Effects of optical axis direction on optical path difference and lateral displacement of Savart polariscope

A simple method is applied to calculating the optical path difference （OPD） of a plane parallel uniaxial plate with an arbitrary optical axis direction. Then, the theoretical expressions of the OPD and lateral displacement （LD） of Savart polariscope under non-ideal conditions are obtained exactly. The variations of OPD and LD are simulated, and some important conclusions are obtained when the optical axis directions have an identical tolerance of ／pm 1^{{／circ}}. An application example is given that the tolerances of optical axis directions are gained according to the spectral resolution tolerances of the stationary polarization interference imaging spectrometer （SPIIS）. Several approximate formulae are obtained for explaining some conclusions above. The work provides a theoretical guidance for the optic design, crystal processing, installation and debugging, data analysis and spectral reconstruction of the SPIIS.

Difference scattering field properties between periodic defect particles and three-dimensional slightly rough optical surface

Based on the practical situation of nondestructive examination, the calculation model of the composite scattering is established by using a three-dimensional half-space finite difference time domain, and the Monte Carlo method is used to solve the problem of the optical surface with roughness in the proposed scheme. Moreover, the defect particles are observed as periodic particles for a more complex situation. In order to obtain the scattering contribution of defects inside the optical surface, a difference radar cross section is added into the model to analyze the selected calculations on the effects of numbers, separation distances, different depths and different materials of defects. The effects of different incident angles are also discussed. The numerical results are analyzed in detail to demonstrate the best position to find the defects in the optical surface by detecting in steps of a fixed degree for the incident angle.

Full-vectorial analysis of optical waveguides by the finite difference method based on polynomial interpolation

Based on the polynomial interpolation, a new finite difference （FD） method in solving the full-vectorial guidedmodes for step-index optical waveguides is proposed. The discontinuities of the normal components of the electric field across abrupt dielectric interfaces are considered in the absence of the limitations of scalar and semivectorial approximation, and the present PD scheme can be applied to both uniform and non-uniform mesh grids. The modal propagation constants and field distributions for buried rectangular waveguides and optical rib waveguides are presented. The hybrid nature of the vectorial modes is demonstrated and the singular behaviours of the minor field components in the corners are observed. Moreover, solutions are in good agreement with those published early, which tests the validity of the present approach.

Laboratory demonstration of geopotential measurement using transportable optical clocks

We report an experimental demonstration of geopotential difference measurement using a pair of transportable ^(40)Ca^(+) optical clocks(TOC-729-1 and TOC-729-3)in the laboratory,each of them has an uncertainty of 1.3×10^(−17) and an instability of 4.8×10^(−15)/√τ.Referenced to a stationary clock of TOC-729-1,the geopotential difference measurements are realized by moving TOC-729-3 to three different locations and the relevant altitude differences are measured with uncertainties at the level of 20 cm.After correcting the systematic shifts(including gravitational red shift),the two-clock frequency difference is measured to be–0.7(2.2)×10^(−17),considering both the statistic(1.0×10^(−17))and the systematic(1.9×10^(−17))uncertainties.The frequency difference between these two clocks is within their respective uncertainties,verifying the reliability of transportable ^(40)Ca^(+) optical clocks at the low level of 10^(−17).

NON-LINEAR OPTICAL IMAGING OF OBESITY-RELATED HEALTH RISKS:REVIEW

This review highlights the recent applications of non-linear optical(NLO)microscopy to study obesity-related health risks.A strong emphasis is given to the applications of coherent anti-Stokes Raman scattering(CARS)microscopy where multiple non-linear optical imaging modalities including CARS,sum-frequency generation(SFG),and two-photon fluorescence are employed simultaneously on a single microscope platform.Specific examples on applications of NLO microscopy to study lipid-droplet biology,obesity-cancer relationship,atherosclerosis,and lipidrich biological structures are discussed.

