(36) Generation and properties of fractal optical fields
¡¡¡¡¡¡Proceedings of International Conference on Optics and Optoelectronics
(ICOL-2005),IT-QOM-2, 2005-12
Recent studies on generation and properties of fractal optical fields, in
particular, multifractal analysis of fractal speckles and generation of nondiffracting
fractal fields, are discussed. We have so far proposed methods for generating
fractal speckles, that is, random optical fields with fractal properties,
and discussed and demonstrated their interesting properties including intensity
clustering and long tails obeying a power-law in their spatial intensity
correlation. However, the fractal speckle is not a simple fractal in some
sense, and seems to involve complicated fractality. To see detailed properties
of such intensities, the multifractal analysis is applied to them. This approach
provides, for a given structure, with not a simple fractal dimension but
a sequence of fractal dimensions called a multifractal spectrum or a singularity
spectrum, which describes the fractality of the structure in details. We
will show that the fractal speckle we proposed is actually multifractal in
certain conditions and that a variation of intensity clustering can be described
by the singularity spectrum.
As another interesting type of fractal fields, nondiffracting fractal and power-law
beams are discussed on the basis of the ordinary theory of nondiffracting beams.
A nondiffracting beam can be produced by illuminating, with coherent light, an
annular aperture placed in the front focal plane of a positive lens. If the amplitude
transmittance of the annular aperture is of a regular fractal function, the generated
nondiffracting beam also has a regular fractal property, while a random fractal
function for the transmittance yields nondiffracting power-law beams. A simple
theoretical approach and simulation results are shown.