An analysis is made of the effect of Doppler broadening on gain without inversion (GWI) from different aspects in a closed lambda-type three-level system with an incoherent pump. It is shown that, regardless of the driving field being on resonance or not, for the counter- or co-propagating of the probe and driving fields (PDF), GWI does not monotonically decrease or increase with increasing Doppler width. Except for the case of counter-propagating PDF with off-resonance driving field, at a suitable Doppler width one can obtain a gain maximum value much larger than that without Doppler broadening; especially in the situation of the resonant driving field, the co-propagating geometry leads to a larger GWI. In addition, for the counter-propagating geometry, when Doppler width is larger enough, GWI oscillation occurs, and the oscillation amplitude and region increase with increasing Doppler width. These conclusions are very different from that obtained in previous investigation (Lukin et al, Laser Phys. 6 436 (1996)).

We investigate the group velocity of the probe light pulse in an open V-type system with spontaneously generated coherence. We find that, not only varying the relative phase between the probe and driving pulses can but varying the atomic exit rate or incoherent pumping rate also can manipulate dramatically the group velocity, even make the pulse propagation switching from subluminal to superluminal; the subliminal propagation can be companied with gain or absorption, but the superluminal propagation is always companied with absorption.

. We studied effects of the relative phase between the probe and driving fields on the absorption and dispersion properties in an open three-level ladder system with spontaneously generated coherence but without incoherent pumping. It is shown that by the phase controlling, switching from absorption to lasing without inversion (LWI) and enhancing remarkablely LWI gain can be realized; large index of refraction with zero absorption and the electromagnetically induced transparency can be obtained. We also find that varying the atomic injection and exit rates has a considerable influence on the phase dependent-absorption property of the probe field, existent of the atomic injection and exit rates gives the necessary condition of the realization of LWI, getting LWI is impossible in the corresponding closed system without incoherent pumping.

We have studied the effect of the spontaneously generated coherence (SGC) on gain of lasing without inversion (LWI) in a closed three-level Λ-type atomic system with Doppler broadening. It is shown that, regardless of the driving and probe fields being co- or counter-propagating, at a suitable value of the Doppler width, we can obtain a much larger LWI gain with SGC than that without SGC; and the region of the LWI gain spectrum with SGC is obviously larger than that without SGC. When the Doppler width takes a constant value, the gain does not monotonically decrease or increase with increasing strength of SGC, the largest LWI gain can be obtained by adjusting strength of SGC. Generally speaking, the co-propagating probe and driving fields is favourable to obtain a larger LWI gain.

It is shown that in an open lambda type atomic system, the gain and dispersion of the probe field are quit sensitive to variation of spontaneously generally coherence (SGC). The value of the parameterp reflects whether SGC effect exists and the size of SGC effect. Under certain condition, whenp=0.002 electromagnetically induced transparency occurs; whenp≠0.002, lasing without inversion can be realized; whenp=0.95, high index of the refraction with zero absorption can be obtained.

The group velocity of the probe light pulse (GVPLP) propagating through an open Lambda-type atomic system with a spontaneously generated coherence is investigated when the weak probe and strong driving light fields have different frequencies. It is found that adjusting the detuning or Rabi frequency of the probe light field can realize switching of the GVPLP from subluminal to superluminal. Changing the relative phase between the probe and driving light. elds or atomic exit and injection rates can lead to GVPLP varying in a wider range, but cannot induce transformation of the property of the GVPLP. The absolute value of the GVPLP always increases with Rabi frequency of the driving light field increasing. For subluminal and superluminal propagation, the system always exhibits the probe absorption, and GVPLP is mainly determined by the slope of the steep dispersion.

The control role of the relative phase between the probe and driving fields on the gain and dispersion in an open Lambda-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.

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.

An analysis is made of the effect of Doppler broadening on the gain for different schemes in an open V type inversionless lasing system. It is shown that except for the case of the off-resonance driving field and the counter-propagating probe and driving fields, in other cases (i.e., the resonant driving field and the counter- or co-propagating geometry, the off-resonance driving field and the co-propagating geometry), the gain does not monotonously decrease with increasing of the Doppler width; particularly, in the situation of the resonant driving field and the co-propagating geometry, at a suitable Doppler width one can get a gain maximum value much larger than that without Doppler broadening; for the counter-propagating geometry, when the Doppler width is larger enough, gain oscillation occurs, and the oscillation amplitude and region increase with increasing of the Doppler width; the co-propagating geometry yields higher gain than the counter-propagating geometry.

Abstract An analysis is made of the effect of Doppler broadening on the gain in an open ladder inversionless lasing system. It is shown that for co-propagating probe and driving fields, the gain does not monotonously decrease or increase with increasing Doppler width, and at a suitable Doppler width one can obtain a maximum value much larger than that without Doppler broadening. For counterpropagating probe and driving fields, when the Doppler width is large enough, gain oscillation occurs, and the oscillation amplitude and region increase with increasing Doppler width. This conclusion is very different from that obtained in the corresponding closed system.

