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Acta Optica Sinica

Theoretical analysis of complex amplitude of vibration for multi-photon optical Instability

Maxim A. Abakumov

Published Jan 1, 1988• 0 citations
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Abstract

In this paper, the theory of linear stability analysis is used in analyzing the complex amplitude of vibration of multi-photon optical bistability which was described by semiolassical Maxwell-Blooh equations. The results of analysis show that after the adiabatio elimination being acted to atomic polarization there is no instability on cooperation branch and one single branch of multi-photon optical bistability characteristic, showing that there is no chaos of multi-photon optical bistability which was caused by the instability of the soft mode at the same time. It has been indicated that the third condition of stability is related to bistable characteristic of multi-photon optical bistability.

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Ikeda instability and degree of stability in optical bistability

Ong J

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.

Acta Optica Sinica•Jan 1, 1985•1 citation
In this paper, the theory of linear stability analysis is used in analyzing the complex amplitude of vibration of multi-photon optical bistability which was described by semiolassical Maxwell-Blooh equations. The results of analysis show that after the adiabatio elimination being acted to atomic polarization there is no instability on cooperation branch and one single branch of multi-photon optical bistability characteristic, showing that there is no chaos of multi-photon optical bistability which was caused by the instability of the soft mode at the same time. It has been indicated that the third condition of stability is related to bistable characteristic of multi-photon optical bistability.
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.
In this paper a quantum mechanics model for describing multiphoton optical bistability is given. Based on this molel, the state equation of multi-photon option1 bistability is obtained. The method which for calculating the threshold of multi-photon optical bistability is also given. After analyzing the potential function, we obtain the statics stability criterion and the explanation of switching characteristics. The stable region and the inferior stable region in the bistability characteristic curve are separated. In fact, multiphoton optical stable states are actually multi-photon optical stable-inferior stable states. We also discuss the phase transition problem of multi-photon optical bistability and multi-photon lasers.
A single-mode dynamical equation is obtained from the Maxwell equation with the slowly varying amplitude approximation and the boundary conditions of the cavity, here the mean field limir and the good quality cavity case have been used. This equation is useful in describing the dynamical behavior of intrinsic optical bistable systems and/or lasers with injected sig-nals for any kinds of materials including two-level atoms. Furthermore, according to the li--near stability analysis, a generalized instability criterion is derived.
A single-mode dynamical equation is obtained from the Maxwell equation with the slowly varying amplitude approximation and the boundary conditions of the cavity, here the mean field limir and the good quality cavity case have been used. This equation is useful in describing the dynamical behavior of intrinsic optical bistable systems and/or lasers with injected sig-nals for any kinds of materials including two-level atoms. Furthermore, according to the li-near stability analysis, a generalized instability criterion is derived.
The cooperative behavior of a system of atoms contained in a ring cavity is investigated under the condition that the fundamental atomic transition is a two photon transition1. Maxwell-Block equations are used to obtain the input vs. output relation by adiabatically eliminating all the atomic variables. The fundamental equation that results is a complex two dimensional map--which in the mean field limit reduces to the standard bistability equations. The characteristics of the two dimensional map are numerically investigated. Such a map is shown to lead to chaotic behavior following the Feigenbaum2 scenario. The sequence of events following first regime of chaos is a set of period halving bifurcations. The characteristics of the power spectrum in the region of chaos are presented. The effect of noise on the period doubling bifurcations in the present model, is also investigated and the connection with the theoretical predictions3 is established. The changes in the dynamical characteristics of the system when atomic inversion relaxes on the same time scale as the cavity round trip time will also be discussed in detail.
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.