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.     

On the nature of “coherent artifact”

The coherent interaction of femtosecond laser pulses in the pump-probe regime has been experimentally studied in the time domain by monitoring light reflection from a tellurium single crystal. The optical response of the probed medium exhibits periodic variations at a frequency equal to that of the exciting laser radiation. Experimental dependences of the observed “coherent artifact” on the pump/probe intensity ratio, the number of accumulated pulses, and the mutual orientation of the polarization vectors of electromagnetic fields and the crystallographic axes are well described by the proposed phenomenological model.     

Bistable lasing of the vertical cavity surface emitting laser with a saturable absorber

The energy characteristics of a quantum-dot (QD) semiconductor laser with a saturable absorber in the regime of bistable lasing, which allow one to implement the device in a monolithic form, are calculated. The active and passive layers of the laser may include the same QDs. The phonon- and collision-related mechanisms of relaxation of carriers, which are substantial for the experiment, are considered. Formulas are derived for the saturation intensity, weak-signal gain/absorption coefficients, and their asymptotic dependence on the pump current. The restriction factor for filling by carriers, Fermions, and the possibility of fast capture of carriers by QDs are taken into account, and distinctions from the two-level model of saturation are demonstrated. It is shown that, to ensure the bistable mode for the laser with a saturable absorber, it is preferable to choose the resonance mode tuned to the excited state of the exciton, with predominant collision-related relaxation mechanism.     

Light transport and correlation length in a random laser

A random laser is a strongly disordered, laser‐active optical medium. The coherent laser feedback, which has been demonstrated experimentally to be present in these systems beyond doubt, requires the existence of spatially localized photonic quasimodes. However, the origin of these quasimodes has remained controversial. We develop an analytical theory for diffusive random lasers by coupling the transport theory of the disordered medium to the semiclassical laser rate equations, accounting for (coherent) stimulated and (incoherent) spontaneous emission. From the causality of wave propagation in an amplifying, diffusive medium we derive a novel length scale which we identify with the average mode radius of the lasing quasi‐modes. We show that truly localized modes do not exist in the system without photon number conservation. However, we find that causality in the amplifying medium implies the existence of a novel, finite intensity correlation length which we identify with the average mode volume of the lasing quasimodes. We show further that the surface of the laser‐active medium is crucial in order to stabilize a stationary lasing state. We solve the laser transport theory with appropriate surface boundary conditions to obtain the spatial distributions of the light intensity and of the occupation inversion. The dependence of the intensity correlation length on the pump rate agrees with experimental findings.     

A three-level model for alkali metal vapor lasers. Part II: broadband optical pumping

The effects of pump laser spectral bandwidth on the performance of longitudinally pumped diode-pumped alkali lasers is explored by extending the analytic, three-level model using longitudinally averaged number densities. By assuming a statistical distribution between the upper two levels, the limiting solution for the quasi-two level system is achieved. A second limiting solution is identified for strongly bleached conditions where the atom recycle rate, limited by spin–orbit relaxation, fully specifies the output power. Performance in the intermediate regime depends significantly on the pump bandwidth relative to the atomic absorption line width and requires numerical simulation. The ratio of populations for the two excited, ²P_3/2,1/2 states completes an analytic solution and depends primarily on pump laser bandwidth, threshold, and alkali concentration. Absorption well into the wings on the atomic profile can be utilized by increasing alkali concentration, but imposes increased pump intensity threshold.     

飞秒时间分辨实验中泵浦-探测交叉相关函数的测量和时间零点的确定

飞秒激光技术的出现使得实时探测与跟踪激发态超快弛豫动力学过程成为可能,并能够给出激发态动力学过程清晰的物理图像。而在飞秒时间分辨实验中,泵浦-探测相关函数和时间零点直接影响实验结果的可靠性和准确性。本文结合飞秒激光在分子激发态超快动力学过程中的应用进展,介绍了根据实验条件和要求,在具体实验过程中泵浦-探测相关函数测量和时间零点确定的几种方法。实验中选择可见光作为泵浦光和探测光时,可以通过测定随泵浦-探测时间延迟变化的泵浦激光与探测激光的和频/差频光强来确定泵浦探测交叉相关函数和时间零点;而选择中心波长在紫外甚至真空紫外的激光脉冲作为泵浦光或探测光时,泵浦-探测交叉相关函数通常采用校正的方法测量。     

Laser relaxation-oscillation frequency imaging

We describe a new imaging technique based on modification of laser relaxation frequency induced by coherent optical feedback from an external target. A direct comparison (both theoretical and experimental) is made with laser feedback interferometry techniques, in which there is a modification of the laser's steady state. We show that, for a laser with a cavity damping rate gamma(c) higher than the population damping rate, gamma(1) , the modification of the laser relaxation frequency can be several orders of magnitude more sensitive than the perturbation of the laser's output power. Application of this technique to imaging is reported.     

