Abstract

We theoretically investigate the properties of second-harmonic generation (SHG) in gold–silicon core–shell nanostructures. We first study a concentric structure. This structure exhibits strong electric field enhancement in the silicon shell due to the combined toroidal dipole mode and electric dipole mode. Efficient SHG can be obtained and the SHG signal is about 5 times as strong as that of the individual Si shell. Further calculations show that the contribution from a surface nonlinear susceptibility at the inner surface of the silicon shell dominates the SHG signal of the core–shell structure. The SHG as a function of wavelength is considered and it shows a resonance behavior. The cases of nonconcentric core–shell structures have also been considered. The SHG is further enhanced in this kind of configuration and the SHG signal can reach about 10 times as strong as that of the concentric case. Our results reveal the strong modification of the SHGs in dielectric nanostructures by using the metal–dielectric hybrid configurations, and could find applications in nanoscale nonlinear devices.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

High-index dielectric nanostructures have recently drawn a lot of attention as they exhibit strong multipolar magnetic and electric optical responses, while their material losses are low [1–3]. The strong optical responses are usually accompanied by significant far field scattering and considerable electric and/or magnetic near field enhancements. Many nanophotonic applications based on dielectric nanostructures have been demonstrated such as metasurfaces [4–6], matematerials [7–9], solar cells [10], structural colors [11, 12], and optical nanoantannas [13–16].

Nonlinear optical responses in dielectric nanostructures have also been demonstrated [17] including the third-harmonic generation (THG) [18–20] and second-harmonic generation (SHG) [21–27]. In these nanostructures, the electromagnetic resonance-induced local electric field enhancements play important roles in the nonlinear responses, as the intensities of SHG/THG responses scale with the fourth/sixth power of the fundamental electric field strength. The resonance-enhanced SHG have been investigated mainly in the noncentrosymmetric structures [21–24], for example, the nanostructures of III−V compounds [21, 22]. Recently, the SHGs in nanostructures with the centrosymmetric material of silicon have been demonstrated [25–27]. The centrosymmetric materials have a vanishing second-order nonlinear susceptibility due to the symmetry reason. Therefore, the SHG can be obtained only in the presence of interfaces or field gradients [28] in these structures. For simple dielectric structures, the electric fields of the resonant modes are usually distributed widely around the entire structure. This kind of distribution, which is unfavorable to getting strong enough electric field enhancements, brings challenge to the further enhancement of the SHG in dielectric nanostructures. Recently studies have shown that the metal−dielectric hybrid nanostructures can strongly modify the linear and nonlinear optical behaviors of the metal/plasmonic or dielectric components [29–34]. These studies motivate us to combine the plasmonic and dielectric nanostructures to modify the SHG of centrosymmetric dielectric nanostructures.

Here we theoretically show that metal−dielectric hybrid nanostructures can exhibit tunable resonances with increased electric field enhancement in deep subwavelength scale, where efficient SHG can be obtained. We study gold–silicon (Au–Si) core–shell nanospheres, where both materials are centrosymmetric. Si is chosen as the dielectric material since it has been widely investigated for photonic applications [35–38]. We first focus on a concentric core–shell nanosphere. A resonance peak appears on the extinction spectrum of the hybrid structure, which is induced by a combined electric dipole mode and toroidal dipole mode. The corresponding electric field distribution in the Si shell especially near the interface between the Au and Si shows an obvious enhancement. Thus, the SH responses of the hybrid structure are several times stronger than that of the individual Si shell or a solid Si sphere with magnetic dipole resonance. The SH responses with different nonlinear sources are calculated independently. The leading nonlinear source that contributes to the SHG is the response of a surface nonlinear susceptibility at the inner surface of the Si shell. The case of nonconcentric core–shell nanospheres has also been considered. The electric field near the interface between the Au and Si shows a larger enhancement. Thus, the SH response is further improved in this kind of configuration and the signal can reach about 10 times higher than that of the concentric case.

