Global rate equation description of a laser

The global integro-differential rate equations describing a multimode laser are analyzed. Expressions for the relaxation oscillation frequencies and their damping rates in the single-mode and two-mode regimes are obtained without specifying either the cavity geometry or the longitudinal pump profile. On the same level of generality, we prove the existence of universal relations relating the peaks of the power spectra in the two-mode regime. For a Fabry-Perot with arbitrary longitudinal pump profile, series expansions of all the physical functions are derived in powers of the pump moments. These moments are averages of the pump profile over cavity modes at linear combinations of the lasing frequencies and their harmonics. These results apply to end-pumped and/or partially filled lasers. For a single mode Fabry-Perot laser, we prove that the contribution to the steady state intensity from the lasing mode varies from 75% close to the lasing threshold to zero at high intensity. The remainder comes from the harmonics of the lasing mode. Analyzing the steady state single mode intensity equation in terms of the pump gratings, we prove that close to the lasing threshold only the space average of the pump and its grating oscillating at twice the lasing wave number do not vanish. This provides a hint towards the justification of the usual modal rate equations which retain only these two functions in the dynamical evolution of a laser. For a Fabry-Perot with constant pump profile, an exact expression for the upper boundary of the stable single mode regime is derived. In that two-mode regime, we prove that there is a critical value of the pump at which the ratio of the two relaxation oscillation frequencies is 2, leading to an internal resonance.     

Theoretical investigation on temporal properties of random lasers pumped by femtosecond-lasing pulses

Pulsing random lasing property has been investigated in both one- and two-dimensional random medium by numerically solving Maxwell’s equations and rate equations in which the pumping rate is described by a time function with duration of 10s or 100s of femtoseconds. The peak intensity, width and delay time of a random lasing pulse are traced with the variation of the peak intensity, duration, shape and numbers of a pumping pulse. Results show that the behavior of random lasing depends strongly on the pumping process, some of which are in agreement with previously reported experiments pumped by femtosecond-lasing pulses. The present work enriches the knowledge about random lasers, especially in temporal regime, and could offer more guidance for relevant experiments.     

Saturation intensity for ultrashort-pulse X-ray laser schemes

Analytic expressions are obtained for the saturation intensity in X-ray laser schemes based on short-pulse high-intensity drivers. For field-ionized plasma schemes, the specific mean saturation intensityJ _sat is time independent and depends only on atomic transition probabilities, level degeneracies, and transition energies. The analytic expression is found to be in good agreement with a detailed numerical calculation. Integrating over space and frequency gives a saturation intensityI _sat of order 2 × 10¹¹ W/cm² for lasing in Li-like Ne at 98 . The low input energy requirements for this scheme (< 1 J), associated with using a confocal geometry, give energy efficiencies of order 10^–6 and greater. For inner-shell photo-ionization schemes, an accurate expression for a time-dependent saturation intensity is obtained. This scheme is calculated to have high saturation intensities,I _sat 10¹³ W/cm², at short wavelengths (5–15 ). The requirement of a line focus geometry leads to higher input energies (5 J) and the short duration of lasing (50 fs) results in lower energy efficiencies ( 10^–7). Repetition rates are important in determining appropriate applications for both schemes.     

Rate equations for an optically-pumped,far infrared laser

Rate equations for an optically-pumped, far infrared laser are developed and solved for the case of a high intensity, pulsed pump beam. Conditions for saturated absorption and for saturated stimulated emission are established. A comparison is made to experimental data for absorption of 9.55 μm, CO₂ laser radiation in CH₃F. Generalized requirements for efficient, high power, FIR laser oscillator-amplifier systems are discussed.     

