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Third-harmonic generation with metallic or dielectric nanoparticles often suffer from, respectively, small modal volumes and weak near-field enhancements. This study propose and demonstrate that a metallic/dielectric hybrid nanostructure composed of a silver double rectangular nanoring and a silicon square nanoplate can be used to overcome these obstacles for enhanced third-harmonic generation. It is shown that the nonradiative anapole mode of the Si plate can be used as a localized source to excite the dark subradiant octupole mode of the Ag ring, and the mode hybridization leads to the formation of an antibonding and a bonding subradiant collective mode, thereby forming anticrossing double Fano resonances. With the strong coupling between individual particles and the effectively suppressed radiative losses of the Fano resonances, several strong hot spots are generated around the Ag ring due to the excitation of the octupole mode, and electromagnetic fields within the Si plate are also strongly amplified, making it possible to confine more incident energy inside the dielectric nanoparticle. Calculation results reveal that the confined energy inside the Si plate and the Ag ring for the hybrid structures can be about, respectively, more than three times and four orders stronger than that of the corresponding isolated nanoparticles, which makes the designed hybrid nanostructure a promising platform for enhanced third-harmonic generation.
© 2016 Optical Society of America
1. Introduction
The manipulation of nonlinear optical effects such as third-harmonic generation (THG) on the nanoscale is very useful for bio-imaging [1, 2], sensing [3–5] and optoelectronics [6]. Because of the intrinsic weak photon-photon interactions, high field intensities are desired to achieve strong third-harmonic (TH) emissions. The incident field can be focused beyond the diffraction limit with localized surface plasmon resonances (LSPRs), and strong near-field enhancements are generated around metallic nanoparticles, which results in the formation of the so called hot spots [7–14]. Therefore, metallic nanostructures are promising platforms for enhanced THG, The third-order nonlinearity can be strongly enhanced with LSPRs [15], and the nonlinear responses are further enhanced with coupled metallic nanoparticles [16] and by using core-shell bimetallic nanostructures [17]. However, there are radiative and nonradiative losses for LSPRs, which are unfavorable to achieve strong near-field enhancements. With the generation of plasmonic Fano resonances, radiative losses can be effectively suppressed due to the excitation of subradiant dark modes, and near-field enhancements are strongly amplified [18–26]. Besides that, it has been shown that Fano resonance is associated with the formation of optical vortices [27], and the anisotropy of a cylinder can be used to generate Fano resonance, which reveals fast reversion between forward and backward scattering [28]. Because of the strong near-field enhancements, Fano resonances can be useful for enhanced nonlinear optical effects [29–34]. Nevertheless, the coupling of incident field to the inner volume of metallic nanoparticles is inherently weak, and strong near-field enhancements are often generated around a tiny gap area, which results in small modal volumes, and it is challenging to further enhance THG with metallic nanostructures.
An alternative approach to enhance THG is by using high-refractive index dielectric nanostructures [35–38]. Compared with that of metallic nanostructures, the incident field can be confined within dielectric nanoparticles, and nonradiative losses of dielectric materials can be very small. With the formation of strong magnetic dipole responses [39–42], a large TH conversion efficiency is achieved using silicon nanodisks [43, 44]. Fano resonance in dielectric metasurfaces can be used to suppress radiative and nonradiative losses simultaneously [45], and the THG conversion efficiency is further enhanced by one order [46]. Not long ago, it has been shown that in addition to the conventional multipolar resonances, a toroidal dipole mode is strongly excited in single dielectric nanodisks, and the destructive interference with the electric dipole mode suppress radiative losses, which leads to the formation of the so called nonradiative anapole mode [47–51]. Experimental results demonstrate that the THG conversion efficiency using the anapole mode with single dielectric nanodisks is comparable with that of the Fano resonant dielectric metasurfaces [52]. However, near-field enhancements inside single dielectric nanoparticles are relatively weak compared with that of plasmonic nanostructures [52], which can be an obstacle to further enhance THG.
