Scattering from fractal superlattices with variable lacunarity

Jaggard, Aaron D.; Jaggard, D.L.

doi:10.1364/josaa.15.001626

Cited by 51 publications

(47 citation statements)

References 12 publications

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“…This new parameter characterizes the distribution of the gaps inside the polyadic Cantor set and becomes a new design parameter, which enhances the control flexibility of these fractal structures in new applications. This ε parameter has also been widely accepted as an indication of the lacunarity parameter in the literature [15].…”

Section: Generalized Polyadic Cantor Setsmentioning

confidence: 99%

“…The rest of the stages are computed recursively from stage s = 1 using Eq. (15). 1) indicates the start and end of each of the Cantor bars in stage s = 1, where i is an integer index that ranges from 1 to 2N.…”

Section: Numerical Models and Lens Designmentioning

confidence: 99%

“…Among different fractal structures, we have focused our attention on polyadic Cantor sets (PCSs). This type of fractals is very easy to construct, being that the main reason why most man-made fractal creations are based on Cantor fractals [10][11][12][13][14][15][16][17]. Nevertheless, focalization in the ultrasonic range requires further attention.…”

Section: Introductionmentioning

confidence: 99%

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Polyadic Cantor Fractals: Characterization, Generation, and Application as Ultrasonic Lenses

Castiñeira-Ibáñez¹,

Tarrazó-Serrano²,

Fuster³

et al. 2017

Fractal Analysis - Applications in Health Sciences and Social Sciences

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The term fractal was coined in 1975 by Benoit Mandelbrot. Since then, fractal structures have been widely used by the international scientific community. Its range of applications includes multiple areas, such as optics, physics, cryptography, medicine, economics, and so on. The application of fractal structures to modulate light beams in the field of optics has been extensively studied, and it has been shown that in some cases these new fractal lenses improve the response of traditional lenses. Fractal lenses are able to provide beamforming capabilities, and allow the optimization of the optical beam according to the specific requirements. In some applications, it may be necessary to improve the focus in a certain area, while in others it may be critical to obtain a sharp attenuation by means of destructive interference. It may even be required a beam profile with multiple focus and a certain control over them. This work investigates the application of fractal structures based on Polyadic Cantor sets as ultrasonic lenses, analyzing how the relation between the different design parameters and the performance of the lens. It is shown that the working frequency becomes a precise control mechanism that can modify dynamically the focus position of the lens.

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Section: Generalized Polyadic Cantor Setsmentioning

confidence: 99%

Section: Numerical Models and Lens Designmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Polyadic Cantor Fractals: Characterization, Generation, and Application as Ultrasonic Lenses

Castiñeira-Ibáñez¹,

Tarrazó-Serrano²,

Fuster³

et al. 2017

Fractal Analysis - Applications in Health Sciences and Social Sciences

View full text Add to dashboard Cite

show abstract

“…(6) has become a common procedure to determine the fractal dimension of aerogels, colloidal aggregates, and polymers from small angle X-ray, neutron, or optical scattering measurements (Sinha, 1989;Schaefer et al, 1990;Jaggard and Jaggard, 1998;Huanling et al, 2006;Melnichenko and Wignall, 2007).…”

Section: Wave Scattering On Fractalsmentioning

confidence: 99%

Mapping soil fractal dimension in agricultural fields with GPR

Oleschko¹,

Korvin

Muñoz³

et al. 2008

Nonlin. Processes Geophys.

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Abstract. We documented that the mapping of the fractal dimension of the backscattered Ground Penetrating Radar traces (Fractal Dimension Mapping, FDM) accomplished over heterogeneous agricultural fields gives statistically sound combined information about the spatial distribution of Andosol' dielectric permittivity, volumetric and gravimetric water content, bulk density, and mechanical resistance under seven different management systems. The roughness of the recorded traces was measured in terms of a single number H , the Hurst exponent, which integrates the competitive effects of volumetric water content, pore topology and mechanical resistance in space and time. We showed the suitability to combine the GPR traces fractal analysis with routine geostatistics (kriging) in order to map the spatial variation of soil properties by nondestructive techniques and to quantify precisely the differences under contrasting tillage systems. Three experimental plots with zero tillage and 33, 66 and 100% of crop residues imprinted the highest roughness to GPR wiggle traces (mean H R/S =0.15), significantly different to Andosol under conventional tillage (H R/S =0.47).

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“…In optics, the first scientific contributions on this topic were addressed to the analysis of light scattered and diffracted by fractal structures usually known as diffractals [2][3][4][5]. Here, it should be recalled that self-similarity means that, within a given distribution (i.e., spatial or frequency distribution), some of its parts have the same shape as the whole set.…”

mentioning

confidence: 99%

Synthesis of fractal light pulses by quasi-direct space-to-time pulse shaping

et al. 2012

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We demonstrated a simple diffractive method to map the self-similar structure shown in squared radial coordinate of any set of circularly symmetric fractal plates into self-similar light pulses in the corresponding temporal domain. The space-to-time mapping of the plates was carried out by means of a kinoform diffractive lens under femtosecond illumination. The spatio-temporal characteristics of the fractal pulses obtained in this way were measured by means of a spectral interferometry technique assisted by a fiber optics coupler (STARFISH). Our proposal allows synthesizing suited sequences of focused fractal femtosecond pulses potentially useful for several current applications, such as femtosecond material processing, atomic, and molecular control of chemical processes or generation of nonlinear effects.

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Scattering from fractal superlattices with variable lacunarity

Cited by 51 publications

References 12 publications

Polyadic Cantor Fractals: Characterization, Generation, and Application as Ultrasonic Lenses

Polyadic Cantor Fractals: Characterization, Generation, and Application as Ultrasonic Lenses

Mapping soil fractal dimension in agricultural fields with GPR

Synthesis of fractal light pulses by quasi-direct space-to-time pulse shaping

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