Abstract
Rapidly growing demands for fast information processing have launched a race for creating compact and highly efficient optical devices that can reliably transmit signals without losses. Recently discovered topological phases of light provide novel opportunities for photonic devices robust against scattering losses and disorder. Combining these topological photonic structures with nonlinear effects will unlock advanced functionalities such as magnet-free nonreciprocity and active tunability. Here, we introduce the emerging field of nonlinear topological photonics and highlight the recent developments in bridging the physics of topological phases with nonlinear optics. This includes the design of novel photonic platforms which combine topological phases of light with appreciable nonlinear response, self-interaction effects leading to edge solitons in topological photonic lattices, frequency conversion, active photonic structures exhibiting lasing from topologically protected modes, and many-body quantum topological phases of light. We also chart future research directions discussing device applications such as mode stabilization in lasers, parametric amplifiers protected against feedback, and ultrafast optical switches employing topological waveguides.
Highlights
Topological insulators represent a recently discovered class of solids, which are insulating in their bulk but exhibit special scatteringresistant conducting states on their surfaces, known as topological edge states.[1]
We introduce the emerging field of nonlinear topological photonics and highlight the recent developments in bridging the physics of topological phases with nonlinear optics. This includes the design of novel photonic platforms which combine topological phases of light with appreciable nonlinear response, self-interaction effects leading to edge solitons in topological photonic lattices, frequency conversion, active photonic structures exhibiting lasing from topologically protected modes, and many-body quantum topological phases of light
A sphere has a genus of g 1⁄4 0, and a torus has a genus of g 1⁄4 1; these two objects cannot transform continuously into each other: Any transformation from a sphere to a torus necessarily involves some discontinuity at which a hole is created; such topological phase transitions are accompanied by a stepwise change in a topological invariant
Summary
Topological insulators represent a recently discovered class of solids, which are insulating in their bulk but exhibit special scatteringresistant conducting states on their surfaces, known as topological edge states.[1]. Topological edge states have been predicted and realized in a wide variety of photonic systems, including gyromagnetic photonic crystals, arrays of coupled optical resonators, metamaterials, helical waveguide arrays, and microcavity polaritons, recently reviewed in Refs. Nonlinear response in photonics and related fields such as Bose–Einstein condensates is expected to open a door toward advanced functionalities of topological photonic structures, including active tunability, genuine nonreciprocity, frequency conversion, and entangled photon generation[6,7,8,9,10,11,12,13,14] (see Fig. 1). IX concludes with a discussion of future prospects and open problems
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