Recently, metallic/dielectric hybrid nanostructures have received considerable attention, where the advantages of metallic and dielectric nanoparticles can be utilized simultaneously for many applications [53, 54]. In order to reliably fabricate hybrid nanostructures, some advanced methods such as laser-induced reshaping have been developed [55]. Due to the mode coupling between the metallic and dielectric nanoparticles, unidirectional emissions are achieved with hybrid structures [56], and it can be used for light switching and routing [57]. Besides that, metallic/dielectric nanostructures are useful for enhanced nonlinear optical effects [58]. For example, when dielectric nanoparticles are placed around the hot spot of a metallic nanorod dimer, enhanced THG can be realized, and the emission intensity is about one times stronger than that of bare metallic nanoantennas [59, 60]. However, there is only one single hot spot for the nanorod dimer, and the modal volume is still small for enhanced nonlinear optical effects. In order to enlarge the area of hot spots and enhance the field intensity inside dielectric nanoparticles, we show that through near-field coupling, the dark octupole mode of a metallic nanoring can be excited by the anapole mode of a dielectric nanoplate, near-field around the hybrid nanostructure are dramatically enhanced with the strong interparticle coupling, and up to six hot spots are generated. The confined energies inside the dielectric plate and the metallic ring for the hybrid structures are significantly enhanced compared with that of the corresponding isolated nanoparticles, which makes the designed hybrid nanostructure promising for enhanced THG.
2. Optical responses of isolated metallic and dielectric nanoparticles
Previous studies have shown that due to the destructive interference between the electric and toroidal dipole modes, the so called anapole mode is excited with single cylinder dielectric nanodisks, and the far-field scattering is strongly suppressed, thereby forming Fano-like lineshape in the scattering spectrum [47–51]. In addition to the cylinder nanodisk, the anapole mode can be excited for other dielectric nanostructures, such as the Si square nanoplate shown in the inset of Fig. 1(a). The optical responses of the plate are calculated with finite-difference time-domain method. In order to better accord with a realistic system, the plate is supposed to be placed on a semi-infinite silica substrate (n = 1.46). The incident field propagates along the z-axis from the side of the substrate, the polarization is along the x-axis, the length of the plate l = 400 nm, the thickness h = 70 nm, and the measured dielectric function of Si is used in the simulations [61].
Fig. 1 (a) Scattering (black line) and absorption (red line) spectra of an isolated Si square nanoplate placed on SiO2 substrate under normal incidence, and (b) an isolated Ag double rectangular nanoring placed in vacuum under grazing incidence, where the insets show the schematic views of the corresponding nanoparticles, the geometry parameters are l = 400 nm, h = 70 nm, L1 = 200 nm, L2 = 400 nm, H = 48 nm, and W = 40 nm. (c) Electric near-field enhancement and field vector distributions of the fundamental anapole mode on the center cross section of the Si plate (the xy-plane), and (d) the dark octupole mode on the surface of the Ag ring (the xy-plane). (e) Magnetic near-field distributions on the center cross section of the yz-plane for the Si plate, and (f) the Ag ring.
The black and red lines in the main panel of Fig. 1(a) represent the scattering and absorption spectra of the Si plate, respectively. There is a pronounced resonance dip around 871 nm in the scattering spectrum, indicating the effectively suppressed radiative losses. Electric field enhancement and field vector distributions in the center cross section of the xy-plane reveal that due to the formation of opposite circular displacement currents in the up and down sides of the plate (see Fig. 1(c)), a circular magnetic moment distribution which is perpendicular to the plate surface is generated, as shown by the magnetic near-field enhancement and field vector distributions in the center cross section of the yz-plane (see Fig. 1(e)). Such near-field distributions provide a strong toroidal moment oriented parallel to the plate surface, and its destructive interference with the electric dipole mode leads to the suppression of radiative damping and the formation of a Fano resonance [47–51]. In this study, the near- and far-field are defined in terms of the distance from the structures. The field less than one wavelength and more than ten wavelengths away from the particles are assigned as the near- and far-field, respectively. It is worth noting that another Fano resonance is excited around 600 nm (see Fig. 1(a)), and it is caused by the excitation of a higher-order anapole mode, which is similar as that of the dielectric nanodisks [48].
Next, the optical responses of a silver double rectangular nanoring are investigated (see the inset of Fig. 1(b)). Due to the structural symmetry, the higher-order (multipolar) plasmon modes of the nanoring cannot be excited under normal incidence. Therefore, the scattering and absorption spectra shown in the main panel of Fig. 1(b) are calculated with grazing incidence, where the ring is supposed to be placed in vacuum, the incident polarization is along the x-axis, the dielectric constants are taken from experimental results [62], the length L1 = 200 nm, L2 = 400 nm, the thickness H = 48 nm, and the width W = 40 nm. Several multipolar resonances appear in the spectra, and Fig. 1(d) and 1(f) show the electric and magnetic near-field distributions for the resonance around 591 nm, respectively. There are six charge lobes around the double rectangular ring, and it is identified as the octupole mode, which is similar as that of a circular nanoring [63]. Besides of the octupole mode, the resonances around 810 and 1000 nm are caused by, respectively, the excitation of the quadrupole and dipole modes.
