Holography with standing surface plasma waves

Holography with standing surface plasma waves, where both reference and object beams propagate in opposite directions, has been investigated using an Al reflection grating coated with evaporated As₂S₃ layers. The image, which appears only for p-polarization and at certain critical angles, is enhanced by the Lippman-Bragg effect and by an increase in intensity over ordinary holography approximately equal to | ?₁| for Al. Also considered is holography with object light alone in photoresist layers, using the beam-splitting properties of the grating.     

Surface structure determination with X-ray standing waves

The X-ray standing-wave technique is reviewed in its application to surface investigations. Element- specific, structural analysis can be performed with high spatial resolution even for low surface coverages. We present several examples. Interface structure determination is discussed briefly. The fundamental principles and possible variations of the technique, the experimental requirements and the quality of structural information obtained from standing-wave measurements are described in detail.     

Lateral resolution enhancement with standing evanescent waves

A high-resolution fluorescence microscopy technique has been developed that achieves a lateral resolution of better than one sixth of the emission wavelength (FWHM). By use of a total-internal-reflection geometry, standing evanescent waves are generated that spatially modulate the excitation of the sample. An enhanced two-dimensional image is formed from a weighted sum of images taken at different phases and directions of the standing wave. The performance of such a system is examined through theoretical calculations of both the point-spread function and the optical transfer function.     

Diffusion processes with singular drift fields

A class of stochastic differential equations with highly singular drift fields is considered. Using a purely probabilistic approach, we can show the unattainability of the nodal set. Moreover, a global existence and uniqueness theorem for diffusion processes with singular drift fields is established. The finite action condition of Carlen and Zheng can be modified. We relate our results to the diffusions which describe the time evolution of quantum systems in stochastic mechanics.     

Energy spectrum of the dirac equation for the Scharzschild and Kerr fields

We consider the effect of relativistic corrections and rotation of the central body on the structure of the energy spectrum of a particle with spin in the Schwarzchild and Kerr fields. A splitting of levels is obtained, which corresponds to the classical shift of the perihelion of the orbit and precession of the plane of the gravitational spin-orbit interaction and several nonlinear spin effects are calculated.Translated from Izvestiya Vysshykh Uchebnykh Zavedenii, Fizika, No. 2, pp. 86–92, February, 1988.     

Strong instability of standing waves for Hartree equation with harmonic potential

This paper is concerned with the standing waves of Hartree equation with harmonic potential. Via construction of a cross-constrained invariant set for Hartree equation with harmonic potential, it is shown that if the initial data is in the invariant set then the corresponding solution blows up in finite time. Under an appropriate assumption on the frequency ω, the strong instability of standing waves is investigated by the above blow-up result. Furthermore, without the assumption we also study the property of the standing waves for Hartree equation with harmonic potential.     

A twistorial description of the dynamics of complexified dirac fields

A method that allows the construction of a twistorial least-action principle for complexified Klein-Gordon fields is adapted to the context of the two-component theory of Dirac fields. It appears that the viability of the adaptation procedures rests crucially upon the freedom in the selection of spinor kernels for the integrands of the universal twistor contour integrals for massive fields carrying arbitrary spin. An intrinsic ambiguity borne by the inner structure of the twistor representation of the dynamics of the spinning fields taken into consideration is then brought out. This feature appears to be reflected by the fact that many Poincaré-invariant Lagrangian densities can be regarded as candidates for entering the new variational principle. It is remarked that all the corresponding equations of motion agree with a single twistor translation of the pertinent field equations. The dynamical expressions that result from the implementation of the procedures turn out to be related to one another through a simple interchange scheme. A set of wave equations for the system allowed for is also obtained. This work was supported financially by the Brazilian agency CNPq.     

Localized nonlinear waves in systems with time- and space-modulated nonlinearities

Using similarity transformations we construct explicit nontrivial solutions of nonlinear Schr?dinger equations with potentials and nonlinearities depending both on time and on the spatial coordinates. We present the general theory and use it to calculate explicitly nontrivial solutions such as periodic (breathers), resonant, or quasiperiodically oscillating solitons. Some implications to the field of matter waves are also discussed.     

非线性驻波的饱和函数

非线性驻波的各个谐波在激发强时都要饱和,现根据饱和的实验规律求出饱和函数,以进一步探讨其物理意义.     

Non-uniqueness of the source for singular gauge fields

We show that the singular Wu-Yang solution for SU(2) gauge fields may be interpreted as due to a point source at the origin. However, the electric or magnetic nature of the source depends on whether one approaches the singularity by means of a “smeared” potential or a “smeared” field strength.     

Nonlinear standing waves in a resonator with feedback control

An experimental study is presented to demonstrate that nonlinear effect on standing waves in a resonator can be reduced by a feedback loop responding to the second harmonic. The resonator was a cylindrical tube sealed at one end and driven by a horn driver unit at another end. The feedback control loop consisted of a pressure sensor, a frequency filter, a phase shifter, and an actuator. The results show that the waveform distortions can be eliminated and large amplitude sinusoidal pressure oscillations are obtained. A simple model is proposed for a qualitative discussion on the control mechanism, which shows that the feedback loop alters the imaginary part of the complex mode frequency so as to suppress (or enhance) the second harmonic.     

Vortex streets in a cavity with higher-order standing waves

Recently a laser analog of vortex generation behind an obstacle in a flow was demonstrated. Vortex generation occurs when tilted waves of different transverse structures are simultaneously excited in a laser. We have generalized this phenomenon to higher-order standing waves. Here typical phenomena expected for optical vortices, such as the excitation and disappearance of single vortices out of and into dark lines and dark areas, as well as vortex-pair creation and annihilation become apparent.     

Resonant interaction of standing acoustic waves with a spin system

A theory is developed of the reaction of a spin system to a resonant action of an acoustic field and an electromagnetic field. It is shown that it is important to allow for the coherent properties of the acoustic field that excites the spin system both for the calculation of the line profile of direct acoustic absorption and for the line profile of saturation of paramagnetic resonance by sound. By studying the influence of the acoustic field on the profile of the absorption line of rf power it becomes possible to determine the magnitude and sign of the spin-phonon interaction constant.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 77–81, October, 1973.We are very grateful to V. R. Nagibarov for discussing the work.     

Mathematical model for non-linear standing waves in a tube

A mathematical model is developed to describe the behavior of one-dimensional, non-linear standing waves in a fluid-filled, rigid-wall tube. The tube is bounded on one end by a piston vibrating with periodic motion and terminated on the other end by an impedance boundary. A numerical procedure for calculations based on this model also is described. Calculations are carried out on a digital computer. The model and computer program are presently restricted to pre-shock conditions. Numerical results obtained for the special case of a rigid reflector and a sinusoidally moving piston are in excellent agreement with the results of Coppens and Sanders (private communication). The general approach is applicable to any one-dimensional system bounded by a velocity condition on one end and an impedance condition on the other end.