Phase singularities in electromagnetic fields became the subject of intense interest in 1974, when Nye and Berry formulated a new wave concept, dealing with nonsmooth wavefronts. If at any point of the cross section of a freely propagating beam amplitude of the field vanishes, then the phase of the complex amplitude at this point is undetermined, and the wavefront around this point is helicoidal. Therefore, the field structures in the vicinity of amplitude zeros are often referred to as optical vortices.
For a long time this chapter of modern optics, called singular optics, was developed within the framework of coherent (monochromatic) approximation. Comprehensive notions on the findings of coherent singular optics can be obtained from Refs. 2 and 3. An original approach to coherent singular optics is contained in Chapter 1 of this book, written by Prof. Mokhun.
It has begun to be understood only at the threshold of the third millennium that complete (both spatial and temporal) coherence is not an indispensable condition for observing phase singularities.
It is worthy to note that amplitude zeros and phase singularities were foretold by Sommerfeld just for the case of a nonmonochromatic and partially spatially coherent field. Calculating the field formed by a few plane waves slightly different in wavelengths and in directions of propagation, Sommerfeld showed a violation of the regularity of the wavefronts and illustrated that the adjacent phase singularities are of opposite signs. The same approximation lies as the basis of consideration in the pioneering paper of Nye and Berry.
The main tendency of modern singular optics consists of coming into being correlation singular optics, i.e., in the study of phase singularities in partially spatially coherent and polychromatic light fields. This tendency is obvious from the comprehensive and regularly updated list of references on singular optics.
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