Multiphoton ionization of molecular hydrogen by single-cycle pulses

Multiphoton ionization, first observed by N.B. Delone in 1965, has been a subject of intense studies ever since. In this paper we consider multiphoton ionization of molecules in the limit of subopticalcycle pulse duration. Moreover, we study the regime where the molecules are first prepared in a coherent vibrational superposition state, and then are subjected to sub-cycle laser pulses synchronized with respect to the phase of the coherent molecular motion. The present approach is based on the Keldysh formalism, which assumes that the final free electron’s state is much more sensitive to the pulse than the bound initial wavefunction [1]. We find that the ionization rate depends not only on the sub-cycle shape of the laser pulses, but also on the time delay between the arrival of pulses and molecular motion.     

Theory of single-mode lasing in coherent quantum cascade lasers

A theory is developed for steady-state single-mode lasing in coherent quantum-well cascade lasers. This laser model is an example of a strictly quantum mechanical problem in which approximate kinetic approaches are not used to account for dissipative scattering processes. Exact wave functions are found for the system in weak and strong electromagnetic fields, so that the output power and frequency can be determined as functions of the coherent pump current and system parameters. It is shown that for pumping by monoenergetic electrons the power has a nonlinear (root) dependence and tends to saturate in strong fields. It is predicted that the coherent pumping efficiency may be increased by adjusting the energy of the pump electrons, which will lead to a linear power dependence, a high efficiency, and low threshold currents. A population inversion is found not be a necessary condition for lasing in the coherent laser. In particular, in the high field regime the population of the lower level exceeds that of the upper, while in the optimally adjusted regime they are the same. Zh. éksp. Teor. Fiz. 112, 483–498 (August 1997)     

相移法测量寿命的理论分析

本文从理论上分析了利用调制的单模激光场共振激发来测量原子或分子的寿命.结果表明:感生荧光或共振荧光信号与调制信号间的相移主要来自三个过程:(1)由原子的横向弛豫时间及激光线宽决定的激发过程;(2)由激发能级及其他能级上粒子数衰减过程;(3)与系统达到平衡态粒子数分布所需的弛豫时间有关的碰撞激发过程.讨论了在不同的情况下它们的影响,并在分析中考虑了多普勒加宽的影响.     

Maximum entropy principle and coherent harmonic generation using a single-pass free-electron laser

Single-pass free-electron lasers constitute an example of systems with long-range interactions. The light-particle interplay leading to the power growth and successive relaxation towards a quasi-stationary state is governed by the Vlasov equation. A maximum entropy principle inspired to Lynden-Bell's theory of “violent relaxation" for the Vlasov equation can be invoked to analytically characterize the behaviour of the saturated system. In particular, we here concentrate on the case of coherent harmonic generation obtained from an externally seeded free-electron laser and provide a simple strategy to predict the laser intensity as well as the final electron-beam energy distribution.     

Two Schemes for Generation of Entanglement for Vibronic Collective States of Multiple Trapped Ions

We propose two schemes to prepare entanglement for the vibronic collective states of multiple trapped ions. The first scheme aims to generating multipartite entanglement for vibrational modes of trapped ions, which only requires a single laser beam tuned to the ionic carrier frequency. Our scheme works in the mediated excitation regime, in which the corresponding Rabi frequency is equal to the trap frequency. Beyond their fundamental importance, these states may be of interest for experimental studies on decoherence since the present scheme operates in a fast way. The second scheme aims to preparing the continuous variable multimode maximal1y Greenberger-Horne-Zeilinger state. The distinct advantage is that the operation time is only limited by the available laser intensity, not by the inherent mechanisms such as off-resonant excitations. This makes it promising to obtain entanglernent of multiple coherent and squeezing states with desired amplitudes in a reasonable time.     

Diffusion and vibrational bottleneck in optically pumped submillimetre lasers

By observing the time dependence of the onset of the submm laser power in the millisecond time scale, just after the switching on of the pump laser, the vibrational bottleneck due to diffusion and vibrational relaxation has been clearly exhibited in CH₃F, D₂CO and HCOOH submm lasers. Experimental results are compared with those deduced from a simplified rate equation model. Both show a diffusion limited regime and a collisional regime.     

Non-Wiener Dynamics of the Generalized Dike Model as a Detector of a Broadband Single-Photon Wave Packet

It has been demonstrated that a quantum state of a broadband single-photon electromagnetic field can be detected and verified by recording the intensity of superradiance of an atomic ensemble governed by non- Wiener dynamics. Under these conditions, the collective relaxation of atoms in the Dike model into vacuum is completely suppressed and only the interaction of the external field with atoms generates a superradiance pulse proportional to the square of the number of atoms. In the case of a single-photon wave packet in a classical state prepared by weakening a broadband source of a family of independent coherent modes, incoherent emission of the same ensemble occurs with the intensity proportional to the number of atoms.     