二维随机激光器的模式选择及阈值与饱和特性

基于将Maxwell方程与四能级原子系统速率方程相结合而建立起随机激光时域理论，并利用有限时域差分法，研究了二维随机介质中激光模式的输出特性与介质尺寸、外形及抽运速率等参数的关系.结果表明，与传统激光模式相似，随机激光模式的强度随抽运速率的变化不仅具有阈值特性，而且具有饱和特性.基于模式特性对介质及抽运参数的依赖关系，提出了二维随机激光器的选模方式，在很大程度上不同于传统激光器的选模方式. 关键词： 随机激光器 模式选择 无序介质中的光学特性     

Influence of Doppler broadening and spontaneously generated coherence on propagation effect in a quasi lambda-type four-level system

In this paper we study influences of Doppler broadening, spontaneously generated coherence, and other system parameters on propagation effect in a quasi lambda-type four-level atomic system. It is shown that when the Doppler broadening is present, generally speaking, the values of gain and intensity of lasing without inversion (i.e. the probe field) in the co-propagating probe and driving fields case are much larger than those in the counter-propagating case; considerably larger gain and intensity of lasing without inversion than those without the Doppler broadening can be obtained by choosing appropriate values of the Doppler broadening width and spontaneously generated coherence strength. The gain and intensity of lasing without inversion increase with the increase of spontaneously generated coherence strength; when spontaneously generated coherence is present, much larger gain and intensity of lasing without inversion than those in the case without spontaneously generated coherence can be obtained. Choosing suitable values of the probe detuning, Rabi frequencies of the driving and pump fields at the entrance of the medium also can remarkably enhance the gain and intensity of lasing without inversion.     

ZnO纳米柱无序介质中泵浦面积对局域模发射的影响

基于ZnO纳米柱制备及发光实验,建立了ZnO纳米柱的位置和大小都是无序的二维介质结构模型.通过构建增益模型,用时域有限差分法数值模拟了无序介质中频谱特性以及ZnO增益频谱范围内的某一个共振峰对应的波源在无序介质中的光场分布情况,发现了局域模的存在.分四种情况讨论了此局域模的受激辐射与泵浦面积的关系:改变泵浦功率,从左到...     

ZnO纳米柱无序介质中泵浦面积对局域模发射的影响

基于ZnO纳米柱制备及发光实验,建立了ZnO纳米柱的位置和大小都是无序的二维介质结构模型.通过构建增益模型,用时域有限差分法数值模拟了无序介质中频谱特性以及ZnO增益频谱范围内的某一个共振峰对应的波源在无序介质中的光场分布情况,发现了局域模的存在.分四种情况讨论了此局域模的受激辐射与泵浦面积的关系:改变泵浦功率,从左到右依次增加两层ZnO纳米柱泵浦和单独泵浦一个局域区域;泵浦功率一定时,增加泵浦局域区域和非局域区域中ZnO纳米柱个数.结果表明:存在一个临界泵浦功率,当泵浦功率小于临界泵浦功率时,无论泵浦面积多大都不能激发局域模;当泵浦功率大于临界泵浦功率时,对于不同的泵浦功率,局域模被激发所需的临界泵浦面积不同;随着泵浦功率的增加,当泵浦面积一定时,光场相对强度呈递增趋势,当泵浦功率超过临界功率时,光场相对强度急剧上升.     

How to achieve lasing in a system with the strong lifetime broadening of working levels?

To minimize and put into an experimentally reachable domain the coherent optical pump intensity needed for radiation amplification on a transition between strongly lifetime broadened levels, an inversionless lasing scheme is suggested. Such a scheme can be used, for example, to achieve lasing in quantum dots with lifetime broadened levels.     

Saturated X-ray lasing in Ni-like Sn at 11.9 nm using the GRIP scheme

We report on gain-saturated operation of the 11.9 nm X-ray lasing line in Ni-like Sn using the grazing-incidence pumping scheme (GRIP). The experiments were done with 2-ps duration pump pulses and energies up to 5 J. Strong gain saturation with multi-microjoule output was measured for the Sn laser at a grazing angle of 30° and a pump pulse energy of 3 J. This was achieved with a 4.5%, 2-ps duration prepulse 2.4 ns ahead of the main pulse and also incident at grazing incidence. Increasing laser output was observed at GRIP angles up to 45°. At this angle, the minimum energy required for saturated lasing was determined as ∼2 J.     

