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Chapter 1:
Introduction to Linear Singular Optics
Propagation of coherent radiation through inhomogeneous media with random fluctuations of local optical characteristics results in the formation of an optical wave that is characterized by random temporal and spatial distributions of its parameters such as intensity, phase, and, in general cases, its state of polarization. The fields formed in this way are referred to as speckle fields. While the parameters of speckle fields are described by the complex functions of general form, one can expect that diverse distinctions (or singularities) are inherent in both pointlike and extended speckle fields. Singularities and stationary points are interconnected in the form of distinct nets. These nets, similar to skeletons, constitute the field structure, and information on their characteristics provides quantitative predictions for the behavior of the field at any point. It must be emphasized that the fundamentals for predicting the behavior of fields were developed in the epochal book Natural Focusing and Fine Structure of Light by J. Nye, published in 1999. The detailed problems discussed by Nye are only mentioned in passing in this chapter, which is intended as a (hopefully successful) addendum and sequel to his outstanding study. Therefore, the focus of this chapter is on the decisive role of various singularities that form the electromagnetic field. The insight provided to the problems of singular optics, as well as the advances of the singular-optics approach in solving optics problems, and the roles played by the nets of singularities as the skeletons of the electromagnetic field is intended to intrigue those involved in modern optics. For the sake of observation, rigorously monochromatic waves are not considered. The optical singularities arising from optical waveguides, nonlinear media, etc. are also not considered, because this is the subject for another comprehensive book. Note, in conclusion, that the number of publications devoted to singular optics has grown as an avalanche in the last few years, and for this reason the list of references may seem to be too short, especially in regard to the concluding section that deals with the singularities of the Poynting vector. Nevertheless, the list of references contains the key publications concerning the main aspects of singularities in electromagnetic fields.
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