VALUE DISTRIBUTION OF MEROMORPHIC SOLUTIONS OF CERTAIN NON-LINEAR DIFFERENCE EQUATIONS

In this article, we consider the non-linear difference equation(f(z + 1)f(z)-1)(f(z)f(z-1)-1) =P(z, f(z))/Q(z, f(z)),where P(z, f(z)) and Q(z, f(z)) are relatively prime polynomials in f(z) with rational coefficients. For the above equation, the order of growth, the exponents of convergence of zeros and poles of its transcendental meromorphic solution f(z), and the exponents of convergence of poles of difference △f(z) and divided difference △f(z)/f(z)are estimated. Furthermore, we study the forms of rational solutions of the above equation.

Synthesis, Structure and Third-order Non-linear Optical Properties of Tungsten Dioxo Complex with 8-Hydroxyquinoline Ligand WO_2(C_9H_6NO)_2

Tungsten dioxo complex WO 2(C 9H 6NO) 2 was obtained via the low temperature solid-state reaction of(NH 4) 2WS 4, 8-hydroxyquinoline(8-hq) and(CH 3) 4NI, and it was characterized by means of elemental analyses, IR spectroscopy and X-ray diffraction analysis. The crystal of the title compound belongs to monoclinic, space group C2/c, with the crystal cell parameters: a=1.3316(3) nm, b=0.94444(19) nm, c=1.3485(3) nm, β=109.66(3)°, V=1.5970(6) nm 3, Z=6. The title compound possesses a supramolecular structure formed through hydrogen bonds and π-π stacking interactions. The third-order non-linear optical(NLO) properties of the title compound were also investigated. The third-order non-linear absorption coefficient α 2 and refractive index n 2 are 0.85×10 -11 m/W -1 and -1.5×10 -19 m 2/W, respectively. The third-order non-linear susceptibility χ (3) is 3.03×10 -13 esu for 3.8×10 -5 mol/L sample concentration.

Unconditionally Explicit Stable Difference Schemes for Solving Some Linear and Non-Linear Parabolic Differential Equation

We present the numerical method for solution of some linear and non-linear parabolic equation. Using idea [1], we will present the explicit unconditional stable scheme which has no restriction on the step size ratio k/h2 where k and h are step sizes for space and time respectively. We will also present numerical results to justify the present scheme.

Investigation on Structural, Optical and Thermal Properties of Diphenyl Urea—An Organic Non-Linear Optical Crystal

Organic non-linear optical crystal diphenyl urea with molecular formula C13H12N2O was synthesized and grown successfully by slow evaporation solution growth technique. The single crystal X-ray diffraction (XRD) confirms that it crystallizes in orthorhombic crystal system with non-centrosymmetric space group Pna21. The various functional groups were identified qualitatively by Fourier transform-infra red (FT-IR) and FT-Raman techniques. The electron absorption spectrum was studied by UV-Vis spectrophotometer. Thermal behavior of the crystal was evidenced by thermogravimetric (TG) and differential scanning calorimetric (DSC) analyses. From DSC the melt ing point of the crystal is found to be 145°C. The existence of second harmonic generation (SHG) signal was evidenced using Kurtz Perry powder test and the efficiency of the crystal was found to be 0.64 times that of the standard KDP crystal.

Tunable Optical Filters Based on Different Configurations with Cholesteric Liquid Crystals

Optical filters with different configurations based on cholesteric liquid crystals （CLCs） are designed. The central wavelength from CLCs can be tuned by the electric field or temperature. For the electric field tuning, the ITO is designed with circular patterns, which can make the tunable range 18 nm. For the temperature tuning, two-layer- CLC configurations are used. The experimental results indicate that a deepened or broadened bandgap from the CLC can be achieved by different handedness or concentrations of chiral dopants. The spectrum study is carried out.

Non-Linear Effects in Optical Systems by Lie Algebra and Symplectic Mapping

The use of signals of different frequencies determines the geometrical deviation with respect to the optical axes of a given beam. This angle can be determined by Sympletic Map (SM), a powerful and simple mathematical tool for the characterization and construction of images in Geometrical Optics. The Sympletic Map constitutes a Lie Group, with an algebra associated: the Lie Algebra. In general, the SM can be expressed as an infinite series, where each term corresponds to different contributions produced by the optical devices that constitute the optical system (lenses, apertures, bandwidth cutoff, etc.). The level of correction to be performed on the image to recover the original object is clear and controllable by SM. This formalism can be extended easily to physical optics to describe diffraction and interference phenomena.

