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Lettere al nuovo cimento della societa italiana di fisica/Lettere al nuovo cimento

Instabilities in the laser with injected signal and laser-phase transition analogy

Luigi A. Lugiato

Published Dec 1, 1978• 49 citations
Publisher
DOI
10.1007/bf02772938

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Traveling and standing waves in a laser with an injected signal

Stefano Longhi

A complex order parameter description of the spatiotemporal dynamics close to threshold for a single-longitudinal-mode, large-aspect-ratio laser with a weak injected signal is presented in one transverse spatial dimension and for a longitudinal cavity frequency smaller than the atomic resonance frequency. It is shown that, when the frequency of the external signal is tuned close to the atomic resonance frequency, the spatiotemporal dynamics of the laser may be described by two coupled Ginzburg-Landau equations with parametric terms analogous to those derived in hydrodynamics to study excitation of parametric waves in oscillatory convection. As a result of the parametric terms, which physically arise by means of a four-wave-intercation process mediated by the external signal, the bifurcating modes which are superimposed to the forced (homogeneous) mode may be either traveling or standing waves. In particular, it is shown that for small frequency detunings of the injected signal standing waves are preferred to traveling waves close to threshold. Stability analysis of traveling and standing waves beyond threshold within the amplitude equations reveals the emergence of both phase (Eckhaus) and amplitude instabilities.

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Instabilities in a laser with injected atomic coherence

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We discuss the influence of injected atomic coherence on laser dynamics. The nonlinear equations of motion for the intensity and phase give the dependence on external parameters (inversion, amplitude of the atomic coherence, and cavity-field detuning). Depending on the inversion, there can be one or three steady-state solutions corresponding to a given value of the injected coherence. The situation is analogous to optical bistability, the atomic coherence playing the role of the injected field. For zero detuning the upper, laser-like branch starts at zero value of the injected coherence and a numerical stability analysis indicates that it is the only stable solution, the lower branch being everywhere unstable. For finite detuning the upper branch starts at a finite threshold value of the injected coherence. For coherences smaller than this threshold the system exhibits oscillatory behavior that corresponds to a stable limit cycle in the phase plane of the laser quadrature variables. The intensity fluctuations of the laser exhibit antibunching for sub-Poissonian pumping statistics.

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A New Classification For Optical Instabilities

Luigi A. Lugiato, M. L. Asquini, Lorenzo M. Narducci

We propose a new scheme for the classification of the optical instabilities that emerge within the framework of the Maxwell-Bloch model. Our scheme is based on an appropriate ex-tension of the notions of amplitude and phase instability advanced in earlier publications and generalized in this work to include the free running laser, optical bistability and the laser with an injected signal. We address our considerations to a unidirectional ring cavity model, in the plane wave approximation and with a homogeneously broadened, two-level active medium.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Oct 14, 1986•0 citations
A complex order parameter description of the spatiotemporal dynamics close to threshold for a single-longitudinal-mode, large-aspect-ratio laser with a weak injected signal is presented in one transverse spatial dimension and for a longitudinal cavity frequency smaller than the atomic resonance frequency. It is shown that, when the frequency of the external signal is tuned close to the atomic resonance frequency, the spatiotemporal dynamics of the laser may be described by two coupled Ginzburg-Landau equations with parametric terms analogous to those derived in hydrodynamics to study excitation of parametric waves in oscillatory convection. As a result of the parametric terms, which physically arise by means of a four-wave-intercation process mediated by the external signal, the bifurcating modes which are superimposed to the forced (homogeneous) mode may be either traveling or standing waves. In particular, it is shown that for small frequency detunings of the injected signal standing waves are preferred to traveling waves close to threshold. Stability analysis of traveling and standing waves beyond threshold within the amplitude equations reveals the emergence of both phase (Eckhaus) and amplitude instabilities.
We discuss the influence of injected atomic coherence on laser dynamics. The nonlinear equations of motion for the intensity and phase give the dependence on external parameters (inversion, amplitude of the atomic coherence, and cavity-field detuning). Depending on the inversion, there can be one or three steady-state solutions corresponding to a given value of the injected coherence. The situation is analogous to optical bistability, the atomic coherence playing the role of the injected field. For zero detuning the upper, laser-like branch starts at zero value of the injected coherence and a numerical stability analysis indicates that it is the only stable solution, the lower branch being everywhere unstable. For finite detuning the upper branch starts at a finite threshold value of the injected coherence. For coherences smaller than this threshold the system exhibits oscillatory behavior that corresponds to a stable limit cycle in the phase plane of the laser quadrature variables. The intensity fluctuations of the laser exhibit antibunching for sub-Poissonian pumping statistics.
We propose a new scheme for the classification of the optical instabilities that emerge within the framework of the Maxwell-Bloch model. Our scheme is based on an appropriate ex-tension of the notions of amplitude and phase instability advanced in earlier publications and generalized in this work to include the free running laser, optical bistability and the laser with an injected signal. We address our considerations to a unidirectional ring cavity model, in the plane wave approximation and with a homogeneously broadened, two-level active medium.