Multiphoton transitions for the harmonic oscillator

2- and 3-photon electric dipole transitions for the harmonic oscillator are shown to have zero intensity. This is extended to the general cases of Δv?=?n and Δv?=?n???2 for n-photon transitions. Although not proved in general, it seems likely that all multiphoton transition moments vanish. This suggests that electric dipole multiphoton transition intensity is due to anharmonicity.     

Nichtlineare Wechselwirkung elektromagnetischer Wellen im Plasma mit konstantem Magnetfeld

The nonlinear interaction of waves in anisotropic plasmas is considered. Solving the hydrodynamics equations with a n-th order perturbation procedure, an equation for the nonlinear electric field is derived. The n-th order current produced by interaction of waves with lower order is represented by means of a nonlinear tensor of conductivity, which is calculated for n = 2. It is shown, that a miced plasma wave with combination frequencies is excited as the result of interaction of two transverse (ordinary) waves propagating perpendicular to the magnetic field.     

用于印刷电路板缺陷检测的光学视觉

本文提出了一种利用光学形态变换探测印刷电路板缺陷的新方法。以非相干光学相关器为基础,构成了一个实现印刷电路板微小缺陷检测的形态变换光学视觉系统给出了原理性实验结果。     

Properties of 2 × 2 h-Deformed Quantum (Super)Matrices

We investigate the h-deformed quantum (super)group of 2 × 2 matrices and use a kind of contraction procedure to prove that the n-th power of this deformed quantum (super)matrix is quantum (super)matrix with the deformation parameter nh.     

多模复共轭虚偶相干态光场的等阶N次方Y压缩与等阶N次方H压缩

本文利用新近建立的多模压缩态理论,详细研究了一种新型的多模复共轭虚偶相干态光场|Ψ_i,e^*(2)>_q的广义非线性等阶N次方Y压缩与等阶N次方H压缩特性.结果发现:1)当压缩阶数N为奇数时,态Ψ_i,e^*(2)>_q在一定条件下总可呈现出周期性变化的、任意阶的等阶N次方Y压缩效应;当腔模总数q与压缩阶数N两者之乘积q·N为奇数时,则在一定条件下态|Ψ_i,e^*(2)>_q又可呈现出周期性变化的、任意阶的等阶N次方H压缩效应.2)态|Ψ_i,e^*(2)>_q与多模偶相干态光场|Ψ_i,e^*(2)>_q与多模虚偶相干态光场|Ψ_i,e⁽²⁾>_q的压缩幅度、压缩条件和压缩特征等完全相同.这一结果再次从理论上证实了多模压缩光中的确存在着“相反压缩”和“压缩简并”这两类新的物理现象.     

Partial coherence in the core–halo picture of Bose–Einstein n-particle correlations

We study the influence of a possible coherent component in the boson source on the two-, three- and n-particle correlation functions in a generalized core–halo-type boson-emitting source. In particular, a simple formula is presented for the strength of the n-particle correlation functions for such systems. Graph rules are obtained to evaluate the correlation functions of arbitrarily high order. The importance of an experimental determination of the 4-th and 5-th order Bose–Einstein correlation function is emphasized. Received: 18 December 1998 / Published online: 20 May 1999     

第Ⅰ类两态叠加多模叠加态光场的非线性高阶压缩特性研究

本文在文献20的基础上进一步提出了多模辐射场的N-Y最小测不准态、N-H最小测不准态、N-Y压缩最小测不准态以及N-H压缩最小测不准态等的定义.构造了由多模(q模)相干态|{Z_j}>_q及其相反态|{-Z_j}>_q的线性叠加所组成的第Ⅰ类两态叠加多模叠加态光场|ψ₁⁽²⁾>_q,利用文献20新近提出的有关多模辐射场的两种非线性高阶压缩的定义,首次对态|ψ₁⁽²⁾>_q的N次方Y压缩及N次方H压缩效应进行了详细研究.结果表明,1)当N为偶数时,态|ψ₁⁽²⁾>_q恒处于N-Y最小测不准态;当N为奇数时,态|ψ₁⁽²⁾>_q在一定条件下可呈现出周期性变化的、任意阶的N次方Y压缩效应.2)当q·N为偶数时,态|ψ₁⁽²⁾>_q恒处于N-H最小测不准态;当q·N为奇数时,在另外的条件下,态|ψ₁⁽²⁾>_q则可呈现出周期性变化的、任意阶的N次方H压缩效应.3)N次方Y压缩及N次方H压缩效应的压缩深度与腔模总数q、压缩参数R_j以及压缩阶数N等非线性相关,后者与上述参量的非线性关联程度要比前者的更强.     