Prepulse dependence ofJ=0−1 lasing at 32.6 nm in neon-like titanium

The dependence of the intensity of the 3p—3s,J = 0–1 lasing line at 32.6 nm in neon-like titanium on the prepulse level has been investigated experimentally. Titanium slabs were irradiated with 1.315 µm/450 ps pulses from the Asterix IV iodine laser using a defined prepulse of 5.2 ns before the main pulse. It is found that for pump energies close to the minimum energy for which lasing is observed, a prepulse level of order 0.5% gives the highest XUV laser intensity, whereas a higher prepulse level, of order 10% and more, is required for optimum XUV lasing far above the threshold. For a 2.7 cm long titanium target lasing was observed down to a pump irradiance of 2.5 TW/cm² (50 J/450 ps) for the 0.5% prepulse.     

Experimental characterisation, optimisation and design of erbium-doped silica fibre lasers

A new characterisation method is described using the new theoretical model for erbium-doped silica fibre lasers (EDSFLs) based on the energy conservation principle. Using this method, we obtained absorption and emission coefficients for the lasing wavelength at lasing operating conditions. After that, an experimental procedure to deduce the spectral profiles of the absorption and emission coefficients is also presented. This procedure allows us to obtain the values of these parameters for the whole fluorescence spectrum through measurements of gain profiles under the lasing operation. Once the absorption and emission coefficients are known, the new model can be applied and a comparison with experimental results for two different laser configurations is shown. The theoretical model is proved to be accurate and in addition some equations are developed to allow the design and optimisation of EDSFLs. This revised version was published online in March 2005. In the previous version, the published online date was missing     

Asymmetric Superradiant Scattering Patterns from Bose--Einstein Condensates

The asymmetric patterns of superradiance from Bose-Einstein condensates are studied for the spatially inhomogeneous pump pulse with the semiclassical Maxwell-Schrodinger equations. The coupling dynamics between the optical field and condensate in the strong pulse and a faded wing in the weak coupling regime are discussed, which not only explain the spatial effects in the process of superradiance, but also supply a new method to control its patterns.     

Generation Dynamics of Coupled Pulses from a Single Active Element of the End-Pumped Solid-State Laser: Experiment and Simulation

Experimental and theoretical study is given to the coupling of pulsed radiation in two adjacent end pump regions of the Nd:YAG solid-state active element in the passively Q-switched Cr:YAG laser. The two-channel laser generates a pair of short pulses with a fixed time delay of a few nanoseconds to 1 μs. The main factors affecting the delay time and spatial radiation profiles are experimentally found. A numerical model of pulsed lasing kinetics in this system is developed, and mechanisms for radiation coupling in the channels are determined. Power scaling in pulsed laser systems, synchronization of pulsed lasing in the submicrosecond duration range, generation of short intense pulse packets, and formation of the temporal envelope of a short laser pulse are discussed.     

微腔中单量子点的激光输出特性研究

研究一个四能级量子点耦合到单模光学腔中的量子系统,利用系统的主方程作数值模拟计算微腔中单量子点的激光输出强度随非相干泵浦的变化关系.结果显示量子点在泵浦作用下激光的输出有一个阈值;且量子点和腔模耦合强度增强时,产生激光的阈值明显减小,输出激光的峰值却增大.当泵浦作用继续增强到一定程度,因激光能级间的相干性被过强的非相干泵浦所破坏,单量子点激光输出变为零----出现了淬灭现象.     

Optical processes in the formation of stimulated emission from ZnO nanowires

This paper studies power dependent photoluminescence spectra, the stimulated emission occurring at ultraviolet (UV) band instead of the green emission band of ZnO nanowires, which are prepared with a chemical reduction method. The dynamics of the UV emission and green emission is given to demonstrate the reason of stimulated emission occurring at UV band but not the green emission band under high excitation, which indicates that the slow decay rate of trap state makes it easy to be fully filled and saturated, while the fast decay rate of near-band-edge exciton state makes the UV emission dominate the radiative recombination under high excitation. The UV emission, as well as the corresponding stimulated emission, occurs in competition with the green deep-trap emission. In addition, when pump fluence further increases, the multiple lasing modes appear. The dependence of these lasing modes on the pump fluence is first discussed. This diagram should be helpful to understand and design the optical nanodevices of ZnO nanowires.     

