We study the influence of graphene Kerr effect on valley-Hall topological modes of a graphene plasmonic crystal waveguide. Extra air holes are introduced to break the spatial-inversion symmetry of the plasmonic metasurface, which can be performed using e-beam lithography. As a result, a gapless Dirac cone and topologically protected edge modes form inside the nontrivial frequency bandgap. Taking advantage of the fact that graphene is a nonlinear optical material possessing an extremely large Kerr coefficient, we demonstrate that an all-optical switch can be implemented in this topological photonic system by controlling an optical signal propagating in the waveguide via a pump beam injected into the bulk modes of the metasurface. This work may lead to new graphene-based active topological photonic nanodevices

Panoiu, NC

Wang, Y

You, JW

English

UCL Discovery

15th International Congress on Artificial Materials for Novel Wave Phenomena - Metamaterials 2021New York, USA, Aug. 2nd - 7th 2021Kerr Effect of Valley-Hall Topological Edge Plasmons on Graphene Nanohole PlasmonicCrystal WaveguideYupei Wang1, J. W. You1,2 and Nicolae C. Panoiu11University College London, Department of Electronic and Electrical Engineering, Torrington Place,WC1E 7JE, London, United Kingdom2Southeast University, State Key Laboratory of Millimeter Waves, No. 2 Southeast University Road,Nanjing, 211189, Chinayupei.wang.18@ucl.ac.ukAbstract – We present and study the Kerr effect of valley topological plasmonic edge modesbased on graphene nanohole plasmonic crystal waveguide. By adding an extra small holes ongraphene nanohole crystal, the spatial-inversion symmetry of whole structure is changed fromC6v toC3v . As a result, the spatial symmetry breaking leads to a gapless Dirac cone and topolog-ically protected edge mode appears inside the nontrivial frequency bandgap which shows unidi-rectional properties. As a nonlinear material with strong nonlinearity enhancement, grapheneprocesses a giant second-order nonlinear refractive index n2 = 6.28 × 10−6cm2/W, which ismore than 9 orders of magnitude larger than other bulk dielectrics. With a pump bulk modechanging the refractive index of the whole system, we observe a remarkable variation of thetransmission of topological signal mode with respect to the applied pump power. This work maydevelop graphene-based robust plasmonic integrated nonlinear applications.I. INTRODUCTIONIn our work, we show the vally-Hall topologically protected edge mode in a graphene nanohole plasmoniccrystal waveguide with the spatial-inversion symmetry breaking, by an extra air hole etched on graphene crystalwaveguide. As a result, the changed spatial-inversion symmetry opens the symmetry-protected Dirac cone andunidirectional topological edge mode is formed inside the nontrivial bandgap. Employing the unidirectional topo-logical property and giant nonlinear refractive index of graphene, we demonstrate the Kerr effect on graphenenanohole plasmonic crystal waveguide. Under pump bulk modes with different group velocities approaching toslow light region, the variation of transmission of signal topological light is quantitatively characterized. All thesimulations are calculated by the optic module of COMSOL Multiphysics 5.6.Research in topological plasmonic egde states has been attracting increasing attention, especially due to thenovel and unique properties, like unidirectional propagation without back-scattering and robustness against in-duced disorder [1]. By breaking the time-reversal symmetry under an external static magnetic field [1], or spatial-inversion symmetry via spatially asymmetric perturbations [2], symmetry-protected Dirac cones are gapped outand topological edge mode appears inside the nontrivial bandgap. Most of the topological photonics studies havefocused on linear systems, but graphene-based topological system with a giant nonlinear interaction shows greatpotential on applications of nonlinear regime [3].II. KERR EFFECT ON GRAPHENE NANOHOLE PLASMONIC CRYSTAL WAVEGUIDEIn this section we present the main results of our work. We first discuss the structure and band diagram of thedesigned graphene nanohole plasmonic crystal waveguide, then show the transmission of unidirectional topologicalsignal mode by applied uniform pump power changing the refractive index of the whole system.15th International Congress on Artificial Materials for Novel Wave Phenomena - Metamaterials 2021New York, USA, Aug. 2nd - 7th 2021A. Topological Bands of Graphene Nanohole Plasmonic Crystal WaveguideThe schematic of the proposed topological graphene nanohole plasmonic crystal waveguide is presented inFig. 1(a). It consists of one graphene layer etched by air holes with two different radius. The graphene waveguidecontains a domain-wall interface formed by left- and right-domains with horizontal mirror symmetry. Each domainis composed by a hexagonal lattice with two air holes of different sizes in the unit cell. The nanohole unit cellstructure and First Brillouin zone (FBZ) of nanohole lattice are shown in Fig. 1(b) and Fig. 1(c), respectively. Wefix the lattice constant a = 400√3nm and radius of big hole R = 140 nm.Fig. 1: (a) Schematic of graphene plasmonic nanohole crystal with a mirror symmetric domain-wall interface alongy-axis. (b) Unit cell of graphene lattice composed of two air holes with radius R and r. (c) First Brillouin zone(FBZ) of a hexagonal graphene lattice, consisting there high symmetric points Γ, K and M . (d) Band diagram ofthe graphene nanohole plasmonic crystal with and without small air hole r. Since the spatial inversion symmetryis broken in the case with small hole r = 50 nm, a nontrivial frequency bandgap emerges.The plasmonic band structure of graphene nanohole