Transition radiation of elastic waves at the interface of two elastic half-planes

Radiation of elastic waves is studied that is emitted by a point load that crosses the interface of two elastic half-planes. It is assumed that the load has a constant magnitude, moves along a straight line normal to the interface, and has a constant speed that is smaller than the minimum shear wave speed in the half-planes. In this case the mechanism of excitation of elastic waves is conventionally referred to as transition radiation. The adopted model allows to obtain an analytical expression for the elastic field excited by the load in the frequency-wavenumber domain. Using this expression, the energy of transition radiation is derived in a closed form. It is shown that transition radiation of the body waves occurs at any non-zero velocity of the load. Additionally, transition radiation of interface waves may occur provided that parameters of the half-planes allow existence of Stoneley waves. A parametric analysis of the directivity diagram of radiated body waves is accomplished focusing on dependence of the diagram on the load speed, load direction, and parameters of the half-planes. Using parameters that allow radiation of interface waves, the energy of this radiation is compared to that of the body waves. It is shown that the energy of the interface waves is greater unless the load velocity is close to the lowest body wave velocity.     

Diffraction of light by a perfectly conducting biaxial periodic surface

The Rayleigh theory is numerically implemented for a crossed sinusoidal grating. It is shown that the scattering pattern of such a structure can be very sensitive to the polarization of a normally-incident plane wave when the surface periodicities are of the order of the wavelength.     

Diffraction of light by weak ultrasonic fields

Assuming the validity ofRaman andNath's simplified theory for small widths of weak sound fields, an elegant and simple method is presented to derive an expression for the intensity of the first order in the case of weak sound fields. Expressions obtained are found to be identical with those ofDavid, andBhatia andNoble. Extending this treatment to the case of diffraction by stationary waves it is shown that the intensity of a first order in this case is half that of the corresponding order for progressive waves and this result has also been verified experimentally.     

Diffraction of light by two spatially separated parallel ultrasonic waves of different frequency

A theory is developed for the diffraction of light by two spatially separated parallel ultrasonic progressive waves of different frequency. The preliminary theories ofRaman andNath [C. V.Raman and N. S.Nath, Proc. Indian Acad. Sci. A2, 406–412; 413–420 (1935)] for normal and oblique incidence are taken to be valid. The resulting equations are extensions of earlier results of R.Mertens, Z. Physik160, 291–296 (1960). The predicted periodicity of the diffraction spectrum with increasing sound beam separation agrees with the well known periodicity of the light intensity distributions in the Fresnel zone of the phase grating formed by the first ultrasonic wave. Results of numerical calculations are presented to illustrate features of the theoretical results, as reflected in the first order of diffraction for 3.0 and 6.0 Mc ultrasonic waves in water.     

Diffraction of light by superposed ultrasonic waves

A method of generating, simultaneously, two sound waves of frequencies in the ratio 1∶n, whose phase difference can be continuously varied, is described. The diffraction of light by such waves is studied, using frequencies in the ratio 1∶2 and 1∶3. Quantitative measurement of the intensities of the various orders is carried out, at phase angles of 0,π/2 and π in case of 1∶2 waves and at phase angles of 0 andρ in case of 1∶3 waves. The measured intensities compared very well with values calculated on the basis of the simple theory worked out by Murty. Photographs, showing the general features of diffraction by superposed waves, have also been reproduced.     

Diffraction of bending waves

This paper is a discussion of the theory of diffraction and scattering of bending waves by mass-impedance loadings of an infinite plane plate. Emphasis is placed on the case of heavy loadings, at which deflexions of the plate are precluded and the scattering is the strongest possible. Examples treated in detail include the diffraction grating, diffraction by a semi-infinite rib, and diffraction by a comb of semi-inifinite ribs.     

Diffraction of optical waves by nonlinearly induced cylinders

The diffraction of optical waves by transparent and opaque cylinders formed by laser beams in defocusing nonlinear media has been investigated for the first time. The wave flow around a single beam (cylinder) and wave signal percolation through the slits formed by closely spaced laser beams have been numerically modeled.     

Diffraction of plane waves by a black wedge

The scattering of plane waves by a black wedge is examined. Two methods are considered for the solution of the problem. A closed-form series solution is derived by performing the technique of the separation of variables using boundary conditions of Macdonald. The second approach is the method of the modified theory of physical optics. The results are compared numerically.     

Diffraction of entangled photon pairs by ultrasonic waves

In this paper, we have presented and established a new theoretical formulation of photon optics based on photon path and Feynman path integral idea. We have used Feynman path integral approach to discuss Fraunhofer, Fresnel diffraction of single photon and entangled photon pairs by ultrasonic wave and obtained the following results: i) quantum state and probability distribution of single photon and entangled photon pairs by Fraunhofer and Fresnel ultrasonic diffraction, ii) oblique incidence Raman-Nath and Bragg diffraction conditions, iii) total correlation state and its probability distribution. Our calculation results are in agreement with the experiment results. Comparing one-photon and two-photon diffraction effects by ultrasonic waves, we have found that two-photon diffraction by ultrasonic waves is also a sub-wavelength diffraction.