On the Number of Photons in a Classical Electromagnetic Field

Relations determining the number of photons in an electromagnetic field are considered from the point of view of a classical electromagnetic field. A relativistically invariant expression is obtained for the number of emitted photons in terms of charges and currents producing the electromagnetic field. Examples are considered for calculating the numbers of photons in the electromagnetic field for the case of the electric dipole radiation field, as well as the field of a finite and spatially restricted electromagnetic pulse.     

Dissecting a brick into bars

Consider the set of all lengths of sides of an N-dimensional parallelepiped. If this set has no more than k elements, the parallelepiped will be called a bar (the definition of a bar depends on k). We prove that a parallelepiped can be dissected into a finite number of bars if and only if the lengths of its sides span a linear space of dimension at most k over \mathbb Q{{\mathbb Q}} . This extends and generalizes a well-known theorem of Max Dehn about the splitting of rectangles into squares. Several other results about dissections of parallelepipeds are obtained.     

On Measure-Valued Processes Generated by Differential Equations

We study the problem of representation of a homogeneous semigroup { _t } _{t 0} of transformations of probability measures on in the form where satisfies a differential equation of a special form dependent on the measure . We give necessary and sufficient conditions for this representation.     

Theory of Reflective X-Ray Multilayer Structures with Graded Period and its Applications

Journal of Russian Laser Research - We report a theory of reflective X-ray multilayer structures with a graded (slowly-varying) period based on the coupled-wave method and quasiclassical asymptotic...     

Theory Of Multilayer X-Ray Mirrors With Slowly Varying Period

Broadening of multilayer-mirror reflection band is achieved by slow variation of its period. The paper is devoted to the theory of such optical elements based on a general theory of wave propagation through a quasi-periodic medium. The calculation results are presented for the reflection coefficient of broadband mirrors in the 1 to 50 Å range. A statement of the inverse problem is also considered, namely, creation of a multilayer structure possessing the prescribed reflection coefficient.     

Optical imaging system with a waveguide

The problem of image transmission through a waveguide is considered. The transfer function of a step rectangular waveguide is obtained, and it is concluded that direct image transmission is possible over large distances without significant loss of quality. An optical system with a waveguide in which an image is formed with a single objective is proposed. The process of image transmission through a step planar dielectric waveguide is experimentally investigated, and the influence of parameters of the waveguide on the resulting image is revealed. The conditions for image transmission through waveguides of other types are discussed.