Goos–Hänchen shift for higher-order Hermite–Gaussian beams

We study the reflection of a Hermite–Gaussian beam at an interface between two dielectric media. We show that unlike Laguerre–Gaussian beams, Hermite–Gaussian beams undergo no significant distortion upon reflection. We report Goos–H?nchen shift for all the spots of a higher-order Hermite–Gaussian beam near the critical angle. The shift is shown to be insignificant away from the critical angle. The calculations are carried out neglecting the longitudinal component along the direction of propagation for a spatially finite, s-polarized, full 3D vector beam. We briefly discuss the difficulties associated with the paraxial approximation pertaining to a vector Gaussian beam.     

Switching behaviour of nonlinear Mach–Zehnder interferometer based on photonic crystal geometry

Nonlinear Mach–Zehnder interferometer (NMZI) created with photonic crystal waveguides (PCW) and with Kerr-type nonlinearity has been investigated in this paper. The NMZI has been simulated using two-dimensional finite difference time domain (2D-FDTD) method. Input verses output (I /O) characteristics have been obtained for different lengths of the nonlinear arm, nonlinear coefficients of the nonlinear arm, wavelengths of the input beam, sizes of defect rods and NMZI offset. The results obtained are compared with earlier published results of NMZI created with conventional step index waveguides (SIW). It is shown that all useful features of light switching offered by SIW-based NMZIs are also possible with PCW-based NMZIs of extremely small dimensions. Moreover, PCW-based NMZIs offer additional useful feature not available with SIW-based NMZIs.     

VISCOELASTIC MODELLING OF ENTRANCE FLOW USING MULTIMODE LEONOV MODEL

A simulation of planar 2D flow of a viscoelastic fluid employing the Leonov constitutive equation has been presented. Triangular finite elements with lower-order interpolations have been employed for velocity and pressure as well as the extra stress tensor arising from the constitutive equation. A generalized Lesaint–Raviart method has been used for an upwind discretization of the material derivative of the extra stress tensor in the constitutive equation. The upwind scheme has been further strengthened in our code by also introducing a non-consistent streamline upwind Petrov–Galerkin method to modify the weighting function of the material derivative term in the variational form of the constitutive equation. A variational equation for configurational incompressibility of the Leonov model has also been satisfied explicitly. The corresponding software has been used to simulate planar 2D entrance flow for a 4:1 abrupt contraction up to a Deborah number of 670 (Weissenberg number of 6·71) for a rubber compound using a three-mode Leonov model. The predicted entrance loss is found to be in good agreement with experimental results from the literature. Corresponding comparisons for a commercial-grade polystyrene, however, indicate that the predicted entrance loss is low by a factor of about four, indicating a need for further investigation. © 1997 by John Wiley & Sons, Ltd.     

RITZ VECTOR APPROACH FOR STATIC AND DYNAMIC ANALYSIS OF PLATES WITH EDGE BEAMS

A Ritz vector approach is used to develop new formulations for evaluating the static and the dynamic characteristics of rectangular plates with edge beams. Unlike previous studies in which stiffness coefficients with specified distributions along the plate edges are used to represent the effect of edge restraints, the effect of elastic edge restraints is accounted for by including appropriate integrals for edge beams in the expressions for total kinetic and potential energies in a Rayleigh-Ritz approach. The effect of various types of boundary conditions at the beam ends is accounted for by considering the corresponding Ritz vectors. The contribution of beam mass to the total kinetic energy is also considered in the proposed approach. This effect has often been neglected in the previous studies but can be significant in some applications. The results obtained from the application of the proposed approach to a variety of examples are compared with the corresponding results obtained from the finite element analysis.     

Optical probing of Eu ions confined in an RF trap

The Eu ions confined in an RF quadrupole trap, has been optically detected. Using a tunable dye laser which is pumped by a Nd-YAG pulsed laser system, the resonance ⁹S₄^9S_4–6p _3/2, J = 5 transition of the Eu ions have been excited and the resulting fluorescence to the metastable ⁹D_4-6^9D_{4-6} state has been detected. In preparation to determine the ground-state hyperfine splitting of the odd isotopes we found the optimum trapping operating point. We have also observed a number of instabilities inside the region of the stability for an ideal trap. These non-linear resonances arise from higher-order contributions to the ideal quadrupole potential.     

Excitation of Bulk-wave on Columns of Magnetized Plasma†

The excitation of the bulk-wave mode on a column of magnetized plasma by a ring of magnetic current outside the plasma is studied. The analysis is based on a solution of the inhomogeneous wave equation by the method of Fourier transforms. It is shown that slow waves with a large E _s field on the axis can be excited with high excitation efficiency.     

Spectroscopy and laser characterization of synthesized supramolecular host cucurbit[7]uril using aqueous Rhodamine B dye

Recent demonstration in augmenting the efficiency of aqueous Rhodamine dye lasers using cucurbit[7]uril (CB[7]), a deaggregating and photostabilizing host, has drawn interest in the synthesis and characterization of spectroscopic grade CB[7] in larger quantities. Synthesis of cucurbituril group of macrocycles always leads to the formation of various homologues of CB[n]s (n=5–7) with CB[7] as the minor product. The literature procedure has been optimized to get pure CB[7] in 12–14% yield by fractional crystallization and the purity was checked by NMR, MS and spectrophotometric titration. Laser performances of the synthesized and commercial CB[7] sample as an additive were evaluated using Nd-YAG (532 nm) pumped Rhodamine B aqueous dye lasers and comparable results were obtained.     

Analysis of a centre-driven antiphase dipole in a warm plasma†

The radiation properties of a thin dipole in a warm plasma, fed with currents in opposite phase, have been theoretically investigated using linearized hydrodynamic theory. Expressions for the far-zone electromagnetic and electroacoustie fields are derived in terms of general propagation constant β. The values of fields and of the radiation resistance are computed using β = β_e and compared with those of a standard dipole. It is found that tho eradiation of the electromagnetic mode is partially suppressed, whereas that of plasma mode remains almost unaltered, suggesting that the antenna could be used for launching electroacoustic waves.     

Single-stage amplifier characteristics of the super-beta composite transistor†

A study has been made of the single-stage amplifier characteristics of the super-beta composite transistor system, in which the circuit has been analysed and the expressions for its voltage gain, current gain, input resistance and the power gain have been obtained in terms of the various parameters of the individual transistor. Further, the expressions obtained have been simplified by taking similar transistors of the composite system. The variations of input resistance, current gain and the power gain with load resistance have also been studied and a set of curves is given showing these variations.     

当方差未知时选取有最大均值总体的两阶段抽样方案

考虑ｋ个有连续分布Ｆｉ＝Ｆ（ｘ－μｉ／σ）的总体，ｉ＝１，．．．，ｋ。其中μｉ和σ均未知，我们通过两阶段抽取样本以得到最大均值的那个总体，第一步根据抽样删去一部分看来不可能的总体，第二步再从余下总体中抽样，取含样本均值最大的那个总体为所需总体，我们用渐过分布方法得到了在所定规则下能选到正确总体的概率下界。特别对Ｌｏｇｉｓｔｉｃ总体计算了有关数值以及关于一次抽样的相对效。