Third-harmonic generation in optical nanoantennas: efficiency enhancement

Optical nanoantennas have attracted a lot of research interest over the last decade owing to their unique characteristics in concentrating far-field radiation into the sub-wavelength dimensions. Also, they have been recently utilized to enhance the functionality of nonlinear optical devices. By inserting a dielectric nanoparticle within the gap of a dipole nanoantenna, the third-harmonic generation (THG) emission can be boosted. In this study, we simulate dipole and bowtie nanoantennas and compare their THG output spectra with and without the presence of indium tin oxide (ITO) nanocrystal in the nanoantennas gap. The results show that with proper design of the nanoantenna and changing the geometry from the dipole to the bowtie structure as well as inserting the ITO nanocrystal, the THG efficiency can be enhanced by a factor of eight. Our work opens a new window to generate more efficient nonlinear phenomena at nanoscale devices.


Introduction
Dipole and bowtie nanoantennas (BNAs) have been used recently in many researches [1][2][3]. Localized field enhancement and spatial confinement of the incident electric field in these nanoantennas are more improved compared to the other coupled plasmon resonantnanoparticle pair geometries [3]. One of the most important physical properties of monopole and dipole optical nanoantennas is their resonance wavelength which is substantially smaller than the free-space incident wavelength λ 0 [4,5]. Recent researches on the optical response of BNAs suggest that the sharp shape of the triangles can be considered for applications in high-resolution imaging, spectroscopy and sensing [6,7]. BNAs can localize the electromagnetic fields higher than other plasmonic nanoparticle resonance structures. Their unique geometry and high electromagnetic coupling between the two antenna arms lead to an increase in the field intensity in the subwavelength gap. This results in an increase of nonlinear effects including second-harmonic generation (SHG) [8] and third-harmonic generation (THG) [9].
Optical nanoantennas have been recently proposed to enhance the efficiency of nonlinear optical processes such as THG which is mainly related to modifying the linear optical properties and the resonance lifetime of the plasmonic antennas [10,11]. The confined plasmonic resonances can be identified from peaks in scattering and absorption cross sections and near-field radiation patterns [10]. This is utilized to build optical nonlinearities at the nanoscale, without any dependency of phase-matching conditions [11]. Resonances of metallic nanoparticles like gold and silver usually take place at UV-visible wavelengths. A nanoparticle with high nonlinear characteristic used in the near field of a plasmonic structure could be beneficial for enhancing nonlinear emissions in nanoscale devices. While nonlinearity in nanophotonics have been concentrated on the inherent coupling from metallic nanostructures, a couple of works have tried to explore the coupling in nonlinear materials integrated with plasmonic devices [12]. Specifically, hybrid dielectric/plasmonic nanostructures gained a lot of interests recently for enhancing the nonlinear responses between the incident light and nanoscale components [13,14].
A hybrid plasmonic nanoantenna has been reported where the interaction of gold and indium tin oxide (ITO) was used for increasing infrared light [15,16]. It has been shown that higher THG conversion efficiency can be achieved by the hybrid crystal in comparison with its bare plasmonic arrangement. In Refs. [9] and [17] a doubled THG intensity has been observed where an ITO nanocrystal with strong third-order susceptibility has been placed in the nanoantenna gap. It is also possible to change the geometry of the optical nanoantenna or place other nonlinear materials [18] and study the nanoantenna characteristics such as the transmission, intensity spectrum at the fundamental resonance frequency.
In this paper, we study dipole and BNAs and compare their intensity spectra with and without ITO nanocrystal inserted within the nanoantennas gap. By employing BNAs in a periodic array, we examine how the nonlinear response can be considerably changed and discuss how the enhanced near-field intensity leads to efficiency enhancement of the THG emission in the proposed hybrid BNAs. Compared with the hybrid dipole nanoantennas, we observed a noticeable increase in the THG output intensity radiated from the BNAs. a e-mail: pakarzadeh@sutech.ac.ir (corresponding author)