3. Anticrossing double Fano resonances
The ability to generate dramatically enhanced near-field is one of the most important optical properties in the studies of nanophotonics. For metallic nanostructures such as a nanoparticle dimer, strong near-field enhancements (hot spots) can only be generated around a tiny gap region. The optical responses of the Ag ring reveal that there are six charge lobes with the excitation of the octupole mode, which makes it possible to generate several hot spots (see Fig. 1(b)). However, the near-field enhancements are relatively weak because of the absence of interparticle plasmon coupling, and the octupole resonance is a dark mode, which cannot be excited with normal incidence. On the other hand, for high-refractive index dielectric nanostructures, optical fields can be confined within the nanoparticles, and the nonradiative damping are inherently weak. However, the displacement fields inside single dielectric nanoparticles are weaker than that of plasmon resonances.
The designed metallic/dielectric hybrid nanostructure shown in the inset of Fig. 2(a) may be used to solve the above problems, where the Ag ring is placed symmetrically on the Si plate with a silica spacer. Since the anapole mode can be seen as three equivalent electric dipoles oscillating out of phase (inset of Fig. 1(a)), the dark octupole mode of the Ag ring could be possibly excited through near-field coupling, and the near-fields around the ring and inside of the plate are expected to be enhanced with interparticle interactions.
Fig. 2 (a) Scattering (solid lines) and absorption (dashed lines) spectra of metallic/dielectric hybrid structures under normal incidence with different length L1 of the Ag ring, where the inset shows the geometry of the hybrid structure, the Ag ring is placed symmetrically on the Si plate with a SiO2 spacer, the separation S = 12 nm, and the other geometry parameters are identical with that of Fig. 1. (b) Contour plots of scattering and (c) absorption spectra of the hybrid structure versus L1 with a step of 20 nm, where the dotted lines indicate the spectra shown in Fig. 2(a), and the dashed lines are for guiding the eye for the two sets of Fano resonances.
To verify this assumption, the scattering and absorption spectra for the hybrid structure with different length L1 of the Ag ring are calculated as shown in the main panel of Fig. 2(a), where the spacer thickness S = 12 nm, and the rest geometry parameters are identical with that of Fig. 1. When L1 = 140 nm (the black lines, Fig. 2(a)), there is a minor change for the Fano resonance around 874 nm compared with that of the single Si plate. Besides that, an additional resonance dip around 755 nm appears in the scattering spectrum, which indicates the excitation of a new Fano resonance. This newly appeared Fano resonance red shifts to about 825 nm when L1 is enlarged to 200 nm, while the other one is slightly red shift to about 899 nm (the red lines, Fig. 2(a)). Further enlarge L1 to 360 nm (the blue lines, Fig. 2(a)), the spectral position of the Fano resonance with higher energy is almost unchanged, while the Fano resonance with lower energy red shift to about 1049 nm.
To better illustrate the far-field responses of the hybrid structure, Fig. 2(b) and 2(c) show, respectively, the variations of the scattering and absorption spectra versus L1 with a step of 20 nm. With the present of the Ag ring, the fundamental Fano resonance of the Si plate splits into two Fano resonances, which shows a clear anticrossing behavior (the first and the second one, which are marked by the red dashed and orange dashed lines, respectively). When L1 < 200 nm, the first Fano resonance red shifts rapidly with the increasing of L1, while there is a minor change for the second one. On the contrary, the first Fano resonance red shifts slightly with the increasing of L1 when it is larger than 200 nm, while the second one shifts to lower energies significantly at the same time.
4. Modes analysis and strong amplified near-field enhancements
Near-field distributions are then investigated to identify the resonance modes corresponding to the Fano resonances. For the hybrid structure with L1 = 140 nm, electric field distributions at the center cross section of the Si plate for the first Fano resonance reveal that the anapole mode is excited (upper panel, Fig. 3(a)), and the field inside the plate is amplified compared with that of the isolated nanoparticle (see Fig. 1(c)). At the same time, the dark octupole mode of the Ag ring is indeed excited through near-field coupling with the anapole mode (middle panel, Fig. 3(a)), and the electric field enhancement is stronger than that of the isolated Ag ring, thereby forming six hot spots around the charge lobes. Due to the same reason, strong induced current density is generated, and there are strong magnetic field enhancements around the Ag ring (lower panel, Fig. 3(a)). It is worth noting that the enhanced fields are extended into the Si plate, making it possible to confine more incident energy into the dielectric nanoparticle. The overall dipole moment of the collective resonance is approaching to zero because of the subradiant nature of the anapole and the octupole modes, and radiative losses are effectively suppressed, which leads to the formation of the first Fano resonance.
