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Yiqi Zhang; Milivoj R. Belić; Huaibin Zheng; Haixia Chen; Changbiao Li; Jianping Song; Yanpeng Zhang
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Akhmediev and Kuznetsov-Ma breathers are rogue wave solutions of the nonlinear Schr\"odinger equation (NLSE). Talbot effect (TE) is an image recurrence phenomenon in the diffraction of light waves. We report the nonlinear TE of rogue waves in a cubic medium. It is different from the linear TE, in that the wave propagates in a NL medium and is an eigenmode of NLSE. Periodic rogue waves impinging on a NL medium exhibit recurrent behavior, but only at the TE length and at the half-TE length...
Topics: Physics, Nonlinear Sciences, Pattern Formation and Solitons, Optics
Source: http://arxiv.org/abs/1402.3017
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Yiqi Zhang; Milivoj R. Belić; Changbiao Li; Zhaoyang Zhang; Yanpeng Zhang; Min Xiao
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We report two new classes of face-centered photonic square lattices with flat bands which we call the Lieb-I and the Lieb-II lattices. There are 5 and 7 sites in the corresponding unit cells of the simplest Lieb-I and Lieb-II lattices, respectively. The number of flat bands $m$ in the new Lieb lattices is related to the number of sites $N$ in the unit cell by $m=(N-1)/2$. Physical properties of the lattices with even and odd number of flat bands are different. We also consider localization of...
Topics: Optics, Physics
Source: http://arxiv.org/abs/1605.04389
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Yiqi Zhang; Milivoj R. Belić; Huaibin Zheng; Haixia Chen; Changbiao Li; Jianeng Xu; Yanpeng Zhang
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We investigate numerically interactions between two bright or dark incoherent localized beams in an strontium barium niobate photorefractive crystal in one dimension, using the coherent density method. For the case of bright beams, if the interacting beams are in-phase, they attract each other during propagation and form bound breathers; if out-of-phase, the beams repel each other and fly away. The bright incoherent beams do not radiate much and form long-lived well-defined breathers or...
Topics: Physics, Nonlinear Sciences, Pattern Formation and Solitons, Optics
Source: http://arxiv.org/abs/1408.2601
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Hua Zhong; Yiqi Zhang; Yi Zhu; Da Zhang; Changbiao Li; Yanpeng Zhang; Fuli Li; Milivoj R. Belić; Min Xiao
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We report on transport properties of the super-honeycomb lattice, the band structure of which possesses a flat band and Dirac cones, according to the tight-binding approximation. This super-honeycomb model combines the honeycomb lattice and the Lieb lattice and displays the properties of both. The super-honeycomb lattice also represents a hybrid fermionic and bosonic system, which is rarely seen in nature. By choosing the phases of input beams properly, the flat-band mode of the super-honeycomb...
Topics: Optics, Physics
Source: http://arxiv.org/abs/1608.06365
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Yiqi Zhang; Milivoj R. Belić; Milan S. Petrović; Huaibin Zheng; Haixia Chen; Changbiao Li; Keqing Lu; Yanpeng Zhang
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We introduce two-dimensional (2D) linear and nonlinear Talbot effects. They are produced by propagating periodic 2D diffraction patterns and can be visualized as 3D stacks of Talbot carpets. The nonlinear Talbot effect originates from 2D rogue waves and forms in a bulk 3D nonlinear medium. The recurrences of an input rogue wave are observed at the Talbot length and at the half-Talbot length, with a \pi phase shift; no other recurrences are observed. Different from the nonlinear Talbot effect,...
Topics: Physics, Nonlinear Sciences, Optics, Pattern Formation and Solitons
Source: http://arxiv.org/abs/1412.0236
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Yiqi Zhang; Milivoj R. Belić; Huaibin Zheng; Haixia Chen; Changbiao Li; Zhiguo Wang; Yanpeng Zhang
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We investigate three-dimensional nonparaxial linear accelerating beams arising from the transverse Whittaker integral. They include different Mathieu, Weber, and Fresnel beams, among other. These beams accelerate along a semicircular trajectory, with almost invariant nondiffracting shapes. The transverse patterns of accelerating beams are determined by their angular spectra, which are constructed from the Mathieu functions, Weber functions, and Fresnel integrals. Our results not only enrich the...
Topics: Physics, Optics
Source: http://arxiv.org/abs/1406.2764
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Hua Zhong; Yiqi Zhang; Milivoj R. Belić; Changbiao Li; Feng Wen; Zhaoyang Zhang; Yanpeng Zhang
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We investigate controllable spatial modulation of circular autofocusing Airy beams, under action of different dynamic linear potentials, both theoretically and numerically. We introduce a novel treatment method in which the circular Airy beam is represented as a superposition of narrow azimuthally-modulated one-dimensional Airy beams that can be analytically treated. The dynamic linear potentials are appropriately designed, so that the autofocusing effect can either be weakened or even...
Topics: Optics, Physics
Source: http://arxiv.org/abs/1603.08349
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Yiqi Zhang; Milivoj R. Belić; Huaibin Zheng; Haixia Chen; Changbiao Li; Yuanyuan Li; Yanpeng Zhang
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We investigate numerically interactions between two in-phase or out-of-phase Airy beams and nonlinear accelerating beams in Kerr and saturable nonlinear media in one transverse dimension. We discuss different cases in which the beams with different intensities are launched into the medium, but accelerate in opposite directions. Since both the Airy beams and nonlinear accelerating beams possess infinite oscillating tails, we discuss interactions between truncated beams, with finite energies....
Topics: Physics, Nonlinear Sciences, Pattern Formation and Solitons, Optics
Source: http://arxiv.org/abs/1403.1952
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Yiqi Zhang; Junfeng Liu; Feng Wen; Changbiao Li; Zhaoyang Zhang; Yanpeng Zhang; Milivoj R. Belić
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We investigate the coherent and incoherent nonparaxial Weber beams, theoretically and numerically. We show that the superposition of coherent self-accelerating Weber beams with transverse displacement cannot display the nonparaxial accelerating Talbot effect. The reason is that their lobes do not accelerate in unison, which is a requirement for the appearance of the effect. While for the incoherent Weber beams, they naturally cannot display the accelerating Talbot effect but can display the...
Topics: Optics, Physics
Source: http://arxiv.org/abs/1605.09525
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Yiqi Zhang; Hua Zhong; Milivoj R. Belić; Changbiao Li; Zhaoyang Zhang; Feng Wen; Yanpeng Zhang; Min Xiao
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We demonstrate the fractional Talbot effect of nonpraxial accelerating beams, theoretically and numerically. It is based on the interference of nonparaxial accelerating solutions of the Helmholtz equation in two dimensions. The effect originates from the interfering lobes of a superposition of the solutions that accelerate along concentric semicircular trajectories with different radii. Talbot images form along certain central angles, which are referred to as the Talbot angles. The fractional...
Topics: Optics, Physics
Source: http://arxiv.org/abs/1603.08339
