Internal flows and energy circulation in light beams

We review optical phenomena associated with the internal energy redistribution which accompany propagation and transformations of monochromatic light fields in homogeneous media. The total energy flow (linear-momentum density, Poynting vector) can be divided into spin part associated with the polarization and orbital part associated with the spatial inhomogeneity. We give general description of the internal flows in the coordinate and momentum (angular spectrum) representations for both nonparaxial and paraxial fields. This enables one to determine local densities and integral values of the spin and orbital angular momenta of the field. We analyse patterns of the internal flows in standard beam models (Gaussian, Laguerre-Gaussian, flat-top beam, etc.), which provide an insightful picture of the energy transport. The emphasize is made to the singular points of the flow fields. We describe the spin-orbit and orbit-orbit interactions in the processes of beam focusing and symmetry breakdown. Finally, we consider how the energy flows manifest themselves in the mechanical action on probing particles and in the transformations of a propagating beam subjected to a transverse perturbation.Comment: 50 pages, 21 figures, 173 references. This is the final version of the manuscript (v1) modified in accord to the referee's remarks and with allowance for the recent development. The main changes are: additional discussion of the energy flows in Bessel beams (section 4.1), a lot of new references are added and the Conclusion is shortened and made more accurat

Internal flows and energy circulation in light beams

We review optical phenomena associated with the internal energy redistribution which accompany propagation and transformations of monochromatic light fields in homogeneous media. The total energy flow (linear-momentum density, Poynting vector) can be divided into a spin part associated with the polarization and an orbital part associated with the spatial inhomogeneity. We give a general description of the internal flows in the coordinate and momentum (angular spectrum) representations for both nonparaxial and paraxial fields. This enables one to determine local densities and integral values of the spin and orbital angular momenta of the field. We analyse patterns of the internal flows in standard beam models (Gaussian, Laguerre-Gaussian, flat-top beam, etc), which provide an insightful picture of the energy transport. Emphasis is given to the singular points of the flow fields. We describe the spin-orbit and orbit-orbit interactions in the processes of beam focusing and symmetry breakdown. Finally, we consider how the energy flows manifest themselves in the mechanical action on probing particles and in the transformations of a propagating beam subjected to a transverse perturbation

The art of goalkeeping: memorializing Lev Yashin

Lev Yashin remains, in the eyes of many, the greatest goalkeeper, ever to have played the game of football. Since his death in 1990, coinciding with the dying days of the Soviet Union, his legacy has played an important role in post-Soviet history, a factor that is gaining more importance as Russia prepares to host the 2018 World Cup tournament. Yashin’s memory is notably being maintained in the public perception not least through the material form of two key sculptures erected in Moscow in the late 1990s. Yet these works, part of a wider international trend to memorialize footballers in the form of public monuments, offer more than a unique insight into Yashin’s career, status and reputation. They also address concerns about the relationship between art and sport as it emerged historically in the Soviet Union and how that cultural legacy is being re-explored in a post-Soviet context. Accordingly this essay examines these two key examples of football statuary as significant case studies through which issues relating to Soviet sport, history and art can be more widely analysed