Fig. 3 Electric near-field distributions on the center cross section of the xy-plane for the Si plate (upper panels), on the surface of the the Ag ring in the xy-plane (middle panels), and magnetic near-field distributions on the center cross section of the yz-plane (lower panels) of the metallic/dielectric hybrid structures for the first (left panels) and the second (right panels) Fano resonances, where (a, d) L1 = 140 nm, (b, e) L1 = 200 nm, and (c, f) L1 = 360 nm.
Figure 3(d) shows the corresponding near-field distributions of the second Fano resonance for the hybrid structure with L1 = 140 nm. Despite of the weaker field enhancements compared with that of the first one (see Fig. 3(a)), the overall near-field distributions are similar to each other, where the anapole mode and the octupole mode are excited in this case. However, the two collective resonances can be identified when the phase difference is considered. From the electric field vector distributions on the upper two panels of Fig. 3(a) and 3(d), one can find that the anapole mode oscillates in phase and out of phase with the octupole mode for the first and the second Fano resonances, respectively.
The interactions of the metallic/dielectric hybrid structure can be better understood with the mode hybridization schemes shown in Fig. 4. The same as plasmon hybridization, the mode hybridization between the anapole mode of the Si plate (see Fig. 4(a)) and the dark octupole mode of the Ag ring (see Fig. 4(c)) leads to splitting of the modal energies into antibonding and bonding hybridized resonances. The two hybridized modes are, respectively, the corresponding subradiant modes of the first and the second Fano resonances (see Fig. 4(b)), and the mode hybridization between the metallic and dielectric resonators results in the spectral anticrossing behavior shown in Fig. 2.
Fig. 4 Schematic diagrams for the mode hybridization between the Si plate and the Ag ring of the hybrid structure. Spectra are for (a) isolated Si plate under normal incidence, (b) hybrid structure under normal incidence, and (c) isolated Ag ring under grazing incidence. The insets show the equivalent electric dipole (Si plate) and charge (Ag ring) distributions at the corresponding resonance energies. The dotted lines indicate the mode hybridization resulting in the subradiant antibonding and bonding collective resonance modes for the two Fano resonances.
When the length L1 is enlarged to 200 and 360 nm, one can expect that the octupole mode will shift to higher energies. Therefore, near-field enhancements around the Ag ring for the first Fano resonance decreases at the same time (middle panels, Fig. 3(b) and 3(c)). Nevertheless, the field enhancements inside the Si plate are still stronger than that of the isolated nanoparticle (upper and lower panels, Fig. 3(b) and 3(c)). It is worth mention that because of the strong interparticle coupling, the octupole mode is strongly red shift compared with that of the isolated Ag ring (see Fig. 1).
On the contrary with that of the first one, near-field enhancements around the Ag ring for the second Fano resonance increase significantly (middle panels, Fig. 3(e) and 3(f)), and the fields inside the Si plate are also enhanced at the same time (upper and lower panels, Fig. 3(e) and 3(f)). For a hybrid structure with a large length L1 (see Fig. 3(f)), because of the strong near-field enhancements around the Ag ring, the fields are strongly extended into the Si plate, and the field profiles are not sustained as that of the anapole mode (see Fig. 1). However, the octupole mode of the Ag ring is indeed excited under normal incidence, which can be attributed to the interactions with the anapole mode.
5. Effective energy confinement for enhanced nonlinear optical effects
The above studies have demonstrated that with the excitation of the double Fano resonances, the incident fields are effectively confined around the hybrid structure, which can be a promising platform for many applications. For example, THG with isolated metallic nanostructures often suffer from small modal volumes, while the fields inside isolated dielectric nanostructures are relatively weak. These obstacles for enhanced THG can be overcome by using the designed metallic/dielectric hybrid structure, where the generation of hot spots is not limited to a single gap area with the excitation of the octupole mode, the interactions with the Si plate lead to very strong near-field enhancements, and the enhanced near-fields are strongly extended into the Si plate, making it possible to confine more incident energy inside the dielectric nanoparticle. Therefore, it is expected that enhanced THG can be achieved with the designed hybrid structure.
