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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Nonlinear output and critical behaviors of an optical multistable amplifier with conjugate polymer

Tingwan Wu, Yunjun Yu, Chao Li

Published Sep 16, 2002• 0 citations
Publisher

Abstract

This paper presents some results on the nonlinear output charactertistics and critical behaviors of a nonlinear optical system with conjugate polymer like polydiacetylenes, in a three-level model. Based on the model of interaction of this kind of matter with the pumping field, probing field and coherent field, the nonlinear susceptibility deduced by the method of the density matrix element, and the multistable output characteristics and effects of lasing or lasing wihtout inversion are furthe studied, using the dynamic equation of the 'forced oscillation model of laser and bistability'. On the other hand, through the approach of 'quasi-thermal dynamics', we analyzed the properites of the critical point of the system. The result shows that when the system is set on a tri-stable situation there exist an unstable critical point of second kind phase transiton and near which the behavior of the system had not been reported before, as we know.

DOI
10.1117/12.483102

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This paper presents some results on the nonlinear output charactertistics and critical behaviors of a nonlinear optical system with conjugate polymer like polydiacetylenes, in a three-level model. Based on the model of interaction of this kind of matter with the pumping field, probing field and coherent field, the nonlinear susceptibility deduced by the method of the density matrix element, and the multistable output characteristics and effects of lasing or lasing wihtout inversion are furthe studied, using the dynamic equation of the 'forced oscillation model of laser and bistability'. On the other hand, through the approach of 'quasi-thermal dynamics', we analyzed the properites of the critical point of the system. The result shows that when the system is set on a tri-stable situation there exist an unstable critical point of second kind phase transiton and near which the behavior of the system had not been reported before, as we know.
This paper studies the characteristics of the nonlinear optical system in a model, which may be considered as that containing conjugate polymer, such as polydiacetylense. The dynamic equations are established through the approach of density matrix elements. The parameter conditions of laser and lasing without inversion (LWI) are discussed and the thresholds of pumping and probing fields to produce LWI are determined. The nonlinear susceptibility of the system is deduced from the density matrix equations and the forced oscillation model of laser and bistability is used to study the bi- or multi-stability of the system under lasing, or inversion without lasing (IWL) and LWI conditions. The results indicate that to realize OB or OM output in IWL or LWI situation, there must be some additional conditions on the relaxation and transition rates, also the critical output light intensity. Finally, theoretical analysis and numerical computing show that there exists unstable critical point of second kind phase transition, in such tri-stable state.
In this paper the results of study on the nonlinear and lasing output characteristics of an organic polymer system, are presented. To describe the dynamics of light field in the medium, the forced oscillation model of optical multi-stable and lasing system are used. For the matter model, the material with the conjugate structure, such as polydiacetylenes which energy structure can be reduced to a three-level system considered; meanwhile the approach of efficient susceptibility is used to deduce the nonlinear susceptibility. Under these conditions, theoretical analyzing and numerical simulation shows that the system appears special output characteristics and dynamic behaviors, also instability, responding to the incident signal, especially when it satisfies both the gain condition of amplifying and that of multi-stable states. Further, the relationship between the detuning and the conditions of light amplification in this system are given out. Moreover, we find the detuning condition can describe and generalize the "frequency pulling effect", in proper situation.
This paper presents some new study results on the threshold conditions and characteristics of lasing output for an organic polymer optical multi-stable system in which the medium is with pumping and the system acted with inject signal. The dynamics of light field in the medium are described with the extended forced oscillation model of optical multi-stable and lasing system. Moreover, through the theoretical analysis and numerical analogue, the gain threshold condition of amplifying under population reversion is discussed. Meanwhile the characteristics of the lasing output state with inject signal inspected. Further, the relationships of the amplifying multiple of the incident light field with the cavity detuning; and that with the two-photon detuning; also that between the two kinds detuning are found by analyzing the stationary equations. Finally, theoretical and numerical analyzing shows that the lasing frequency characteristic of such an organic polymer system with pumping and inject signal is different from the common laser. These results should be significant in some degree for both theoretical and experimental research, also application purpose.
In this paper, some new results of the study on the bistability and the instability of semiconductor optical amplifier are presented, which may be expected to be available to a class of excitonic optical bistable and amplifying systems. For these systems, both saturation and increasing absorptive bistability will product, depending on the competition among the interactions in the medium, especially the nonlinear couplings, and the lasing conditions. Particularly, the output curve appears a novel feature of optical hysteresis, with amplifying effect as well. On the other hand, the instability of the stationary states is investigated by linear stability analyzing. Some new phenomena of 'critical slowing down' are discovered near the relevant critical points, in the dynamic responding course.
The semiclassical equations which describe the behaviours of three-level lasers were derived. The method of nonlinear mechanics was used to treat the electromagnetic oscillations coupled with the dipole moments of molecules. It is shown that when the pumping power is larger than the critical value, the amplitude of output oscillations is stable (corresponding to a stable equilibrium point in phase space), only if the homogeneous line width of molecules (1/T 2 ) is larger than the damping width of the resonan-tor (q). The appearance of instability of output oscillations is due to the effect of coherence. Furthermore, a stable limit cycle was shown to appear when the above mentioned equilibrium point becomes unstable as qT 2 increases. Therefore, it seems true that there is no limit cycle near the equilibrium point when it is stable. These results may account for the instability of amplitude of output oscillations observed by some authors in ruby lasers, and should be checked in detail with gas lasers.
For a polymer inside an optical cavity, optical multistability mediated by phonon modes and virtual exciton coupling is investigated. The cavity field, excitons, and phonon modes are treated as damped oscillators, and the equations of motion for the dynamical variables are obtained by applying Dekker's theory for dissipative systems. Steady-state results are obtained numerically for polydiacetylene [bis(p-toluene sulfonate)] with the input field frequency on or off resonance with the cavity field. The variation of the cavity-field intensity follows a reversed hysteresis loop on resonance, while it may follow either a normal or a reversed hysteresis loop off resonance depending on the course of change of the driving-field intensity at the unstable turning point. The variation is inverted when the detuning changes its sign. It is also found that the virtual excitons, phonon modes, and feedback of the cavity are all indispensable to such tristability.