Theory and simulation method
To simulate our proposed nanoantenna, the three-dimensional (3D) finite-difference time-domain (FDTD) numerical method is employed. It is worth noting that owing to the strong coupling between neighboring nanoantennas for the array configuration, we traced the source of the nonlinear signal by extraction of figures from a single cell of the nanocrystal (isolated hybrid nanostructure). Periodic boundary conditions have been used for the linear and nonlinear simulations of the structure where electric and magnetic walls were set in the direction of x and y, respectively. This is while the perfectly matched layers (PMLs) boundary conditions were set in z-direction in order to avoid numerical reflections of the incident field. Following these boundaries, an infinite array in x-and y-direction is placed over a silicon substrate which is excited by a plane-wave source polarized in x-direction.
Palik's material data [19] are used for gold and silicon. For transmittance and reflectance, a monitor is placed at 2.5 μm above and below the silicon-gold interface, respectively, parallel to the interfaces [20]. The transmittance is obtained as a function of frequency (wavelength) using: where P m,s denotes the Poynting vector at the monitor and source location, f is the frequency and S is the surface of the reference plane where the transmittance is computed. Equation (1) is also used to calculate the reflectance R of the system by changing S to the appropriate reference plane. The absorbance is then determined as The linear and nonlinear responses simulated at the same time in which the nonlinear investigations started by measuring the THG spectra from the hybrid and bare plasmonic nanoantenna. By having an excitation at frequency ω, the third-order susceptibility χ (3) of the material induces a nonlinear polarization P (3) (3ω) defined by [11]: It is worth mentioning that we have numerically examined two cases where for the first case, the ITO material of the hybrid nanoantenna is considered to be linear i.e., χ  [21] and neglect the nonlinearity of the substrate. We have simulated gold dipole nanoantenna with a 3 nm Cr adhesion layer and compared our results with the same structure consisting of two gold rods shown in Fig. 1a, with height of h 40 nm, width of W 50 nm, length of L 180 nm and the gap distance of g 20 nm. Figure 1b shows the dipole nanoantenna gap filled with the ITO nanocrystal. By studying the results of Ref. [15], we have decided to change our structure to BNA with the same boundary conditions to compare our new results.
We have simulated gold BNA with thickness of h 40 nm and Cr adhesion layer thickness of h Cr 3 nm using the FDTD method [22] to reach the enhanced resonance behavior of a single BNAs and their near-field intensity enhancement |E| 2 |E incident | 2 for our study. As the BNA resonance has a strong dependency on the polarization of the applied optical field, the incident polarization used in this simulation is parallel to the bowtie axis, which it is known as horizontal polarization. Two equilateral triangles with length of L 150 nm separated by gap distance of g 15 nm have been shaped a single BNA as it is illustrated in Fig. 2a. Also the thickness of the substrate for both cases is h sub 100 nm. Figure 2b shows the ITO nanocrystal which is considered as a cylinder with diameter of d ITO 7.5-nm in the center of the bowtie nanoantenna gap.  Fig. 3. Extinction is defined by transmission (extinction − log(T )). As it is seen, the extinction peak shifts about 75 nm toward higher wavelengths; this can be explained by changing the refractive index of the nanoantenna. In fact, the refractive index of the bare nanoantenna gap is equal to that of the air (n 1) before adding the ITO nanocrystal, while this is increased to (n 2.9) by adding ITO nanocrystal [23]. The solid and dashed lines refer to the bare antenna and ITO incorporated within the nanoantenna gap where the fundamental resonances take place at 1050 nm and 1125 nm, respectively.
The output spectrum of THG intensity for the dipole nanoantenna with ITO nanocrystal is shown in Fig. 4a where the nonlinearity of the gold and nanocrystal is considered in this study. On the other hand, when the ITO nanocrystal is inserted in the nanoantenna gap with the third-order susceptibility of χ the main resonance and the THG peaks are changed. It can be seen in Fig. 4a that the fundamental resonance and THG peak of the structure occur at 1125 nm and 380 nm, respectively.
In Fig. 4b, one can see a comparison of the presence of ITO nanocrystal and its absence in the dipole nanoantenna gap, which shows a resonance shift of about 30 nm due to an increase in the total refractive index of the system by adding ITO nanocrystal in its gap. Even more importantly, it is observed that the enhancement is increased about twofold in comparison of the THG intensity by incorporation of the ITO nanocrystals. In addition to THG, it has been recently observed that the ITO has been found various applications in different areas such plasmon-enhanced infrared spectroscopy, nanowire network and optoelectronics [24][25][26].