It is hard to determine quantitative and wavelength-dependent values for the third order susceptibilities χ3(ω) for noble metals. Hence, first we consider the electric energy inside the nanoparticles at the fundamental wavelength, which can be used to describe the excitation power for THG. Previous studies have shown that when there are no resonances at the TH wavelength, THG emission intensity can be interpreted by the variation of the third power of the electric energy, and the energy inside the Si plate can be calculated by [52],
where nSi is the refractive index of Si, and the small imaginary part is neglected in the calculations. The solid lines in Fig. 5(a) show the wavelength dependent confined energy inside the Si plate for the hybrid structures with different Ag ring, and the gray dashed lines represent the confined energy for the isolated Si plate, which are identical with each other. To better show the variations of the confined energy inside the Si plate, Fig. 5(c) represents the calculation results versus L1 with a step of 20 nm. It is found that indeed the incident energy can be effectively confined within the Si plate with the excitation of the two Fano resonances. For the first Fano resonance (red arrows in Fig. 5(a), and red dashed line in Fig. 5(c)), the energy only decreases slightly with the increasing of L1, and the confined energy for the hybrid structure can be about one times stronger than that of the isolated Si plate (black arrows in Fig. 5(a)). As for the second Fano resonance (orange arrows in Fig. 5(a), and orange dashed line in Fig. 5(c)), the confined energy is comparable with the isolated Si plate for the hybrid structure with L1 = 140 nm. However, the energy increases dramatically with the increasing of L1, and it is more than three times stronger than that of the isolated Si plate when L1 = 360 nm.Fig. 5 Normalized energy confined within (a) the Si plate, and (b) the Ag rings for the hybrid structures (solid lines) and the corresponding isolated nanoparticles (dashed lines), where the red and orange arrows indicate, respectively, the spectral positions of the first and the second Fano resonances, the black arrows in Fig. 5(a) and Fig. 5(b) indicate the spectral positions of the anapole mode and the octupole modes, respectively. The rest geometry parameters and the excitation conditions for the isolated and hybrid structures are identical with that of Fig. 1 and 2, and the values of the energy confined within isolated Ag rings are scaled by a factor of 104. (c) Contour plots of the energy confined within the Si plate, and (d) the Ag rings for the hybrid structures versus L1 with a step of 20 nm, where the dotted lines indicate the spectra shown in Fig. 5(a) and 5(b), and the dashed lines are for guiding the eye for the two sets of Fano resonances.
Next, the energy confined inside the Ag ring will be investigated. To avoid to get a negative energy value when the permittivity is smaller than zero for noble metals, the energy inside the Ag ring is calculated by [64],
where εAg is the permittivity of silver, and γ is the damping constant (γ = 0.06 eV in the calculations). The solid lines in Fig. 5(b) show the calculated confined energy in the Ag ring for different hybrid structures, and the dashed lines represent the calculated results for the corresponding isolated Ag ring under grazing incidence. More calculations for the hybrid structures are presented in Fig. 5(d). The energy around the first Fano resonance decreases rapidly with the increasing of L1 (red arrows in Fig. 5(b), and red dashed line in Fig. 5(d)), which can be attributed to the red shifting of the octupole mode. On the contrary, the confined energy increases dramatically at the same time for the second Fano resonance (orange arrows in Fig. 5(b), and orange dashed line in Fig. 5(d)). Compared with the isolated Ag rings (black arrows in Fig. 5(b)), the confined energy inside the metallic nanoparticles for the hybrid structure can be about four orders stronger due to the strong interparticle coupling.The excitation power for THG can be described by the energy confined inside nanoparticles at the fundamental wavelength. The calculation results reveal that the confined energies inside the metallic and dielectric nanoparticles are significantly amplified compared with that of the isolated nanoparticles, thereby forming strong enhanced nonlinear excitation source for TH emission. As a third order nonlinear effect, the emission intensity of THG is proportional to the third power of the confined energy at the fundamental wavelength. It has been shown that by using the anapole mode of single dielectric nanodisks, the measured wavelength dependent TH emissions agree quantitatively well with the calculated wavelength dependent third power of the confined energy [52]. The confined energies can be further amplified with the designed hybrid structures. For example, for the second Fano resonance with L1 = 360 nm (upper panel, Fig. 5(a)), a 64-fold increase of the third power of the confined energy within the Si plate can be achieved compared with that of the anapole mode of the isolated dielectric nanoparticles. Even for the first Fano resonance, there is an 8-fold increase of the third power of the confined energy inside the Si plate. Therefore, one can expect that TH emission can be significantly enhanced with the designed metallic/dielectric hybrid nanostructures.
