From Helmholtz equation of the harmonic electromagnetic waves, the integral equations of the light field at the medium boundaries are obtained by use of the Green's theorem and are discretized into linear equation set with the values of the light field and its derivative as the unknowns. On solving the linear equation set, we realize the rigorous computations of the light fields at the boundaries. Then the intensities of the light waves scattered by the random self-affine fractal surfaces in the optical near-field are calculated, and the propagation characteristics, the evolutions of the contrast and the intensity probability density function of the near-field speckles are studied in detail. The near-field speckles are much different from the conventional speckles in the diffraction regions and in the imaging systems. There are obvious local fluctuations in the intensity distributions of the near-field speckles and such fluctuations disappear after propagating a distance of one wavelength from the medium surfaces. For the random surfaces with smaller lateral correlation lengths, the speckle contrasts approach the saturation values and the speckle fields approach Gaussian distribution within the near-field, while for the random surfaces with larger lateral correlation lengths, such evolutions become comparatively slow.
CHENG Chuanfu1, 2, SONG Hongsheng2, LIU Chunxiang2, REN Xiaorong2, ZHANG Ningyu3, TENG Shuyun1 & XU Zhizhan1 1. Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, P. O. Box 800-211, Shanghai 201800, China
The relations between the specular reflection component of the intensity scattered by random surfaces and the height distributions of the surfaces are analyzed theoretically. In the extraction of the height distribution, both the phase and the amplitude of the specular wave are required. The measured specular intensity data versus the perpendicular component of the wave vector are used for the retrieval of the phase distribution of the specular wave, in which the Gerchberg-Saxton iterative algorithm is employed, and the characterization of the height distribution of random surfaces is accomplished. In the experiment, two samples with Gaussian and quasi-two level height distributions, respectively, are practically measured and the results of the height probability density function obtained by light scattering method are in good accordance with those by atomic force microscopy. The method of this paper is of important significance for the characterizations and studies of random surfaces.
