Positive and negative dispersion in a three-level Λ system driven by a single pump

We extend our previous study of a nearly degenerate Λ three-level system that exhibits population trapping when driven by a single pump and produces an absorption or gain doublet in the probe absorption spectrum. In particular, we show that the probe dispersion is positive or negative between the doublet lines, and can survive Doppler broadening. For certain values of the pump Rabi frequency, the sign of the dispersion can be changed by altering the ratio of the splitting between the lower levels to the Doppler width.     

Phase time delay and Hartman effect in a one-dimensional photonic crystal with four-level atomic defect layer

The Hartman effect is revisited using a Gaussian beam incident on a one-dimensional photonic crystal (1DPC) having a defect layer doped with four-level atoms. It is considered that each atom of the defect layer interacts with three driving fields, whereas a Gaussian beam of width w is used as a probe light to study Hartman effect. The atom–field interaction inside the defect layer exhibits electromagnetically induced transparency (EIT). The 1DPC acts as positive index material (PIM) and negative index material (NIM) corresponding to the normal and anomalous dispersion of the defect layer, respectively, via control of the phase associated with the driving fields and probe detuning. The positive and negative Hartman effects are noticed for PIM and NIM, respectively, via control of the relative phase corresponding to the driving fields and probe detuning. The advantage of using four-level EIT system is that a much smaller absorption of the transmitted beam occurs as compared to three-level EIT system corresponding to the anomalous dispersion, leading to negative Hartman effect.     

Three-photon electromagnetically induced absorption and transparency in an inhomogeneously broadened atomic vapour

We study both theoretically and experimentally three-photon electromagnetically induced transparency and electromagnetically induced absorption resonances in inhomogeneously broadened 85 Rb atomic vapour driven by probe and drive laser radiations. We observe narrow Doppler-free absorption as well as transmission resonances for the probe field when the driving laser field is redshifted from the D₁ or D₂ lines of ⁸⁵Rb; the frequency difference between the drive and probe fields is equal to the hyperfine splitting of the ground state of the atoms, and the probe field is tuned to the centre of the Doppler broadened atomic transition. We theoretically study the spectroscopic effect in both homogeneously and inhomogeneously broadened media. Our numerical simulations are in good agreement with the experimental results.     

Enhanced gain and narrow linewidth of an optical cavity by the Doppler effect in a four-level atomic system

Abstract

A scheme for high gain and narrow linewidth of an optical cavity with a four-level atomic system is proposed by the Doppler effect via active Raman gain (ARG) process. Atomic motion leads to Doppler frequency shift which induces constructive interference for the linear susceptibility. The enhanced normal dispersion greatly narrows the cavity linewidth, and the amplified gain gives rise to a high cavity transmission. Simulation results show that the cavity linewidth based on ARG is about one order of magnitude narrower than that based on electromagnetically-induced transparency under the same conditions, and the cavity transmission intensity could be enhanced by nearly 30 times.     

The effect of probe coherence and atomic coherence on the response of an open lambda-type pump–probe system

The response of a coherently prepared four-level λ-type system, interacting with two electromagnetic fields in a Doppler-free pump–probe configuration is analytically formulated. Under density matrix formalism the probe coherence (field-dependent phase) and atomic coherence (field-independent phase) are introduced through the off-diagonal matrix elements. The coherent effects on probe response is investigated for probe coherence, as well as for the driving contribution (coherence) of the pump field. We show how probe coherence can modify the Rabi splitting and two-photon absorption, through shifting and broadening of spectral lines for on- and off-resonance pumping, respectively. In addition, we report on the enhancement of absorptionless dispersion (i.e. refractive index for on and around probe resonance) and two-photon absorption, via coherent control of the driving contribution of the pump field.     

Group velocity of probe light pulse in an open lambda system

The group velocity of the probe light pulse (GVPLP) propagating through an open Λ-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 fields 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.     

Laser Instabilities and Chaos in Inhomogeneously Broadened Dense Media

Abstract

We study numerically the effects of local-field corrections originating from near dipole—dipole interactions on the dynamics of a single mode, inhomogeneously broadened laser. Our analysis is based on a set of generalized Maxwell–Bloch equations in which the inhomogeneous nature of gain broadening is accounted for by introducing two new dynamical variables and a single parameter that governs the extent of inhomogeneous broadening. Our results show that local-field effects occurring in a dense gain medium reduce the range of continuous wave operation and lead to instabilities and chaos at much lower pumping levels.     

The Effect of Phase Fluctuation on Electromagnetically Induced Transparency,Inversionless Lasing and Refractive Index Enhancement in a Λ System

Abstract

The steady-state behaviour for a Λ-type, three-level atomic system has been analysed by taking into account the effect of the phase fluctuation. It is shown that, for a monochromatic driving field, even if the probe field is in resonance with the corresponding atomic transition, a large refraction index can still be generated; for a finite linewidth of the driving field, inversionless lasing and index enhancement tends to disappear. Furthermore, the linewidth prevents the transparency of the medium.     