crystal is calculated through the high symmetric points Γ,K and M of the FBZ. In the graphene nanohole crystal without small air hole r = 0, the spatial symmetry of theperiodic system is C6v , which protects the Dirac cone at K point, as shown in blue curves of Fig. 1(d). Whenthe small hole r = 50 nm is etched on the graphene crystal, the C3v spatial symmetry opens the Dirac cone and anontrivial bandgap emerges at the location of Dirac point (red curves in Fig. 1(d)).The projected band diagram of a finite graphene nanohole waveguide consisting a domain-wall interface iscomputed, and the graphene nanohole structure and projected band are presented in Fig. 2(a) and Fig. 2(b), re-spectively. The red line represents topological mode inside the bandgap whereas blue regions represent the bulkmode. Moreover, the corresponding field distribution of topological edge mode and bulk mode are discussed.Under a left-circularly polarized (LCP) source, the field distribution of topological mode (Fig. 2(c)) at 11.4 THz,corresponding toEs in Fig. 2(b), shows highly-confined and unidirectional properties at the domain-wall interface.Besides, the field distribution of bulk mode is uniform and extended around the whole graphene waveguide, whichis shown in Fig. 2(d).B. Kerr Effect of Topological Valley Edge ModeThe unidirectional propagation feature of topological interfacial mode and graphene nonlinearity can be appliedon graphene-based nonlinear nanodevices. In this work, we studies the Kerr effect on graphene nanohole plasmonicwaveguide pumped by bulk modes with different group velocities. As seen in Fig. 3(a), bulk mode Eb with highpower uniformly pumps the whole system whereas the topological signal mode Es is excited by a low powerLCP source at 11.4 THz. The length and height of graphene nanohole waveguide are L = 35a and W = 19a,respectively. As a nonlinear material with large nonlinear refractive index n2 = 6.28×10−6cm2/W [3], graphenewaveguide shows tunable refractive index excited by the power of pump mode, which can also shift the frequencyof bandgap. Consequently, the topological signal mode can be switched to a leaky and scattered bulk mode, whichcan sharply decrease the transmission η = Psout/Psin (the ratio between the output and input power) of the signalmode.15th International Congress on Artificial Materials for Novel Wave Phenomena - Metamaterials 2021New York, USA, Aug. 2nd - 7th 2021Fig. 2: (a) Domain-wall interface with a vertical mirror symmetry of the graphene nanohole crystal supercell. (b)Projected band diagram of graphene nanohole crystal waveguide with r = 50 nm, topological protected interfacialmode (red) appears inside the nontrivial bandgap. (c) Unidirectional propagation along the domain-wall interface,when the finite graphene nanohole waveguide excited by a left-circularly polarized (LCP) source at 11.4 THz,corresponding to the topological mode Es in Fig. 2(b). (d) Field distribution of uniform bulk along the wholegraphene nanohole waveguide, corresponding to the bulk mode Eb in Fig. 2(b).The variation of signal transmission with respect to the pump power is shown in Fig. 3(b). Under there pumpbulk mode (Eb1, Eb2 and Eb3 in Fig. 2(b)) with different group velocities approaching to slow light region, thetransmission of signal mode shows sharply decreases to 0.1 when the power of pump mode increases, however,the required power of bulk mode Eb3 at slow light region is lowest compared with other two bulk modes. Thecloser pump mode is to the slow light region, the lower required pump power is to achieve the same transmissionof signal mode.Fig. 3: (a) Schematic of the Kerr effect based on the graphene nanohole plasmonic crystal waveguide. Light ofuniform bulk mode Eb (yellow) pumps the whole waveguide. The unidirectional signal mode Es at 11.4 THzcarries an input power Psin and output power Psout . (b)Transmission of signal light with respect to the variationof pump power under the cases pumped by there electric fields of bulk modes in Fig. 2(b).III. CONCLUSIONWe proposed valley-Hall topological plasmons on graphene nanohole plasmonic crystal waveguide. The changeof spatial-inversion symmetry realizes a gapless Dirac cone and topological interfacial mode with unidirectionalproperty. Kerr effect on the designed graphene nanohole waveguide is studied based on the large nonlinear refrac-15th International Congress on Artificial Materials for Novel Wave Phenomena - Metamaterials 2021New York, USA, Aug. 2nd - 7th 2021tive index of graphene. Our results shows the transmission of signal mode sharply decreases with the increasingpump power and the less pump power is required when the pump mode is closed to slow light region.ACKNOWLEDGEMENTThis work has been supported by the European Research Council (ERC), Grant Agreement no. ERC-2014-CoG-648328, China Scholarship Council (CSC) and University College London (UCL)..REFERENCES[1] L. Lu, J. D. Joannopoulos, and M. Soljacic, “Topological photonics,” Nature photonics, vol. 8, p. 821, 2014.[2] J.W. You, Z. Lan, Q. Bao and N.C. Panoiu,“Valley-Hall topological plasmons in a graphene nanohole plasmonic crystalwaveguide,” IEEE Journal of Selected Topics in Quantum Electronics, vol. 26, p. 1, 2020.[3] S. Thakur, B. Semnani, S. Safavi-Naeini and A.H. Majedi, “Experimental characterization of the ultrafast, tunable andbroadband optical Kerr nonlinearity in graphene,” Scientific reports, vol. 9, p. 1, 2019.

All-optically Control of Light Propagation in Valley-Hall Topological Waveguides of Graphene Metasurfaces

https://discovery.ucl.ac.uk/id/eprint/10139957/1/ValleyHallNl.pdf

All-optically Control of Light Propagation in Valley-Hall Topological Waveguides of Graphene Metasurfaces

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