Singular and Correlation Optics

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Background

Singular optics is a relatively young area of modern optics, whose age does not exceed 40 years. If we consider research in the field of singular optics, then its concept can be divided into three main paradigms that define the essence of research in this area:

(I) It can be stated that practically any spatially distributed value (two-dimensional or three-dimensional) can be characterized by a system of singular or special points, which may be connected in some network by certain lines. For example, for the phase distribution of scalar fields they are equiphase lines, for the distribution of polarization parameters they are equiazimutal lines, etc. Such a network is the skeleton of a spatially distributed parameter and determines, at least at the qualitative (probabilistic) level, the value of the parameter at any point in space.
At the same time, singular networks associated with different characteristics of a wave are somehow interconnected. Thus, we can speak of a global connection between all, without exception, the parameters of the wave. This implies the relevance of studies of specific types of connections between the various characteristics of a light wave and their singular networks. The results of such studies can lead to the development of new algorithms for the restoration of wave characteristics in the analysis of other, seemingly unrelated, field parameters. For example, field phase recovery algorithms based on the analysis of the distribution of its intensity, etc.

(II) The presence of certain topological features, such as a non-zero topological charge or index, leads to the fact that singular structures, in contrast to "smooth" waves, are more stable when they propagate in media with various physical disturbances. It should be added that the difference in the topological characteristics of singular beams automatically leads to the orthogonality of such beams in terms of the orbital angular momentum. Such a property of singular beams of various types can be useful in creating telecommunication systems of a new type, developing new methods for information compression, diagnostic equipment, etc.

(III) Finally, perhaps the main and most interesting aspect of singular optics today is related to the fact that in the field formed by optical singularity, the wave acquires unique physical properties, unusual for any other optical structures. For example, in the region of singularity, a specific angular momentum of the field arises, the energy flows have a unique character, the dimensions of the focused spot of the polarized beam are less than the diffraction limit, etc. These facts that make it possible to hope for the development of optical equipment of a new type, for example; unique optical tweezers, technological equipment (equipment for effective laser welding), super-resolution systems, etc.

Based on the above, the following areas and local topics can be included in the subject of singular optics (and the Research Topic in particular):

1. General principles of coherent singular optics, as in the case of scalar and vector electromagnetic waves.
2. Singular optics of partially coherent and polychromatic waves.
3. Investigation of the energy fluxes, the angular momentum of the field, in the field of optical singularities in both coherent and polychromatic fields.
4. Development of tools for the formation of optical singularities, such as optical converters that convert smooth beams into singular ones.
5. Critical points, singularities in integrated and fiber optics.
6. Investigation of the possibility of developing a new type of optical equipment (diagnostic, technological) based on the principles of singular optics.
7. The practical applications of singular optics in creating new types of optical traps and optical tweezers.

In this regard, the Research Topic will include at least 3-4 review articles in addition to original research.

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