Modulational instability and solitary waves in polariton topological insulators

Kartashov, Yaroslav V.; Skryabin, Dmitry V.

doi:10.1364/optica.3.001228

Cited by 143 publications

(147 citation statements)

References 41 publications

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“…Achieving large polarization energy splitting has been important, since the beginning of the studies of microcavity polaritons, in the context of the polariton spin Hall effect [33,34], see also [4] for a detailed review of the previous work. Currently, the design of strong SOC is getting crucially important for the work towards experimental observation and applications of polariton topological insulators [5,[35][36][37].…”

Section: Analytical and Numerical Results For The Symmetric System 2mentioning

confidence: 99%

Spin–orbit coupling and nonlinear modes of the polariton condensate in a harmonic trap

2017

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We consider a model of the exciton-polariton condensate based on a system of two Gross-Pitaevskii equations coupled by the second-order differential operator, which represents the spin-orbit coupling in the system. Also included are the linear gain, effective diffusion, nonlinear loss, and the standard harmonic-oscillator trapping potential, as well as the Zeeman splitting. By means of combined analytical and numerical methods, we identify stable two-dimensional modes supported by the nonlinear system. In the absence of the Zeeman splitting, these are mixed modes, which combine zero and nonzero vorticities in each of the two spinor components, and vortex-antivortex complexes. We have also found a range of parameters where the mixed-mode and vortex-antivortex states coexist and are stable. Sufficiently strong Zeeman splitting creates stable semi-vortex states, with vorticities 0 in one component and 2 in the other. mixed modes, which combine fundamental and vortex terms with S 1 =  in both field components [7]. Stability of nonlinear states in SOC systems is radically different with respect to the ones without SOC [18,19]. Indeed, the GPE in the free 2D space with the cubic self-attraction, or a system of two GPEs with self-and cross attraction, gives rise to families of zero-vorticity, alias fundamental (Townes' [9]) and vorticity-carrying [10][11][12] bright solitons which are completely unstable either due to the critical collapse [13][14][15] or due to the ringsplitting instabilities [16,17], respectively. On the other hand, the SOC terms come with a coefficient which fixes an inverse length scale in the system, thus breaking the scaling invariance which makes norms of all the solitons belonging to the Townes' family exactly equal to the critical value necessary for the onset of the collapse. As a OPEN ACCESS RECEIVED

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Section: Analytical and Numerical Results For The Symmetric System 2mentioning

confidence: 99%

Spin–orbit coupling and nonlinear modes of the polariton condensate in a harmonic trap

2017

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“…These include modulational instability and topological edge solitons, which inherit topological protection against scattering into the bulk modes and remain localized upon motion along the edge of a topological insulator. To date, topological edge solitons have been studied mainly in undriven systems, such as polariton topological insulators 44 admitting bright 45 and dark 46,47 quasi-solitons, as well as rich bistability effects. 48 Solitons in Floquet insulators have received less attention.…”

Section: Introductionmentioning

confidence: 99%

Vector Topological Edge Solitons in Floquet Insulators

et al. 2020

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We introduce topological vector edge solitons in a Floquet insulator, consisting of two honeycomb arrays of helical waveguides with opposite directions of rotation in a focusing nonlinear optical medium. Zigzag edges of two arrays placed in contact create a zigzag-zigzag interface between two structures with different topology. A characteristic feature of such a photonic insulator is that, in the linear limit, it simultaneously supports two topologically protected chiral edge states at the interface between the two arrays. In the presence of nonlinearity, either bright or dark scalar Floquet edge soliton can bifurcate from a linear topological edge state. Such solitons are unidirectional and are localized in both directions, along the interface due to nonlinear selfaction, and across the interface as being an edge state. The presence of two edge states with equal averaged group velocities enables the existence of stable topological vector edge solitons. In our case these are nonlinearly coupled bright and dark solitons bifurcating from different branches of the topological Floquet edge states. Here we put forward a new mathematical description of scalar and vector small-amplitude Floquet envelope solitons in the above-mentioned continuous system. Importantly for the design of future photonic devices based on Floquet edge solitons, we find that the latter can be described by nonlinear Schrödinger equations for the mode envelopes obtained by averaging over one rotation period in the evolution coordinate.

