Short-and resonant-range interactions between scales in turbulence and their applications

Interactions between different scales in turbulence were studied starting from the incompressible Navier-Stokes equations. The integral and differential formulae of the short-range viscous stresses, which express the short-range interactions between contiguous scales in turbulence, were given. A concept of the resonant-range interactions between extreme contiguous scales was introduced and the differential formula of the resonant-range viscous stresses was obtained. The short- and resonant-range viscous stresses were applied to deduce the large-eddy simulation (LES) equations as well as the multiscale equations, which are approximately closed and do not contain any empirical constants or relations. The properties and advantages of using the multiscale equations to compute turbulent flows were discussed. The short-range character of the interactions between the scales in turbulence means that the multiscale simulation is a very valuable technique for the calculation of turbulent flows. A few numerical examples were also given.

Resonant mode analysis in toroidal cavities with elliptic cross-sections

Resonant cavity modes in a torus with elliptical cross section are studied by means of a direct variational method. The nonlinear effects of toroidicity and ellipticity on the frequency of the basic mode are analyzed simply and systematically without the restriction of linear theory. It is shown that the toroidicity effect on the m = 0 transverse magnetic mode is less-than-or-equal-to 11%. The frequency of the mode shifts approximately 11-29% when the elongation of the cross section changes from 1 to 2. The effects of toroidicity and ellipticity differ for each resonant mode.

Locally resonant phononic woodpile: A wide band anomalous underwater acoustic absorbing material

To meet the demand of modern acoustic absorbing material for which acoustic absorbing frequency region can be readily tailored, we introduced woodpile structure into locally resonant phononic crystal (LRPC) and fabricated an underwater acoustic absorbing material, which is called locally resonant phononic woodpile (LRPW). Experimental results show that LRPW has a strong capability of absorbing sound in a wide frequency range. Further theoretical research revealed that LRPC units and woodpile structure in LRPW play an important role in realization of wide band underwater strong acoustic absorption.

Generation of intense extreme supercontinuum radiation via resonant propagation effects

Confinement of electromagnetic energy into a single well-controlled oscillation of light is very important for generation of intense supercontinuum radiation. We find that the pulse breakup of few-cycle ultrashort laser pulses via resonant propagation effects can achieve this aim. By extracting such pulses and then focusing them to drive the He atoms, about 200 eV intense supercontinuum radiation can be generated, which is capable of supporting similar to 20 attosecond isolated pulse generation.

Spatiotemporal evolution and multiple self-focusing of ultrashort pulses in a resonant two-level medium

The spatiotemporal evolutions of ultrashort pulses in two dimensions are investigated numerically by solving the coupled Maxwell-Bloch equations without invoking the slowly varying envelope approximation and rotating-wave approximation. For an on-axis 2n pi sech pulse, local delay makes the temporal split 2 pi sech pulses crescent-shaped in the transverse distribution. Due to the transverse effect, the temporal split 2 pi sech pulses become unstable and experience reshaping during the propagation process. Then, interference occurs between the successive crescent-shaped pulses and multiple self-focusing can form.

Propagation of an arbitrary elliptically polarized few-cycle ultrashort laser pulse in resonant two-level quantum systems

We investigate the propagation of an arbitrary elliptically polarized few-cycle ultrashort laser pulse in resonant two-level quantum systems using an iterative predictor-corrector finite-difference time-domain method. It is shown that when the initial effective area is equal to 2 pi, the effective area will remain invariant during the course of propagation, and a complete Rabi oscillation can be achieved. However, for an elliptically polarized few-cycle ultrashort laser pulse, polarization conversion can occur. Eventually, the laser pulse will evolve into two separate circularly polarized laser pulses with opposite helicities.

A new method of measuring the waveguide dispersion factor and the thermo-optic coefficient of long-period fiber gratings

Based on the Mach-Zehnder effect between the core mode and the cladding modes, the interference fringes are formed by a pair of cascaded long-period fiber gratings (CLPFGs). Theoretical analyses show that the spectral spacing and the wavelength of these fringes are functions of the waveguide dispersion factor gamma, which is a characterizing parameter to LPFG and with theoretical and applicational significance. By measuring the characteristics of the transmission spectra of CLPFGs, the absolute value of gamma can be obtained. At the same time, the thermo-optic coefficient of effective refractive index difference between core and cladding modes, p, can also be obtained by measured the temperature sensitivity of these fringes. In the experiments, \gamma\ and mu were measured by this method to be 0.874 and 4.08 x 10(-5) degreesC(-1), respectively, for LPFGs with period of 450 mum and with a HE14 resonant peak at 1554 nm. (C) 2004 Elsevier B.V. All rights reserved.

Cascaded Fresnel digital hologram and its application to watermarking

A cascaded Fresnel digital hologram (CFDH) is proposed, together with its mathematical derivation. Its application to watermarking has been demonstrated by a simulation procedure, in which the watermark image to be hidden is encoded into the phase of the host image. The watermark image can be deciphered by the CFDH setup, the reconstructed image shows good quality and the error is almost close to zero. Compared with previous technique, this is a lensless architecture which minimizes the hardware requirement, and it is used for the encryption of digital image.

Watermarks encrypted in the cascaded Fresnel digital hologram

A cascaded Fresnel digital hologram (CFDH) is proposed, together with its mathematical derivation. Its application to watermarking has been demonstrated by a simulation procedure, in which the watermark image to be hidden is encoded into the phase of the host image. The watermark image can be deciphered by the CFDH setup, the reconstructed image shows good quality and the error is almost closed to zeros. Compared with previous technique, this is a lensless architecture, which minimizes the hardware requirement. (c) 2006 Elsevier GmbH. All rights reserved.

Non-resonant third-order non-linear optical properties of amorphous GeSe2 film

The real and imaginary parts of third-order susceptibility of amorphous GeSe2 film were measured by the method of the femtosecond optical heterodyne detection of optical Kerr effect at 805 nm with the 80 fs ultra fast pulses. The results indicated that the values of real and imaginary parts were 8.8 x 10(-12) esu and -3.0 x 10(-12) esu, respectively. An amorphous GeSe2 film also showed a very fast response within 200 fs. The ultra fast response and large third-order non-linearity are attributed to the ultra fast distortion of the electron orbits surrounding the average positions of the nucleus of Ge and Se atoms. (c) 2005 Elsevier B.V. All rights reserved.

Precise determination of anomalous scattering factors of Ge by using X-ray resonant scattering

Variations of peak position of the rocking curve in the Bragg case are measured from a Ge thin crystal near the K-absorption edge. The variations are caused by a phase change of the real part of the atomic scattering factor. Based on the measurement, the values of the real part are determined with an accuracy of better than 1%. The values are the most reliable ones among those reported values so far as they are directly determined from the normal atomic scattering factors.

Guided-mode resonant grating filter with an antireflective surface for the multiple channels

In this paper, a new type of guided-mode resonant grating (GMRG) filter with an antireflective surface called the 'moth-eye structure' for the multiple channels is presented by using rigorous coupled-wave analysis (RCWA) and the S-matrix method. Long range, low sidebands and multiple channels are found when the GMRG filters with antireflective surface are illuminated with incident polarization light. It is calculated that the multiple channel phenomenon can be shown when the depth of antireflective surface is increased. Moreover, the wavelengths of the multiple channels can be easily shifted by changing the depth of the homogenous layer which is under the antireflective surface, and the optical properties of GMRG filters such as low sideband reflection and narrow band are not badly spoiled when the depth is changed.