A New Fourth Order Difference Approximation for the Solution of Three-dimensional Non-linear Biharmonic Equations Using Coupled Approach

This paper deals with a new higher order compact difference scheme, which is, O(h4) using coupled approach on the 19-point 3D stencil for the solution of three dimensional nonlinear biharmonic equations. At each internal grid point, the solution u(x,y,z) and its Laplacian Δ4u are obtained. The resulting stencil algo-rithm is presented and hence this new algorithm can be easily incorporated to solve many problems. The present discretization allows us to use the Dirichlet boundary conditions only and there is no need to discretize the derivative boundary conditions near the boundary. We also show that special treatment is required to handle the boundary conditions. Convergence analysis for a model problem is briefly discussed. The method is tested on three problems and compares very favourably with the corresponding second order approximation which we also discuss using coupled approach.

Molecular Structure, Vibrational Assignments and Non-Linear Optical Properties of 4,4’ Dimethylaminocyanobiphenyl (DMACB) by DFT and <i>ab Initio</i>HF Calculations

In the present study, structural properties of 4,4’ dimethylaminocyanobiphenyl (DMACB) have been studied extensively by using ab initio Hartree Fock (HF) and density functional theory (DFT) employing B3LYP/B3PW91 exchange correlation levels of theory. The vibrational frequencies of DMACB in the ground state have been calculated by using Hartree Fock level and density functional method (B3LYP/B3PW91) with 6-31G(d, p), basis set. Nonlinear optical (NLO) behavior of the examined molecule is investigated by the determination of the electric dipole moment μ, the polarizability α, and the hyperpolarizability β by using the B3LYP/B3PW91 methods.

The optical nonreciprocal response based on a four-mode optomechanical system

We propose a scheme for realizing the optical nonreciprocal response based a four-mode optomechanical system,consisting of two charged mechanical modes and two linearly coupled optical modes. Two charged mechanical modes are coupled by Coulomb interaction, and two optical modes are coupled to one of mechanical modes by radiation pressure. We numerically evaluate the transmission probability of the probe field to obtain the optimum optical nonreciprocal response parameters. Also, we show that the optical nonreciprocal response is caused by the quantum interference between the optomechanical couplings and the linearly coupled interaction that breaks the time-reversal symmetry.

Gender difference in the neuroprotective effect of rat bone marrow mesenchymal cells against hypoxiainduced apoptosis of retinal ganglion cells

Bone marrow mesenchymal stem cells can reduce retinal ganglion cell death and effectively prevent vision loss. Previously, we found that during differentiation, female rhesus monkey bone marrow mesenchymal stem cells acquire a higher neurogenic potential compared with male rhesus monkey bone marrow mesenchymal stem cells. This suggests that female bone marrow mesenchymal stem cells have a stronger neuroprotective effect than male bone marrow mesenchymal stem cells. Here, we first isolated and cultured bone marrow mesenchymal stem cells from female and male rats by density gradient centrifugation. Retinal tissue from newborn rats was prepared by enzymatic digestion to obtain primary retinal ganglion cells. Using the transwell system, retinal ganglion cells were co-cultured with bone marrow mesenchymal stem cells under hypoxia. Cell apoptosis was detected by flow cytometry and caspase-3 activity assay. We found a marked increase in apoptotic rate and caspase-3 activity of retinal ganglion cells after 24 hours of hypoxia compared with normoxia. Moreover, apoptotic rate and caspase-3 activity of retinal ganglion cells significantly decreased with both female and male bone marrow mesenchymal stem cell co-culture under hypoxia compared with culture alone, with more significant effects from female bone marrow mesenchymal stem cells. Our results indicate that bone marrow mesenchymal stem cells exert a neuroprotective effect against hypoxia-induced apoptosis of retinal ganglion cells, and also that female cells have greater neuroprotective ability compared with male cells.