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“…This property may be used for realization of fascinating applications, such as superlensing (which breaks the diffraction limit of imaging [81]), and optical cloaking (lending partial invisibility to small objects [82]). Other well-known examples of purposely designed artificial optical media with extraordinary properties include hyperbolic metamaterials, whose tensors of the dielectric permittivity and/or magnetic permeability feature principal values of opposite signs [83,84], planar metasurfaces [85,86], epsilon-near-zero materials, in which the refractive index nearly vanishes [87], photonic topological insulators [88,89] (which exemplify the area of topological photonics [90]), and others. The use of such media opens numerous possibilities to implement diverse optical effects, including nonlinear ones [91] and guided-wave propagation, in forms that were not known previously (for instance, in the form of the surface waveguiding in photonic topological insulators, which is immune to scattering on defects because the scattering is suppressed by the topology of the guiding system), and are unified under the name of metaoptics [92,93].…”

Section: Waveguides Built Of Artificial Materialsmentioning

confidence: 99%

Editorial: Guided-Wave Optics

Malomed

2017

Applied Sciences

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Guided waves represent a vast class of phenomena in which the propagation of collective excitations in various media is steered in required directions by fixed (or, sometimes, reconfigurable) conduits. Arguably, the most well-known and practically important waveguides are single-mode and multi-mode optical fibers [1,2], including their more sophisticated version in the form of photonic crystal fibers [3] and hollow metallic structures transmitting microwave radiation [4]. Light pipes, in the form of hollow tubes with reflecting inner surfaces, are used in illumination techniques. On the other hand, medical stethoscopes offer a commonly known example of a practically important acoustic waveguide. New directions of studies in photonics are focused on waveguides for plasmonic waves on metallic surfaces [5][6][7] (which provide the possibility of using wavelengths much smaller than those corresponding to the traditional optical range, and thus offer opportunities to build much more compact photonic devices) and on the other hand, on the guided transmission of terahertz waves, which also have a great potential for applications [8].Outside of the realm of photonics (optics and plasmonics) and acoustics, wave propagation plays a profoundly important role in many other areas; accordingly, waveguiding settings have drawn a great deal of interest in those areas as well. In particular, as concerns hydrodynamics, natural waveguides-which may be very long-exist for internal waves propagating in stratified liquids (e.g., in the ocean) [9]. Various settings in the form of waveguides for matter waves are well known in studies of Bose-Einstein condensates in ultracold bosonic gases [10,11]. In solid-state physics, guided propagation regimes for magnon waves in ferromagnetic media are a subject of theoretical and experimental studies [12]. In superconductivity, long Josephson junctions are waveguides for plasma waves [8,13]. The significance of waveguiding in plasma physics is also well-known; e.g., Ref [14][15][16].Below, a very brief overview of basic theoretical models and experimental realizations of various physical implementations of the waveguiding phenomenology is given. The text is structured according to the character of the guided wave propagation: linear or nonlinear and conservative or dissipative, as well as according to the materials used in the underlying settings, natural or artificial.This presentation definitely does not aim to include an exhaustive bibliography on this vast research area. References are given chiefly to review articles and books summarizing the known results, rather than to original papers where the results were first published. However, in some cases original papers are also cited if it is necessary in the context of the presentation. Linear WaveguidesThe basic waveguiding structure is a single-mode conduit, designed with a sufficiently small transverse size and boundary conditions at the boundary between the guiding core and surrounding cladding, which admits the propagation of a single tr...

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Modulational instability and solitary waves in polariton topological insulators

Cited by 143 publications

References 41 publications

Spin–orbit coupling and nonlinear modes of the polariton condensate in a harmonic trap

Spin–orbit coupling and nonlinear modes of the polariton condensate in a harmonic trap

Vector Topological Edge Solitons in Floquet Insulators

Editorial: Guided-Wave Optics

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