To further show the ability to enhance THG with the hybrid structure, the nonlinear optical responses are calculated by introducing constant third order susceptibilities, where the susceptibilities χ(3) of silver and silicon are supposed to be, respectively, 6 x 10−9 and 1 x 10−12 esu, and the nonlinear response of silica substrate has been neglected [57]. In the calculations, a single pulse with 150 fs pulse width is used to excite the nanoparticles, the peak pump intensity is about 13.3 MW/cm2, and the center wavelengths are adjusted to match with the resonances of individual structures. The green line in Fig. 6 represents the scattered power spectrum of the Ag ring under grazing incidence, where the refractive index of the surrounding medium is supposed to be 1.46, and the octupole mode red shift to about 1018 nm. It is found that in addition to the incident pulse, an emission peak is observed around 340 nm, indicating the THG of the Ag ring. For the Si plate under normal incidence, the center wavelength of the incidence is adjusted to 871 nm to match with the anapole mode. However, there is no TH emission in the spectrum (the blue line, Fig. 6), which can be attributed to the strong absorption losses of silicon within the ultra-violet spectral range. The red line in Fig. 6 shows the nonlinear emission spectrum of the hybrid structure when the incident is around the first Fano resonance. It is found that although the TH wavelength is within the inter-band transition range of silver (273 nm), the THG intensity is only slightly weaker than that of the single Ag ring. In addition, there is an emission peak around 350 nm, and it is more than four orders weaker than the TH emission, which may be caused by numerical errors. As for the second Fano resonance (the orange line, Fig. 6), the incidence and the TH emission are around the same spectral ranges as that of the Ag ring. Because of the strongly enhanced near-field with the hybrid structure, the TH emission is about 20 times stronger compared with that of the octupole mode of the Ag ring.
Fig. 6 TH emission spectra of the single Ag ring under grazing incidence around the octupole mode (green line), the single Si plate under normal incidence around the anapole mode (blue line), and the hybrid structure under normal incidence around the first (red line) and the second (orange line) Fano resonances, where a pulse with 150 fs pulse width is used to excite the nanoparticles, the peak pump intensity is 13.3 MW/cm2, and the susceptibilities χ(3) of silver and silicon are 6 x 10−9 and 1 x 10−12 esu, respectively. To have a better comparison with the hybrid structure, the refractive index of the surrounding medium around the single Ag ring is supposed to be 1.46. The Ag ring length L1 = 360 nm, and the rest geometry parameters and excitation conditions are identical with that of Fig. 1 and Fig. 2.
6. Conclusion
In conclusion, the optical responses of metallic/dielectric hybrid nanostructures composed of an Ag double rectangular nanoring and a Si square nanoplate are investigated, and the obstacles for enhanced THG with isolated metallic or dielectric nanoparticles can be overcome by using the designed hybrid nanostructures. It is shown that the dark subradiant octupole mode of the Ag ring can be excited through near-field coupling with the nonradiative anapole mode of the Si plate. The mode hybridization leads to splitting of the modal energies into antibonding and bonding subradiant combinations, thereby forming double Fano resonances with a spectral anticrossing behavior. Due to the effectively suppressed radiative losses with the excitation of the Fano resonances, and the strong interparticle coupling, the incident energy can be more effectively confined around the hybrid nanostructures. It is shown that six strong hot spots are generated around the Ag ring, and the electromagnetic fields within the Si plate are also strongly amplified. The calculation results reveal that the confined energy inside the Si plate and Ag ring for the hybrid structures can be about, respectively, more than three times and four orders stronger than that of the corresponding isolated nanoparticles, which indicates that the metallic/dielectric hybrid structure can be a promising platform for enhanced THG.
Funding
National Natural Science Foundation of China (NSFC) (11304219, 11574228, and 61471254); the Project of International Cooperation of Shanxi Province (2015081025 and 201601D021005); the Program for the Top Young Academic Leaders of Higher Learning Institutions of Shanxi.
Acknowledgments
We thank Prof. Xudong Fan in Key Lab of Advanced Transducers and Intelligent Control System for the helpful discussions.
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