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Journal of Optoelectronics·laser

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

Fan Xi

Published Jan 1, 2001• 0 citations
OpenAlex

Abstract

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.

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Chinese Journal of Quantum Electronics•Jan 1, 2008•0 citations
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 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 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.
This paper investigates the control role of the relative phase between the probe and driving fields on the gain, dispersion and populations in an open Λ system with spontaneously generated coherence (SGC). It shows that by adjusting the value of the relative phase, a change from lasing with inversion to lasing without inversion can be realized; the values and frequency spectrum regions of the inversionless gain and dispersion can be obviously varied; high refractive index with zero absorption and electromagnetically induced transparency can be achieved. It is also found that when the driving field is resonant, the shapes of the dispersion and the gain curves versus the probe detuning are very similar if the relative phase of the dispersion lags π/2 than that of the gain, however for the off-resonant driving field the similarity will disappear; the gain, dispersion and populations are periodical functions of the relative phase, the modulation period is always 2π; the contribution of SGC to the inversionless gain and dispersion is much larger than that of the dynamically induced coherence.
Begin with the density matrix equations of motion under the conditions of the rotating wave,slowly varying amplitude and mean field approximations,by using the numerical calculation results,the time evolution laws of the probe laser field and populations corresponding to two cases in producing inversionless lasing (i.e.,through the Pitchfork bifurcation giving rise to continuous wave lasing emission and through the Hopf bifurcation giving rise to self-pulsing lasing emission) in an open V-type resonant system are studied,and the effects of the system parameters varying on the time evolution laws are discussed.
The control role of the relative phase between the probe and driving fields on the gain and dispersion in an open Λ-type inversionless lasing system with spontaneously generated coherence (SGC) is investigated. It is shown that the inversionless gain and dispersion are quite sensitive to variation in the relative phase; by adjusting the value of the relative phase, electromagnetically induced transparency (EIT), a high refractive index with zero absorption and a larger inversionless gain can be realized. It is also shown that, in the contributions to the inversionless gain (absorption) and dispersion, the contribution from SGC is always much larger than that from the dynamically induced coherence for any value of the relative phase. Our analysis shows that variation in the SGC effect will cause the spectrum regions and values of the inversionless gain and dispersion to vary evidently. We also found that, under the same conditions, the values of the inversionless gain and dispersion in the open system are evidently larger than those in the corresponding closed system; EIT occurs in the open system but cannot occur in the closed system.
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.