Light in curved two-dimensional space

Schultheiss, Vincent H.; Batz, Sascha; Peschel, Ulf

doi:10.1080/23746149.2020.1759451

Cited by 8 publications

(4 citation statements)

References 104 publications

(114 reference statements)

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“…Engineering topological gaps that host robust edge modes based on aperiodic principles is an extremely active area of research, spreading over several research fields such as condensed matter [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20], photonics [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36], acoustics [37][38][39] and mechanics [40][41][42][43][44][45][46][47][48][49][50]. The basic working principles for all these studies rest on the existenc...…”

Section: Introductionmentioning

confidence: 99%

Topological gaps in quasiperiodic spin chains: A numerical and K-theoretic analysis

2022

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Topological phases supported by quasi-periodic spin-chain models and their bulk-boundary principles are investigated by numerical and K-theoretic methods. We show that, for both the un-correlated and correlated phases, the operator algebras that generate the Hamiltonians are non-commutative tori, hence the quasi-periodic chains display physics akin to the quantum Hall effect in two and higher dimensions. The robust topological edge modes are found to be strongly shaped by the interaction and, generically, they have hybrid edge-localized and chain-delocalized structures. Our findings lay the foundations for topological spin pumping using the phason of a quasi-periodic pattern as an adiabatic parameter, where selectively chosen quantized bits of magnetization can be transferred from one edge of the chain to the other.

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Section: Introductionmentioning

confidence: 99%

Topological gaps in quasiperiodic spin chains: A numerical and K-theoretic analysis

2022

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“…A surface's two most crucial curvature functions are Gaussian and mean curvature [45]. The Gaussian curvature is an intrinsic measure, and the mean curvature is an extrinsic measure [51]. In [16], the extracted curvature that yielded the best performance was derived from the mean curvature.…”

Section: The Proposed Curvature Best Basis Methodsmentioning

confidence: 99%

Curvature Best Basis: A Novel Criterion to Dynamically Select a Single Best Basis as the Extracted Feature for Periocular Recognition

et al. 2022

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Aiming at the problems in the best basis selection, this paper presents a novel criterion based on the statistical measurement of the curvature wavelet coefficient to dynamically select the single best basis of the quad-tree wavelet packet transformation. The selected single best basis works as an extracted feature for biometric periocular recognition system. The proposed method first extracts the mean curvature of wavelet coefficients inside the quad-tree wavelet packet transform. Second, the method finds the most distinctive features based on the largest standard deviation and dynamically selects the extracted curvature wavelet coefficients as the single best basis. Third, the selected single curvature best basis works as an extracted feature, and then it is combined with the histogram of oriented gradients method. Finally, the support vector machine is employed to perform classification. Two datasets of two-dimensional periocular digital images are tested against the proposed method. To show the extended ability, we analyze the curvature best basis method against wavelet functions and characteristics and test the proposed method against the plain face and masked face recognition. The proposed method achieves the highest performance results inside periocular recognition (97.53% accuracy for UBIPr-1 and 97.77% accuracy for EYB-P1), masked face recognition (98.11% accuracy), and plain face recognition (98.26% accuracy). The proposed method is robust against glasses occlusion, artificial geometry transformations, Gaussian and salt pepper noise. Comparison with other works in a similar recognition system shows that our proposed curvature best basis method yields the highest performance results.INDEX TERMS Best basis, curvature, periocular recognition, wavelet packet transform.

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“…A notable exception are spherical Schell sources [4][5][6] being important for the modeling of sunlight coherence [7,8]. Among other curved source models [9], cylindrical structures can be treated with simple mathematical tools. In this connection, we note that the scattering problem of stationary light from a cylinder was solved in Ref.…”

Section: Other Items To Checkmentioning

confidence: 99%

Cylindrical partially coherent scalar sources

Martı́nez-Herrero¹,

Korotkova²,

Santarsiero³

et al. 2022

Opt. Lett.

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Partially coherent scalar sources with cylindrical symmetry radiating outwards are introduced. Homogeneous cross-spectral densities are shown to possess angularly modulated Hankel modes, whose amplitudes are subject to a filtering process during propagation. Simple criteria for treating such sources are given. For the case of an incoherent cylinder, the number of effective modes is found and spatial coherence is shown to appear in the radiated light. The radial coherence of the radiated field is then examined. Non-homogeneous cylindrical sources are also introduced.

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Light in curved two-dimensional space

Cited by 8 publications

References 104 publications

Topological gaps in quasiperiodic spin chains: A numerical and K-theoretic analysis

Topological gaps in quasiperiodic spin chains: A numerical and K-theoretic analysis

Curvature Best Basis: A Novel Criterion to Dynamically Select a Single Best Basis as the Extracted Feature for Periocular Recognition

Cylindrical partially coherent scalar sources

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