Quantummechanical solutions of the laser masterequation. II

A Fokker-Planck equation for a distribution function over the macroscopic observables of the laser essentially equivalent to that recently obtained byRisken,Schmid andWeidlich is derived from the fundamental quantummechanical laser masterequation. The general method used is the expansion of the statistical operator in a complete set of projection operators of the atoms and the lightfield. The assumptions leading from the microscopic equation of motion to the macroscopic semiclassical Fokker-Planck equation are explicitly introduced and discussed.     

Quantum mechanical solutions of the laser masterequation

We treat a laser consisting of one mode described by a running wave and a set of atoms with two optically active levels which are homogeneously broadened. We start from the laser density matrix equations ofWeidlich andHaake and define a distribution functionf for lightfield and atomic variables, where we use for the lightfield the coherent state representation and for the atomic system a modified version of the distribution function used bySchmid andRisken in a previous paper. We derive a partial differential equation forf which is completely exact and is of the type of a generalized Fokker-Planck equation, i.e. it contains higher derivatives. Using a recently stated theorem ofHaken andWeidlich we show that this distribution function allows to calculate single-time as well as multitime quantum mechanical correlation functions. If the leading terms of the generalized Fokker-Planck equation are retained we find the semiclassical Fokker-Planck equation ofRisken,Schmid andWeidlich. Our treatment can be extended to several modes connected with standing waves and multilevel atoms.     

The time dependent solution of the masterequation for a laser system

Calculations of the cross sections for collision-induced transitions between Zeeman sublevels of excited alcali atoms are proposed, which are independent from dynamical models. 1. Supposing that the spin of the valence electron does not flip, the transition matrix, describing collision-induced deorientation of the orbital angular momentum, is analysed considering invariance principles only. Consequently the cross sections for depolarizing collisions are given by two dynamical parameters. 2. The full transition matrix, describing deorientation of the orbital angular momentum as well as of the spin of the valence electron, is analysed in the same way. In this general case the depolarizing cross sections are given by six dynamical parameters.     

Quantummechanical treatment of the penetration through a two-dimensional fission barrier

The collective Hamiltonian is idealized by making a harmonic approximation for the motion perpendicular to the fission path. This is done within a properly defined set of coordinates. The frequency for the transverse oscillations depends on the fission coordinate which leads to a coupling between the two degrees of freedom. Its influence is discussed within the language of scattering theory. Using the Born approximation, formulas for the transmission amplitudes are deduced. These formulas are applied to a simple example. All calculations are done analytically, taking into account the variation of the inertia for the fission mode.     

Quantum mechanical masterequation and Fokker-Planck equation for the damped harmonic oscillator

For the statistical operator of the damped harmonic oscillator a Masterequation is given in operator form describing both inelastic and elastic, purely phase destroying processes. By expressing the statistical operator in the diagonal representation with respect toGlauber's coherent states the Masterequation is transformed into a Fokker-Planck equation forGlauber's quasiprobability distribution function. The general solution of this Fokker-Planck equation is calculated. It is shown how the solution of a Masterequation can be used for calculating correlation functions and expressions are given for the amplitude and intensity correlation functions which are in complete formal agreement with the corresponding classical formulae.     

Self-similar solutions of laser produced blast waves

The aerodynamics of the blast wave produced by laser ablation is studied using the piston analogy. The unsteady one-dimensional gasdynamic equations governing the flow are solved under assumption of self-similarity. The solutions are utilized to obtain analytical expressions for the velocity, density, pressure and temperature distributions. The results predict all the experimentally observed features of the laser produced blast waves.     

固溶态染料激光物质的研究

本文从不同改进的掺Rh6G聚甲基丙烯酸甲脂(PMMA)固溶态物质获得了有效的激光.热稳定性得到改善以及工作寿命得到延长.研究了它们的激射和光谱特性.     

Continuation of periodic solutions in the waveguide array mode-locked laser

We apply the adjoint continuation method to construct highly accurate, periodic solutions that are observed to play a critical role in the multi-pulsing transition of mode-locked laser cavities. The method allows for the construction of solution branches and the identification of their bifurcation structure. Supplementing the adjoint continuation method with a computation of the Floquet multipliers allows for explicit determination of the stability of each branch. This method reveals that, when gain is increased, the multi-pulsing transition starts with a Hopf bifurcation, followed by a period-doubling bifurcation, and a saddle-node bifurcation for limit cycles. Finally, the system exhibits chaotic dynamics and transitions to the double-pulse solutions. Although this method is applied specifically to the waveguide array mode-locking model, the multi-pulsing transition is conjectured to be ubiquitous and these results agree with experimental and computational results from other models.     

New exact solutions of the dirac equation. I

Three new types of external electromagnetic fields, allowing exact solution of the Dirac and Klein-Gordon equations, are found in this paper. The wave functions are expressed in terms of quadratures. Solutions of the corresponding classical relativistic equations of motion are also found.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, Vol. 16, No. 7, pp. 95–101, July, 1973.     

