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Chapter 3:
Coherent-Mode Representation of Propagation-Invariant Fields
As is well known, a bounded optical field propagating in free space undergoes diffractive spreading that changes its transverse intensity distribution. Nevertheless, it is not always the case if the field has an infinite extent. Almost two decades ago, Durnin found an exact solution for the wave propagation equation that describes a whole class of so-called nondiffracting fields. It has been shown that any nondiffracting field represents the superposition of plane waves with wave vectors lying on a cone. In this case, all the wave vectors possess the same projection along, say, the z-axis and the constituent plane waves suffer one and the same phase change on propagation. Accordingly, they interfere in the same way at any constant z plane. The simplest member of the class of nondiffracting fields is the fundamental Bessel beam. The sharply peaked intensity profile of this beam, together with its propagation-invariant property, has generated wide interest to nondiffracting beams. The new models of nondiffracting beams have been studied and compared, the possibility of their physical generation has been demonstrated in experiments, and their potential practical applications have been discussed. It is not out of place to mention here that nondiffracting beams have also received attention in acoustic science (see, e.g., Ref. 60). The nondiffracting beams defined by Durnin's solution represent completely coherent optical fields. At the same time, as has been shown by Ohtsuka et al. and Gori et al., some partially coherent fields can also exhibit propagation-invariant properties. Turunen et al. have generalized the concept of diffraction-free propagation into a domain of partially coherent fields, and have deduced the general expression for the cross-spectral density function, which defines a wide class of partially coherent propagation-invariant fields. In spite of a great number of published results, the theory of propagation-invariant fields is still far from completion. Recently, Ostrovsky et al., while trying to describe all the possible classes of propagation-invariant fields, have deduced the coherent-mode structure of propagation-invariant fields that allowed, in particular, predicting the existence of new peculiar propagation-invariant optical beams. Below, we consider this representation and the results obtained on its basis.
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