Bowtie nanoantenna
Now, we proceed to simulate the same boundary conditions but for the bowtie structure. The basic result of the bowtie simulation is shown in Fig. 5; where the resonance wavelength of new nanoantenna has been located around 780 nm.
The output spectrum of THG intensity for the bowtie nanoantenna with ITO nanocrystal is shown in Fig. 6a where the nonlinearities of the gold and nanocrystal are included in simulations. The THG peak occurs around 260 nm, and the fundamental resonance of nanoantenna is about 780 nm.   Fig. 6b. Also, the resonance wavelength of the nanoantenna in presence of ITO nanocrystal is shifted about 20 nm to higher wavelengths compared with the resonance wavelength of the bare nanoantenna. Furthermore, the third harmonic signal appeared at 263 nm, the maximum magnitude of the third harmonic intensity is significant, with the intensity of the third harmonic. The state of ITO nanocrystal within the nanoantenna gap has a maximum value about 6.5 × 10 10 , which in fact increased about three times greater than the bare nanoantenna.
In Fig. 6a, there are two peaks showing the fundamental wavelength around 780 nm along with its THG wavelength around 260 nm where it is equal to 1/3 of the fundamental wavelength. Figure 6b compares the THG wavelengths of two different BNAs Fig. 6 a Output spectrum of the BNA in presence of ITO nanocrystal. The THG intensity peak is shown around 260 nm; and b comparison of THG spectra in presence (dashed line) and absence (solid line) of ITO nanocrystal in the BNA with and without ITO. Obviously, the dashed-pink peak in Fig. 6b is the same as the THG peak in Fig. 6a. However, it should be noted that spectrum details around the 260 nm-peak in Fig. 6a refers to some numerical artifact. In fact, as we increased the accuracy in Fig. 6b, there is only one real peak around 260 nm without any artefact. The third-harmonic intensity enhancement curves for the two structures with/without the presence of ITO nanocrystal in bowtie nanoantenna are compared in Fig. 6b. The detection point located at the same place for two structures, which is at the center of gap between the two bowties. For a better comparison, the result of THG spectrum in Fig. 6a is smoothened, so one can see that the peak of the dashed-pink line is more than three-fold increased than the solid blue line. This means that owing to the sharp tips of the BNA structure and enhanced local fields, the THG intensity is enhanced compared with that of dipole nanoantennas.
We have compared THG intensity of each nanoantenna (dipole or bowtie) to itself when ITO nanocrystal is present or absent. Therefore, as it is seen from Fig. 4b the ratio of THG intensities for the dipole nanoantenna with and without ITO is 8/4.25 which is approximately equal to 2 and matches very well with the results reported in Ref. [15]. This ratio for the BNA with and without ITO is 6.5/1.9 which is approximately equal to 3.5 as shown in Fig. 6b. However, if one compares the THG peak intensity of the dipole nanoantenna to that of the BNA both with ITO nanocrystal, an eight-fold increase in efficiency is obtained.

Conclusion
We have simulated linear and nonlinear spectra of both dipole and bowtie nanoantennas (BNAs) and investigated the role of ITO nanocrystal when incorporated in the nanoantennas gap. It was shown that in general, the presence of ITO nanocrystal in the nanoantenna gap led to the efficiency enhancement of the THG so that in the dipole nanoantenna the enhancement factor reached twice. This is while in particular, by changing the geometry of the nanoantenna from the dipole to the bowtie structure and inserting ITO nanocrystal, the THG efficiency was enhanced by a factor of eight. Thus, our proposed BNAs with enhanced nonlinear efficiency provide new opportunities for designing tunable and sensitive nanophotonic devices for nonlinear-optics applications.