Lasing without inversion is investigated from a nonlinear dynamics viewpoint for the open resonant lower-ladder and V systems. We find that, for the two systems, destabilization of the non-lasing solution can occur through pitchfork bifurcation, giving rise to continuous-wave lasing emission, and also through Hopf bifurcation, giving rise to self-pulsing lasing emission. This conclusion is very different from that obtained from the corresponding closed systems by Mompart in 1998. The effects of the gain parameter, damping rate, ratio of the atomic injection rates and atomic exit rate on the two types of destabilization are also analysed.

An exact nonlinear analytical solution of an open V-type inversionless lasing system with two incoherent pump fields, off-resonant driving and probe fields is given. Through qualitative and quantitative comparison of the gain, dispersion and population differences of the linear and nonlinear cases, some conclusions concerning the Rabi frequencies of the driving and the probe fields are drawn and discussed in detail.

We study the law of time evolution of atomic response in an open Λ-type inversi onless lasing system,elucidate the light amplification mechanism without inversi on,and find that the character of the time evolution of atomic response in an open system is obviously different from that in a corresponding closed system. Weconsider that the variation of the oscillation frequency and anharmonic oscillat ion in the process of time evolution originate from the stochastic coherence pro perty of atom oscillators in the system.

A theoretical explanation for L core-shell absorption edge of electron energy loss spectrum of Al, an analysis of the electronic populations and a comparison between different partial cross sections are given. The edge was first normalized to the same atomic ionization cross section (per atom per electronvolt). The contributions for the cross section come from three respects:the first one is the electronic transitions from the core-shell to valence-shell calculated by extended Hückel band model, the second one is the final ionization state obtained by electron gas model, the third comes from the elastic backscatting of outgoing waves by the atoms that neighbor the excited atom. The agreement between the calculation result and the experimental result is good.

The Al L near-edge fine structures of aluminum and its compounds with nitrogen and oxygen are studied using electron energy loss microspectroscopy in a transmission electron microscope. These edges are normalized to the same scattering cross section per Al atom per electronvolt. The cross section is calculated by using the Born approximation. The contributions to the cross section are from the valence shell crystal states obtained by using the extended Huckel band calculation and the ionization states obtained by using the electron gas model. The chemical effects in the ionization region are taken into account by including the contributions from the elastic backscattering of outgoing plane waves by the atoms that neighbor the excited atoms. The results by theoretical calculation agree semiquantitatively with experimental results.

AlL and OK near edge fine structures in sapphire are studied using electron energy loss microspectroscopy in a transmission electron microscope;an analysis of the electronic populations of atoms Al and O,and a comparison between different partial cross sections are given.We consider the ionization of an atom in a homogeneous solid to interpret the elemental effects in the ionization region near edges.The chemical effects in the region near edge onset are interpreted by using extended Hückel molecular orbital theory and Bloch's theorem including the effects of translation symmetry in crystals to calculate the electronic transitions from core-shell to unoccupied valence-shell.We also consider the additional chemical effects, which arise from the elastic backscattering of the atomic ionization waves by the atoms neighboring the exited atom,giving rise to the so-called extended fine structure in the ionization region.The agreement between the calculated results and the experimental energy loss spectra of sapphire from single-phase region is good.

Under the strong driving field approximation, the conditions for realizing non-inversion lasing in an open V-type three-level system were discussed. The dependence of the gain behavior of the system on the Rabi frequency of the driving field, on the spontaneous rate, on the ratio of the atomic injection rates for the two lower levels, and on the rate by which the atoms exit from the cavity after interacting with the probe laser field, was analyzed.

The optical bistability in a dye-ring cavity laser was investigated by using the theory of Maxwell-Bloch equation of band model. In the study, the real distribution of the cavity field with Gaussian transverse profile was used. The optical bistability area is wider than that of two-level model. When �� (lack of harmony) value, C (expansion coefficient) and ��0 (imbalance parameter) change, the bistability area and threshold of bistability change obviously. The results was compared with those which were obtained by using plane wave approximation based on the band model and the two-level model in one transverse mode approximation, respectively.

In this paper, the general ring cavity model of passive and active optical systems is presented. In the mean field and the Gaussian one transverse mode approximations, the steady state and stability properties of the systems are analyzed for mixed absorptive and dispersive cases. It is found that when the transmissivity ratio M (equals T1/T2) varies, the bistable loop changes its size and even the systematic behavior varies from the bistability mode into the amplification mode, and the instability domain on the steady state curve varies obviously. The mode-pulling formula and bistable threshold with varying values of M are also discussed.