Dielectric metasurfaces have opened novel routes for nonlinear optics in recent years. In this work, we integrate a nonlinear metasurface with monolayer molybdenum disulfide (MoS2) to enhance second-harmonic generation (SHG) from atomically thin MoS2. By utilizing bound states in the continuum, we achieve about 600× of SHG enhancement from monolayer MoS2 on a resonant metasurface relative to suspended monolayer MoS2. Moreover, an eigenmode expansion approach is exploited to express second-harmonic power and the corresponding analytical results agree well with the rigorous calculations

Panoiu, NC

Wang, JT

You, JW

English

UCL Discovery

15th International Congress on Artificial Materials for Novel Wave Phenomena - Metamaterials 2021New York, USA, Aug. 2nd - 7th 2021Enhanced Second-Harmonic Generation in Monolayer MoS2 Driven by a BIC-basedNonlinear MetasurfaceJ.T. 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, Chinajitong.wang@ucl.ac.ukAbstract – Dielectric metasurfaces have opened novel routes for nonlinear optics in recentyears. In this work, we integrate a nonlinear metasurface with monolayer molybdenum disulfide(MoS2) to enhance second-harmonic generation (SHG) from atomically thin MoS2. By utilizingbound states in the continuum, we achieve about 600× of SHG enhancement from monolayerMoS2 on a resonant metasurface relative to suspended monolayer MoS2. Moreover, an eigen-mode expansion approach is exploited to express second-harmonic power and the correspondinganalytical results agree well with the rigorous calculations.I. INTRODUCTIONOptical metasurfaces have been studied widely in the context of nonlinear optics due to their ability to generatelarge local field enhancement. Recently, symmetry-breaking dielectric metasurfaces governed by bound states inthe continuum (BICs) have opened up a new way for engineering optical resonances with large quality-factors(Q-factors) [1]. This promising approach makes metasurfaces a compelling platform to enhance light-matter in-teractions in atomically thin transition metal dichalcogenides (TMDs), which possess large second-order opticalnonlinearity arising from their non-centrosymmetric structure [2].In this work, we propose a nonlinear optical system for giant SHG from monolayer MoS2 on a silicon metasur-face. The optical system that supports a symmetry-protected BIC is engineered to be asymmetric so that high-Qresonances can be achieved. In addition, we utilize a recently proposed theoretical approach based on an eigen-mode expansion method to express the second-harmonic (SH) power generated from monolayer MoS2. The resultsderived from the analytical model agree with the conclusions based on rigorous numerical calculations.II. RESULTS AND DISCUSSIONA. Geometrical ConfigurationAs described in Fig. 1, our optical system consists of a cruciform silicon metasurface placed on a quartz substrateand a MoS2 monolayer placed on top of the silicon crosses. The period of the metasurface along both x and ydirections is Λ = 506 nm. For each arm of the cruciform nanoresonator, the long and short sides are 316 nm and126 nm, respectively, and the depth is 122 nm. The monolayer MoS2 has the same pattern with cruciform siliconand its thickness is 0.615 nm. In the symmetric case, the centers of the two crossed arms coincide. To employ theBIC-inspired mechanism for enhancing the nonlinear optical response of the metasurface, one arm is shifted so asto break the in-plane inversion symmetry. Then, we can define an asymmetry parameter s = ∆a/a to quantify theasymmetry of the metasurface, where a = 95 nm is the maximum shift distance. Impinging perpendicularly uponthis system is an x-polarized plane wave, which acts as external excitation at the fundamental frequency (FF).B. Linear Optical Response of a BIC-based MetasurfaceWe first investigate the angle-dependent transmission map and corresponding band diagram of the silicon meta-surface under symmetric condition (s = 0). By comparing the two panels in Fig. 2a, the band structure of transverse15th International Congress on Artificial Materials for Novel Wave Phenomena - Metamaterials 2021New York, USA, Aug. 2nd - 7th 2021Fig. 1: Schematics of a nonlinear optical system for enhanced harmonic generation (left), design of a unit cell(upper right) and definition of a asymmetry parameter s (lower right).electric (TE)-like modes shows consistent behavior with the transmission map. A BIC is clearly observed underTE-polarized wave at the Γ point with frequency of 345.8 THz. The resonance line-width of the BIC vanishes atthe Γ point because of the symmetry incompatibility and increases gradually away from the Γ point.The existence of a symmetry-protected BIC provides us with a simple approach to obtain high-Q resonancesin the form of quasi-BIC. To show the dependence of the BIC on s, we sweep s from 0 to 1 under x-polarizedplane-wave excitation. The results are given in Fig. 2b and the sharp resonances are