2. Results and discussion

The schematic of a concentric core–shell nanostructure is shown in Fig. 1(a). The origin of the coordinate is chosen at the center of the structure. The polarization and wave vector of the excitation plane wave are along the y-axis and negative z-axis directions, respectively. The optical responses are calculated by using finite-element-solver COMSOL Multiphysics. The dielectric constants of Au and Si are taken from Palik’s book [39]. Figure 1(b) shows the extinction spectra of the Au–Si core–shell nanosphere, Au core and individual Si shell. The radius of the Au core is 50 nm. The outer radius of the Si shell is 73 nm. A pronounced new peak appears at λ = 800 nm for the core–shell structure. Electric and magnetic near field distributions (Figs. 1(d) and 1(e)) show that this peak is induced by a combined electric dipole mode and toroidal dipole mode. The slightly asymmetrical distribution of the magnetic field in Fig. 1(e) is due to the retardation effect, as the structure has a certain size compared to the resonant wavelength. The electric dipole mode is associated with the redshifted plasmon dipole mode of the Au core in the appearance of dielectric surrounding [40, 41]. The toroidal dipole mode corresponds to a rotating magnetic field [42], which has been demonstrated in many dielectric based nanostructures [43–45]. The coherent combination of the two modes is also viewed as an anapole mode in some literatures [44]. In Fig. 1(d), the electric dipole mode corresponds to the electric field outside the Si shell and the toroidal dipole mode corresponds to the electric field near the interface between the Si shell and Au core. As it has been pointed out that the excitation of toroidal dipole and its destructive interference with the electric dipole leads to suppressed scattering [43,44], which means that the absorption becomes relatively larger. This is confirmed by our results in Fig. 1(c), where the absorption of the coupled structure is much larger than the individual segments. Compared to the case of an individual Si shell (Fig. 1(f)), the electric field in the Si shell of the core–shell structure is largely enhanced near the interface between the Si shell and Au core (Fig. 1(d)) due to the toroidal dipole response. We have also carried out the calculations based on the analytical Mie theory which has been widely used for spherical structures [41, 46–48]. The results (data not shown) show good agreement with the results above, indicating the high accuracy of our COMSOL simulations.

 figure: Fig. 1

Fig. 1 Linear optical responses. (a) Schematic of a core–shell nanostructure. The origin of the coordinate system is located at the center of the structure. (b) Extinction spectra of a core–shell structure, an Au sphere and an individual Si shell. The radius of the Au core is 50 nm. The outer radius of the Si shell is 73 nm. (c) Absorption and scattering spectra of the core–shell structure. The absorption of the individual Si shell and Au core are also shown (dashed lines). (d) Electric field enhancement of the core–shell structure on the y-z plane at λ = 800 nm. (e) Magnetic field enhancement of the core–shell structure on the x-z plane at λ = 800 nm. (f) Electric field enhancement of the individual Si nanoshell on the y-z plane at λ = 800 nm.

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We now turn to the second-harmonic (SH) responses of the core–shell structure. It has been well known that the second-order polarization P(2ω) in centrosymmetric materials can be written as a superposition of surface and bulk contributions [25,49]

Psurf(2ω)=Psurf(2ω)+Pbulk(2ω),
Psurf(2ω)=ε0χs(2):E(ω)(r)E(ω)(r)δ(rrs),
Pbulk(2ω)=ε0[βE(ω)(E(ω))+γ(E(ω)E(ω))+δ(E(ω))E(ω)],
where χs(2) is the second-order surface nonlinear susceptibility. ε0 is the dielectric permittivity of vacuum. E(ω) is the electric field vector at the fundamental wavelength. rs defines the interface surface. β,γ and δ' are the bulk nonlinear susceptibilities. The β term can be omitted as ∇·E vanishes in the bulk of a homogeneous medium. In the spherical coordinate system, Psurf(2ω) can be written as
Psurf(2ω)=ε0δ(rrs)[χ(2)(Er(ω))2r^+χ||||(2)(Eθ(ω))2r^+χ||||(2)(Eφ(ω))2r^+2χ||||(2)Er(ω)Eθ(ω)+θ^+2χ||||(2)Er(ω)Eφ(ω)φ^],
where χ(2),χ||||(2) and χ(2) are the elements of the surface nonlinear susceptibility. ⊥ and‖correspond to the spatial components perpendicular and parallel to the surface. Au is also a centrosymmetric material and the χ(2) component dominates the nonlinear responses [50]. So, only this contribution is taken for our SHG calculations of Au (denoted by χAu, (2)). This assumption has been widely used for most of the relevant calculations [50]. For the Si nanostructures, we consider the contributions from all the components of the nonlinear susceptibility (for simplicity, the nonlinear components for Si are denoted by χ(2),χ||||(2), χ(2), γ andδ'). According to [51], we take χ(2) = 65 × 10−19 m2/V, χ(2) = 3.5 × 10−19 m2/V, and both χ||||(2) and γ are roughly assumed to be 1 × 10−19 m2/V. Based on the results in [27], we estimate the δ' to be δ' ≈1 × 10−19 m2/V. The corresponding fundamental wavelength is λ = 800 nm.

