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Adiabatic Dynamics of Edge Waves in Photonic Graphene
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In this paper, the propagation of localized edge modes in photonic honeycomb lattices, formed from an array of adiabatically varying periodic helical waveguides, is considered.Abstract:
The propagation of localized edge modes in photonic honeycomb lattices, formed from an array of adiabatically varying periodic helical waveguides, is considered. Asymptotic analysis leads to an explicit description of the underlying dynamics. Depending on parameters, edge states can exist over an entire period or only part of a period; in the latter case an edge mode can effectively disintegrate and scatter into the bulk. In the presence of nonlinearity, a `time'-dependent one-dimensional nonlinear Schr\"odinger (NLS) equation describes the envelope dynamics of edge modes. When the average of the `time varying' coefficients yields a focusing NLS equation, soliton propagation is exhibited. For both linear and nonlinear systems, certain long lived traveling modes with minimal backscattering are found; they exhibit properties of topologically protected states.read more
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Journal ArticleDOI
Topological Photonics
Tomoki Ozawa,Hannah M. Price,Alberto Amo,Nathan Goldman,Mohammad Hafezi,Ling Lu,Mikael C. Rechtsman,David Schuster,Jonathan Simon,Oded Zilberberg,Iacopo Carusotto +10 more
TL;DR: Topological photonics is a rapidly emerging field of research in which geometrical and topological ideas are exploited to design and control the behavior of light as mentioned in this paper, which holds great promise for applications.
Journal ArticleDOI
Bifurcations of edge states—topologically protected and non-protected—in continuous 2D honeycomb structures
TL;DR: In this paper, the authors consider a family of Schrodinger Hamiltonians consisting of a bulk honeycomb potential and a perturbing edge potential, and show that the topologically protected edge state bifurcation is seeded by the zero-energy eigenstate of a one-dimensional Dirac operator.
Journal ArticleDOI
Hinge solitons in three-dimensional second-order topological insulators
TL;DR: In this article, the existence of stable solitons localized on the hinges of a second-order topological insulator in three dimensions was shown by means of a systematic numerical study, and the soliton propagates along the hinge unidirectionally without changing its shape.
Posted Content
Weakly Nonlinear Analysis of Vortex Formation in a Dissipative Variant of the Gross-Pitaevskii Equation
TL;DR: It is shown that the mechanism responsible for initiating vortex formation is a modulational instability of the amplitude equation, and the role of dissipation in the symmetry breaking process is illustrated.
Journal ArticleDOI
Topology puts solitons in the corner
TL;DR: In a nonlinear photonic higher-order topological insulator, solitons localize on the corners together with the topological modes as mentioned in this paper, where the topology and nonlinearity are linked to symmetry.
References
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TL;DR: The first observation of conical diffraction arising from k-space singularities in the band-structure of a periodic potential is predicted and presented.
Journal ArticleDOI
Edge states in the integer quantum Hall effect and the Riemann surface of the Bloch function.
TL;DR: It is found that the energies of the edge states are given by the zero points of the Bloch function on some Riemann surface (RS) (complex energy surface) when the system size is commensurate with the flux.
Journal ArticleDOI
Observation of unconventional edge states in ‘photonic graphene’
Yonatan Plotnik,Mikael C. Rechtsman,Daohong Song,Matthias Heinrich,Julia M. Zeuner,Stefan Nolte,Yaakov Lumer,Natalia Malkova,Jingjun Xu,Alexander Szameit,Zhigang Chen,Zhigang Chen,Mordechai Segev +12 more
TL;DR: A new type of edge state is found: one residing on the bearded edge that has never been predicted or observed in graphene, and can be classified as a Tamm-like state lacking any surface defect.