characterized by the Q factorpresented in Fig. 2c. The transmission spectra are fitted with Fano formula: TFano = |a1 + ia2 + bω−ω0+iγ |,where a1, a2, and B are constant real parameters, ω0 is resonant frequency, and γ represents the leakage rate of theresonance. Then, the Q factor can be calculated as Q = ω0/2γ [3].To gain deeper insights into the physical properties of the TE-like modes, we present the electric and magneticfield profiles determined at points A and B in Fig. 2d from eigenmode analysis. At point A, the electric andmagnetic field patterns of the BIC state possess in-plane inversion symmetry, indicating the complete decouplingof the BIC from the normally incident plane wave. In contrast, the quasi-BIC (point B) reveals asymmetric fielddistributions and therefore manifests itself in transmission spectra as sharp resonances with high Q factor.Fig. 2: (a) Angle dependence of transmission map (left) and corresponding eigenmode analysis (right). (b) Trans-mission spectra vs. s. The blue dashed line indicates the resonant frequency, and letters A and B indicate BIC(s = 0) and quasi-BIC (s = 0.63) states, respectively. (c) Evolution of Q factor with s. (d) In-plane (xy plane)electric and magnetic filed patterns of TE-like eigenmodes computed at the two s points A and B.15th International Congress on Artificial Materials for Novel Wave Phenomena - Metamaterials 2021New York, USA, Aug. 2nd - 7th 2021C. Giant Second-Harmonic Generation from Monolayer MoS2The monolayer MoS2 generates enhanced second-order nonlinear optical response due to the BIC mechanism.In Fig. 3a, we notice that SHG from monolayer MoS2 on the resonant metasurface is about 600× larger than thatfrom suspended monolayer MoS2, appearing at s = 0.63 with frequency of 699 THz. Moreover, it is of particularinterest to explore the underlying relation between s and SH intensity. Thus, we use a recently proposed eigenmodeexpansion method to study the nonlinear SHG process. The main idea is to find the induced field using Green’sfunctions that are expanded in eigenfunctions of an optical resonance system. At the FF, linear optical response issupposed to be governed by a resonant state, E1, while near the SH a single resonant state E2 dominates the fieldgenerated by nonlinear polarization sources. Then, the SH power PSH(2ω) is determined as explained in [4]:PSH(2ω) = [P (ω)κ1(ω)Q1L1(ω)]2κ12Q2L2(2ω)κ2α(2ω). (1)Here, P (ω) is total incident power, κ1(ω) is the coupling between excitation and E1, κ2 is the out-couplingcoefficient, κ12 is the overlap factor between the modes E1 and E2, Qj and Lj , j = 1, 2, are Q factor and spectralmismatch, respectively, and α(2ω) is smooth envelope factor.Fig. 3: Harmonic generation from monolayer MoS2. (a) s-dependent SHG enhancement with maximal enhance-ment at s = 0.63. (b) Comparison of normalized SH intensity determined using numerical and analytical methods.The results of analytical model from (1) are compared with those of rigorous numerical calculations, as shownin Fig. 3b. The two methods show a maximum up-conversion efficiency at s = 0.63 and s = 0.53, respectively.The difference in s is explained by the assumption of single-mode field expansion in the analytical model. Adouble-resonance phenomenon at s = 0.64 is also observed, which further enhances SHG.III. CONCLUSIONIn this contribution, a nearly 600 times enhancement of SH intensity is shown from monolayer MoS2 in aBIC-based metasurface relative to suspended monolayer MoS2. In our quantitative analysis of this phenomenon,we employ an eigenmode expansion method to obtain the SH power. Our design suggests a promising way forintegrated TMD-based nanodevices in photonic applications.ACKNOWLEDGEMENTThis work was supported by the European Research Council (ERC) (ERC-2014-CoG-648328).REFERENCES[1] K. Koshelev, S. Lepeshov, M. Liu, A. Bogdanov, and Y. Kivshar, “Asymmetric Metasurfaces with High-Q ResonancesGoverned by Bound States in the Continuum,” Physical Review Letters, vol. 121, art. no. 193903, 2018.[2] M. Weismann and N. C. Panoiu, “Theoretical and computational analysis of second- and third-harmonic generation inperiodically patterned graphene and transition-metal dichalcogenide monolayers,” Physical Review B, vol. 94, art. no.035435, 2016.[3] Y. Yang, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “All-dielectric metasurface analogue of electromagneticallyinduced transparency,” Nature Communications, vol. 5, p. 5753, 2014.[4] K. Koshelev, S. Kruk, E. Melik-Gaykazyan, J.-H. Choi, A. Bogdanov, H.-G. Park, and Y. Kivshar, “Subwavelengthdielectric resonators for nonlinear nanophotonics,” Science, vol. 367, p. 288, 2020.

Enhanced Second-Harmonic Generation in Monolayer MoS2 Driven by a BIC-based Nonlinear Metasurface

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Enhanced Second-Harmonic Generation in Monolayer MoS2 Driven by a BIC-based Nonlinear Metasurface

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