experimental parameters and an elaborated
comparison with the earlier results for in-
dividual nanoresonators is presented in part
13 of the supplementary text ( 25 ). The SHG
efficiency of an individual nanoantenna dem-
onstrated here is qualitatively comparable
to the best-to-date efficiencies of nonlinear
metasurfaces ( 29 , 30 ) based on hybrid multiple-
quantum-well structures, whereas a quantitative
comparison cannot be done without some
ambiguity. Although high nonlinear coeffi-
cientsP^2 pw=ðPpwÞ^2 were demonstrated in such
systems in the far- to mid-infrared spectral
ranges, the reported conversion efficiencies
P^2 pw=Pwp of 2 × 10–^4 %( 29 )and7.5×10–^2 %
( 30 ), respectively, remain low and are lim-ited by a peak pump power of 100 mW that
they can sustain, compared with 10 W for our
nanoresonator.
Our results illustrate, for the first time to our
knowledge, manifestation of high Q-factor op-
tical modes in individual nanoresonators in
the linear and nonlinear regimes governed by
the physics of bound states in the continuum.Koshelevet al.,Science 367 , 288–292 (2020) 17 January 2020 4of5
Fig. 3. Experimental characterization of the SHG enhancement.(A) 3D map of SH intensity measured as a function of the pump wavelength and particle diameter
for an azimuthally polarized beam. The SH intensity is normalized on the square of the pump power. (BtoD) Top views of the maps of SHG with the azimuthal,
radial, and linear pump, respectively. (EandF) Experimentally measured directionality diagrams of SHG for a nanoresonator with a diameter of ~930 nm in the
(E) backward and (F) forward direction.
Fig. 4. Experimental nonlinear conversion efficiency.(AandB) Measured SH intensity as a function of the pump wavelength for the nanoresonator with
the diameter of ~930 nm (A) and as a function of the nanoresonator diameter at a 1570-nm pump wavelength (B) for different pump polarizations. The SH intensity
is normalized on the square of the pump power. (C) Measured peak SH power versus the peak pump power for a nanoresonator with a diameter of ~930 nm
(log 10 – log 10 scale). Line shows the fit with a quadratic dependence with the nonlinear conversion coefficient 1.3 × 10−^6 W−^1.
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