Investigation of transient process and steady output of lasing without inversion

The transient evolution processes and steady outputs of continuous wave lasing without inversion (LWI) and self-pulsing LWI in a resonant open V type three-level system are studied. It was found that the two kinds of LWI have some obvious differences not only from the steady outputs but also from the transient evolution processes. The effects of the unsaturated gain coefficient, cavity loss coefficient, ratio of the atomic injection rates and atomic exit rate on the transient evolution processes and steady outputs are discussed.

Group velocity of probe light pulse in an open lambda system

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.

A mathematical study of finite-amplitude rock-folding

The problem of the finite-amplitude folding of an isolated, linearly viscous layer under compression and imbedded in a medium of lower viscosity is treated theoretically by using a variational method to derive finite difference equations which are solved on a digital computer. The problem depends on a single physical parameter, the ratio of the fold wavelength, L, to the "dominant wavelength" of the infinitesimal-amplitude treatment, L_d. Therefore, the natural range of physical parameters is covered by the computation of three folds, with L/L_d = 0, 1, and 4.6, up to a maximum dip of 90°.

Significant differences in fold shape are found among the three folds; folds with higher L/L_d have sharper crests. Folds with L/L_d = 0 and L/L_d = 1 become fan folds at high amplitude. A description of the shape in terms of a harmonic analysis of inclination as a function of arc length shows this systematic variation with L/L_d and is relatively insensitive to the initial shape of the layer. This method of shape description is proposed as a convenient way of measuring the shape of natural folds.

The infinitesimal-amplitude treatment does not predict fold-shape development satisfactorily beyond a limb-dip of 5°. A proposed extension of the treatment continues the wavelength-selection mechanism of the infinitesimal treatment up to a limb-dip of 15°; after this stage the wavelength-selection mechanism no longer operates and fold shape is mainly determined by L/L_d and limb-dip.

Strain-rates and finite strains in the medium are calculated f or all stages of the L/L_d = 1 and L/L_d = 4.6 folds. At limb-dips greater than 45° the planes of maximum flattening and maximum flattening rat e show the characteristic orientation and fanning of axial-plane cleavage.

Effect of phases on the dynamic evolution of a Lambda system with spontaneously generated coherence

The dynamic evolution of a A system coupled by two strong coherent fields is investigated by taking spontaneously generated coherence (SGC) into account. By numericaly simulation, it is shown that the relative phase of the two coherent fields affects significantly the time scale to the coherent population trapping state. In addition, an analytical expression to the evolution rate which is consistent with the numerical results is given. (c) 2005 Elsevier B.V. All rights reserved.

Lasing without or with inversion in an open four-level system with a phase-fluctuation driving field

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.

Effects of Lorentz local field correction on propagation properties of few-cycle pulse in dense Λ-type atomic medium

By solving numerically the full Maxwell-Bloch equations without the slowly varying envelope approximation and the rotating-wave approximation, we investigate the effects of Lorentz local field correction (LFC) on the propagation properties of few-cycle laser pulse in a dense A-type three-level atomic medium. We find that: when the area of the input pulse is larger, split of pulse occurs and the number of the sub-pulses with LFC is larger than that without LFC; at the same distance, the time interval between the first sub-pulse and the second sub-pulse in the case without LFC is longer than that with LFC, the time of pulse appearing in the case without LFC is later than that in the case with LFC, and the two phenomena are more obvious with propagation distance increasing; time evolution rules of the populations of levels vertical bar 1 >, vertical bar 2 > and vertical bar 3 > in the two cases with and without LFC are much different. When the area of the input pulse is smaller, effects of LFC on time evolutions of the pulse and populations are remarkably smaller than those in the case of larger area pulse. (c) 2008 Elsevier B.V. All rights reserved.

Phase-dependent properties for absorption and dispersion in a closed equispaced three-level ladder system

It is shown that in a closed equispaced three-level ladder system, by controlling the relative phase of two applied coherent fields, the conversion from absorption with inversion to lasing without inversion (LWI) can be realized; a large index of the refraction with zero absorption can be gotten; considerable increasing of the spectrum region and value of the LWI gain can be achieved. Our study also reveals that the incoherent pumping will produce a remarkable effect oil the phase-dependent properties of the system. Modifying value of the incoherent pumping can change the property of the system from absorption to amplification and enhance significantly LWI gain. If the incoherent pumping is absent, we cannot get any gain for any value of the relative phase. (c) 2007 Elsevier GmbH. All rights reserved.

Tools for the study of dynamical spacetimes

This thesis covers a range of topics in numerical and analytical relativity, centered around introducing tools and methodologies for the study of dynamical spacetimes. The scope of the studies is limited to classical (as opposed to quantum) vacuum spacetimes described by Einstein's general theory of relativity. The numerical works presented here are carried out within the Spectral Einstein Code (SpEC) infrastructure, while analytical calculations extensively utilize Wolfram's Mathematica program.

We begin by examining highly dynamical spacetimes such as binary black hole mergers, which can be investigated using numerical simulations. However, there are difficulties in interpreting the output of such simulations. One difficulty stems from the lack of a canonical coordinate system (henceforth referred to as gauge freedom) and tetrad, against which quantities such as Newman-Penrose Psi_4 (usually interpreted as the gravitational wave part of curvature) should be measured. We tackle this problem in Chapter 2 by introducing a set of geometrically motivated coordinates that are independent of the simulation gauge choice, as well as a quasi-Kinnersley tetrad, also invariant under gauge changes in addition to being optimally suited to the task of gravitational wave extraction.

Another difficulty arises from the need to condense the overwhelming amount of data generated by the numerical simulations. In order to extract physical information in a succinct and transparent manner, one may define a version of gravitational field lines and field strength using spatial projections of the Weyl curvature tensor. Introduction, investigation and utilization of these quantities will constitute the main content in Chapters 3 through 6.

For the last two chapters, we turn to the analytical study of a simpler dynamical spacetime, namely a perturbed Kerr black hole. We will introduce in Chapter 7 a new analytical approximation to the quasi-normal mode (QNM) frequencies, and relate various properties of these modes to wave packets traveling on unstable photon orbits around the black hole. In Chapter 8, we study a bifurcation in the QNM spectrum as the spin of the black hole a approaches extremality.

Phase control of gain and dispersion in an open lambda-type inversionless lasing system

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.

Atom localization via interference of dark resonances

A scheme of atom localization based on the interference of resonance of double-dark states is proposed, in which the atom interacts with a classical standing-wave field. It is found that the localization property is significantly improved due to the interaction of double-dark resonances. It is realized that the atom is localized just at the nodes of the standing-wave field with higher precision. Moreover, an improvement by a factor of 2 in the detecting probability of a single atom within the subwavelength domain can be achieved by adjusting the probe-field detuning. This scheme shows more advantages than other schemes of atom localization.

Phase control of gain and dispersion in an open V-type 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.

Effects of relative phase in an open ladder system without incoherent pumping

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 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.

Group velocity of the light pulse in an open V-type system

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. (c) 2006 Elsevier GmbH. All rights reserved.