Table of contents

This paper discusses theoretical and experimental results of the investigation of light beams that retain their intensity strusture during propagation and focusing. We describe a family of laser beams termed spiral whose intensity remains invariable, up to scale and rotation, during propagation. Several properties of spiral beams are of practical interest for laser technologies, medicine, and microbiology. The problem of synthesis of spiral beams with the intensity distribution given by an arbitrary planar curve is considered. We emphasize the feasibility, in principle, of making lasers that directly generate beams with desired properties without additional unconventional optics.

Isolated waveguide modes of intense light fields are unique physical objects, which can never be observed in standard optical fibers, hollow waveguides, plasma filaments, or in the bulk of a transparent dielectric or gas. Hollow photonic-crystal fibers can for the first time produce robust isolated truly guided spatial modes of subgigawatt ultrashort light pulses, perform efficient nonlinear-optical transformations of laser fields in such states, and implement new waveguide regimes of coherent excitation and probing of molecular Raman-active modes in the gas phase.

It is shown that the current problems related to the nuclear power cycle can be resolved if the conventional fission process is complemented with the 'photoneutron reprocessing' of fissile nuclei directly in spent uranium by using the energy of relativistic storage-ring electrons and transforming it to synchrotron/undulator gamma radiation, and by utilizing the fission products as neutron sources while at the same time transmuting them into stable isotopes. A suitable method of 'gamma–neutron transmutation' is described, and the values of its parameters that make the corresponding 'electrophotonuclear' power cycle closed and waste-free are determined.

The teaching of optical phenomena can be enhanced through the use of analogies to the motion of a bi-freguency pendulum. In this text we target demonstrations to four groups of students and scientists: younger schoolchildren to high school seniors; 7th graders to college juniors; college juniors to final-year graduate students in physics, optics and engineering; and college seniors to research scientists. The main defference between the groups is in the level of mathematics required to make the analogy to optical phenomena. Most of the physical ideas may be understood and appreciated even in junior high school and serve as a motivation for deeper study of mathematics and science.

It is shown that a necessary and sufficient condition for β-stability of the nucleus in a neutral atom is that the mass of the atom be a minimum within the isobaric series, which is not always the same as the requirement of minimum nuclear mass often cited in the literature.

A laser beam introduced into a simple soap film unexpectedly breaks out into thin (micron-thick) branching channels which keep unspread (without divergence) sometimes for as long as tens of centimeters as they go along the film. The physical interpretation and possible applications of the phenomenon are discussed in this paper.

This article is dedicated to John von Neumann, one of the most outstanding scholars of the 20th century. His life was short but bright, and his contribution to almost all branches of mathematics, as well as to physics, economics, biology, and astronomy was enormous. He constructed some of the first computers and he was among the key persons in the American atomic project. Development of his ideas will continue to play a vital part in various areas of pure and applied mathematics.