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Acta Optica Sinica

Ikeda instability and degree of stability in optical bistability

Ong J

Published Jan 1, 1985• 1 citation
OpenAlex

Abstract

The degree of stability which describes intensity of feedback is introduced into the dynamic equations of optical bistability with delayed feedback. In addition to relative delay time, the degree of stability also affects the instability behaviors of the system, including threshold condition and oscillation modes of instability. The threshold condition of instability is (S≥2 for long delay and S≥1+π/2Q for short delay. The experiment by a hybrid OBD shows oscillation, bifurcation and chaos and verities theoretical analysis. The results show the close relation between Ikeda instability and stability in OBD. New basis to realize Ikeda instability in intrinsic OBD has been provided.

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The periodic and chaotic behaviors for both long and short delay time are demonstrated successfully using a hybrid OBD. The degree of stability S is introduced into the dynamic equations of optical bistability with a delayed feedback. The instability threshold is S = 2 for long delay time and S = 1 + π/2 Q for short delay time.

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In the linear instability analysis of the difference-differential equation which describes the dynamic behaviors of optical bistability with delayed feedback, introducing degree of stability S, which is defined as the ratio between relative variations of input and output intensities(1), we find that for long delay time instability condition is S≥2 and possible oscillation periods are approximately T ¯ = 2 T / ( 2 n + 1 ) but for short delay time the condition is S≥1 + πτ/2T and the periods are T ¯ = 4 T / ( 4 n + 1 ) . So the generation of instability for long delay time is easier than for short one, as shown in Fig.1.

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Although the discovery of oscillatory instabilities (both single-mode and multimode) in free-running lasers was achieved in the 1960s, investigations on oscillatory instabilities in optical bistability did not take place until the 1970s and 1980s. The first section of this chapter does not deal with oscillatory instabilities, but instead concerns an interesting dynamical phenomenon in optical bistability that arises when the input field approaches a boundary of the bistable domain, and is called critical slowing down . This has been investigated both theoretically and experimentally. The remainder of this chapter is entirely devoted to oscillatory instabilities, following a historical order. With an inverse approach with respect to the laser case, we discuss multimode instabilities first. In Section 24.2.1 we start with the description of the instability which arises under exactly resonant conditions. While this is the counterpart in optical bistability of the resonant multimode laser instability discussed in Section 22.5, a striking difference from the laser case is that in the passive configuration there is no corresponding single-mode instability. This difference disappears, however, when we consider the generalization of the multimode instability of optical bistability to the detuned configuration. Finally we show that in the detuned case it has been possible to achieve a convincing experimental observation of the multimode instability in a long microwave cavity. After some relevant miscellaneous considerations in Section 24.2.2, in Section 24.2.3 we address the subject of the multimode Ikeda instability which leads to period doubling and chaos and aroused a lot of interest in optical chaos. We emphasize also the intrinsic connections with the standard multimode instability discussed in Section 24.2.1, showing, in particular, that the Ikeda instability requires conditions far from the low-transmission limit, i.e. that ∝L is not small. In Section 24.3 we discuss single-mode instabilities in optical bistability. In Section 24.3.1 we illustrate a configuration for the single-mode instability that includes also the Gaussian shape of the electric field in the beam section, and leads to periodic, close-to-sinusoidal self-pulsations.

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

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A single-mode dynamic equation is obtained from the Maxwell equation with the slowly-varying amplitude approximation, and the boundary conditions of the cavity. Here the mean-field limit and the good-quality cavity case have been used. This equation is useful in describing the dynamic behavior of intrinsic optical bistable systems and/or lasers with injected signals for any kinds of materials, including two-level atoms. Furthermore, according to the linear stability analysis, a generalized instability criterion is derived.

