Mechanism of micro-waviness induced KH₂PO₄ crystal laser damage and the corresponding vibration source

The low laser induced damage threshold of the KH2PO4 crystal seriously restricts the output power of inertial confinement fusion.The micro-waviness on the KH2PO4 surface processed by single point diamond turning has a significant influence on the damage threshold.In this paper,the influence of micro-waviness on the damage threshold of the KH2PO4 crystal and the chief sources introducing the micro-waviness are analysed based on the combination of the Fourier modal theory and the power spectrum density method.Research results indicate that among the sub-wavinesses with different characteristic spatial frequencies there exists the most dangerous frequency which greatly reduces the damage threshold,although it may not occupy the largest proportion in the original surface.The experimental damage threshold is basically consistent with the theoretical calculation.For the processing parameters used,the leading frequency of micro-waviness which causes the damage threshold to decrease is between 350-1 μm-1 and 30-1 μm-1,especially between 90-1 μm-1 and 200-1 μm-1.Based on the classification study of the time frequencies of microwaviness,we find that the axial vibration of the spindle is the chief source introducing the micro-waviness,nearly all the leading frequencies are related to the practical spindle frequency(about 6.68 Hz,400 r/min) and a special middle frequency(between 1.029 Hz and 1.143 Hz).     

Study on incident laser modulation using surface micro-defects on KH2PO4 crystal

KH2PO4 crystal is a crucial optical component of inertial confinement fusion. Modulation of an incident laser by surface micro-defects will induce the growth of surface damage, which largely restricts the enhancement of the laser induced damage threshold. The modulation of an incident laser by using different kinds of surface defects are simulated by employing the three-dimensional finite-difference time-domain method. The results indicate that after the modulation of surface defects, the light intensity distribution inside the crystal is badly distorted, with the light intensity enhanced symmetrically. The relations between modulation properties and defect geometries （e.g., width, morphology, and depth of defects） are quite different for different defects. The modulation action is most obvious when the width of surface defects reaches 1.064 p-m. For defects with smooth morphology, such as spherical pits, the degree of modulation is the smallest and the light intensity distribution seems relatively uniform. The degree of modulation increases rapidly with the increase of the depth of surface defects and becomes stable when the depth reaches a critical value. The critical depth is 1.064 μm for cuboid pits and radial cracks, while for ellipsoidal pits the value depends on both the width and the length of the defects.     

Application of thermal stress model to paint removal by Q-switched Nd:YAG laser

In this paper, we demonstrate that thermal stress is the main mechanism in the process of paint removal by Q-switched Nd：YAG laser （λ = 1064 nm, τ = 10 ns）. A theoretical model ofpaint removal by short-pulse laser is established from the perspective of thermal stress. Thermal stress is generated by thermal expansion, and the temperatures of different samples are calculated according to the one-dimensional （1D） heat conduction equation. The theoretical cleaning threshold can be obtained by comparing thermal stress with the adhesion of paint, and the theoretical damage threshold is obtained by calculating the temperature. Moreover, the theoretical calculations are verified by experimental results. It is shown that the thermal stress model of the laser cleaning is very useful to choose the appropriate laser fluence in the practical applications of paint removal by Q-switched Nd： YAG laser because our model can validly balance the efficiency of laser cleaning and the safety of the substrate.     

Analysis on Far-Field of Slab Waveguide and Its Gaussian Approximation

This paper researches end diffraction of slab waveguide and then matching efficiency between the far-field and its Gaussian approximate field is analyzed leads to a new definition of divergence half-angle. Finally, why the far-field can be approximated by a Gaussian function is presented according to characteristic of beam propagation factor.     

Characterization of calcium phosphate coatings doped with Mg, deposited by pulsed laser deposition technique using ArF excimer laser

Calcium phosphate layers were deposited on Ti6Al4V substrates with TiN buffer layers by use of pulsed laser deposition method. With this technique three pressed pellets consisted of tricalcium phosphate (TCP, Ca(3)(PO(4))(2)), hydroxyapatite (HA, Ca(10)(PO(4))(6)(OH)(2)) and hydroxyapatite-doped with magnesium (HA with 4% of Mg and trace amount of (Ca,Mg)(3)(PO(4))(2)) were ablated using ArF excimer laser (lambda=193 nm). The using of different targets enabled to determine the influence of target composition on the nature of deposited layers. The obtained deposits were characterized by means of Fourier transform infrared spectroscopy (FTIR) and X-ray diffraction method (XRD). The obtained Fourier spectras revealed differences in terms of intensity of spectral bands of different layers. The analysis from XRD showed that Mg-doped HA layer has crystalline structure and TCP and HA layers composition is characterized by amorphous nature.     

Binding Energy of D^- and D^0 Centers Confined by Spherical Quantum Dots

We study a negative donor center, a neutral donor in a spherical Gaussian potential quantum dot by using the matrix diagonalization of Hamiltonian within the effective-mass approximation. We calculate the energy E（ D^-） as functions of Gaussian potential size and depth, the same calculations as performed with the parabolic approximation. The dependence of the ground state of the neutral shallow donor and the negatively charged donor on the dot size and the potential depth is investigated.     

