718-7_57

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Abstract We analyse the simplest model that describes the dynamics of a two-level, optically bistable system in a ring cavity, and incorporates a Gaussian radial variation of the electric field. We find that the most favourable situation to achieve self-pulsing instabilities is that of atomic and cavity detunings with opposite sign. The results are compared with those of plane-wave theory. We show that noise plays a primary role at the onset of self-oscillatory instabilities, and that its effects are governed by an equation formally identical to the Risken equation for the laser.

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Effects of the Radial Variation of the Electric Field on Some Instabilities in Lasers and in Optical Bistability.

Luigi A. Lugiato, M. Milani

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.

Topical Meeting on Optical Bistability (OB)•Jan 1, 1983•0 citations
Abstract We analyse the simplest model that describes the dynamics of a two-level, optically bistable system in a ring cavity, and incorporates a Gaussian radial variation of the electric field. We find that the most favourable situation to achieve self-pulsing instabilities is that of atomic and cavity detunings with opposite sign. The results are compared with those of plane-wave theory. We show that noise plays a primary role at the onset of self-oscillatory instabilities, and that its effects are governed by an equation formally identical to the Risken equation for the laser.
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.