Z-scan analytical theories for characterizing multiphoton absorbers

The open-aperture Gaussian-beam Z-scan measurements for characterizing an optically thin multiphoton-absorbing material were systematically investigated. Two widely used temporal profiles of the laser pulses on Z-scan traces were considered as well. The analytical polynomial expressions of Z-scan traces were presented for a thin sample with only one nonlinear process at a time [two-, three-, four-, or five-photon absorption (2PA, 3PA, 4PA, or 5PA)] and concurrence of two different processes (e.g., 2PA and 3PA, 3PA and 4PA, or 4PA and 5PA), respectively. A simple yet highly efficient approach was presented for identifying and evaluating the simultaneous n- and (n+1)-photon absorption coefficients.     

α-SiN:H薄膜的光学声子与VO2基Mott相变场效应晶体管的红外吸收特性

从器件构成材料中α-SiN:H，VO₂，Al薄膜介电常数弥散特性的Lorentz多谐振模型出发，研究了器件在金属表面等离子体与VO₂，特别是α-SiN:H薄膜光学声子共同作用下的红外吸收特性；得到了在不同的光谱范围器件的红外吸收特性随着α-SiN: H钝化层几何厚度的变化关系，与中心工作波长10μm对应的且经过位相修正以后钝化层的几何厚度为λ/4n时的红外吸收光谱、以及VO₂的相变对吸收光谱的影响. 关键词： 红外吸收特性 Mott相变 场效应晶体管 二氧化钒     

Change of photon statistics due to multi-photon absorption

Simple approximative equations governing the temporal behaviour of both the mean photon number, $\text{n}$, and its mean square deviation, Δn², in the process of k-photon absorption (k = 1, 2, …) are derived and solved for initial photon distributions characterized by $\text{n}$ ? 1 and Δn² ? $\text{n}$^-2. It is readily shown that such an initial distribution, in the course of attenuation, tends to a distribution for which $\text{Δn}{}^2\text{= k (2 k - 1)}{}^{-1}\text{n}$. Hence, for k > 1, the distribution is narrower than a Poisson distribution which means that photon antibunching occurs. The feasibility of a Hanbury Brown and Twiss type experiment allowing to detect this effect utilizing two-photon absorption is discussed, and an estimation of the required order of magnitude of the two-photon absorption cross-section is presented.     

Quenchedn-vectorp-spin model

A disorderedn-vector model withp spin interactions previously introduced is studied for the quenched case by means of the replica method and a generalized Parisi theory. We present formal solutions for generaln andp and then study the casep . The high-temperature solution is stable at all temperatures and there is only one phase transition at a temperatureT _g. Only longitudinal lowtemperature solutions are possible. There is one spin-glass solution, and it is stable for allT _g. The phase transition atT _g is of first order and displays a jump discontinuity in the order parametersq _j ^(L) andd. The spin-glass free energy is temperature dependent forn > 1 while it is constant whenn = 1.     

Nonlinear light absorption on the surface of a transparent wide-gap crystal: I. Direct interband transitions

For a semi-infinite wide-gap crystal, expressions for the rates of one- and two-photon transitions caused by the action of linearly polarized light are obtained in the basis set of model surface and bulk functions. The transition probability is shown to significantly depend on the angle between the light polarization vector and the normal to the surface Ψ. At a light intensity of 10 MW/cm², the probability of one-photon transitions between surface states is in the range 10²⁴−10²⁶ s⁻¹ cm⁻² (ψ = π/2 and ψ = 0, respectively). It is shown that, in the case wherein the light polarization vector is perpendicular to the surface, the rates of allowed n-photon transitions (n = 1, 2) decrease more slowly with increasing n than in the case in which the polarization vector lies in the plane of the surface.     

Multiphoton transitions and the resonant optical Stark effect in AgBr nanocrystals

Nonlinear absorption of 30-ps light pulses with λ = 560 nm in AgBr nanocrystals is experimentally studied in the range of intensities 10⁸–10¹⁰ W/cm². The results of a theoretical analysis show that the absorption is related to direct interband n-photon transitions. With increasing light intensity j, the number n increases and the region of the k-space changes for the transitions predominantly contributing to the absorption. It is shown that, due to specific features of the AgBr electronic band structure, the probabilities of two-photon transitions for the light at λ = 560 nm are anomalously low, while those of four-photon transitions are anomalously high. In addition, the increase in the two-photon transition rate with increasing intensity is blocked at j ? 10⁸ W/cm² due to the resonant optical Stark effect and due to a gap arising in the band spectrum, rearranged because of the interaction with light.     

Isotopically selective IR multiphoton dissociation of 1,3,5-trioxane

Searching for oxygen-isotope selectivity, we investigated the infrared multiphoton dissociation of the formaldehyde trimer around 10 µm, in a range where the molecule has a degenerate and a non-degenerate CO stretch vibration and a degenerate CH₂ deformation vibration. In the region of the two latter, the wavelength dependence of the dissociation yield exhibits sharp structures. They were assigned ton-photon resonances (n = 2, 3, 5) by the help of the IR spectrum in the fundamental and overtone region. The O and C selectivities were very small (1.05) near the non-degenerate CO stretch band, but surprisingly large (2–4) in the CH₂ deformation, which has no isotopic shift. The selectivity is not controlled by the first (n-photon) excitation step, but only by a later step. Its assignment is attempted. The pressure dependence of the dissociation is peculiar: Only after an initial decrease, the yield exhibits the usual rise with pressure. We attribute the decrease to a relaxation which perturbs the two-photon resonance.     