运用“部分受激拉曼绝热通道”制备串行Λ系统相干叠加态

讨论了在串行Λ系统中制备初态和末态的连续叠加态的方法,这种方法是部分受激拉曼绝热通道的扩充.但是它又不同于部分受激拉曼绝热通道,每个斯托克斯脉冲先行相应的泵浦脉冲,但是所有的中间脉冲提前并且同时消失,而第一束斯托克斯脉冲和最后一束泵浦脉冲稍后同时消失.应用数值方法讨论了脉冲驰豫时间和失谐量对该方法的影响.数值结果表明要制备任意的叠加态,不仅要满足双光子共振,而且要满足单光子共振.     

KrF准分子激光的饱和参量与最佳激光输出

本文研究了在激光达到饱和强度下的上能级弛豫速率及泵浦速率两个参量与激光输出强度的关系。激光达到饱和强度时,上能级弛豫速率等于受激跃迁几率。根据这一特性,研究了Ar在4个大气压到6个大气压之间的四组N_(Ar)和N_(F_2),粒子数密度的Ar—Kr-F_2系统。计算了在给定激发速率和外耦合下的激光输出能量密度随Kr所占混合气体的比例而变化的关系。最后,从饱和强度下的上能级弛豫速率和泵浦速率得到了最大激光输出的条件,相应的激发速率、气压和气体混合的比例。     

利用全光纤结构Michelson腔实现两路高功率双包层光纤激光器相干合成

Michelson腔技术是实现激光相干合成的有效方案. 利用Michelson腔技术, 实现了全光纤结构下的两路光纤激光器的相干合成, 获得了功率为11.75 W, 效率为95.76%的相干输出. 实验研究了相干合成效率与激光腔长差的关系以及抽运对称性对相干合成效率的影响. 实验表明相干合成效率极易受激光腔长差的影响, 不同腔长差下相干合成效率差异可达18%以上, 且存在最佳腔长差; 抽运对称性对相干合成效率的影响在2%以内.     

飞秒激光参数对非绝热耦合分子态布居的影响

利用含时波包法研究强飞秒泵浦-探测激光场中激光脉宽、波长和场强对非绝热耦合NaI分子各态布居的影响.波包在势能面上做周期性运动,周期约为1 000 fs.延时为200 fs时,波包第一次到达交叉区域分裂成两部分.波包在交叉区域的分裂情况影响各态布居.脉宽增长,NaI分子的激发概率增大,而解离概率减小.泵浦波长为共振波长318 nm时,激发概率最大.泵浦波长增长,NaI分子的解离概率减小.泵浦场强增大,激发概率增大,但解离概率不变.探测激光波长和场强不影响NaI分子各态布居分布.调节激光场参数可实现对波包运动的控制从而控制态布居的选择性分布.研究结果为实验上实现分子的光控制过程提供参考.     

Switchable different operation states in an erbium-doped fiber laser cavity with normal dispersion

We demonstrate different operation states which can be switched by the polarization control in an erbium-doped fiber laser cavity with normal dispersion, including passive single-pulse and multiple-pulse mode-locking, coherent pulse pattern, and passive Q-switching. The mode-locked single pulse has a smooth and broad rectangular-shaped spectrum. With increasing pump power, multiple pulses appear and finally six pulses are observed, where the pulses have no interaction with each other. Keeping the pump power at 407 mW and adjusting the polarization state, we observe the coherent pulse pattern with the pulse numbers from 2 to 5. It is the first time five coherent pulses in the 1.55 μm normal dispersion cavity have been observed, to our knowledge. The mode-locked spectra are highly modulated and the largest pulse separation of 31.9 ps is observed for the two-pulse case. When the pump power exceeds 180 mW, the mode-locked operation can be switched to the passively Q-switched operation by controlling the polarization state. The repetition rate and pulse width can be changed by pump power variation, and the spectrum is tunable in the range of 8.45 nm.     

反馈调谐CO2激光器的静态与动态行为

建立了反馈调谐CO_2激光器的物理数学模型.稳态分析结果表明,只有当反馈系数大于某一临界值之后,才能出现激光器泵浦速率与激光输出之间的光学双稳性.线性稳定性分析的结果表明,系统失稳的必要条件是失谐量的Debye弛豫速率(反馈系统的带宽)必须超过布居反转的衰减速率.只有当激光泵浦落在某一范围内时,才出现不稳性.数值分析的结果证明了系统输出倍的周期分岔混沌行为.线性稳定性分析预言的Hopf分岔频率与数值分析的结果符合得很好.