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Chinese Journal of Luminescence

Phase Diffusion Effect on Inversionless Lasing in a Three-level Upper-ladder System

朱孟正 Zhu Meng-zheng, 赵春然 Zhao Chun-ran, 尹新国 YIN Xin-guo

Published Jan 1, 2011• 1 citation
Publisher

Abstract

In the rotating wave and slowly varying envelope approximations,the density-matrix motion equations for the three-level cascade system equation are solved under the influence of driving-field phase diffusion.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 effects of phase diffusion on absorption,dispersion and population difference in a three-level upper-ladder system and on the time of steady-state limit in the course of time evolution have been analyzed by using the numerical simulation from the steady linear,analytical solution and density-matrix motion equations.Gain of the probe field will be decreased due to the driving-field phase diffusion.The presence of the finite linewidth induced by the driving-field phase diffusion prevents the ladder system from obtaining a high refractive index along with zero absorption.Variation of the linewidth can not change the property of the lasing in the upper-ladder system.The linewidth as a result of the driving-field phase diffusion has influence to the time of steady state limit and the phase diffusion leads to a decay of the coherence in the course of time evolution.

DOI
10.3788/fgxb20113202.0174

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In the rotating wave and slowly varying envelope approximations,the density-matrix motion equations for the three-level cascade system equation are solved under the influence of driving-field phase diffusion.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 effects of phase diffusion on absorption,dispersion and population difference in a three-level upper-ladder system and on the time of steady-state limit in the course of time evolution have been analyzed by using the numerical simulation from the steady linear,analytical solution and density-matrix motion equations.Gain of the probe field will be decreased due to the driving-field phase diffusion.The presence of the finite linewidth induced by the driving-field phase diffusion prevents the ladder system from obtaining a high refractive index along with zero absorption.Variation of the linewidth can not change the property of the lasing in the upper-ladder system.The linewidth as a result of the driving-field phase diffusion has influence to the time of steady state limit and the phase diffusion leads to a decay of the coherence in the course of time evolution.
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.
A steady analytical solution of an open four-level inversionless lasing system with a driving field having the phase fluctuation has been given, and the effects of the finite width due to the phase fluctuation on the gain, dispersion, and population difference have been analyzed by using the numerical simulation from the steady analytical solution. It is found that: with the linewidth increasing, the gain decreases and the absolute value of population difference between levels coupled by the probe field increases, but the variation of the linewidth cannot change the properties of the inversionless lasing and refractive index increase of the system; when the linewidth does not equal to zero, the system can still get a high refractive index with zero absorption, and these conclusions have very obvious difference from those obtained in other inversionless lasing systems.
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 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 effect of exit rate and the ratio of atomic injection rate on gain behaviour has been investigated, and the effects of phase fluctuation on absorption, dispersion and population difference in an open four-level system have been analysed by using numerical simulation from the steady linear, analytical solution. The variation of the linewidth, Rabi frequency of the driving field, the exit rate or the ratio of atomic injection rate can change the lasing properties in the open system. The presence of finite linewidth due to driving-field phase fluctuation prevents the open four-level atomic system from obtaining a high refractive index along with zero absorption.
The model of an open four-level atomic system is presented on the basis of the closed four-level atomic system. In the rotating wave, slowly varying envelope and mean field approximations, the density-matrix motion equations of the system are solved, and the linear analytical solution in the steady state is obtained. The numerical calculation from the steady-state solution of the open system is presented. It is shown that a change from LWI to lasing with inversion action can occur due to the Rabi frequency of the driving field increasing; another change from lasing with inversion to LWI action can also occur as the exit rate or ratio of injection rates increases; high refractive index without absorption can be obtained; the curve of ρ33-ρ11(vs Δ2) presents the shape of the rectangle wave.