Golden spiral photonic crystal fiber: polarization and dispersion properties

Agrawal, Arti; Kejalakshmy, N.; Chen, J; Rahman, B. M. A.; Grattan, K. T. V.

doi:10.1364/ol.33.002716

Cited by 74 publications

(49 citation statements)

References 12 publications

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“…PBGs in weakly modulated quasi-crystals are often excluded, even though the approximants may be too small to retain elements of long-range order present in the lattice. In particular, fractal patterns [7,10] may exhibit extremely long-range order owing to their inherent selfsimilarity.In this Letter, we analyze a point set mimicking the head of a sunflower, previously studied in both planar [11] and fiber geometries [12]. Mathematically, this pattern (herein "the sunflower") is a form of Fermat's spiral representing an optimal packing of points evolving about a polar origin.…”

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Low-contrast bandgaps of a planar parabolic spiral lattice

Pollard

Parker

2009

Opt. Lett.

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We show that a planar aperiodic lattice, mimicking the appearance of a sunflower, supports photonic bandgaps for weak dielectric contrast. The pattern's high orientational order and spatially uniform modal pitch yields an isotropic Fourier space. A 2D structure of cylinders ͑⑀ =2͒ in air possesses a wide 21% TM bandgap, versus 5.6% for a sixfold lattice or 14% for a 12-fold fractal tiling. The isotropic gap frequencies imply flat bands, and thus application in nonlinear optics and low threshold lasers, where a reduced group velocity in all directions may be desired. [8]. Intuitively, the ideal Fourier space for 2D band gaps is a circle, i.e., a "Bragg ring." One such pattern with this property is the infinite pinwheel tiling [9]. However, the circular symmetry is not preserved in real (finite) samples.Photonic quasi-crystals are often modeled using periodic "approximants" [8]. In the infinite limit, these approximants recover the properties of the true quasi-periodic parent lattice. PBGs in weakly modulated quasi-crystals are often excluded, even though the approximants may be too small to retain elements of long-range order present in the lattice. In particular, fractal patterns [7,10] may exhibit extremely long-range order owing to their inherent selfsimilarity.In this Letter, we analyze a point set mimicking the head of a sunflower, previously studied in both planar [11] and fiber geometries [12]. Mathematically, this pattern (herein "the sunflower") is a form of Fermat's spiral representing an optimal packing of points evolving about a polar origin. The number of visible spirals, or parastichies, in each direction appear as consecutive numbers in the Fibonacci series, the ratio of which approximates the golden ratio . Formally, an N-point pattern is expressed bywhere ͕n 0:N͖, A is a scaling factor and ⌿ =2 / 2 is the golden angle [13]. This remarkably simple definition contrasts sharply with conventional quasicrystals, typically generated by matching rules, projection, substitution, or multigrids. Figure 1 shows the scanning electron microscopy (SEM) image, Delaunay triangulation, and both calculated and experimental diffraction patterns of a 500 point sunflower fabricated by e-beam lithography. The pattern has a strong modal nearestneighbor pitch a = 2.2 m, derived from Delaunay triangulation [ Fig. 1(b)] of the SEM image ͑r / a = 0.245͒. Expressing the real space density distribution ͑r͒ as a finite sum of plane waves,

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confidence: 99%

“…In this Letter, we analyze a point set mimicking the head of a sunflower, previously studied in both planar [11] and fiber geometries [12]. Mathematically, this pattern (herein "the sunflower") is a form of Fermat's spiral representing an optimal packing of points evolving about a polar origin.…”

mentioning

confidence: 99%

Low-contrast bandgaps of a planar parabolic spiral lattice

Pollard

Parker

2009

Opt. Lett.

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“…Reported [17] offers dispersion coefficient approximately -239.51 ps/(nm.km) with a birefringence of 1.67×10 -2 . In reported [18] reveals negative dispersion of -400 ps/(nm.km) at the operating wavelength of 1550 nm and they got the birefringence of 1.60×10 -2 . In both cases the value of birefringence is low while this is an important factor nowadays for many sensing applications.…”

Section: Dispersionmentioning

confidence: 85%

Design of a Polarization Maintaining Large Negative Dispersion PCF Using Rectangular Lattice

Ali¹,

Ahmed²,

Islam³

et al. 2017

IJIEE

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Abstract-In this paper, we demonstrate a new & simple rectangular photonic crystal fiber (RPCF) for high negative dispersion covering the E to U communication band with ultra-high birefringence, large nonlinearity. According to the simulation results, the designed fiber shows negative dispersion coefficient of -776 to -1591 ps/(nm.km) over E to L communication bands with the relative dispersion slope (RDS) is perfectly matched to that of a single mode fiber. In addition, the proposed RPCF offers a high value of birefringence 2.97×10-2 and a large nonlinear coefficient of 44.5W-1km-1, both at the operating wavelength of 1550 nm. Moreover, the proposed RPCF achieved two zero-dispersion wavelengths in the visible and near IR regions for both of the x and y polarization modes.Index Terms-Photonic crystal fiber, negative dispersion, high birefringence, rectangular lattice.

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“…For example, Douady and Couder (1992) successfully obtained Fibonacci spirals with drops of ferrofluid under the influence of a magnetic field. Spiral structures are emerging as powerful nanophotonic platforms with distinctive optical properties for multiple engineering applications (Agrawal et al, 2008;Trevino et al, 2008;Negro et al, Copyright c Society for Science on Form, Japan.…”

Section: Introductionmentioning

confidence: 99%

Determining Parastichy Numbers Using Discrete Fourier Transforms

Negishi¹,

Sekiguchi²,

Totsuka³

et al. 2017

Forma

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We report a practical method to assign parastichy numbers to spiral patterns formed by sunflower seeds and pineapple ramenta using a discrete Fourier transform. We designed various simulation models of sunflower seeds and pineapple ramenta and simulated their point patterns. The parastichy numbers can be directly and accurately assigned using the discrete Fourier transform method to analyze point patterns even when the parastichy numbers contain a divergence angle that results in two or more generalized Fibonacci numbers. The presented method can be applied to extract the structural features of any spiral pattern.

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Golden spiral photonic crystal fiber: polarization and dispersion properties

Cited by 74 publications

References 12 publications

Low-contrast bandgaps of a planar parabolic spiral lattice

Low-contrast bandgaps of a planar parabolic spiral lattice

Design of a Polarization Maintaining Large Negative Dispersion PCF Using Rectangular Lattice

Determining Parastichy Numbers Using Discrete Fourier Transforms

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