Scaling in the Optical Characteristics of Aperiodic Structures with Self-Similarity Symmetry

Zotov, A. M.; Korolenko, P. V.; Mishin, A. Yu.

doi:10.1134/s1063774510060106

Cited by 7 publications

(3 citation statements)

References 8 publications

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“…We shall now make use of the discussed symmetry properties to express the resulting diffraction pattern. Let us split the complex function, (8), into positive and negative frequency parts, such that…”

Section: B Diffraction Peaks and Modulating Envelope For Mirror-symme...mentioning

confidence: 99%

“…In X-ray diffraction, for instance, completely disordered or amorphous media do not give rise to sharp diffraction peaks, while aperiodic lattices with long-range order (quasi-crystals) manifest diffraction signatures similar to periodic lattices [5,6]. Interference from aperiodic structures has also been studied in the context of photonic and plasmonic quasi-crystals [7][8][9]. Besides, studies on the focusing and deflection properties of aperiodic gratings have been carried out [10][11][12][13], with attention to structures ruled by Fibonacci sequences [14][15][16].…”

Section: Introductionmentioning

confidence: 99%

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Optical computing of quantum revivals

Maia,

Jonathan,

Oliveira

et al. 2022

Preprint

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Interference is the mechanism through which waves can be structured into the most fascinating patterns. While for sensing, imaging, trapping, or in fundamental investigations, structured waves play nowadays an important role and are becoming subject of many interesting studies. Using a coherent optical field as a probe, we show how to structure light into distributions presenting collapse and revival structures in its wavefront. These distributions are obtained from the Fourier spectrum of an arrangement of aperiodic diffracting structures. Interestingly, the resulting interference may present quasiperiodic structures of diffraction peaks on a number of distance scales, even though the diffracting structure is not periodic. We establish an analogy with revival phenomena in the evolution of quantum mechanical systems and illustrate this computation numerically and experimentally, obtaining excellent agreement with the proposed theory.

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Section: B Diffraction Peaks and Modulating Envelope For Mirror-symme...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Optical computing of quantum revivals

Maia,

Jonathan,

Oliveira

et al. 2022

Preprint

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show abstract

“…The concept of fractals provide a general technique for analyzing the physical phenomena in different fields, for example, the fractal theory used for image inpainting algorithm [2] , the fractal characterization of surface morphology [3] , the fractal structure excitation in soliton-supporting systems [4] and the evolution of self-written waveguides [5] . Although fractals are common in the one-dimensional quasicrystals structures [6] , the fractal characteristics of twodimensional (2-D) quasicrystals structures have not been deeply known. Only a few of significant studies have been carried out, including the transmission resonances in Penrose quasicrystal [7] , the photonic-plasmonic scattering resonances in Fibonacci, Thue-Morse (TM) and Rudin-Shapiro array [8] .…”

mentioning

confidence: 99%

Fractal characteristics of far-field diffraction patterns for two-dimensional Thue-Morse quasicrystals

Yang

Zhou

Petti

et al. 2011

Optoelectron. Lett.

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Tianjin University of Technology and Springer-Verlag Berlin Heidelberg 2011 C We report a numerical method to analyze the fractal characteristics of far-field diffraction patterns for two-dimensional Thue-Morse (2-D TM) structures. The far-field diffraction patterns of the 2-D TM structures can be obtained by the numerical method, and they have a good agreement with the experimental ones. The analysis shows that the fractal characteristics of far-field diffraction patterns for the 2-D TM structures are determined by the inflation rule, which have potential applications in the design of optical diffraction devices.The fractal phenomenon is easily found in nature, by definition, fractal objects exhibit the self-similarity in their geometric structures which are determined by an iterative rule [1] . The concept of fractals provide a general technique for analyzing the physical phenomena in different fields, for example, the fractal theory used for image inpainting algorithm [2] , the fractal characterization of surface morphology [3] , the fractal structure excitation in soliton-supporting systems [4] and the evolution of self-written waveguides [5] . Although fractals are common in the one-dimensional quasicrystals structures [6] , the fractal characteristics of twodimensional (2-D) quasicrystals structures have not been deeply known. Only a few of significant studies have been carried out, including the transmission resonances in Penrose quasicrystal [7] , the photonic-plasmonic scattering resonances in Fibonacci, Thue-Morse (TM) and Rudin-Shapiro array [8] .In this work, we present a numerical study to demonstrate that the far-field diffraction patterns of the 2-D TM structure, which have the fractal characteristics determined by the inflation rule of TM sequence. In addition, two kinds of 2-D TM chips are fabricated by electron beam lithography (EBL) technique and their far-field diffraction patterns are experimentally recorded by CCD detector. By comparing the numerical far-field diffraction patterns with the experimental photos, it is verified that the numerical method can finely simulate the far-field diffraction results. And, the analysis of fabrication tolerance of the 2-D TM chips shows that the far-field diffraction patterns of 2-D TM structure have high fractal stability.To construct the 2-D TM structure, a one-dimensional binary TM sequence is firstly constructed using the following rule. First of all, let , s give an arbitrary sequence of two symbols, A=0 and B=1, and then a new sequence is formed by replacing each occurrence of A with the pair (A, B) and each occurrence of B with the pair (B, A) [9] . By inflation rule, the one-dimensional TM sequence can be generalized to the two-dimensional TM structure by introducing a substitutional matrix S N+1[9] :

show abstract

Optical computing of quantum revivals

et al. 2022

View full text Add to dashboard Cite

Interference is the mechanism through which waves can be structured into the most fascinating patterns. While for sensing, imaging, trapping, or in fundamental investigations, structured waves play nowadays an important role and are becoming the subject of many interesting studies. Using a coherent optical field as a probe, we show how to structure light into distributions presenting collapse and revival structures in its wavefront. These distributions are obtained from the Fourier spectrum of an arrangement of aperiodic diffracting structures. Interestingly, the resulting interference may present quasiperiodic structures of diffraction peaks on a number of distance scales, even though the diffracting structure is not periodic. We establish an analogy with revival phenomena in the evolution of quantum mechanical systems and illustrate this computation numerically and experimentally, obtaining excellent agreement with the proposed theory.

show abstract

Scaling in the Optical Characteristics of Aperiodic Structures with Self-Similarity Symmetry

Cited by 7 publications

References 8 publications

Optical computing of quantum revivals

Optical computing of quantum revivals

Fractal characteristics of far-field diffraction patterns for two-dimensional Thue-Morse quasicrystals

Optical computing of quantum revivals

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