Photo-stability of laser dye solutions under Copper-vapour-laser excitation

The photo-stability of laser dyes, Rhodamine-6G, Rhodamine-B, and Kiton-Red, under high repetition rate (6.3 kHz) Copper-vapour-laser (CVL) irradiation has been investigated. Exhaustive photo-bleaching of these dyes in different solvents has been carried out to study the extent to which the dye photo-degraded products would interfere with the lasing process in high-power CVL-pumped dye lasers. Our results indicate that the photo-degradation of dyes occurs predominantly through excited-state intermolecular reactions, involving the singlet state, rather than the process of nonlinear optical absorption in individual molecules. Received: 13 March 2000 / Revised version: 2 August 2000 / Published online: 21 March 2001     

Determination of the dynamics of microcharacteristics of solutions by time laser spectroscopy

The development of simple methods used to analyze the available data and separate the contributions from the main physicochemical processes responsible for the kinetics of instantaneous emission spectra is of considerable interest due to the intensive investigation of the time-resolved characteristics of fluorescence of various quantum objects that are used to examine the most important photophysical and photochemical reactions in excited states. The relation between the functions of the shift in the instantaneous spectra of spontaneous emission of molecules (obtained using kinetic spectroscopy methods) and the time variations in the configurational structure of solvates, as well as the charge transfer in the excited singlet state of molecules of the luminescent probe, has been shown using simple analytical expressions of solvatofluorochromism. The fluorescence of solutions of one of the most important molecular probes, namely, 1-(phenylamino)naphthalene in glycerol, has been investigated with a picosecond time resolution. This molecular probe is known because its electric dipole moment is formed in the excited singlet state, which almost instantaneously initiates processes of intermolecular rearrangement of solvent molecules. It has been demonstrated that it is possible to determine the time dependence of the function of the dielectric response of the polar solvent to the dipole of this probe and, hence, the time evolution of the microcharacteristics of the solvent that determine the above function.     

LRS Bianchi type I perfect fluid solutions generated from known solutions

Some LRS Bianchi type I perfect fluid solutions are generated from known solutions of this type. The solutions represent spatially homogeneous and anisotropic cosmological models which would give essentially empty space for large time. The physical and kinematic properties of the models are discussed.     

Analytical solutions for laser modes in misaligned resonators

Laser modes of misaligned resonators transversally limited in gain are obtained analytically within the paraxial approximation. The eigenfunctions are shown to be complex Hermite-Gaussian functions, not centered either in intensity or in curvature center. Eigenvalues are also obtained, and the effect of resonator parameters and misalignment is analyzed, revealing the lack of selectivity of misalignment on order mode. The changes in the appearance of the modes are also shown.     

超短脉冲激光烧蚀金属靶热分布的数值解与解析解

研究了超短脉冲激光烧蚀靶材的整个过程,对描述超短脉烧蚀过程热行为的双温度方程进行了分析简化,得出了超快激光烧蚀金属材料的解析解. 以铜靶材为例,对双温度模型的数值解与解析解做了对比分析,得到了靶材温度随时间和深度的变化规律,结果显示解析解的计算结果比较好的符合了数值解的计算结果.     

Spatiotemporal characteristics of laser emission. I

The first chapter describes the general premises of the electrodynamic theory of the laser as a nonstationary nonlinear oscillatory system with spatially distributed parameters. Maxwell's equations are used to derive an equation for the complex amplitude of the electromagnetic field in a cavity filled with transversely inhomogeneous active medium. The self-conssitent analysis includes a simultaneous solution of the equations for the field and for the inverted population. In the second chapter, electrodynamic theory is applied to injection and electron-beampumped semiconductor lasers. The threshold characteristics, the field structure in the near and far zones, the lasing regimes of semiconductor lasers, and the influence of nonlinearity of the refractive index are considered.Division of Quantum Radiophysics, Lebedev Physics Institute. Translated from Preprint No. 33, Lebedev Physics Institute, Moscow, 1990.     

Calorimetric study of thiophene-benzene solutions(I)

Molar heat capacities were measured on seven mixtures [(1 − x)thiophene + x benzene] using an adiabatic calorimeter in the 14 and 300 K temperature range. The measurements were made at x = 0.0016, 0.0030, 0.0050, 0.0061, 0.0070, 0.0183 and 0.0210, respectively. Transitions between various phases in stable and metastable sequences of thiophene crystal were found to be affected more or less by the benzene doping in this thiophene-rich region. Among others, the II₂-II₁ transition in the metastablephase sequence was affected drastically by the dopant. The significant effect of benzene on the transitional behavior was discussed in relation to the incommensurate structure of phase II,. Glass transitions observed in phase II₁ or II₂ were analyzed in terms of the Kohlrausch-Williams-Watts equation to derive kinetic parameters characterizing the relaxation processes. Non-exponential behavior of enthalpy relaxation was discussed in the light of possible distribution of relaxation times in the solid solution.