The near field and far field SH responses of the core–shell structure are shown in Figs. 2(a) and 2(e), respectively. The SH far field can be calculated directly by the COMSOL simulations. The results are the electric far field for a selected number of angles on a unit circle (in 2D) or a unit sphere (in 3D), where the radius of the circle/sphere is 1 m. Compared to the case of the individual Si shell (Figs. 2(b) and 2(f)), the SH signals of the core–shell structure are greatly enhanced. The maximal SH electric far field (Efar(2ω)) of the core–shell is 5 times larger than that of the individual Si shell. Here in this paper, the maximal Efar(2ω) means the largest value of the Efar(2ω) at an angle in the Efar(2ω) distribution pattern. Note that the absolute value of the maximal Efar(2ω) / E0 for the individual shell is about 4.3 × 10−15. The Efar(2ω) for other cases are normalized to this value for clearer comparison. The contribution of χAu, (2) to the SH responses of the core–shell structure has also been included in the calculations for Figs. 2(a) and 2(e). But calculations show that the Si dominates the SH responses of the core–shell structure. Figures 2(c) and 2(g) show a case where only χAu, (2) is taken for the calculation of the SH responses of the core–shell structure. The χAu, (2) signal is much smaller than the case where all the nonlinear susceptibilities are considered (Figs. 2(a) and 2(e)). We have also calculated the SH responses of a resonant solid Si sphere (Figs. 2(d) and 2(h)), where the radius 103 nm corresponds to a magnetic dipole resonance at λ = 800 nm. Compared to the core–shell structure, the solid Si sphere has less than half of the Efar(2ω) response but more than twice the volume. It is noted that the Efar(2ω) (or SH radiation) patterns for these cases are different. This is closely related to the multipolar mode emissions [49].

 figure: Fig. 2

Fig. 2 The SHG near field and far field properties of the core-shell structure and a solid Si sphere at λ = 400 nm. The radius of the solid Si sphere is 103 nm. The SH near fields (Log(|E(2ω)|/|E0|)) for core-shell (a), individual shell (b), core-shell with only χAu, (2) source (c) and solid sphere (d). The SH far field Efar(2ω) for core-shell (e), individual shell (f), core-shell with only χAu, (2) source (g) and solid sphere (h).

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The contributions from different nonlinear coefficients to the SH responses of the core–shell nanostructure are also considered. We calculated the different terms in the nonlinear sources (Eqs. (1) and (2)) independently, and the results are shown in Fig. 3(a). Here the Efar(2ω) patterns on the y-z plane are shown as they cover the maximal Efar(2ω) responses. The χ(2) source dominates the SH responses, which is more than twice larger than the χ(2) signal. The other three sources (χ(2),γ andδ') are more than 10 times weaker than the χ(2) signal. The Si shell has two surfaces that contribute to the χ(2) signal. They are the inner and outer surfaces, which are located at the radii 50 nm and 73 nm of the core–shell structure, respectively. Figure 3(b) shows the Efar(2ω) on the y-z plane by calculating the SH responses with χ(2) on only the inner or outer surface. The χ(2) signal of inner surface is about 3 times stronger than that of outer surface, and dominates the χ(2) response. The case for the individual Si shell is also calculated and the results are shown in Fig. 3(c). Compared to the individual Si shell (Fig. 3(c)), the core–shell structure has a slightly stronger Efar(2ω) of outer surface but has more than 60 times stronger Efar(2ω) of inner surface. The results in Fig. 3 are in consistent with that in Fig. 1, where an important feature is that the electric field around the inner surface of the Si shell is significantly enhanced. Here, it should be pointed out that the SH responses are generated coherently by the different terms in the nonlinear sources (χ(2),χ||||(2), χ(2), γ andδ'). Thus, the total SH response is not equal to the sum of the SH responses calculated independently from the different nonlinear sources. But the separate calculations with the different nonlinear sources reveal important information about their contributions.