Full-vectorial finite-difference beam propagation method based on the modified alternating direction implicit method

A modified alternating direction implicit algorithm is proposed to solve the full-vectorial finite-difference beam propagation method formulation based on H fields. The cross-coupling terms are neglected in the first sub-step, but evaluated and doubly used in the second sub-step. The order of two sub-steps is reversed for each transverse magnetic field component so that the cross-coupling terms are always expressed in implicit form, thus the calculation is very efficient and stable. Moreover, an improved six-point finite-difference scheme with high accuracy independent of specific structures of waveguide is also constructed to approximate the cross-coupling terms along the transverse directions. The imaginary-distance procedure is used to assess the validity and utility of the present method. The field patterns and the normalized propagation constants of the fundamental mode for a buried rectangular waveguide and a rib waveguide are presented. Solutions are in excellent agreement with the benchmark results from the modal transverse resonance method.

Universal form of the power spectrum of the aero-optical aberration caused by the supersonic turbulent boundary layer

Based on the measurement of one-dimensional （1D） optical path difference （OPD） of the supersonic turbulent bound- ary layer, an analytical form for the power spectrum of the two-dimensional （2D） OPD is obtained with its structure function and under the locally homogeneous isotropic assumption. The universality of this spectrum is argued, and its validity is checked by the comparison with experimental result. The potential applications of this model in theoretical and numerical studies are emphasized. Another contribution of this work is around the application of correlation function to analyzing the statistics of OPD. Based on our results and other results published elsewhere, we show that the OPD is often not stationary, and one should be cautious about using this tool.

Analysing the structure of the optical path length of a supersonic mixing layer by using wavelet methods

The nano-particle-based planar laser scattering （NPLS） technique is used to measure the density distribution in the supersonic mixing layer of the convective Mach number 0.12, and the optical path difference （OPL）, which is quite crucial for the study of aero-optics, is obtained by post processing. Based on the high spatiotemporal resolutions of the NPLS, the structure of the OPL is ana]ysed using wavelet methods. The coherent structures of the OPL are extracted using three methods, including the methods of thresholding the coefficients of the orthogonal wavelet transform and the wavelet packet transform, and preserving a number of wavelet packet coefficients with the largest amplitudes determined by the entropy dimension. Their performances are compared, and the method using the wavelet packet is the best. Based on the viewpoint of multifractals, we study the OPL by the wavelet transform maxima method （WTMM）, and the result indicates that its scaling behaviour is evident.

Design of supercontinuum generating photonic crystal fiber at 1.06, 1.31 and 1.55 µm wavelengths for medical imaging and optical transmission systems

We propose broad supercontinuum spectrum generating highly nonlinear photonic crystal fiber (HN-PCF) which can be used in ultrahigh- resolution optical coherence tomography and optical transmission systems. Using full vector finite difference method, we investigated the different properties of HN-PCF. Broadband su-percontinuum spectrum is numerically calculated by using nonlinear Schr?dinger equation. Investigation showed that it is possible to obtain longitudinal resolution in a biological tissue of 1.3 μm, 1.2 μm and 1.1 μm by using picosecond continuum light at center wavelengths of 1.06 μm, 1.31 μm and 1.55 μm, respectively.

Structural, Thermal and Optical Studies of Oxypeucedanin Hydrate Monoacetate Micro-Crystals from <i>Prangos pabularia</i>

Oxypeucedanin hydrate monoacetate (Mol. Formula = C18H18O7) micro-crystals were obtained by acetylation of oxy-peucedanin hydrate, a furanocoumarin, isolated from the roots of Prangos pabularia. The composition related structural, thermal and optical properties were investigated. All the crystals were found to have triclinic structure. From thermal studies of these crystals, stability, melting point and other relevant informations were obtained. Their blue emission, less absorption in entire visible range and band gap predicts these crystals as good candidate for modern optoelectronic devices.