Two series of nanodisk arrays were designed. The first one was fabricated out of a silicon-on-insulator (SOI) wafer using electron-beam lithography and a reactive-ion etching process. The top layer of a SOI wafer is a 260-nm layer of monocrystalline (100)-cut silicon. We consider three square 400x400 μm2 arrays distinguished by the disk diameter values – 340, 345 and 360 nm, respectively; the period of the nanodisk ordering in the array amounted to 2.85 μm – this value allows for regarding the disks as isolated ones in terms of optical coupling. The nanodisk diameter choice specifies the magnetic dipolar (MD) resonance wavelength . The second series of arrays was made of a 130-nm hydrogenated amorphous silicon (a-Si:H) film grown by plasma-enhanced chemical vapor deposition on a thin glass substrate.
In order to study the nonlinear optical response of the nanodisks and verify the multipole resonances roles, we conducted third-harmonic generation (THG) spectroscopy measurements using a tunable (1.0-1.5 μm) optical parametric oscillator (200 fs pulses with the repetition rate of 76 MHz) pumped by a Ti:Sapphire laser. The laser beam waist diameter was set at 11 μm by an aspheric lens. The full thickness of both the SOI and glass wafers (∼500 μm each) was less than the waist depth. The resulting peak intensity reached the values of about 1 GW/cm2 in the sample plane. The laser beam polarization was linear as controlled by a Glan-Taylor laser prism. The transmitted and collimated THG signal was selected by a set of blue filters and detected by a photomultiplier tube connected with a lock-in amplifier. This signal was proven to be of TH origin by checking its cubic dependence on the pump power and by direct measurements of its spectrum. It was also verified that the THG beam was polarized parallel to the orientation of the pump beam polarization. It should be pointed out that the penetration depth of the THG into silicon does not exceed the nanodisk height.
The experimental technique  of nonlinear spectroscopy consists of defining the ratio of the TH signal from the nanostructured area to the successively measured signal from the nearby area where the top layer of silicon was etched away (in the case of the SOI wafer) or to the signal from a reference channel (in the case of the a-Si:H film). These ratios reveal the enhanced third-order optical response; moreover, the dispersion of the silicon nonlinear susceptibility is thereby taken into account. The resultant normalized THG signal represents the nanodisks and their resonant contribution.
In this contribution, we have shown the third-harmonic response of silicon nanodisks at their electric and magnetic dipolar resonances. The enhanced up-conversion efficiency at the MD resonance of the nanodisks is observed, whereas the electric dipolar resonance yields less nonlinear conversion. The maximum area-normalized THG enhancement is around 30. In this work, the observed linear and nonlinear spectra are confirmed by numerical calculations.
 I. Staude, et al., ACS Nano, 7, 7824 (2013).
 M.R. Shcherbakov, et al., Nano Lett., 14, 6488 (2014).
Elizaveta V. Melik-Gaykazyan, Alexander S. Shorokhov, Maxim R. Shcherbakov, Isabelle Staude, Daria A. Smirnova, Andrey E. Miroshnichenko, Igal Brener, Dragomir N. Neshev, Andrey A. Fedyanin, and Yuri S. Kivshar, "Third harmonic generation in isolated all dielectric meta-atoms
(Conference Presentation)," Proc. SPIE 9894, Nonlinear Optics and its Applications IV, 98940X (Presented at SPIE Photonics Europe: April 06, 2016; Published: 4 August 2016); https://doi.org/10.1117/12.2228249.5042345731001.
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