Non-stationary Two-photon Doppler-free Coherent Spectroscopy in an Atomic Gas in the Presence of Depolarizing Collisions

Abstract

Non-stationary two-photon absorption coherent spectroscopy free of Doppler broadening in an atomic gas has been considered in detail. Correct account has been taken of the level degeneracy and depolarizing collisions. This two-photon Doppler-free spectroscopy has been developed for determining the relaxation rates of the atomic multipole moments in gas. A criterion to test the adopted model of the depolarizing collisions has been developed. A possible method for the identification of the atomic transitions in the angular momentum has been formulated. A technique of precisely determining the separation between the energy levels of the two-photon transition has been proposed. The conditions under which the Stokes wave is conjugated with respect to the probe pulse in amplitude, phase and polarization have been determined for the atomic gas in the presence of depolarizing collisions.     

Spectrum of Doppler ultrasound signals from nonstationary blood flow

A new formulation for the Doppler signal generation process in pulsatile flow has been developed enabling easier identification and quantification of the mechanisms involved in spectral broadening and the development of a simple estimation formula for the measured rms spectral width. The accuracy of the estimation formula was tested by comparing it with the spectral widths found by using conventional spectral estimation on simulated Doppler signals from pulsatile flow. The influence of acceleration, sample volume size, and time window duration on the Doppler spectral width was investigated for flow with blunt and parabolic velocity profiles passing through Gaussian-shaped sample volumes. Our results show that, for short duration windows, the spectral width is dominated by window broadening and that acceleration has a small effect on the spectral width. For long duration windows, the effect of acceleration must be taken into account. The size of the sample volume affects the spectral width of the Doppler signal in two ways: by intrinsic broadening and by the range of velocities passing through it. These effects act in opposite directions. The simple spectral width estimation formula was shown to have excellent agreement with widths calculated using the model and indicates the potential for correcting not only for window and nonstationarity broadening but also for intrinsic broadening.     

Effects of a Moving Mass Centre on Atomic Dynamics in Locally Inhomogeneous Quantized Cavity Field

Abstract

By invoking an exactly solvable model as the generalization of the Jaynes-Cummings model, the influence of spatial motion of atomic centre on the dynamics of a single-mode cavity-two-level atom system are studied for various initial conditions. These investigations show that the Doppler effect exercised by the motion of atom in a locally inhomogeneous cavity field can lead to the phenomenon of oscillation collapse and revival in the transition probability and the atomic population inversion.     

A positron annihilation study on the defect properties of doped diamond films

Doppler broadening measurements were performed on undoped, boron doped, and sulfur doped diamond films. The defect properties in these different diamond films were analyzed and the effect of boron concentration in the B-doped diamond films on these properties was studied. The Doppler broadening measurements were characterized with the shape parameter S and the wing parameter W. From these fitted characteristic S and W values of the diamond films and plots of S vs. position implantation energy, it was deduced that undoped and S-doped diamond films are rich of vacancy-like defects, while B-doped diamond films are poor of vacancy-like defects. This difference may originate from possible different charge state of the vacancy-like defects and from the incorporation of impurities in the different growth ambient of the films. By comparing the parameters obtained in the Doppler broadening measurements of diamond films with different boron concentration, we found that S values of B-doped diamond did not decreased with the increasing of boron concentration, which suggests that more damaged regions form in the higher boron concentration samples.     

Spatially resolved positron annihilation spectroscopy on friction stir weld induced defects

Abstract

A friction stir welded (FSW) Al alloy sample was investigated by Doppler broadening spectroscopy (DBS) of the positron annihilation line. The spatially resolved defect distribution showed that the material in the joint zone becomes completely annealed during the welding process at the shoulder of the FSW tool, whereas at the tip, annealing is prevailed by the deterioration of the material due to the tool movement. This might be responsible for the increased probability of cracking in the heat affected zone of friction stir welds. Examination of a material pairing of steel S235 and the Al alloy Silafont36 by coincident Doppler broadening spectroscopy (CDBS) indicates the formation of annealed steel clusters in the Al alloy component of the sample. The clear visibility of Fe in the CDB spectra is explained by the very efficient trapping at the interface between steel cluster and bulk.     

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 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.     

光纤中基于SBS实现慢光的数值研究

通过运用带有预测.校正的隐格式有限差分法对基于光纤的受激布里渊散射耦合方程组进行了数值求解.在增益0～16范围内考察了布里渊增益系数、增益带宽以及有效模面积对时间延迟和脉冲展宽的影响.结果表明,较小的增益系数和增益带宽、较大的有效模面积使得Stokes信号具有更大的饱和增益值,相应的时间延迟也较大.在固定泵浦功率并保证增益参数在小信号范围的情况下,时间延迟及脉冲展宽因子随着增益系数的增加而增加,但随着增益带宽以及有效模面积的增加而减少.     