An improved deconvolution method for X-ray coded imaging in inertial confinement fusion

In inertial confinement fusion （ICF）, X-ray coded imaging is considered as the most potential means to diagnose the compressed core. The traditional Richardson-Lucy （RL） method has a strong ability to deblur the image where the noise follows the Poisson distribution. However, it always suffers from over-fitting and noise amplification, especially when the signal-to-noise ratio of image is relatively low. In this paper, we propose an improved deconvolution method for X-ray coded imaging. We model the image data as a set of independent Gaussian distributions and derive the iterative solution with a maximum-likelihood scheme. The experimental results on X-ray coded imaging data demonstrate that this method is superior to the RL method in terms of anti-overfitting and noise suppression.     

Transient Properties of a Bistable System with Delay Time Driven by Non-Gaussian and Gaussian Noises： Mean First-Passage Time

The mean first-passage time of a bistable system with time-delayed feedback driven by multiplicative non-Gaussian noise and additive Gaussian white noise is investigated. Firstly, the non-Markov process is reduced to the Markov process through a path-integral approach; Secondly, the approximate Fokker-Planck equation is obtained by applying the unified coloured noise approximation, the small time delay approximation and the Novikov Theorem. The functional analysis and simplification are employed to obtain the approximate expressions of MFPT. The effects of non-Gaussian parameter （measures deviation from Gaussian character） r, the delay time τ, the noise correlation time to, the intensities D and a of noise on the MFPT are discussed. It is found that the escape time could be reduced by increasing the delay time τ, the noise correlation time τ0, or by reducing the intensities D and α. As far as we know, this is the first time to consider the effect of delay time on the mean first-passage time in the stochastic dynamical system.     

Realization of quantum Fourier transform over ZN

Since the difficulty in preparing the equal superposition state of amplitude is 1/√N, we construct a quantile transform of quantum Fourier transform （QFT） over ZN based on the elementary transforms, such as Hadamard transform and Pauli transform. The QFT over Z_N can then be realized by the quantile transform, and used to further design its quantum circuit and analyze the requirements for the quantum register and quantum gates. However, the transform needs considerable quantum computational resources and it is difficult to construct a high-dimensional quantum register. Hence, we investigate the design of t-bit quantile transform, and introduce the definition of t-bit semiclassical QFT over Z_N. According to probability amplitude, we prove that the transform can be used to realize QFT over ZN and further design its quantum circuit. For this transform, the requirements for the quantum register, the one-qubit gate, and two-qubit gate reduce obviously when compared with those for the QFT over Z_N.     

Theoretical study of the structure and analytic potential energy function for the ground state of the PO2 molecule

In this paper, the energy, equilibrium geometry, and harmonic frequency of the ground electronic state of PO2 are computed using the B3LYP, B3P86, CCSD（T）, and QCISD（T） methods in conjunction with the 6-311＋＋G（3df, 3pd） and cc-pVTZ basis sets. A comparison between the computational results and the experimental values indicates that the B3P86/6-311＋＋G（3df, 3pd） method can give better energy calculation results for the PO2 molecule. It is shown that the ground state of the PO2 molecule has C2v symmetry and its ground electronic state is X2A1. The equilibrium parameters of the structure are Rp-o = 0.1465 am, ZOPO = 134.96°, and the dissociation energy is Ed = 19.218 eV. The bent vibrational frequency Ul = 386 cm-1, symmetric stretching frequency v2 = 1095 cm-1, and asymmetric stretching frequency ua = 1333 em-1 are obtained. On the basis of atomic and molecular reaction statics, a reasonable dissociation limit for the ground state of the PO2 molecule is determined. Then the analytic potential energy function of the PO2 molecule is derived using many-body expansion theory. The potential curves correctly reproduce the configurations and the dissociation energy for the PO2 molecule.     

熔石英亚表面修复形貌对光场的调制

基于标量衍射理论, 计算了熔石英亚表面高斯型修复形貌对于光场的调制，用Matlab对结果进行了仿真并与实验结果进行了比较。所得结果表明，二者有较好的一致性, 一定尺度的高斯面型修复形貌会对光场产生调制，且调制度随光场传输位置变化，通过适当选择后续光学元件位置，可降低光场调制造成光学元件损伤的风险。     

Source function extracted from single-event HBT correlation functions of hydrodynamical sources

We investigate the single-event two-pion correlation functions for the hydrodynamic particle-emitting sources with the fluctuating initial conditions generated by the Heavy Ion Jet Interaction Generator （HIJING）. Using a three-dimension fast Fourier transform （FFT）, we further extract the source functions from the single-event correlation functions. It is found that the inhomogeneity of the hydrodynamic sources with the fluctuating initial conditions lead to event-by-event fluctuations of the correlation functions and source functions.     