Optical edge modes in photonic liquid crystals

An analytic theory of localized edge modes in chiral liquid crystals (CLCs) is developed. Equations determining the edge-mode frequencies are found and analytically solved in the case of low decaying modes and are solved numerically for the problem parameter values typical for the experiment. The discrete edge-mode frequencies specified by the integer numbers n are located close to the stop-band edge frequencies outside the band. The expressions for the spatial distribution of the n’s mode field in a CLC layer and for its temporal decay are presented. The possibilities of a reduction of the lasing threshold due to the anomalously strong absorption effect are theoretically investigated for a distributed feedback lasing in CLCs. It is shown that a minimum of the threshold pumping wave intensity may be reached, generally, for the pumping wave propagating at an angle to the helical axis. However, for lucky values of the related parameters, it may be reached for the pumping wave propagating along the helical axis. The lowest threshold pumping wave intensity occurs for the lasing at the first low-frequency band-edge lasing mode and the pumping wave propagating at an angle to the spiral axis corresponding to the first angular absorption maximum of the anomalously strong absorption effect at the high-frequency edge of the stop band. The study is performed in the case of the average dielectric constant of the liquid crystal coinciding with the dielectric constant of the ambient material. Numerical calculations of the distributed feedback lasing threshold at the edge-mode frequencies are performed for typical values of the relevant parameters.     

Optical pumping of the Zeeman components in the rubidium vapor

We investigated the optical pumping of the Zeeman components of rubidium atoms, in the presence of the external magnetic field ranging from the geomagnetic up to 130 Gauss. Using the saturated absorption spectroscopy with linearly polarized pump and probe laser beams, the rubidium Doppler-free spectra at different magnetic field strengths were measured. The dips (negative intensity signals) in the saturated absorption spectra of the ⁸⁷Rb hyperfine transition lines were observed. They come as a result of the alignment process induced by the incoherent population transfer due to the hyperfine optical pumping. By inspection of the dips for different magnetic field strengths we were able to conclude about the dynamics of the alignment process in the external magnetic field. Present work is a part of the investigations concerning the influence of the magnetic field on the velocity selective optical pumping of the rubidium atoms induced by femtosecond frequency comb [D. Aumiler, T. Ban, H. Skenderovi?, G. Pichler, Phys. Rev. Lett. 95 (2005) 233001; T. Ban, D. Aumiler, H. Skenderovi?, G. Pichler, Phys. Rev. A 73 (2006) 043407].     

Determination of the Auger upconversion rate in fiber-coupled diode end-pumped Nd:YAG and Nd:YVO4 crystals

An analytical model is developed to study the influence of the Auger upconversion process on the thermal loading under lasing and nonlasing conditions. With the developed model, Auger upconversion rates can be determined by comparing theoretical calculations with experimental results for the ratio of the thermal loading under lasing and nonlasing conditions. The upconversion rates obtained with the present method are compared with the results measured from the fluorescence decay experiment. Received: 7 June 1999 / Revised version: 3 August 1999 / Published online: 30 November 1999     

Bichromatic coherent random lasing from dye-doped polymer stabilized blue phase liquid crystals controlled by pump light polarization

In this paper, we investigate the bichromatic coherent random lasing actions from the dye-doped polymer stabilized blue phase liquid crystals. Two groups of lasing peaks, of which the full widith at half maximum is about 0.3 nm, are clearly observed. The shorter- and longer-wavelength modes are associated with the excitation of the single laser dye (DCM) monomers and dimers respectively. The experimental results show that the competition between the two groups of the lasing peaks can be controlled by varying the polarization of the pump light. When the polarization of the pump light is rotated from 0° to 90°, the intensity of the shorter-wavelength lasing peak group reduces while the intensity of the longer-wavelength lasing peak group increases. In addition, a red shift of the longer-wavelength modes is also observed and the physical mechanisms behind the red-shift phenomenon are discussed.