Least-energy path planning and oscillation analysis of robotic manipulator using direct collocation with nonlinear programming

ABSTRACT

Direct collocation is a method that converts a two-point boundary-value problem into a nonlinear programming problem by approximating the state variables and controls into parameters. It has been broadly used in studies of space and orbital mechanics yet has been rarely applied in the fields of robotics. This study builds up a mathematical model of a five-linked manipulator arm. Gradually reducing the upper and lower bounds of the five joint actuator outputs, this paper explores the variations in the least-energy cost function and the final time. Special attention has been focused on whether restrictions would ever arouse any un-anticipated oscillation in the joints. The numerical results show some irony. Excessively restricting the upper and lower output bounds of actuators does not actually gain traction in minimizing the cost index. On the contrary, the value of the cost index is increased by 41.77% from 924.87 to 1310.44 for a tunnel case whose radius is 1.5 m. The simulation cautions that unwanted frequency of oscillation begins to surface due to this wishful restricting. This paper demonstrates how Direct Collocation with Nonlinear Programming can be successfully applied to solve robotic path planning problems. It also cautions the users and designers of the manipulator about the unwanted frequency drift so that the users and designers can amend it before the oscillation builds up.     

Propagation of (2 + 1)-dimensional solitary waves in dissipative/active saturable nonlinear media

Abstract

We investigate the propagation of (2 + 1)D bright solitary waves in a saturable nonlinear medium perturbed with gain or loss. We find that in the presence of loss (gain) the amplitude and width of the (2 + 1)D bright solitary waves may both increase (decrease) with their product varying adiabatically during evolution. This is in contrast to the (1 + 1)D Kerr bright (dark) solitons or (2 + 1)D vortex solitons whose amplitude decreases (increases) at the same rate as the width increases (decreases), keeping their product unchanged with the propagation distance. For a very weak nonlinear saturation approaching Kerr nonlinearity, it is found that the amplitude and the width change at a rate faster than the (1 + 1)D Kerr bright and dark solitons, whereas their variation in highly saturable media is slower than the (1 + 1) or (2 + 1)D Kerr dark solitons. In a medium of moderate nonlinear saturation, the beam width and amplitude may vary in the way following that of high nonlinear saturation or weak nonlinear saturation or a combination of the two, depending on loss or gain and propagation distance.     

Subluminal and superluminal light propagation via electromagnetically induced transparency in radiatively and inhomogeneously broadened media

Contrary to popular belief, we demonstrate the feasibility of generating superluminal (and subluminal) probe (and signal) light via electromagnetically induced transparency in a medium comprising coupled double-ladder systems. This scheme can be realized in both homogeneously (radiative) as well as in inhomogeneously (Doppler) broadened atomic systems. Unlike more intricate earlier schemes, our scheme is based simply on steady-state propagation dynamics resulting from compensation of the inevitable absorption losses by large nonlinear gain generated through appropriate choice of the pump and coupling fields. We show how easily in this scheme the speed of weak probe (and signal) fields can be switched from subluminal to superluminal by simply varying the strengths of the coherent pump and coupling fields. Furthermore, it is shown that under these conditions both the signal and probe fields are intensity matched and both propagate with the same subluminal (or superluminal) group velocity without suffering loss or gain for long distance in the medium.     

Numerical simulation of the oscillation line width in synchronous multi-element Josephson structures

A method of simulating the dynamics of systems with Josephson junctions with allowance for thermal fluctuations is developed using the PSCAN program package followed by calculation of the Josephson oscillation spectrum using an autoregression method. An investigation is made of the synchronous Josephson oscillation line width in several types of Josephson structures. Pis’ma Zh. Tekh. Fiz. 24, 52–59 (August 12, 1998)     

Axisymmetric damped natural frequencies in a slowly spinning cylindrical container filled with viscous liquid

The axisymmetric fundamental natural damped frequency of the free surface in a slowly rotating cylindrical container is determined for incompressible viscous liquid. It was found that with increasing liquid height ratio h/a oscillation frequencies and decay magnitude both exhibit increased values. The influence of the surface tension parameter σ*=σa/?ν² shows for increasing magnitude increasing oscillation frequencies and decreasing decay magnitudes. For increasing Bond number Bo the oscillation frequency increases while the decay magnitude decreases. The effect of increasing the spin parameter ω₀=Ω₀ a ²/ν is manifested by an increase of the oscillation frequency and decay magnitude, i.e. for faster spin a liquid disturbance decays faster with larger oscillation frequency.