 figure: Fig. 3

Fig. 3 (a) The Efar(2ω) distributions on the y-z plane of the core–shell structure, which are calculated based on different nonlinear source terms. The angle 0 corresponds to the + y-axis direction. The results for the χ||||(2), σ, γ have been multiplied by 5, respectively, for clearer demonstration. (b) The Efar(2ω) calculated with only the χ(2) source on the outer (black) and inner surface (red) of the core–shell structure. The results are shown on the same plane as that in (a). (c) The same contents as that in (b) for the individual Si nanoshell. The result of the inner surface has been multiplied by 10 for clearer demonstration.

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We have focused on the fundamental wavelength λ = 800 nm which corresponds to a resonance peak on the extinction spectrum of the core–shell structure. We now turn to the SH responses of the structure at other fundamental wavelengths. Here we assume that the values of the nonlinear coefficients for Si at other wavelengths (in the range from 700 to 900 nm) are the same as that at λ = 800 nm, as these values are not well established yet. The nonlinear coefficients for Au at other wavelengths are also assumed to be the same as that at λ = 800 nm for simplicity. The calculated maximal Efar(2ω) as a function of fundamental wavelength is shown in Fig. 4(a). The SHG signal shows a peak around the fundamental wavelength λ = 800 nm. The result indicates that the resonant field enhancement at the fundamental wavelength λ = 800 nm plays an important role in the SH responses. In fact, the electric field distributions indeed show that the field enhancement (E(ω) / E0) at λ = 800 nm is obviously larger than that at other wavelengths, for example, λ = 700 and 900 nm (Fig. 4(a)). Based on the results in Fig. 4(a), it is reasonable to expect that by varying the shell thickness, the SH response at λ = 800 nm reaches maximal when the outer radius of the Si shell is Rout = 73 nm, which has been confirmed by our calculations (data not shown). This is due to the fact that the core–shell structures with larger or smaller radii are off resonant at λ = 800 nm. Thus, the electric field E(ω) / E0 of Rout = 73 nm is larger than that of Rout of other values.

 figure: Fig. 4

Fig. 4 (a) The maximal Efar(2ω) of the core–shell structure as a function of fundamental wavelength. The size of the structure is the same as above. The insets show the E(ω) / E0 at λ = 700 and 900 nm. The color bar for them is the same. (b) The resonant maximal Efar(2ω) of the core–shell structures with varying inner radius. The resonance for each case is kept at λ = 800 nm. The insets show the E(ω) / E0 of Rin = 45 and 55 nm.

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The effect of the radius of the Au core (or the inner radius of the Si shell, Rin) is also considered. Here, the working wavelength is also fixed at λ = 800 nm. It is found that for each Rin, the thickness of the shell should be around Rout - Rin = 23 nm to match the resonance at λ = 800 nm. Figure 4(b) shows the maximal Efar(2ω) as a function of the inner radius (Rin). A peak value appears at Rin = 50 nm. The maximal Efar(2ω) for the other Rin become smaller but still remain above ~80% (in the range from 40 to 60 nm) of the peak value. The behavior of Efar(2ω) with varying Rin can be explained by considering their surface sizes and the electric field enhancements at fundamental wavelength E(ω)/E0. The E(ω)/E0 (Figs. 4(b) and 1(d)) near the Au–Si interface decreases while the surface size increases with Rin. The combination of these two factors induces the peak SH response at Rin = 50 nm.

