Mode analysis in optics through fractional transforms

The relationship between the mode content and the fractional Fourier and fractional Hankel transforms of a function is established. It is shown that the Laguerre-Gauss spectrum of a rotationally symmetric wave front can be determined from the wave front's fractional Hankel transforms taken at the optical axis.     

Shaping Solid-State Supramolecular Cavities: Chemically Induced Accordionlike Movement of gamma-Zirconium Phosphate Containing Polyethylenoxide Pillars

The hydrophilic oxygen atoms of polyethylenoxide chains inserted as pillars in gamma-zirconium phosphate form hydrogen bonds with the acid groups of the host. As a result the pillars are almost perpendicular to the gamma layers. Upon changing the pH level of the supernatant solution the hydrogen bonds are broken and the pillars become almost perpendicular to the layers (shown schematically). Thus there is a reversible enlargement-shortening of the interlayer space.     

Swirling and Impinging Effects in an Annular Nonpremixed Jet Flame

The effects of swirl and downstream wall confinement on an annular nonpremixed flame were investigated using direct numerical simulation (DNS). Fully three-dimensional parallel DNS was performed employing high-order numerical methods and high-fidelity boundary conditions to solve governing equations for variable-density flow and finite-rate Arrhenius chemistry. Three swirl numbers have been examined: 0 (without swirl), 0.4 and 0.8, while the effects of downstream wall confinement have been examined for swirl numbers 0 and 0.4. Results have been presented in terms of instantaneous and time-averaged flow quantities, which have also been analysed using energy spectra and proper orthogonal decomposition (POD). Effects of swirl on the fluid dynamic behaviour of the annular nonpremixed flame were found to be significant. The fluid dynamic behaviour of the flame is greatly affected by the interaction between the geometrical recirculation zone (GRZ) near the jet nozzle exit due to the annular configuration, the central recirculation zone (CRZ) associated with swirl, the unsteady vortical structures in the jet column due to the shear instability, and the downstream wall confinement. Depending on the degree of swirl, the GRZ near the burner mouth and the CRZ may co-exist or one zone may be overwhelmed by another. At a moderate swirl number, the co-existence leads to a flame with strong reaction attached to the burner mouth; while at a high swirl number, the CRZ dominates over the GRZ. The precessing vortex core was observed to exist in the swirling flow fields. The Nusselt number distribution of the annular impinging flames differs from that of round impinging jets. The POD analysis revealed that wall effects on the flow field are mainly associated with the higher mode numbers.     

First-order optical systems with real eigenvalues

It is shown that a lossless first-order optical system whose real symplectic ray transformation matrix can be diagonalized and has only real eigenvalues, is similar to a separable hyperbolic expander in the sense that the respective ray transformation matrices are related by means of a similarity transformation. Moreover, it is shown how eigenfunctions of such a system can be determined, based on the fact that simple powers are eigenfunctions of a separable magnifier. As an example, a set of eigenfunctions of a hyperbolic expander is determined and the resemblance between these functions and the well-known Hermite-Gauss modes is exploited.     

The wigner distribution function and Hamilton''s characteristics of a geometric-optical system

Four system functions have been defined for an optical system; each of these functions describes the system completely in terms of Fourier optics. From the system functions the Wigner distribution function of an optical system has been defined; although derived from Fourier optics, this Wigner distribution function can directly be interpreted in terms of geometrical optics. In the special case of a geometric-optical system, the Wigner distribution function clearly demonstrates the relations that exist between the four system functions and the four Hamilton's characteristics of the system.     

The calculation of electron density and temperature in Ar spectroscopic plasmas from continuum and line spectra

The measurement of electron temperature and electron density from line and continuum radiation in Ar plasmas used for spectroscopic purposes is discussed. The correct equations for the calculation of these parameters from experimentally observable quantities are identified. Such expressions yield the theoretical spectral irradiance expected from line and continuum radiation. To aid calculations, grouped constants from these equations are calculated using SI units of measure. The sources of accurate values for the parameters and correction factors appearing in the irradiance equations are listed. In addition the approximations made in order to simplify electron temperature and electron density determinations are reviewed. Practical aspects of making accurate measurements of these parameters in Ar plasmas are considered. Theoretical plots of line to continuum emission ratio vs electron temperature and of continuum irradiance vs electron density are presented as an illustration using parameters appropriate for Ar emission at 430 nm and the spectrally adjacent continuum.