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Wang JT, Tonkaev P, Koshelev K et al. Resonantly enhanced second- and third-harmonic generation in dielectric nonlinear metasurfaces. Opto-Electron Adv 7, 230186 (2024). doi: 10.29026/oea.2024.230186
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Resonantly enhanced second- and third-harmonic generation in dielectric nonlinear metasurfaces
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Abstract
Nonlinear dielectric metasurfaces provide a promising approach to control and manipulate frequency conversion optical processes at the nanoscale, thus facilitating both advances in fundamental research and the development of new practical applications in photonics, lasing, and sensing. Here, we employ symmetry-broken metasurfaces made of centrosymmetric amorphous silicon for resonantly enhanced second- and third-order nonlinear optical response. Exploiting the rich physics of optical quasi-bound states in the continuum and guided mode resonances, we comprehensively study through rigorous numerical calculations the relative contribution of surface and bulk effects to second-harmonic generation (SHG) and the bulk contribution to third-harmonic generation (THG) from the meta-atoms. Next, we experimentally achieve optical resonances with high quality factors, which greatly boosts light-matter interaction, resulting in about 550 times SHG enhancement and nearly 5000-fold increase of THG. A good agreement between theoretical predictions and experimental measurements is observed. To gain deeper insights into the physics of the investigated nonlinear optical processes, we further numerically study the relation between nonlinear emission and the structural asymmetry of the metasurface and reveal that the generated harmonic signals arising from linear sharp resonances are highly dependent on the asymmetry of the meta-atoms. Our work suggests a fruitful strategy to enhance the harmonic generation and effectively control different orders of harmonics in all-dielectric metasurfaces, enabling the development of efficient active photonic nanodevices. -
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References
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Wang JT, Tonkaev P, Koshelev K et al. Resonantly enhanced second- and third-harmonic generation in dielectric nonlinear metasurfaces. Opto-Electron Adv 7, 230186 (2024). doi: 10.29026/oea.2024.230186
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Figure 1.
Enhanced second- and third-harmonic generation from an asymmetric nonlinear metasurface. Schematics of a nonlinear metasurface consisting of a periodic array of pairs of amorphous silicon bars placed on top of a glass substrate. The geometric asymmetry parameter, α, of the meta-atom is defined as α = ∆w/w.
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Figure 2.
Simulated linear transmission spectra of the metasurface. (a) Dependence of transmission on the asymmetry parameter α under normal incidence and for x-polarized plane-wave excitation. The green dashed line corresponds to α = 0.075. (b) Dependence of transmission on the angle of incidence θ, determined for α = 0.075 and for x-polarized plane-wave excitation. (c, d) Same as in (a) and (b), respectively, but determined for y-polarized plane-wave excitation.
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Figure 3.
Eigenmode analysis in case of α = 0.075. Band diagrams with respect to (a) ky and (b) kx. Only modes with Q-factors larger than 50 are included. Red solid (blue dotted) lines are modes excited by x-polarized (y-polarized) plane-waves. (c-h) In-plane electric field profiles of the eigenmodes at the Γ point, presented in order of increasing wavelength. The yellow dashed lines indicate the interfaces between amorphous silicon and air.
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Figure 4.
Simulated dependence of Q-factor of the metasurface eigenmodes on the structural asymmetry parameter α for modes excited by (a) x-polarized and (b) y-polarized incident plane-waves. The calculations are performed at the Г point.
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Figure 5.
(a) Top-view SEM image of a fabricated metasurface corresponding to α = 0.075. (b) Comparison of experimentally measured linear transmittance and the corresponding numerically calculated spectrum at α = 0.075. The purple arrow denotes the resonance that is used to illustrate the measured power-dependent second-harmonic and third-harmonic signals presented in (c). (c) Measured power-dependent output SH (red dots) and TH (blue dots) signals from the fabricated sample with α = 0.075. The dependence of nonlinear emissions is measured at the resonance with (pump) wavelength of 1620 nm under field polarization oriented along the x-axis. The dots represent the measured data while the black dashed lines denote the fitting lines of SHG and THG power.
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Figure 6.
Enhancement factor ηE of the averaged electric field amplitude within the amorphous silicon resonators under plane- wave illumination with the asymmetry of the metasurface being α = 0.075.
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Figure 7.
(a) Measured enhancement factor ηSHG of SHG from the all-dielectric metasurface with α = 0.075. An amorphous silicon slab with the same thickness as that of the metasurface is used as a reference. The inset shows a zoom-in of the enhancement factor. (b) Simulated linear transmittance for asymmetry parameter α = 0.075. (c, d) Numerically calculated surface and bulk contributions to SHG, respectively, when α = 0.075. Red (blue) lines correspond x-polarized (y-polarized)
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Figure 8.
(a) Measured enhancement factor of THG from the resonant metasurface described by α = 0.075. (b) Numerically calculated TH intensity spectra corresponding to the same metasurface. Red (blue) lines correspond to x-polarized (y- polarized) incident plane-waves. In both figures, the upper ticks of the x-axis denote the TH wavelength.
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Figure 9.
Fourier analysis of numerically calculated (a) transmitted SHG at 1590 nm (under x-polarized incident plane-wave), which corresponds to the resonant peak of highest measured SHG enhancement, and (b) transmitted THG at 1747 nm (under y- polarized incident plane-wave), which corresponds to the resonant peak of largest THG enhancement in experiments. Fourier analysis is performed for an asymmetry parameter of α = 0.075.
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Figure 10.
Simulated dependence of SHG from the amorphous silicon metasurface with respect to the structural asymmetry parameters α in cases of (a) surface contribution under x-polaried excitation, (b) surface contribution under y-polarized excitation, (c) bulk contribution under x-polarized excitation, and (d) bulk contribution under y-polarized excitation.
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Figure 11.
Numerical simulation of asymmetry-dependent TH intensity under plane wave excitation with polarization along (a) x and (b) y directions, respectively. In both figures, the upper ticks of the x-axis denote the TH wavelength.