The cases of nonconcentric core–shell nanostructures are also considered as shown in Fig. 5. The Au core is moved on the y-axis while the shell is fixed. Figure 5(b) shows the linear optical spectral responses of a nonconcentric structure, where the size of the Au core and Si shell are the same as that in Fig. 1, and the offset distance between the centers of the core and shell is 15 nm. The nonconcentric structure shows a strong resonance peak around λ = 820 nm which is similar to that of the concentric case (Fig. 1(b)). But compared to the concentric case, the ratio of absorption to scattering becomes higher while the total extinction cross section is reduced. This indicates that the proportion of the toroidal dipole mode is increased and the corresponding destructive interference becomes stronger in the nonconcentric case. As a result, the electric field around the Au–Si interface (toroidal dipole mode) is further enhanced while the electric field outside the Si shell (electric dipole mode) is decreased (Figs. 5(c) and 1(d)). Figure 5(d) shows the Efar(2ω) distribution at λ = 410 nm. The Efar(2ω) is improved remarkably in comparison to the concentric nanosphere (Fig. 2(b)). Calculations show that the leading contribution to the SHG is also the χ(2) at the inner surface of the Si shell (data not shown). The SH response is in association with the results at the fundamental wavelength, namely, the further enhancement of the electric field around the Au–Si interface. The SHG of the individual Si shell is similar to the concentric shell (data not shown). The situation with varying the offset distance between the centers of the core and shell is also considered. The maximal Efar(2ω) increases with the offset distance (Fig. 5(e)), where the distance 0 corresponds to the concentric case. This increment behavior is also supported by the calculated E(ω)/E0 results, where the E(ω)/E0 near the Au–Si interface increases with the offset distance. The maximal Efar(2ω) can reach about 10 times (distance 20 nm) as large as that of the concentric case. The further enhancement of SHG with the nonconcentric configuration also applies for other radii of the Au core, where the behaviors are similar to that in Fig. 5 (data not shown).

 figure: Fig. 5

Fig. 5 SHG of nonconcentric core-shell nanostructures. (a) Schematic of a nonconcentric core-shell nanostructure excited by a plane wave. The size of the Au core and Si shell are the same as that in Fig. 1. (b) Absorption, scattering and extinction spectra of the core–shell structure. (c) Electric field enhancement of the core-shell structure on the y-z plane at λ = 820 nm. The distance between the centers of the core and shell is 15 nm. (d) The 3D Efar(2ω) distribution for the core-shell at λ = 410 nm. The distance between the centers of the core and shell is 15 nm. (e) The maximal SH far field as a function of the distance between the centers of the core and shell. The resonance wavelengths for the distances 0, 5, 10, 15 and 20 nm are λ = 400, 400, 405, 410, 410 nm, respectively, which are slightly different.

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3. Conclusion

In conclusion, we investigate Au–Si core–shell nanostructures and find that efficient SHGs can be obtained. In a concentric core–shell structure, an obvious field enhancement appears near the inner surface of the Si shell due to a combined toroidal dipole mode and electric dipole mode. The corresponding SH far field response is about 5 times stronger than that of the individual Si shell, and more than twice stronger than that of a resonant larger solid Si sphere. Different nonlinear sources that contribute to the SHG are considered independently. The contribution from a surface component at the inner surface of the Si shell dominates the SHG signal. This result is in consistent with the electric near field distributions at the fundamental wavelength. The SH response as a function of fundamental wavelength shows a resonance peak, which is similar to the behavior of the extinction spectrum. The case of nonconcentric core–shell structure has also been considered. The SHG is further enhanced in this configuration. The SHG signal can reach about 10 times as strong as that of the concentric case. The SHG may be further improved by more careful design. It is reasonable to expect that the THG could also be modified in this kind of design. Although experimental realization of such Au–Si core-shell structures has not been well established, some physical or chemical methods for similar structures provide constructive guidance [32, 52–54]. Our results reveal that the SHG in dielectric nanostructure can be largely modified in the metal–dielectric hybrid nanostructures, and could find applications in deep subwavelgth nonlinear devices.

Funding

The authors acknowledge financial support from the National Natural Science Foundation of China (Grant no. 11704416) and the Hunan Provincial Natural Science Foundation of China (Grant no. 2017JJ3408).