Acta Physica Sinica•Jul 1, 1989•0 citations

Spatial and temporal instabilities of light fields in cavity-free optical bistable systems

Vyacheslav A. Trofimov

Physical reasons for the development of spatial and temporal instabilities realizing in optical bistability (OB) cavity- free systems are analyzed. It is shown that there are certain types of instability. We describe diffraction instability of light beams due to its propagation through a boundary on a high absorption domain. We consider instability generated by nonlinear dependence of a relaxation time of excited states of atoms (molecules) on vibration temperature or on room temperature under the condition of presence (or absence) of nonlinear absorption. We investigate instability due to an influence of laser- induced electric field and instability caused by the delay in a scheme with additional lateral feedback and instability in a scheme with mirror having a hole at its axis caused by dynamical lenses.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Jan 28, 1999•3 citations
The degree of stability which describes intensity of feedback is introduced into the dynamic equations of optical bistability with delayed feedback. In addition to relative delay time, the degree of stability also affects the instability behaviors of the system, including threshold condition and oscillation modes of instability. The threshold condition of instability is (S≥2 for long delay and S≥1+π/2Q for short delay. The experiment by a hybrid OBD shows oscillation, bifurcation and chaos and verities theoretical analysis. The results show the close relation between Ikeda instability and stability in OBD. New basis to realize Ikeda instability in intrinsic OBD has been provided.
In the linear instability analysis of the difference-differential equation which describes the dynamic behaviors of optical bistability with delayed feedback, introducing degree of stability S, which is defined as the ratio between relative variations of input and output intensities(1), we find that for long delay time instability condition is S≥2 and possible oscillation periods are approximately T ¯ = 2 T / ( 2 n + 1 ) but for short delay time the condition is S≥1 + πτ/2T and the periods are T ¯ = 4 T / ( 4 n + 1 ) . So the generation of instability for long delay time is easier than for short one, as shown in Fig.1.
Although the discovery of oscillatory instabilities (both single-mode and multimode) in free-running lasers was achieved in the 1960s, investigations on oscillatory instabilities in optical bistability did not take place until the 1970s and 1980s. The first section of this chapter does not deal with oscillatory instabilities, but instead concerns an interesting dynamical phenomenon in optical bistability that arises when the input field approaches a boundary of the bistable domain, and is called critical slowing down . This has been investigated both theoretically and experimentally. The remainder of this chapter is entirely devoted to oscillatory instabilities, following a historical order. With an inverse approach with respect to the laser case, we discuss multimode instabilities first. In Section 24.2.1 we start with the description of the instability which arises under exactly resonant conditions. While this is the counterpart in optical bistability of the resonant multimode laser instability discussed in Section 22.5, a striking difference from the laser case is that in the passive configuration there is no corresponding single-mode instability. This difference disappears, however, when we consider the generalization of the multimode instability of optical bistability to the detuned configuration. Finally we show that in the detuned case it has been possible to achieve a convincing experimental observation of the multimode instability in a long microwave cavity. After some relevant miscellaneous considerations in Section 24.2.2, in Section 24.2.3 we address the subject of the multimode Ikeda instability which leads to period doubling and chaos and aroused a lot of interest in optical chaos. We emphasize also the intrinsic connections with the standard multimode instability discussed in Section 24.2.1, showing, in particular, that the Ikeda instability requires conditions far from the low-transmission limit, i.e. that ∝L is not small. In Section 24.3 we discuss single-mode instabilities in optical bistability. In Section 24.3.1 we illustrate a configuration for the single-mode instability that includes also the Gaussian shape of the electric field in the beam section, and leads to periodic, close-to-sinusoidal self-pulsations.
A single-mode dynamic equation is obtained from the Maxwell equation with the slowly-varying amplitude approximation, and the boundary conditions of the cavity. Here the mean-field limit and the good-quality cavity case have been used. This equation is useful in describing the dynamic behavior of intrinsic optical bistable systems and/or lasers with injected signals for any kinds of materials, including two-level atoms. Furthermore, according to the linear stability analysis, a generalized instability criterion is derived.
Physical reasons for the development of spatial and temporal instabilities realizing in optical bistability (OB) cavity- free systems are analyzed. It is shown that there are certain types of instability. We describe diffraction instability of light beams due to its propagation through a boundary on a high absorption domain. We consider instability generated by nonlinear dependence of a relaxation time of excited states of atoms (molecules) on vibration temperature or on room temperature under the condition of presence (or absence) of nonlinear absorption. We investigate instability due to an influence of laser- induced electric field and instability caused by the delay in a scheme with additional lateral feedback and instability in a scheme with mirror having a hole at its axis caused by dynamical lenses.