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Chinese Journal of Quantum Electronics

Transient analysis of laser without inversion in an open system

Haiying Liu

Published Jan 1, 2008• 0 citations
OpenAlex

Abstract

In an open V-type system,by numerical results of differential equations,the physical mechanism of laser without inversion(LWI) was analyzed,and the effects of the probe and driving fields detunings, the Rabi frequencies of the driving fields,and the initial values of the populations on LWI transient were discussed.The conclusions show that the populations of the two levels coupled by the driving field have the same oscillation frequency,however,exist a phase differenceπ.The dispersion equals to zero and two- photon coherent item is real number when the driving and the probe fields are both resonant.Oscillation period of the gain,coherent item and population difference reduce with the increase of the Rabi frequencies of the driving field.The initial vaiues of the populations mainly affect the oscillation amplitudes of the gain, coherent item and population difference but don't affect their values in the steady state.

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Journal of Optoelectronics·laser•Jan 1, 2002•0 citations
In an open V-type system,by numerical results of differential equations,the physical mechanism of laser without inversion(LWI) was analyzed,and the effects of the probe and driving fields detunings, the Rabi frequencies of the driving fields,and the initial values of the populations on LWI transient were discussed.The conclusions show that the populations of the two levels coupled by the driving field have the same oscillation frequency,however,exist a phase differenceπ.The dispersion equals to zero and two- photon coherent item is real number when the driving and the probe fields are both resonant.Oscillation period of the gain,coherent item and population difference reduce with the increase of the Rabi frequencies of the driving field.The initial vaiues of the populations mainly affect the oscillation amplitudes of the gain, coherent item and population difference but don't affect their values in the steady state.
With the density matrix equations of motion under the electric dipole and the rotating wave approximations,the mechanism of LWI gain was analyzed.By numerical results,the effects of the Rabi frequencies of the driving fields and nonlinear term on the gain without inversion and the population difference of the system were studied.Theoretical model of an openⅤ-type four-level atomic system was presented.Through calculation,when both the probing and driving fields are resonant,the dispersion equals to zero.A LWI gain was got during the region of Rabi frequencies of the driving fields.The gain was saturated because of nonlinear term.
The law of time evolution of atomic response in an open V type lasing without inversion (LWI) system with two incoherent pumps is investigated by the numerical results.Following conclusions are shown:the time evolution of the populations of the two levels coupled by the probe field has the same oscillation frequency,however,exists a phase difference π;the initial values of the populations affect mainly the oscillation amplitudes of the gain,coherent item and population difference but dont affect their values in the steady state;the ratio of the atomic injection rates increasing will results in an increase of the gain and a decrease of the population difference in the steady state;the atomic exit rate increasing will make both the gain and population difference in the steady state decreasing.
A model for an open four-level atomic system driven by two fields is presented.Density matrix equations of motion are obtained by electric dipole and rotating wave approximations.Physical mechanism of lasing without inversion(LWI) is discussed.Effects of detuning on gain without inversion and population difference are studied.Dispersion equals to zero as two driving and probe fields are resonant.As one driving field(probe field) is resonant,the gain and the population difference versus detuning of driving field(probe field)show even symmetry,and the dispersion shows central symmetry.As two or three of driving and probe fields are off-resonance,the symmetries disappear.LWI gain is obtained when the dispersion equals to zero.When both driving and probe fields are off-resonance,the gain,the dispersion and the population difference change greatly.High dispersion without absorption is obtained by adjusting suitable parameters of the system.
Theoretical model of an open four-level atomic system driven by two fields was presented. The density matrix equations of motion were obtained by the electric dipole and the rotating wave approximations. Under resonance of corresponding fields, the physical mechanism of lasing without inversion (LWI) was discussed and its linear analytical solution was obtained. By numerical results, we studied the effects of the spontaneous decay rates between atomic levels, incoherent pump rate, the injection rates, and the exit rate on the gain without inversion and the population difference of the system. The difference between the linear and nonlinear gain and the population difference of the system were discussed. A LWI gain was got during the region of the spontaneous decay rates between atomic levels. The LWI gain can obtain by adjusting suitably incoherent pump rate, the atomic injection ratio and the exit rate. The curves of the linear gain and the nonlinear gain were similar with the Rabi frequencies of the driving fields. The curves of the linear population difference and the nonlinear population difference were similar too. The linear stable value of the gain was larger than the nonlinear stable value of the gain.
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.