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ACTA PHOTONICA SINICA

Studies of Lasing Without or with Inversion in Open Four-Level Atomic System

Guangyuan Li

Published Jan 1, 2007• 0 citations
OpenAlex

Abstract

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.

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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.
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 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.
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.
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.
The LWI operation condition for an open Λ-type three level atomic system is obtained by solving the steady-state density-matrix equation with the system being driven by a strong coherent field while the inherent pumping rate and decay rate being arbitrary.It is shown that the inversions of inherent pumping rate and spontaneous decay rate replace the inversion of population,and together help to realize lasing without population inversion.Furthermore,the LWI can be realized if just either one of the two inversions is fulfilled.A schrodinger equation of three-level atomic system with appropriate conditions is analytically solved to explain the quantum interference process that leads to LWI.