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Register a new userBragg solitons in topological Floquet insulators
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We consider a topological Floquet insulator consisting of two honeycomb arrays of identical waveguides having opposite helicities. The interface between the arrays supports two distinct topological edge states, which can be resonantly coupled by additional weak longitudinal refractive index modulation with a period larger than the helix period. In the presence of Kerr nonlinearity, such coupled edge states enable topological Bragg solitons. Theory and examples of such solitons are presented.
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We describe topological edge solitons in a continuous dislocated Lieb array of helical waveguides. The linear Floquet spectrum of this structure is characterized by the presence of two topological gaps with edge states residing in them. A focusing nonlinearity enables families of topological edge solitons bifurcating from the linear edge states. Such solitons are localized both along and across the edge of the array. Due to the non-monotonic dependence of the propagation constant of the edge states on the Bloch momentum, one can construct topological edge solitons that either propagate in different directions along the same boundary or do not move. This allows us to study collisions of edge solitons moving in the opposite directions. Such solitons always interpenetrate each other without noticeable radiative losses; however, they exhibit a spatial shift that depends on the initial phase difference.
Edge modes in topological insulators are known to be robust against defects. We investigate if this also holds true when the defect is not static, but varies in time. We study the influence of defects with time-dependent coupling on the robustness of the transport along the edge in a Floquet system of helically curved waveguides. Waveguide arrays are fabricated via direct laser writing in a negative tone photoresist. We find that single dynamic defects do not destroy the chiral edge current, even when the temporal modulation is strong. Quantitative numerical simulation of the intensity in the bulk and edge waveguides confirms our observation.
We address linear and nonlinear topological interface states in polariton condensates excited at the interface of the honeycomb and Lieb arrays of microcavity pillars in the presence of spin-orbit coupling and Zeeman splitting in the external magnetic field. Such interface states appear only in total energy gaps of the composite structure when parameters of the honeycomb and Lieb arrays are selected such that some topological gaps in the spectrum of one of the arrays overlap with topological or nontopological gaps in the spectrum of the other array. This is in contrast to conventional edge states at the interface of periodic topological and uniform trivial insulators, whose behavior is determined exclusively by the spectrum of the topological medium. The number of emerging interface states is determined by the difference of the Chern numbers of the overlapping gaps. Illustrative examples with one or two coexisting unidirectional interface states are provided. The representative feature of the system is the possibility of wide tuning of the concentration of power of the interface states between two limiting cases when practically all power is concentrated either in the Lieb or the honeycomb array. Localization of the interface states and their penetration depth into arrays drastically vary with Bloch momentum or upon modification of the amplitude of the interface state in the nonlinear regime. We illustrate topological protection of the interface states manifested in the absence of backscattering on interface defects, and study their modulation instability in the nonlinear regime. The latter leads to formation of quasisolitons whose penetration into different arrays also depends on Bloch momentum. In addition, we discuss the impact of losses and coherent pump leading to bistability of the interface states.
We theoretically introduce a new type of topological dipole solitons propagating in a Floquet topological insulator based on a kagome array of helical waveguides. Such solitons bifurcate from two edge states belonging to different topological gaps and have bright envelopes of different symmetries: fundamental for one component, and dipole for the other. The formation of dipole solitons is enabled by unique spectral features of the kagome array which allow the simultaneous coexistence of two topological edge states from different gaps at the same boundary. Notably, these states have equal and nearly vanishing group velocities as well as the same sign of the effective dispersion coefficients. We derive envelope equations describing components of dipole solitons and demonstrate in full continuous simulations that such states indeed can survive over hundreds of helix periods without any noticeable radiation into the bulk.
Periodically driven systems can host so called anomalous topological phases, in which protected boundary states coexist with topologically trivial Floquet bulk bands. We introduce an anomalous version of reflection symmetry protected topological crystalline insulators, obtained as a stack of weakly-coupled two-dimensional layers. The system has tunable and robust surface Dirac cones even though the mirror Chern numbers of the Floquet bulk bands vanish. The number of surface Dirac cones is given by a new topological invariant determined from the scattering matrix of the system. Further, we find that due to particle-hole symmetry, the positions of Dirac cones in the surface Brillouin zone are controlled by an additional invariant, counting the parity of modes present at high symmetry points.
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