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Chinese Optics Letters

Effect of phase fluctuation on Hopf bifurcation in a ladder type atomic system

Chengpu Liu, Shangqing Gong, Zhenxun Zheng, Zhizhan Xu

Published Jul 20, 2003• 0 citations
OpenAlex

Abstract

Hopf bifurcation inducing lasing without inversion has been analyzed by taking into account the effect of phase fluctuation in the driving field based on a closed three level ladder-type atomic model. It is shown that due to the phase fluctuation of the driving field, the necessary threshold increases significantly. Furthermore the area domain to get lasing without inversion decreases as the driving field's linewidth increases.

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Hopf bifurcation inducing lasing without inversion has been analyzed by taking into account the effect of phase fluctuation in the driving field based on a closed three level ladder-type atomic model. It is shown that due to the phase fluctuation of the driving field, the necessary threshold increases significantly. Furthermore the area domain to get lasing without inversion decreases as the driving field's linewidth increases.
The steady-state behavior of a simple three-level atomic system has been investigated by taking into account the effect of phase fluctuations in the driving field. For a monochromatic driving field, lasing with or without inversion can be established over a wide frequency range for the probe and driving fields. A large refractive index can also be generated even if the population inversion is positive. For a finite linewidth of the driving field, the refractive index enhancement tends to decrease. Furthermore, a behavior change from inversion laser to noninversion laser can occur as the driving field linewidth increases.
The influence of driving field phase fluctuation on lasing without population inversion in a three-level cascade system was studied. In the rotating wave and slowly varying envelope approximations, the density-matrix motion equations for the three-level cascade system, considered the influence of driving-field phase diffusion is solved, and the exact linear analytical solutions of the three-level cascade system with the driving field having the phase fluctuation in the steady state are obtained. The dependence of LWI gain, dispersion and the populations on the probe field detuning and the strengths of coherent pumping, respectively, are examined and simulated numerically. It was shown from the results of numerical calculation about the steady-state solutions of three-level cascade system that the gain of lasing without population inversion will be decreased due to driving-field phase-fluctuation The effect ran he compensated by increased driving-field intensities. However, the effect that LWI gain is decreased due to driving- field phase-fluctuation can not be always compensated by increased driving field Rabi frequency. Lasing without population inversion is still obtained even if the linewidth due to driving-field phase-fluctuation is large enough. The presence of the linewidth prevents the cascade system from obtaining a high refractive index along with zero absorption. The cascade system can still exhibit a larger refractive index and zero absorption at the lesser linewidth. The linewidth tends to destroy lasing without population inversion and refractive index enhancement. There is no population inversion for the lasing transition and for the driving transition under the given condition. And the condition without population inversion has nothing to do with the variety of linewidth in the steady-state analytical solutions. That is to say, there is not possibility for the cascade system that a change from lasing with population inversion to lasing without population inversion can occur with the linewidth increasing or with the Rabi frequency of driving-field increasing. The conclusion is very different from that obtained in other inversionless lasing system.
The analytical solutions of the gain,dispersion and population difference in the steady state of an open ladder lasing without inversion(LWI) system are at first given when the phase fluctuation of the driving field is considered.Then the effects of the driving field phase fluctuation on the gain,dispersion and population difference are analyzed by the numerical results from the analytical solutions.Our research shows that the phase fluctuation of the driving field will results in a finite line width;with the line width increasing,the gain decreases monotonously,however,variation of the dispersion isnt monotonous,it has a maximum value when the line width takes some value;the line width varying cant lead to change lasing from without to with population inversion.
The steady-state behaviour for a Λ-type, three-level atomic system has been analysed by taking into account the effect of the phase fluctuation. It is shown that, for a monochromatic driving field, even if the probe field is in resonance with the corresponding atomic transition, a large refraction index can still be generated; for a finite linewidth of the driving field, inversionless lasing and index enhancement tends to disappear. Furthermore, the linewidth prevents the transparency of the medium.