The representation of 3D gaussian beams by means of inhomogeneous waves

There are different methods to mathematically represent a bounded beam. Perhaps the most famous method is the classical Fourier method that consists of the superposition of pure homogeneous plane waves all traveling in different directions and having an amplitude that can be found by the Fourier transform of the required profile. This method works perfectly for 2D as well as for 3D bounded beams. However, some researchers prefer the inhomogeneous wave theory to represent a bounded beam because some phenomena, e.g. the Schoch effect, are explained by this method by means of concepts that agree better with intuition. There are several papers dealing with this method for 2D gaussian beams. Until now, it has never been considered possible to represent 3D gaussian beams as well. The present paper shows a method to overcome this shortcoming and presents different sorts of 3D gaussian beams that are built up by means of inhomogeneous plane waves.     

The reflection of bounded inhomogeneous waves on a liquid/solid interface

Fourier analysis and normal mode theory are used to describe the reflection of bounded inhomogeneous waves on a liquid/solid interface. Nonspecular reflection phenomena in the Rayleigh angle are studied in detail. In this way, an explanation is given for the Rayleigh dip phenomenon for positive inhomogeneity factors and the related result of a reflection coefficient larger than unity when the sign of the inhomogeneity factor is reversed. In the limit of large beamwidths, the reflection coefficient predicted by the infinite plane inhomogeneous wave theory is obtained. These results are entirely consistent with the experimental work published by Deschamps [J. Acoust. Soc. Am. 96, 2841-2848 (1994)]. The energy efficiency of Rayleigh wave excitation is investigated as well. It is shown that for large beamwidths, the energy efficiency for bounded inhomogeneous waves is considerably higher in comparison with Gaussian and square-profiled beams.     

Extension of the mode method for viscoelastic media and focused ultrasonic beams

In the present study viscoelasticity is introduced in the mode model and the orthogonality condition is adapted for viscous media. The expansion of convergent acoustic Gaussian beams in terms of radiation modes for viscoelastic media is studied as well. The effects on the reflected and transmitted profiles of acoustic beams incident from an ideal liquid onto a viscoelastic plate are shown and physically explained. It is shown that focusing the incident beam can suppress divergence effects and gives the possibility to measure shear wave attenuation coefficients.     

Collinear acousto-optic diffraction using two nearby sound frequencies

Collinear acousto-optic spectrometers with sound consisting of one frequency have a spectral transfer function with many good characteristics, such as a narrow bandwidth, ... the side lobes, however, are rather high. To reduce these side lobes, one can try to apodize the sound in the acousto-optic cell by using a sound wave consisting out of two frequencies. At certain times, this produces a more smoothened sound field in the cell than in the one-frequency case. The resulting transfer function will contain lower side lobes. Also, the influence of all the sound field parameters--the amplitude, frequency difference, and time--on the transmission function is studied. Out of these results, better-performing collinear spectrometers can be designed.     

α-Distonic ions as transient species in the reactions of metastable alkyl benzoate radical cations

The key intermediates to the fragmentation of metastable methyl and ethyl benzoate radical cations are α- and β-distonic isomers of the molecular ions. The α-distocic isomers are also formed by fragmentation of longer chain alkyl benzoates, but may not be long-lived, stable species. Rearrangement of the α-distonic ions prior to fragmentation can take place, but (re)formation of the benzoate molecular ions does not occur.     

Spectroscopic study of BixEu1−xVO4 and BiyGd1−yVO4 mixed oxides

The mixed oxides Bi_xEu_1−xVO₄ and Bi_yGd_1−yVO₄ crystallize in a zircon-type structure, for 0 <x < 0.6 and 0 < y < 0.64, and in a fergusonite-type structure, for 0.94 < x < 1 and 0.93 < y < 1. A process of competition between the dominant and the constrained effects of the lone-pair 6s² of Bi³⁺ is discussed. The diffuse reflectance spectroscopic studies of these mixed oxides are presented. The observed broad bands are attributed to charge transfer processes and the sharp peaks in the Bi_xEu_1−xVO₄ spectra are ascribed to intra-configurational 4f – 4ftransitions of the Eu³⁺ ion. The broad absorption shift in BiLnVO₄ (Ln : Eu and Gd) compounds to the longer wavelengths range, when Bi is introduced in the LnVO₄ lattice, is ascribed to charge transfer processes in a Bi-VO₄ center and are interpreted assuming a Jahn-Teller effect in the excited state of Bi³⁺. The concept of an internal pressure of Bi³⁺ ions is also used to explain the broad A-band shifts.     

Peptide sequence mediated self-assembly of molybdenum blue nanowheel superstructures

The precise control over the formation of complex nanostructures, e.g. polyoxometalates (POMs), at the sub-nanoscale is challenging but critical if non-covalent architectures are to be designed. Combining biologically-evolved systems with inorganic nanostructures could lead to sequence-mediated assembly. Herein, we exploit oligopeptides as multidentate structure-directing ligands via metal-coordination and hydrogen bonded interactions to modulate the self-assembly of POM superstructures. Six oligopeptides (GH, AH, SH, G₂H, G₄H and G₅H) are incorporated into the cavities of Molybdenum Blue (MB) POM nanowheels. It is found that the helicity of the nanowheel can be readily switched (Δ to Λ) by simply altering the N-terminal amino acid on the peptide chain rather than their overall stereochemistry. We also reveal a delicate balance between the Mo-coordination and the hydrogen bonds found within the internal cavity of the inorganic nanowheels which results in the sequence mediated formation of two unprecedented asymmetrical nanowheel frameworks: {Mo₁₂₂Ce₅} and {Mo₁₂₆Ce₄}.

Peptide sequence can be used to control the self-assembly and structures of nanoscale molybdenum blue polyoxometalate (POM) wheel-shaped clusters.