Optical propagation of fractal fields. Experimental analysis in a single display

Trabocchi, Osvaldo; Granieri, Sergio; Furlan, Walter D.

doi:10.1080/09500340108231767

Cited by 11 publications

(4 citation statements)

References 8 publications

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“…In fact, this study is inspired by optical diffraction of fractal screen. [5,17,18] FRFT of more complex fractals seems to be more meaningful, but the severe problems of mathematical definition and physical realization are encountered. We hope that both theoretical and experimental researchers are interested in our model.…”

Section: Model and Methodsmentioning

confidence: 99%

Fractional Fourier transform of Cantor sets: further numerical study

2008

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This paper is a further work of the authors' paper published previously (Liao T H and Gao Q 2005 Chin. Phys. Lett. 22 2316). The amplitudes of fractional Fourier transform of Cantor sets are analysed from the viewpoint of multifractal by wavelet transform maxima method (WTMM). An integral operation is carried out before the application of WTMM, such that the function obtained can be considered as the perturbed devil staircase. Also, wavelets with large number of vanishing moments are used, which makes the complete singularity spectrum more accessible. The validity of multifractal formalism is guaranteed by restricting parameter q to a proper range, so that the phenomenon of multifractal phase transition can be explained reasonably. Particularly, the method of determining the range of parameter q in the above paper is developed to be more operational and rigorous.

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Section: Model and Methodsmentioning

confidence: 99%

Fractional Fourier transform of Cantor sets: further numerical study

2008

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“…In optics, fractal structures ranging from simple one-dimensional (1D) systems [4,5] to complex 2D objects [6,7] have been extensively studied. Specifically, diffraction gratings based on the fractal Cantor set sequences have been analysed [8,9].…”

Section: Introductionmentioning

confidence: 99%

Undergraduate experiment with fractal diffraction gratings

et al. 2011

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We present a simple diffraction experiment with fractal gratings based on the Triadic Cantor Set. Diffraction by fractals is proposed as a motivating strategy for the students of optics about the potential applications of optical processing. The Fraunhofer diffraction patterns were obtained with the standard equipment present in most undergraduate physics labs and compared with that obtained with conventional periodic gratings. It is shown that fractal gratings produce self-similar diffraction patterns which can be evaluated analytically. A very good accuracy is obtained between experimental and numerical results.

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“…In optics, fractal structures, ranging from simple one-dimensional (1D) objects [2] to complex 2D systems [3][4][5] have been extensively studied. Specifically, 1D dielectric multilayers characterized by a refractive-index distribution that follows Cantor [6,7] sequences have been analyzed.…”

Section: Introductionmentioning

confidence: 99%