Figure 1: Schematics of a nonlinear metasurface with monolayer MoS2 on top of its cruciform-shaped silicon unit cell.
1. Pre-reading
Nonlinear all-dielectric metasurfaces open up new avenues in nonlinear optics through their remarkable capability of enhancing the frequency conversion efficiency of nonlinear optical interactions. Availability of materials with large optical nonlinearity and development of innovative approaches that enable improved light-matter coupling at deep-subwavelength scale are a prerequisite to enhanced nonlinear optical interactions. Recently, a novel field enhancement mechanism based on bound states in the continuum (BICs) has been introduced in periodically structured metasurfaces to boost the local field enhancement at the fundamental frequency (FF) and thus the nonlinear optical interactions in 2D materials such as transition metal dichalcogenides (TMDs). However, the highly nontrivial case in which BICs exist at multiple frequencies has yet to be investigated.
To solve this challenge, Prof. Nicolae C. Panoiu’s group from University College London has proposed a metasurface consisting of a square array of cruciform-shaped silicon building blocks covered by a monolayer molybdenum disulfide (MoS2). By designing the metasurface so that it supports optical BICs at the FF and second-harmonic (SH), nearly 600× enhancement of the second-harmonic generation (SHG) in the MoS2monolayer as compared to that of the same MoS2 monolayer suspended in air is achieved. To gain deeper insights into the physics of the enhanced nonlinear optical response of the metasurface, an eigenmode expansion method is employed to analytically investigate the main characteristics of SHG. In addition, a versatile nonlinear homogenization approach is used to highlight and understand the interplay between the BICs of the metasurface and the efficiency of the SHG process. This work suggests a promising method to enhance the nonlinear optical processes in two-dimensional materials, enabling the development of advanced active photonic devices.
2. Background
Optical metasurfaces have attracted rapidly growing research interest in recent years, chiefly due to their remarkable versatility in light manipulation, including phase control, distribution of the optical nearfield, and light polarization. Notably, the ability of metasurfaces to produce significant enhancement of the local optical field makes them a prominent and promising platform for nonlinear optics. In this context, to further boost the efficiency of frequency conversion processes, it is of critical importance to find materials with large optical nonlinearity and to develop innovative approaches that enable improved light-matter coupling at deep-subwavelength scale.
The discovery of monolayer semiconducting 2D materials, including TMDs, has provided a fertile ground for the development of fundamental new ideas and device applications in optoelectronics and photonics. Moreover, the non-centrosymmetric nature of the atomic structure of monolayer TMDs allows for a broader set of nonlinear optical interactions, which in turn offers increased versatility in the design of novel active photonic nanodevices.
Recently, a novel field enhancement mechanism based on BICs has been introduced, and its effectiveness in enhancing the optical coupling between light and periodically structured metasurfaces has been demonstrated. In principle, optical BICs do not couple to free-space radiative modes, a property that implies a practically infinite quality-(Q) factor and vanishingly small spectral line-width. However, in practice, due to roughness and other inherent fabrication imperfections, ideal BICs transition to optical resonances with finite Q-factor called quasi-BICs. In nonlinear optics, BICs provide a novel approach to generate a large enhancement of nonlinear optical interactions, mainly via significant spatial confinement and enhancement of the optical near-field.
3. Innovative research
In this work, a metasurface consisting of a square array of cruciform-shaped silicon building blocks covered by a monolayer MoS2is proposed. The designed metasurface supports BIC-type resonances at both FF and SH so as to enhance the light-matter interaction at multiple frequencies.The signature of the quasi-BIC mode is imprinted in the transmission spectra as a sharp and asymmetric resonance with Fano-line shape (Figure 2A). The Q-factor of the corresponding resonance is extracted by fitting the transmission spectrum with the Fano formula and the results are presented in Figure 2B. To illustrate the dual-resonance effect (Figure 2C), the dependence of the TE-like eigenmodes located nearby the SH (700 THz) on the asymmetry parameter 𝑠 is investigated, from which it can be observed that the FF and SH bands cross at about 𝑠 = 0.6. In addition, the linewidth of the SH mode is denoted in error bars to demonstrate the coupling regime between the two modes.
Figure 2: Characterization of the BIC mode at the FF and the double-resonance effect.
To illustrate the enhanced SHG arising from the double-resonance mechanism, the simulated frequency dependence of the SHG enhancement factor using the same MoS2 monolayer suspended in air as reference is determined for several values of the asymmetry parameter 𝑠. As it can be seen in Figure 3A, the maximum SHG enhancement in monolayer MoS2 is as large as 600 and is reached for 𝑠= 0.63 and frequency of 699 THz. To gain deeper insights into the physics of the metasurface-induced enhancement of nonlinear optical interactions, an eigenmode expansion method is employed to semi-analytically investigate the main characteristics of SHG and the results show a good agreement with the results obtained via full-wave numerical simulations, as per Figure 3B. Note that the various factors embedded in the semi-analytical model used in the calculation of the SHG are summarized in Figure 3C.
Figure 3: Enhancement of SHG (A) and the comparison between full-wave simulations and a semi-analytical model, (B) and (C).
4. Applications and perspectives
This work suggests a promising method to enhance the nonlinear optical processes in two-dimensional materials by designing metasurfaces that possess at both interacting frequencies a special type of optical resonances. This could result in the development of advanced photonic nanodevices and spur further research in nonlinear optical systems and new applications of photonics.
These research results are published online with the title “Giant second-harmonic generation in monolayer MoS2 boosted by dual bound states in the continuum” in Nanophotonics.
The authors of this article are Ji Tong Wang, Jian Wei You, and Nicolae C. Panoiu. Nicolae C. Panoiu is the corresponding author of this work. Prof. Nicolae C. Panoiu’s research group is affiliated to the Department of Electronic and Electrical Engineering, University College London, London WC1E 7JE, UK.
