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Topical Meeting on Optical Bistability (OB)

Self-Pulsing, Breathing and Chaos in Optical Bistability and the Laser with Injected Signal

L. A. Lugiato, Lorenzo M. Narducci

Published Jan 1, 1983• 2 citations
Publisher

Abstract

The subject of spontaneous pulsations in Optical Bistability has stimulated considerable interest following its prediction by Bonifacio, and Lugiato1 in the framework of the plane-wave, ring cavity model and the realization by McCall2 of an electro-optical converter of cw coherent light into pulsed radiation. In a subsequent important development Ikeda3 showed that, in the dispersive case, the Bonifacio-Lugiato instability leads to chaotic behavior (optical turbulence). This was later observed in a hybrid device by Gibbs, et al4.

DOI
10.1364/obi.1983.whb2

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Self-pulsing in other optical systems

Luigi A. Lugiato, Franco Prati, Massimo Brambilla

This chapter concludes the discussion about temporal instabilities and self-oscillations, considering the instabilities that arise in the systems analyzed in Chapter 13, with the exception of optical bistability, which has been discussed separately in Chapter 11. Section 25.1 focuses on the laser with an injected signal. As already mentioned in Section 13.1, in this system self-pulsing instabilities are rather ubiquitous, and on exploring the parameter space one meets an extremely rich variety of oscillatory behaviors. For example, under extremely high-gain conditions, breathing, spiking and chaos have been identified over various ranges of the driving field strength [294]. In this section we show some results that arise under parametric conditions that are more accessible experimentally. We illustrate especially the coexistence, for the same parametric values, of different oscillatory behaviors that are reached by starting from different initial conditions. On the other hand, Section 25.2 deals with a laser with a saturable absorber. In this system even the full scenario of stationary intensity solutions in the single-mode model is very complex. For the sake of simplicity, in this section we focus on a simpler rate-equation model that is obtained from the single-mode model of Eqs. (13.13)–(13.17) by adiabatically eliminating the atomic polarization of both active and passive medium. As in Chapter 13, we assume that the atomic transition frequencies are equal and also coincide with a cavity frequency. In this way all the variables in the model can be assumed real, and the linearization around the stationary solution described in Section 13.2 leads to a cubic eigenvalue equation. The spontaneous oscillations which arise from this instability are called repetitive passive Q-switching in the literature. Section 25.3 considers the stability of the stationary solutions of the degenerate optical parametric oscillator described in Section 13.4 and outlines the scenario of period doubling and chaos that arises under appropriate parametric conditions.

Cambridge University Press eBooks•Feb 28, 2015•0 citations

Self-Pulsing, Breathing and Chaos in Optical Bistability and in a Laser with Injected Signal

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The effect of transverse intensity variation on the various instabilities associated with optical bistability seems to be catastrophic in the case of pure absorptive bistability1,2 but benign in the mixed absorptive-dispersive case.2,3 In particular, recent results of Lugiato et al.2 indicate that the mean-field single-mode instability is not destroyed by the assumption of a Gaussian transverse intensity profile, and that it should be observable for experimentally accessible parameter values. Stimulated by these results, we have looked for and observed self-pulsing due to the single-mode instability in the predicted region of parameter space.

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

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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
The subject of spontaneous pulsations in Optical Bistability has stimulated considerable interest following its prediction by Bonifacio, and Lugiato1 in the framework of the plane-wave, ring cavity model and the realization by McCall2 of an electro-optical converter of cw coherent light into pulsed radiation. In a subsequent important development Ikeda3 showed that, in the dispersive case, the Bonifacio-Lugiato instability leads to chaotic behavior (optical turbulence). This was later observed in a hybrid device by Gibbs, et al4.
This chapter concludes the discussion about temporal instabilities and self-oscillations, considering the instabilities that arise in the systems analyzed in Chapter 13, with the exception of optical bistability, which has been discussed separately in Chapter 11. Section 25.1 focuses on the laser with an injected signal. As already mentioned in Section 13.1, in this system self-pulsing instabilities are rather ubiquitous, and on exploring the parameter space one meets an extremely rich variety of oscillatory behaviors. For example, under extremely high-gain conditions, breathing, spiking and chaos have been identified over various ranges of the driving field strength [294]. In this section we show some results that arise under parametric conditions that are more accessible experimentally. We illustrate especially the coexistence, for the same parametric values, of different oscillatory behaviors that are reached by starting from different initial conditions. On the other hand, Section 25.2 deals with a laser with a saturable absorber. In this system even the full scenario of stationary intensity solutions in the single-mode model is very complex. For the sake of simplicity, in this section we focus on a simpler rate-equation model that is obtained from the single-mode model of Eqs. (13.13)–(13.17) by adiabatically eliminating the atomic polarization of both active and passive medium. As in Chapter 13, we assume that the atomic transition frequencies are equal and also coincide with a cavity frequency. In this way all the variables in the model can be assumed real, and the linearization around the stationary solution described in Section 13.2 leads to a cubic eigenvalue equation. The spontaneous oscillations which arise from this instability are called repetitive passive Q-switching in the literature. Section 25.3 considers the stability of the stationary solutions of the degenerate optical parametric oscillator described in Section 13.4 and outlines the scenario of period doubling and chaos that arises under appropriate parametric conditions.
The effect of transverse intensity variation on the various instabilities associated with optical bistability seems to be catastrophic in the case of pure absorptive bistability1,2 but benign in the mixed absorptive-dispersive case.2,3 In particular, recent results of Lugiato et al.2 indicate that the mean-field single-mode instability is not destroyed by the assumption of a Gaussian transverse intensity profile, and that it should be observable for experimentally accessible parameter values. Stimulated by these results, we have looked for and observed self-pulsing due to the single-mode instability in the predicted region of parameter space.
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.