Proceedings Article | 30 May 2001
Proc. SPIE. 4403, Second International Conference on Singular Optics (Optical Vortices): Fundamentals and Applications
KEYWORDS: Speckle, Fourier transforms, Speckle pattern, Wave propagation, Black bodies, Beam propagation method, Spiral phase plates, Information operations, Anisotropy, Correlation function
This paper is a review and extension of recent work by Berry and Dennis (Proc. Roy. Soc. Lond. A456, pp. 2059-2079, 2000; A457, pp. 141-155, 2001), where the geometric structure of phase singularities (wave dislocations) in waves is studied, particularly for singularities in isotropic random wavefields. The anisotropy ellipse of a generic dislocation is defined, and I derive an angular momentum rule for its phase. Random wavefields are discussed, and statistical results for density, anisotropy ellipse eccentricity, and planar correlation functions are stated. The properties of the correlation functions are compared to analogous features from ionic structure theory, and are discussed in those terms. The results are given explicitly for four particular spectra: monochromatic waves propagating in the plane, monochromatic waves propagating in space, a speckle pattern in the transverse plane of a paraxial beam, and the Planck spectrum for blackbody radiation.