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34. W.-C. Zhai, T.-Z. Qiao, D.-J. Cai, W.-J. Wang, J.-D. Chen, Z.-H. Chen, and S.-D. Liu, “Anticrossing double Fano resonances generated in metallic/dielectric hybrid nanostructures using nonradiative anapole modes for enhanced nonlinear optical effects,” Opt. Express 24(24), 27858–27869 (2016). [CrossRef]   [PubMed]  

35. I. Staude and J. Schilling, “Metamaterial-inspired silicon nanophotonics,” Nat. Photonics 11(5), 274–284 (2017). [CrossRef]  

36. J. Leuthold, C. Koos, and W. Freude, “Nonlinear silicon photonics,” Nat. Photonics 4(8), 535–544 (2010). [CrossRef]  

37. F. Priolo, T. Gregorkiewicz, M. Galli, and T. F. Krauss, “Silicon nanostructures for photonics and photovoltaics,” Nat. Nanotechnol. 9(1), 19–32 (2014). [CrossRef]   [PubMed]  

38. M. Cazzanelli and J. Schilling, “Second order optical nonlinearity in silicon by symmetry breaking,” Appl. Phys. Rev. 3(1), 011104 (2016). [CrossRef]  

39. E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, 1985).

40. W. Liu, A. E. Miroshnichenko, D. N. Neshev, and Y. S. Kivshar, “Broadband Unidirectional Scattering by Magneto-Electric Core-Shell Nanoparticles,” ACS Nano 6(6), 5489–5497 (2012). [CrossRef]   [PubMed]  

41. Z.-J. Yang, Q.-Q. Wang, and H.-Q. Lin, “Tunable two types of Fano resonances in metal–dielectric core–shell nanoparticle clusters,” Appl. Phys. Lett. 103(11), 111115 (2013). [CrossRef]  

42. N. Papasimakis, V. A. Fedotov, V. Savinov, T. A. Raybould, and N. I. Zheludev, “Electromagnetic toroidal excitations in matter and free space,” Nat. Mater. 15(3), 263–271 (2016). [CrossRef]   [PubMed]  

43. W. Liu, J. Zhang, B. Lei, H. Hu, and A. E. Miroshnichenko, “Invisible nanowires with interfering electric and toroidal dipoles,” Opt. Lett. 40(10), 2293–2296 (2015). [CrossRef]   [PubMed]  

44. T. Feng, Y. Xu, W. Zhang, and A. E. Miroshnichenko, “Ideal Magnetic Dipole Scattering,” Phys. Rev. Lett. 118(17), 173901 (2017). [CrossRef]   [PubMed]  

45. W. Liu, J. Zhang, and A. E. Miroshnichenko, “Toroidal dipole‐induced transparency in core–shell nanoparticles,” Laser Photonics Rev. 9(5), 564–570 (2015). [CrossRef]  

46. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (John Wiley & Sons, 2008).

47. A. García-Etxarri, R. Gómez-Medina, L. S. Froufe-Pérez, C. López, L. Chantada, F. Scheffold, J. Aizpurua, M. Nieto-Vesperinas, and J. J. Sáenz, “Strong magnetic response of submicron silicon particles in the infrared,” Opt. Express 19(6), 4815–4826 (2011). [CrossRef]   [PubMed]  

48. Q. Zhao, Z.-J. Yang, and J. He, “Fano resonances in heterogeneous dimers ofvsilicon and gold nanospheres,” Front. Phys. 13(3), 137801 (2018). [CrossRef]  

49. J. I. Dadap, J. Shan, and T. F. Heinz, “Theory of optical second-harmonic generation from a sphere of centrosymmetric material: small-particle limit,” J. Opt. Soc. Am. B 21(7), 1328–1347 (2004). [CrossRef]  

50. J. Butet, P.-F. Brevet, and O. J. F. Martin, “Optical Second Harmonic Generation in Plasmonic Nanostructures: From Fundamental Principles to Advanced Applications,” ACS Nano 9(11), 10545–10562 (2015). [CrossRef]   [PubMed]  

51. M. Falasconi, L. C. Andreani, A. M. Malvezzi, M. Patrini, V. Mulloni, and L. Pavesi, “Bulk and surface contributions to second-order susceptibility in crystalline and porous silicon by second-harmonic generation,” Surf. Sci. 481(1-3), 105–112 (2001). [CrossRef]  

52. A. Rudenko, K. Ladutenko, S. Makarov, and T. E. Itina, “Photogenerated Free Carrier-Induced Symmetry Breaking in Spherical Silicon Nanoparticle,” Adv. Opt. Mat. 6, 1701153 (2018). [CrossRef]  

