# Boosting Second Harmonic Radiation from AlGaAs Nanoantennas with Epsilon-Near-Zero Materials
## 2 Results and Discussion
Figure 2: Electric field enhancement at the fundamental wavelength FW (second harmonic SH) in the case of nanocylinder of radius 232 nm, and height \(h\) equal to 400 nm placed over the ENZ ((**a**) at FW and (**d**) at SH), the dielectric ((**b**) at FW(**e**) at SH) and the gold substrate ((**c**) at FW and (**f**) at SH). Moreover, by using the eigenfrequency analysis in COMSOL Multiphysics, one can estimate the \(Q\) factor of the mode for the proposed structure in the different scenarios. The linear scattering power spectra for the different substrates are reported in Figure 4a, for a nanodisk with \(r=232\) nm and \(h=400\) nm. For the ENZ substrate, the scattering spectra showed a Fano-like behavior. A Fano resonance originates from the coupling between a broad \"bright\" mode resonator, that is accessible from free space, and a narrow \"dark\" mode resonator which is less-accessible, or inaccessible, from free-space. When the two resonances are brought in close proximity in both the spatial and frequency domains, a coupling is possible. This leads to a total resonance in the system, coming from the interference between the two pathways. We could attribuite this Fano resonance to the excitation of the broad magnetic dipolar resonance in the AlGaAs nanodisk that interfered with the SPP excited at the interface between the ENZ material and the dielectric resonator. The mode of the ENZ substrate (Figure 4b) has a \(Q\) factor of 25 for a pump wavelength of 1550 nm. If the cylinder is slightly moved upwards from the substrate one can find a field distribution as shown in Figure 4c with \(Q\) factor that decreases by increasing the distance of the cylinder from the substrate. In the limit case of infinite distance, the dielectric antenna can be considered as completely surrounded by air. In this latter situation, the closest mode (which is a magnetic resonance) has a \(Q\) factor of 9 at the wavelength of about 1695 nm, as shown in Figure 4d. The analysis of the nanostructure placed at different heights from the substrate demonstrates that the high enhancement of the field at the interface was due to the excitation of surface plasmon polaritons of the underlying ENZ substrate by the AlGaAs nanodisk on top. The dielectric nanoparticle helps provides the appropriate momentum (\(k\)-vector) to couple light at the interface. As far as concerning the substrate with refractive index 1.6, the closest mode that one can excite is a magnetic resonance with a \(Q\) factor of 6 for a wavelength equal to 1710 nm (Figure 4e). This is in perfect agreement with the known effect of broadening and redshifting of the resonances that are obtained when a nanostructure is placed on a dielectric substrate with respect to the case of structure in homogenous media (usually assumed to be air). Finally, when the AlGaAs nanocylinder was placed over the gold substrate, the closest mode had a \(Q\) factor equal to 20 for a wavelength of 1460 nm, see Figure 4f. Therefore, to conclude, the mode with the highest \(Q\) factor excitable at 1550 nm is the one obtained in the case of ENZ substrate. This high-quality mode is supported by the nanoantenna results in the enhanced near-field distribution, as represented in Figure 2a. Figure 3: SH Far Field in the case of AlGaAs cylinder (\(r=232\) nm, \(h=400\) nm) placed over (**a**) the ENZ, (**b**) the dielectric and (**c**) the gold substrate when excited by a plane wave.