Stochastic beams are highly-directional fields whose amplitudes and phases fluctuate randomly in time. Such beams may be characterized by probability density functions involving their amplitudes and phases or by a complete set of their statistical moments. In practice, however, except in a very few cases such complete information can be prescribed or measured. Usually moments up to the second order (more seldom to the fourth order) are available.
We will first review the basic theory concerning stochastic beams, particularly their generation, propagation and interaction with different types of media and their detection. We will consider both scalar and electromagnetic beams. In the later case we will concentrate on the phenomenon discovered relatively recently, relating to changes in polarization properties as the beam propagates.
In the second part of the talk we will consider some applications of stochastic beams. Primarily, we will discuss the advantages of employing such beams as carriers of signals in communication through random media (e.g. the turbulent atmosphere). In addition important applications to medical imaging and diagnostics will be mentioned.