Deep subsurface optical waveguides produced by direct writing with femtosecond laser pulses in fused silica and phosphate glass

In the present work, we have analyzed the use of elliptical beam shaping along with low numerical aperture focusing optics in order to produce circular cross-section waveguides in different materials at large processing depths by direct femtosecond laser writing (100 fs, 800 nm, 1 kHz). A variable slit located before the focusing optics allows to generate a nearly elliptical beam shape and also to reduce the effective numerical aperture of the beam along the shat axis of the ellipse. The focusing optics allows to focus the beam deep inside the sample, which is translated at a constant speed transversely to the writing beam direction. The influence of several experimental parameters (energy per pulse, slit width, processing depth) on the properties of the produced waveguides has been analyzed. The influence of the intrinsic properties of the material (refractive index, composition) has been analyzed by comparing results obtained in fused silica and Er:Yb co-doped phosphate glass. The results obtained show that this approach leads to the successful production of deep subsurface (up to 7 mm) waveguides with circular cross-sections. Preliminary results using chirped pulses in the phosphate glass suggest that temporal pulse shaping can be used as an additional parameter to optimize the guided mode symmetry.     

再论各向异性单轴晶体的布儒斯特角

从各向同性介质和各向异性单轴晶体界面间的菲涅耳公式出发,进一步研究了当自然光从各向同性介质射向各向异性且光轴任意取向的单轴晶体界面上时,其反射光成为垂直入射面的线偏振光时所对应的入射角,即布儒斯特角是否存在的问题,并对该问题进行了较全面的论述,计算了相应条件下的布儒斯特角和有关参量的数值,得到了正确的结论,同时也指出了某些文献在论述该问题时的不妥之处.     

Unconditionally Stable Complex Envelope Wave Equation PML Algorithm for Band Limited FDTD Simulations

Unconditionally stable complex envelope (CE) perfectly matched layer (PML) absorbing boundary conditions (ABCs) are presented for truncating the scalar wave-equation finite difference time domain (WE-FDTD) grids. The formulations are based on incorporating the alternating direction implicit (ADI) scheme into the CE FDTD implementations of the scalar wave-equation derived in the PML region at the domain boundaries. Numerical example carried out in two dimensional domain shows that the proposed formulations are more accurate than the classical ADI scalar wave equation PML formulations when it is used for modelling band limited electromagnetic applications.     

A second-order accurate numerical method for the two-dimensional fractional diffusion equation

Spatially fractional order diffusion equations are generalizations of classical diffusion equations which are used in modeling practical superdiffusive problems in fluid flow, finance and others. In this paper, we present an accurate and efficient numerical method to solve a fractional superdiffusive differential equation. This numerical method combines the alternating directions implicit (ADI) approach with a Crank–Nicolson discretization and a Richardson extrapolation to obtain an unconditionally stable second-order accurate finite difference method. The stability and the consistency of the method are established. Numerical solutions for an example super-diffusion equation with a known analytic solution are obtained and the behavior of the errors are analyzed to demonstrate the order of convergence of the method.     

显示反射全息图单光束相干复制技术

描述用单光束激光复活制银盐白光显示反射全息图的技术，本技术的关键：１）母全息图的颜色必须恢复到满足其布拉格条件；２）复制所用的光波与记录母全息图时的参考的相同；（３）复制所用的激光采用平行偏振，以减少界面反射；９４）采用白糖溶液作为折射率匹配液，取得极佳效果。     

Greatest Descent Algorithms in Unconstrained Optimization

We show that, for an unconstrained optimization problem, the long-term optimal trajectory consists of a sequence of greatest descent directions and a Newton method in the final iteration. The greatest descent direction can be computed approximately by using a Levenberg-Marquardt like formula. This implies the view that the Newton method approximates a Levenberg-Marquardt like formula at a finite distance from the minimum point, instead of the standard view that the Levenberg-Marquadt formula is a way to approximate the Newton method. With the insight gained from this analysis, we develop a two-dimensional version of a Levenberg-Marquardt like formula. We make use of the two numerically largest components of the gradient vector to define here new search directions. In this way, we avoid the need of inverting a high-dimensional matrix. This reduces also the storage requirements for the full Hessian matrix in problems with a large number of variables. The author thanks Mark Wu, Professors Sanyang Liu, Junmin Li, Shuisheng Zhou and Feng Ye for support and help in this research as well as the referees for helpful comments.     

Used digital speckle correlation method to realize orientation function of optical mouse

Used digital speckle correlation method (DSCM) to realize orientation function of optical mouse is researched. The experiment is designed to obtain the dynamic speckle patterns which are shot by CCD, then the DSCM is used to process the sequential images and also the experiment is simulated. The experimental results show the DSCM can confirm orientation function of the optical mouse, and have a good agreement with the simulation results, and the resolution we obtained is higher than the resolution of mouse on the market.     

Growth and raman scattering of aluminium gallium orthophosphate piezoelectric crystals

A new series of non-ferroelectric crystals, the piezoelectric solid solution aluminium gallium orthophosphate Al_1-xGa_xPO₄ (AGP, 0 < x < 1) system has been successfully developed by a hydrothermal method. The AGP crystal with X = 0.10 shows a phase transition temperature T_−β = 587 ± 3 °C with a cell parameters A = b = 0.49386(3) and C = 1.09563(2) nm. Raman spectra including directional dispersion in AGP are similar to those from -AIPO4 and -quartz crystals, indicating all of them belong to an isomorphic family, the short-range interaction being dominant in AGP. Comparison with -AIPO4 crystals, there exists an apparent red shift of the mode frequency and a smaller TO/LO mode splitting of the E species in the AGP crystals.     

Efficient interval partitioning for constrained global optimization

A new efficient interval partitioning approach to solve constrained global optimization problems is proposed. This involves a new parallel subdivision direction selection method as well as an adaptive tree search. The latter explores nodes (intervals in variable domains) using a restricted hybrid depth-first and best-first branching strategy. This hybrid approach is also used for activating local search to identify feasible stationary points. The new tree search management technique results in improved performance across standard solution and computational indicators when compared to previously proposed techniques. On the other hand, the new parallel subdivision direction selection rule detects infeasible and suboptimal boxes earlier than existing rules, and this contributes to performance by enabling earlier reliable deletion of such subintervals from the search space.     

Self-avoiding walks in slits and slabs with interactive walls

Self-avoiding walk models of a polymer confined between two parallel attractive walls in two and three dimensions (slits and slabs, respectively) have recently had a revival of interest. They were first studied as simple models of steric stabilisation and sensitised flocculation in colloids. The revival has been catalysed by new exact solution techniques, that have allowed the solution of directed walk models in two dimensions in full generality, and by new Monte Carlo techniques that have allowed the simulation of the full parameter space in the three-dimensional slab model. Additionally, rigorous techniques applied to the slab problem have also yielded new results. The contributions to the study of this problem that have been recently added include a novel phase diagram for the “infinite-slab” (when the walls are a macroscopic distance apart but both walls may still “see” the polymer) the delineation of the repulsive and attractive regimes of the parameter space, and a conjectured scaling theory for the problem in general dimensions.