Orientation dependence in high harmonics of ZnO with polarization corrections to counteract the birefringent effect

We investigate the influence of the birefringence on the high-order harmonics in an a-cut Zn O crystal with midinfrared laser pulses. The high harmonics exhibit strong dependence on the alignment of the crystal with respect to the laser polarization. We introduce the Jones calculus to counteract the birefringent effect and obtain the harmonics with polarization corrections in Zn O. We show that the birefringent effect plays an important role in the orientation dependence of HHG.     

Shape stability of a gas bubble in a soft solid

Predicting the onset of non-spherical oscillations of bubbles in soft matter is a fundamental cavitation problem with implications to sonoprocessing, polymeric materials synthesis, and biomedical ultrasound applications. The shape stability of a bubble in a Kelvin-Voigt viscoelastic medium with nonlinear elasticity, the simplest constitutive model for soft solids, is analytically investigated and compared to experiments. Using perturbation methods, we develop a model reducing the equations of motion to two sets of evolution equations: a Rayleigh-Plesset-type equation for the mean (volume-equivalent) bubble radius and an equation for the non-spherical mode amplitudes. Parametric instability is predicted by examining the natural frequency and the Mathieu equation for the non-spherical modes, which are obtained from our model. Our theoretical results show good agreement with published experiments of the shape oscillations of a bubble in a gelatin gel. We further examine the impact of viscoelasticity on the time evolution of non-spherical mode amplitudes. In particular, we find that viscosity increases the damping rate, thus suppressing the shape instability, while shear modulus increases the natural frequency, which changes the unstable mode. We also explain the contributions of rotational and irrotational fields to the viscoelastic stresses in the surroundings and at the bubble surface, as these contributions affect the damping rate and the unstable mode. Our analysis on the role of viscoelasticity is potentially useful to measure viscoelastic properties of soft materials by experimentally observing the shape oscillations of a bubble.     

Yield enhancement of elliptical high harmonics driven by bicircular laser pulses

We theoretically investigate the yield enhancement of elliptical high harmonics in the interaction of molecules with bicircular laser pulses by solving the time-dependent Schrödinger equation. It is shown that by adjusting the relative intensity ratio of the two bicircular field components in specific ranges the yield of the molecular high harmonics for the plateau and cutoff regions can be respectively enhanced. To analyze this enhancement phenomenon, we calculate the weights of the electron classical trajectories. Additionally, we also study the ellipticity distribution of harmonics for different intensity ratios. We find that these enhanced harmonics are elliptically polarized, which we mainly attribute to the recombination dipole moment of the major weighted trajectories. These enhanced elliptical extreme ultraviolet and soft x-ray radiations may serve as essential tools for exploring the ultrafast dynamics in magnetic materials and chiral media.     

Comment on “On the Neumann function and the method of images in spherical and ellipsoidal geometry”

In this note, we point out two errors in the article “On the Neumann function and the method of images in spherical and ellipsoidal geometry” by Dassios and Sten. Two corrections are then proposed.     

H_2~+分子与共振相关的阈下谐波的取向效应

通过数值模拟的方法研究了H_2~+阈下谐波的取向效应.数值模拟过程中,主要关注波长为760nm的阈下谐波,通过逐次减去激发态贡献的方法,研究共振相关谐波不同取向角下的变化规律.结果表明:阈下平行、垂直谐波展示的复杂取向依赖与共振效应密切相关,该现象主要由与基态共振的各激发态的轴对称性导致.另外,用包含跃迁偶极子的简单模型对取向效应进行了概括描述,并以H_2~+第一激发态为演化初始态进行了验证.本文结果可为阈下谐波取向效应的实验研究提供参考.     

Influence of higher harmonics of the undulator in X‐ray polarimetry and crystal monochromator design

The spectrum of the undulator radiation of beamline P01 at Petra III has been measured after passing a multiple reflection channel‐cut polarimeter. Odd and even harmonics up to the 15th order, as well as Compton peaks which were produced by the high harmonics in the spectrum, could been measured. These additional contributions can have a tremendous influence on the performance of the polarimeter and have to be taken into account for further polarimeter designs.     

A polynomial expression for the Hilbert series of the quotient ring of diagonal coinvariants

A special case of Haiman?s identity [M. Haiman, Vanishing theorems and character formulas for the Hilbert scheme of points in the plane, Invent. Math. 149 (2002) 371–407] for the character of the quotient ring of diagonal coinvariants under the diagonal action of the symmetric group yields a formula for the bigraded Hilbert series as a sum of rational functions in q,t. In this paper we show how a summation identity of Garsia and Zabrocki for Macdonald polynomial Pieri coefficients can be used to transform Haiman?s formula for the Hilbert series into an explicit polynomial in q,t with integer coefficients. We also provide an equivalent formula for the Hilbert series as the constant term in a multivariate Laurent series.     

Mixed needlets

The construction of needlet-type wavelets on sections of the spin line bundles over the sphere has been recently addressed in Geller and Marinucci (2008) [14], and Geller et al. (2008, 2009) [12] and [13]. Here we focus on an alternative proposal for needlets on this spin line bundle, in which needlet coefficients arise from the usual, rather than the spin, spherical harmonics, as in the previous constructions. We label this system mixed needlets and investigate in full their properties, including localization, the exact tight frame characterization, reconstruction formula, decomposition of functional spaces, and asymptotic uncorrelation in the stochastic case. We outline astrophysical applications.     

Calculation of geometrical coupling coefficients for the hyperspherical harmonics approach

An elegant and fast method for the calculation of geometrical structure coefficients needed for an expansion of a few-body wavefunction and interaction in hyperspherical harmonics has been proposed. A sum rule for the GSC has also been derived, which is useful for an independent check of the coefficients. The proposed method of computation is many orders of magnitude faster than conventional methods.