Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Jisuan wuli

Detuning in Open Four-level Inversionless Lasing Systems

Ping Li

Published Jan 1, 2008• 0 citations
OpenAlex

Abstract

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.

Related papers

Study on an open four-level inversionless lasing system driven by two intense fields

Pei‐ji Wang

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.

Chinese Journal of Quantum Electronics•Jan 1, 2007•0 citations

Study on an Open V-Type Four-Level Inversionless Lasing System

Xinlian Chen

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.

Journal of Shandong Jiaotong University•Jan 1, 2010•0 citations

Effect of Relative Phase on Probe Response in Open Four-level System

Fan Xi-jun

The effect of the relative phase Φ between the probe and driving fields on gain and dispersion from different aspects in an open quasi-type four-level system by the numerical solution of the steady state was investigated.The results show that by adjusting the value of the relative phase the inversionless gain and dispersion can be periodically amplified and attenuated.High dispersion (refractive index) without absorption can be achieved.The dispersion curve corresponding to Φ=α is similar to the gain curve corresponding to Φ=α+π/2.When the probe field is on resonance,the largest lasing without inversion (LWI) gain can be obtained by adjusting the relative phase.The effect of the atomic exit and injection rates on the LWI gain for different values of the relative phase is also studied.

ACTA PHOTONICA SINICA•Jan 1, 2008•0 citations

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

Guangyuan Li

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.

ACTA PHOTONICA SINICA•Jan 1, 2007•0 citations

Effect of Detuning on the Time Evolution of an Open Inversionless Lasing System

Fan Xi

We study the time evolution law of the atomic response in an open Λ type inversionless lasing system when the probe or driving field is off resonance,and compare the law with that obtained when the probe and driving fields are resonant.We find that the detuning has considerable effects on the time evolution law:When the probe or driving fields is off resonance,the dispersive responses for the probe and driving fields are no longer 0 and the two photon coherence is no longer a pure real;The variation of the probe detuning can make the time evolution law of the population distributions and the gain (absorbtion) of the driving field changing obviously;With detuning increasing,the time evolution behavior of the gain (absorbtion),dispersion of the probe field and the two photon coherence will gradually diviate from the evolution law of the standard damped oscillator;With the driving detuning increasing,the oscillating time of the dispersion of the driving field becomes longer,the amplitude and the stationary value increase.

Journal of Optoelectronics·laser•Jan 1, 2001•0 citations

Effects of phase fluctuation in an open four-level inversionless lasing system

樊锡君, 朱孟正, 洪正平 +2 more

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.

Chinese Optics Letters•Jan 1, 2004•1 citation
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.
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 effect of the relative phase Φ between the probe and driving fields on gain and dispersion from different aspects in an open quasi-type four-level system by the numerical solution of the steady state was investigated.The results show that by adjusting the value of the relative phase the inversionless gain and dispersion can be periodically amplified and attenuated.High dispersion (refractive index) without absorption can be achieved.The dispersion curve corresponding to Φ=α is similar to the gain curve corresponding to Φ=α+π/2.When the probe field is on resonance,the largest lasing without inversion (LWI) gain can be obtained by adjusting the relative phase.The effect of the atomic exit and injection rates on the LWI gain for different values of the relative phase is also studied.
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.
We study the time evolution law of the atomic response in an open Λ type inversionless lasing system when the probe or driving field is off resonance,and compare the law with that obtained when the probe and driving fields are resonant.We find that the detuning has considerable effects on the time evolution law:When the probe or driving fields is off resonance,the dispersive responses for the probe and driving fields are no longer 0 and the two photon coherence is no longer a pure real;The variation of the probe detuning can make the time evolution law of the population distributions and the gain (absorbtion) of the driving field changing obviously;With detuning increasing,the time evolution behavior of the gain (absorbtion),dispersion of the probe field and the two photon coherence will gradually diviate from the evolution law of the standard damped oscillator;With the driving detuning increasing,the oscillating time of the dispersion of the driving field becomes longer,the amplitude and the stationary value increase.
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.