Considerations to Rayleigh’s hypothesis

In 1907 Lord Rayleigh published a paper on the dynamic theory of gratings. In this paper he presented a rigorous approach for solving plane wave scattering on periodic surfaces. Moreover he derived explicit expressions for a perfectly conducting sinusoidal surface, and for perpendicular incidence of the electromagnetic plane wave. This paper was criticized by Lippmann in 1953 for he assumed Rayleigh’s approach to be incomplete. Since this time there have been published several arguments, proofs, and discussions concerning the correctness and the range of validity of Rayleigh’s approach not only for plane wave scattering on gratings but also for light scattering on nonspherical structures, in general. In the paper at hand we will discuss the different point of views on what is called “Rayleigh’s hypothesis” as well as the relevance of a found theoretical limit for its validity. Furthermore we present a numerical treatment of the original scattering problem of a p-polarized plane wave perpendicularly incident on a perfectly conducting sinusoidal surface (i.e., the scalar Dirichlet problem). In doing so we emphasizes the near-field solution especially within the grooves of the grating up to points on the surface, and below the surface. Two different Green’s function formulations of Huygens’ principle are used as starting points. One of this formulation results in the general T-matrix approach which is considered to be affected by Rayleigh’s hypothesis especially for near-field calculations. The other formulation provides a conventional boundary integral equation which is in accordance with Lippmann’s point of view and free of problems with Rayleigh’s hypothesis. But the obtained results show that Lippmann’s argumentation do not withstand a critical numerical analysis, and that the independence of least-squares approaches from Rayleigh’s hypothesis, as understood and proven by Millar, seems to hold also for certain methods which does not fit into such an approach.     

Effects of group-delay difference on ultrashort pulse propagation in an active nonlinear LPFG

The effects of group-delay difference in an active nonlinear long-period fiber grating (LPFG) made in an erbium-doped amplifying fiber (EDF) are investigated by proposing a general model that include the effects of detuning, group-delay difference, gain saturation, gain bandwidth and Kerr nonlinearity. In particular, we observe a new feature caused by the interaction between the group-delay difference and the gain bandwidth: the pulse breakup effect due to the group-delay difference can be suppressed by the finite bandwidth of the linear gain.     

Time-Dependent Variational Approach to Ground-State Phase Transition and Phonon Dispersion Relation of the Quantum Double-Well Model

The ground-state phase transition and the phonon dispersion relation of the quantum double-well model are studied by means of the time-dependent variational approach combined with a Hartree-type many-body trial wavefunction. The single-particle state is taken to be a frozen Jackiw-Kerman wavefunction. Under the condition of minimum uncertainty relation, we obtain an effective classical Hamiltonian for the system and equations of motion for the particle＇s expectation values. It is shown that the effective substrate potential transits from a symmetric double-well potential to a symmetric single-well potential, and the ground state exhibits a transition from a broken symmetry phase to a restored symmetry phase as increasing the strength of quantum fluctuations. We also obtain the phonon dispersion relations and the phonon gaps at the two phases.     

Superimposed nanostructured diffraction gratings as high capacity barcodes for biological and chemical applications

We describe a new non-contact high capacity optical tagging technique for bead based assays, based on the use of nanostructured barcodes. The tags are generated from a number of superimposed diffraction gratings. With one-dimensional diffraction, capacity for up to 68,000 distinguishable tags has been demonstrated, with a theoretical capacity of up to 10⁹ tags. Extension into two dimensions increases this theoretical limit to 10²¹ tags.     

Macroscopic-microscopic theory of semi-spheroidal atomic cluster

The macroscopic-microscopic method is adapted to atomic clusters deposited on a surface. Analytical relationships for the deformation-dependent liquid drop model (LDM) energies of oblate and prolate semi-spheroidal atomic clusters have been obtained. A superdeformed prolate semi-spheroid is the most stable semi-spheroidal shape within LDM. It is also the shape with maximum degeneracy of quantum states of the semi-spheroidal harmonic oscillator used to compute the shell and pairing corrections. The microscopic corrections as well as total deformation energy show parabolic valley and ridges of the potential energy surfaces in the plane (deformation, number of atoms). The ground state and isomeric state deformation of clusters of various sizes depends on the interplay between the minima of LDM and shell correction energies.     

Extraordinary optical transmission for TE wave through metallic sub-wavelength grating with slits filled with dielectric

A metallic sub-wavelength grating with slits filled with dielectric was proposed to achieve broadband and enhanced Extraordinary Optical Transmission (EOT) for Transverse Electric (TE) wave. The physical mechanism for the improvements of the transmission spectrum was also revealed. It was found that the Fabry–Perot cavity resonance in the grating slits was the cause of the enhancement of the EOT and the waveguide modes theory was the fundamental mechanism for the broadened bandwidth of the transmission.     

First order phase change detection using planar waveguide Bragg grating refractometer

Solid-to-liquid and gas-to-liquid phase changes in water and ordered-to-isotropic phase changes in a nematic liquid crystal are detected with an optical sensor. A planar Bragg grating defined purely by refractive index modulation is covered with a water or liquid crystal overcladding and the temperature is controlled to trigger phase changes. Measurement of the Bragg wavelength allows changes of effective refractive index to be detected and discontinuities in behaviour caused by phase transitions can be clearly identified.     

Solving coupled Dyson-Schwinger equations on a compact manifold

We present results for the gluon and ghost propagators in SU (N) Yang-Mills theory on a four-torus at zero and non-zero temperatures from a truncated set of Dyson-Schwinger equations. When compared to continuum solutions at zero temperature sizeable modifications due to the finite volume of the manifold, especially in the infrared, are found. Effects due to non-vanishing temperatures T, on the other hand, are minute for T < 250 MeV.     

Towards the design of elliptical-polarization rejection filters

Ambichiral layered structures can be designed to function reasonably well as rejection filters for elliptical polarization states, although the proposed design strategy is inadequate for linear and quasilinear polarization states.