Exact Time-Dependent Wave Functions of a Confined Time-Dependent Harmonic Oscillator with Two Moving Boundaries

By applying the standard analytical techniques of solving partial differential equations, we have obtained the exact solution in terms of the Fourier sine series to the time-dependent Schrodinger equation describing a quantum one-dimensional harmonic oscillator of time-dependent frequency confined in an infinite square well with the two walls moving along some parametric trajectories. Based upon the orthonormal basis of quasi-stationary wave functions, the exact propagator of the system has also been analytically derived. Special eases like （i） a confined free particle, （ii） a confined time-independent harmonic oscillator, and （iii） an aging oscillator are examined, and the corresponding time- dependent wave functions are explicitly determined. Besides, the approach has been extended to solve the case of a confined generalized time-dependent harmonic oscillator for some parametric moving boundaries as well.     

Convolution Theorem of Fractional Fourier Transformation Derived by Representation Transformation in Quantum Mechancis

Based on our previous paper （Commun. Theor. Phys. 39 （2003） 417） we derive the convolution theorem of fractional Fourier transformation in the context of quantum mechanics, which seems a convenient and neat way. Generalization of this method to the complex fractional Fourier transformation case is also possible.     

A novel orthogonally linearly polarized Nd:YVO4 laser

<正>We presented a novel orthogonally linearly polarized Nd:YVO₄ laser.Two pieces of a-cut grown-together composite YVO₄/Nd:YVO₄ crystals were placed in the resonant cavity with the c-axis of the two crystals orthogonally.The polarization and power performance of the orthogonally polarized laser were investigated.A 26.2-W orthogonally linearly polarized laser was obtained.The power ratio between the two orthogonally polarized lasers was varied with the pump power caused by the polarized mode coupling.The longitudinal modes competition and the corresponding variable optical beats were also observed from the orthogonally polarized laser.We also adjusted the crystals with their c-axis parallele to each other,and a 40.7-W linearly polarized TEMoo laser was obtained,and the beam quality factors were M_x²=1.37 and M_y² =1.25.     

Implementation of Quantum Fourier Transform and Its Applications via Quantum-Dot Spins and Microcavity

A scheme for implementing discrete quantum Fourier transform is proposed via quantum dots embedded in a microcavity, and then some of its applications are investigated, i.e., Deutsch 3ozsa. algorithm and Shor＇s quantum factoring. In particular, the detailed process of implementing one~qubit Deutsch Jozsa algorithm and the factorization of N = 15 are given. The microcavity mode is only virtually excited in the whole interaction, so the effective decoherent has slight effect on the current scheme. These schemes would be an important step to fabricate a solid quantum computer.     

Application of Fourier Slice Theorem in Wigner Operator Theory and New Complete Representation

By applying the Fourier slice theorem, Sθ（λ） =∫^∞-∞Pθ（t）e^-iλt=F（λcosθ,λsinθ）,where Pθ（t） is a projection of f（x,p）=^∞∫∫-∞F（u,v）e^i（uz＋up） dudv along lines of constant, to the Wigner operator we are naturally led to a projection operator （pure state）, which results in a new complete representation. The Weyl orderimg formalism of the Wigner operator is used in the derivation.     

Average vector field methods for the coupled Schr/idinger-KdV equations

The energy preserving average vector field （AVF） method is applied to the coupled Schr6dinger-KdV equations. Two energy preserving schemes are constructed by using Fourier pseudospectral method in space direction discretization. In order to accelerate our simulation, the split-step technique is used. The numerical experiments show that the non-splitting scheme and splitting scheme are both effective, and have excellent long time numerical behavior. The comparisons show that the splitting scheme is faster than the non-splitting scheme, but it is not as good as the non-splitting scheme in preserving the invariants.     

Multi-symplectic method for the coupled Schrodinger-KdV equations

In this paper, we present a multi-symplectic Hamiltonian formulation of the coupled Schrtidinger-KdV equations （CS＇KE） with periodic boundary conditions. Then we develop a novel multi-symplectic Fourier pseudospectral （MSFP） scheme for the CSKE. In numerical experiments, we compare the MSFP method with the Crank-Nicholson （CN） method. Our results show high accuracy, effectiveness, and good ability of conserving the invariants of the MSFP method.     

Numerical simulation of the modulation to incident laser by the repaired damage site in a fused silica subsurface

One of the main factors of laser induced damage is the modulation to incident laser which is caused by the defect in the subsurface of the fused silica.In this work,the repaired damage site irradiated by CO 2 laser is simplified to a Gaussian rotation according to the corresponding experimental results.Then,the three-dimensional finite-difference time-domain method is employed to simulate the electric field intensity distribution in the vicinity of this kind of defect in fused silica front subsurface.The simulated results show that the modulation is notable,the E max is about 2.6 times the irradiated electric field intensity in the fused silica with the damage site (the width is 1.5 μm and depth is 2.3 μm) though the damage site is repaired by CO 2 laser.The phenomenon and the theoretical result of the annular laser enhancement existed on the rear surface are first verified effectively,which agrees well with the corresponding experimental results.The relations between the maximal electric field intensity in fused silica with defect depth and width are given respectively.Meanwhile,the corresponding physical mechanism is analysed theoretically in detail.