态|Ψn(2)>q的广义非线性等阶N次方H压缩效应

构造了一种新型的多模叠加态|Ψ_n⁽²⁾>_q=C_n^(R)|{-iZ_j^*}>_q+C_n⁽⁰⁾|{O_j}>_q;并首次详细地研究了此量子态的等阶N次方H压缩特性.大量的计算和分析表明:态|Ψ_n⁽²⁾>_q是一种多模典型的非经典光场;还发现了"相似压缩"等现象.     

Multiphoton absorption controlled by the resonance optical stark effect in crystals

Probabilities of n-photon transitions between upper valence and lower conduction bands under conditions in which the frequency of light is in resonance with the frequency of adjacent transition between two conduction bands are calculated for arbitrary integer n. The case of n = 3 is investigated in detail. Effects caused by transformation of the electronic band spectrum due to the resonance optical Stark effect are analyzed. It is shown that the rate of photogeneration of electron-hole pairs as a function of radiation intensity j is nonmonotonic and includes areas of extremely fast rise and/or decrease due to the appearance of new van Hove singularities in the modified band spectrum.     

Annealedn-vectorp-spin model

A disorderedn-vector model withp spin interactions is introduced and studied in mean field theory for the annealed case. We present complete solutions for the casesn=2 andn=3, and have obtained explicit order parameter equations for all the stable solutions for arbitraryn. For alln andp we find one stable high-temperature phase and one stable low-temperature phase. The phase transition is of first order. Forn=2, it is continuous in the order parameters for p4 and has a jump discontinuity in the order parameters ifp>4. Forn=3, it has a jump discontinuity in the order parameters for allp.     

Theorem on the Distribution of Short-Time Particle Displacements with Physical Applications

The distribution of the initial short-time displacements of particles is considered for a class of classical systems under rather general conditions on the dynamics and with Gaussian initial velocity distributions, while the positions could have an arbitrary distribution. This class of systems contains canonical equilibrium of a Hamiltonian system as a special case. We prove that for this class of systems the nth order cumulants of the initial short-time displacements behave as the 2n-th power of time for all n > 2, rather than exhibiting an nth power scaling. This has direct applications to the initial short-time behavior of the Van Hove self-correlation function, to its non-equilibrium generalizations the Green's functions for mass transport, and to the non-Gaussian parameters used in supercooled liquids and glasses. PACS Number: 05.20.-y, 02.30.Mv, 66.10.-x, 78.70.Nx, 05.60.Cd     

一种新型的多模虚偶相干态光场的等阶N次方Y压缩与等阶N次方H压缩

本文利用新近建立的多模压缩态理论,详细研究了一种新型的多模虚偶相干态光场|Ψ_i,e⁽²⁾>_q的广义非线性等阶N次方Y压缩与等阶N次方H压缩特性.结果发现:1)态|Ψ_i,e⁽²⁾>_q是一种典型的多模非经典光场,当压缩阶数N为奇数时,态|Ψ_i,e⁽²⁾>_q在一定条件下总可呈现出周期性变化的、任意阶的等阶N次方Y压缩效应;当腔模总数q与压缩阶数N这两者的乘积q·N为奇数时,则在一定条件下态|Ψ_i,e⁽²⁾>_q又可呈现出周期性变化的、任意阶的等阶N次方H压缩效应.2)态|Ψ_i,e⁽²⁾>_q的等阶N次方Y压缩与等阶N次方H压缩效应这两者的压缩程度和压缩深度分别与几率幅γ_q^(e)、压缩参数R_j、各模的初始相位φ_j(或者各模的初始相位和 φ_j)、压缩阶数N以及腔模(指纵模)总数q等呈较强的非线性关联,等阶N次方H压缩效应与上述诸参量之间的非线性关联程度要比等阶N次方Y压缩效应的更强.3)多模虚偶相干态光场|Ψ_i,e⁽²⁾>_q与多模偶相干态光场|Ψ_,e>_q及多模复共轭偶相干态光场|Ψ*_,e⁽²⁾>_q这后两者的等阶N次方Y压缩效应和等阶N次方H压缩效应的压缩条件和压缩特性正好相反,这种现象就称为相反压缩.     

Exact analytical solution for the change of the photon statistics due tok-photon absorption

For unsaturatedk-photon absorption the exact solution of the master equation for the diagonal elements is presented. This solution is found by Laplace-transformation and recursion. It has the form of a double sum over the initial values. Commuting the order of summation we then show, that fork2 the photon distribution does not depend on the initial distribution if the initial mean photon number is sufficiently high and the square of the resulting photon number is small against the initial photon number.