Topologically enhanced harmonic generation in a nonlinear transmission line metamaterial

Wang, You; Lang, Li-Jun; Lee, Ching Hua; Zhang, Baile; Chong, Yidong

doi:10.1038/s41467-019-08966-9

Cited by 128 publications

(107 citation statements)

References 55 publications

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“…In addition, the planar geometry and ultrathin thickness of the metasurface will facilitate its integration with existing electronic systems. This includes electronic topological insulators as well as PTIs based on lumped‐circuit components . Attractively, the addition of electrical elements to the proposed PCB‐compatible design would enable tunable/switchable topological states and reconfigurable pathways .…”

Section: Resultsmentioning

confidence: 99%

Electromagnetic‐Dual Metasurfaces for Topological States along a 1D Interface

Bisharat

Sievenpiper

2019

Laser & Photonics Reviews

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The discovery of topological insulators was rapidly followed by the advent of their photonic analogues, motivated by the prospect of backscattering‐immune light propagation. So far, however, implementations have mainly relied on engineering bulk modes in photonic crystals and waveguide arrays in two‐dimensional (2D) systems, which closely mimic their electronic counterparts. In addition, metamaterials‐based implementations subject to electromagnetic duality and bianisotropy conditions suffer from intricate designs and narrow operating bandwidths. Here, it is shown that symmetry‐protected topological states akin to the quantum spin‐Hall effect can be realized in a straightforward manner by coupling surface modes over metasurfaces of complementary electromagnetic responses. Specifically, stacking unit cells of such metasurfaces directly results in double Dirac cones of degenerate transverse‐electric (TE) and transverse‐magnetic (TM) modes, which break into a wide nontrivial bandgap at small interlayer separation. Consequently, the ultrathin structure supports robust gapless edge states, which are confined along a one‐dimensional (1D) line rather than a surface interface, as demonstrated at microwave frequencies by near‐field imaging. The simplicity and versatility of the proposed approach proves attractive as a tabletop platform for the study of classical topological phases, as well as for applications benefiting the compactness of metasurfaces and the potential of topological insulators.

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Section: Resultsmentioning

confidence: 99%

Electromagnetic‐Dual Metasurfaces for Topological States along a 1D Interface

Bisharat

Sievenpiper

2019

Laser & Photonics Reviews

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“…The major challenge here is the difficulty in implementation of sizeable nonlinearities manifested already at the two-photon level [16]. To overcome this difficulty and to bridge the gap between quantum-optical topological states and physics of interacting systems, we adopt the concept of topolectrical circuits [17,18,19,20,21,22] applying them to emulate an interacting two-body problem in one dimension. As detailed below, this approach is based on mathematically rigorous mapping of quantum two-body problem onto the classical setup of higher dimensionality, and this correspondence renders the topolectrical platform a powerful tool to study topological states of interacting photons.…”

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confidence: 99%

Topological edge states of interacting photon pairs emulated in a topolectrical circuit

et al. 2020

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|0⟩ |1⟩ |2⟩ 4 J J J J P P 5 C J C P C U L Figure 1: Topolectrical circuit model. a, Artistic view of two-photon excitations in the array of microresonators with tunneling couplings. The depicted state isâ † 1â † 3 |0 . b, Extended version of Bose-Hubbard model considered in the present article. Single-photon tunnelings J are shown by blue solid lines, direct two-photon tunnelings P are indicated by purple wavy lines. c, Top view of the equivalent two-dimensional topolectrical circuit with a voltage at the site (m, n) corresponding to probability amplitude βmn for one photon to be located at the m th resonator of the array with another one located at the n th resonator [cf. Eq. (2)]. Colored regions show characteristic voltage patterns for two-photon scattering states (green), doublons (red), and doublon edge state (blue). External voltage source applied for the system excitation and voltmeter are shown to the right. Side view of the diagonal (lower inset) and off-diagonal (upper inset) sites of the topolectrical circuit, where grounding elements are shown. d, The photograph of experimental setup having the size of 15 × 15 nodes. Inset shows the enlarged fragment of the circuit which includes two unit cells. d c b a J J P J P J J P J

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“…Indeed, it has been shown that when a photonic topological insulator is embedded in an optical medium with Kerr nonlinearity, lattice edge solitons could arise [13,14]. The possibility to enhance the conversion efficiency of harmonic generation in the presence of topological edge states has also been studied [15,16]. Moreover, traveling-wave amplifiers [17], topological sources of quan-arXiv:1907.00444v1 [physics.optics]…”

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confidence: 99%

Nonlinear one-way edge-mode interactions for frequency mixing in topological photonic crystals

2020

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Topological photonics aims to utilize topological photonic bands and corresponding edge modes to implement robust light manipulation, which can be readily achieved in the linear regime of light-matter interaction. Importantly, unlike solid state physics, the common test bed for new ideas in topological physics, topological photonics provide an ideal platform to study wave mixing and other nonlinear interactions. These are well-known topics in classical nonlinear optics but largely unexplored in the context of topological photonics. Here, we investigate nonlinear interactions of one-way edge-modes in frequency mixing processes in topological photonic crystals. We present a detailed analysis of the band topology of two-dimensional photonic crystals with hexagonal symmetry and demonstrate that nonlinear optical processes, such as second-and third-harmonic generation can be conveniently implemented via one-way edge modes of this setup. Moreover, we demonstrate that more exotic phenomena, such as slow-light enhancement of nonlinear interactions and harmonic generation upon interaction of backwardpropagating (left-handed) edge modes can also be realized. Our work opens up new avenues towards topologyprotected frequency mixing processes in photonics.One of the most important developments in condensed matter physics in the past decades is the discovery of topological insulating materials [1,2]. These materials feature gapped bulk but gapless edge modes, which propagate unidirectionally along the system edge and are immune to local disorder, thus opening a promising avenue towards robust wave manipulation protected by topology. Inspired by this development, the emerging field of topological photonics aims to extend these topology related ideas to the realm of photonics [3][4][5][6], which holds great promises for innovative optical devices by exploiting robust, scattering-free light propagation and manipulation. As the concept of energy band exists at the single particle level both in condensed matter physics and photonics, the goal of realizing photonic topological insulators can be readily achieved in the linear regime of light matter interaction. Indeed, topological phenomena of electromagnetic waves in a linear medium can be understood by mapping Maxwell equations to the Schrödinger equation [7,8].Photonics, however, has several features not present in solid-state physics. For example, optical gain and loss can be utilized to implement non-Hermitian photonics based on parity-time symmetry [9]. The recently realized topological insulator laser demonstrates the power of this new ingredient and could deepen our understanding of the interplay between non-hermiticity and topology in active optical systems k ω ω 0 Ω 2 = 2ω 0 Ω 3 = 3ω 0 y x z a b FIG. 1. Nonlinear one-way edge mode interaction in 2D topological photonic crystals. a, Schematic band structure showing the emergent edge modes due to the nontrivial topology of the bulk frequency bands. The edge modes can couple via SHG and THG frequency mixing processes. b, Real ...

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Topologically enhanced harmonic generation in a nonlinear transmission line metamaterial

Cited by 128 publications

References 55 publications

Electromagnetic‐Dual Metasurfaces for Topological States along a 1D Interface

Electromagnetic‐Dual Metasurfaces for Topological States along a 1D Interface

Topological edge states of interacting photon pairs emulated in a topolectrical circuit

Nonlinear one-way edge-mode interactions for frequency mixing in topological photonic crystals

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