53. B. Liu and H. C. Zeng, “Symmetric and asymmetric Ostwald ripening in the fabrication of homogeneous core-shell semiconductors,” Small 1(5), 566–571 (2005). [CrossRef]   [PubMed]  

54. D. A. Zuev, S. V. Makarov, I. S. Mukhin, V. A. Milichko, S. V. Starikov, I. A. Morozov, I. I. Shishkin, A. E. Krasnok, and P. A. Belov, “Fabrication of hybrid nanostructures via nanoscale laser-induced reshaping for advanced light manipulation,” Adv. Mater. 28(16), 3087–3093 (2016). [CrossRef]   [PubMed]  

References

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  43. W. Liu, J. Zhang, B. Lei, H. Hu, and A. E. Miroshnichenko, “Invisible nanowires with interfering electric and toroidal dipoles,” Opt. Lett. 40(10), 2293–2296 (2015).
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  45. W. Liu, J. Zhang, and A. E. Miroshnichenko, “Toroidal dipole‐induced transparency in core–shell nanoparticles,” Laser Photonics Rev. 9(5), 564–570 (2015).
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  47. A. García-Etxarri, R. Gómez-Medina, L. S. Froufe-Pérez, C. López, L. Chantada, F. Scheffold, J. Aizpurua, M. Nieto-Vesperinas, and J. J. Sáenz, “Strong magnetic response of submicron silicon particles in the infrared,” Opt. Express 19(6), 4815–4826 (2011).
    [Crossref] [PubMed]
  48. Q. Zhao, Z.-J. Yang, and J. He, “Fano resonances in heterogeneous dimers ofvsilicon and gold nanospheres,” Front. Phys. 13(3), 137801 (2018).
    [Crossref]
  49. J. I. Dadap, J. Shan, and T. F. Heinz, “Theory of optical second-harmonic generation from a sphere of centrosymmetric material: small-particle limit,” J. Opt. Soc. Am. B 21(7), 1328–1347 (2004).
    [Crossref]
  50. J. Butet, P.-F. Brevet, and O. J. F. Martin, “Optical Second Harmonic Generation in Plasmonic Nanostructures: From Fundamental Principles to Advanced Applications,” ACS Nano 9(11), 10545–10562 (2015).
    [Crossref] [PubMed]
  51. M. Falasconi, L. C. Andreani, A. M. Malvezzi, M. Patrini, V. Mulloni, and L. Pavesi, “Bulk and surface contributions to second-order susceptibility in crystalline and porous silicon by second-harmonic generation,” Surf. Sci. 481(1-3), 105–112 (2001).
    [Crossref]
  52. A. Rudenko, K. Ladutenko, S. Makarov, and T. E. Itina, “Photogenerated Free Carrier-Induced Symmetry Breaking in Spherical Silicon Nanoparticle,” Adv. Opt. Mat. 6, 1701153 (2018).
    [Crossref]
  53. B. Liu and H. C. Zeng, “Symmetric and asymmetric Ostwald ripening in the fabrication of homogeneous core-shell semiconductors,” Small 1(5), 566–571 (2005).
    [Crossref] [PubMed]
  54. D. A. Zuev, S. V. Makarov, I. S. Mukhin, V. A. Milichko, S. V. Starikov, I. A. Morozov, I. I. Shishkin, A. E. Krasnok, and P. A. Belov, “Fabrication of hybrid nanostructures via nanoscale laser-induced reshaping for advanced light manipulation,” Adv. Mater. 28(16), 3087–3093 (2016).
    [Crossref] [PubMed]

2018 (2)

Q. Zhao, Z.-J. Yang, and J. He, “Fano resonances in heterogeneous dimers ofvsilicon and gold nanospheres,” Front. Phys. 13(3), 137801 (2018).
[Crossref]

A. Rudenko, K. Ladutenko, S. Makarov, and T. E. Itina, “Photogenerated Free Carrier-Induced Symmetry Breaking in Spherical Silicon Nanoparticle,” Adv. Opt. Mat. 6, 1701153 (2018).
[Crossref]

2017 (9)

T. Feng, