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ACTA PHOTONICA SINICA

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

Fan Xi-jun

Published Jan 1, 2008• 0 citations
OpenAlex

Abstract

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.

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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 control role of the relative phase between the probe and driving fields on gain, dispersion and populations in an open V-type three-level system with spontaneously generated coherence is studied. The result shows that by adjusting the value of the relative phase, the transformation between lasing with inversion and lasing without inversion (LWI) can be realized and high dispersion (refractive index) without absorption can be obtained. The shape and value range of the dispersion curve are similar to those of the gain curve, and this similarity is closely related to the relative phase. The effects of the atomic exit and injection rates and the incoherent pump rate on the control role of the relative phase are also analysed. It is found easier to get LWI by adjusting the value of the relative phase using the open system rather than the closed system, and using an incoherent pump rather than without using the incoherent pump. Moreover the open system can give a larger LWI gain than the closed system.
Based on matrix theory,the absorption and dispersion properties of a Y-type four-level system driven by three coherent fields are investigated on the condition of effect spontaneously induced coherence.The result obtained by means of numerical method indicates that by adjusting the relative phase of the coherent field in the steady state,the dispersion(gain) and dispersion of the probe field can be significantly magnified and weakened periodically.Using appropriately parameters,the dispersion curve corresponding to =α is similar to the absorption(gain) curve corresponding to =α+π/2.In addition,the evolution of dispersion with the relative phase of coherent fields shows explicitly optical bistability.
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.
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.
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.
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.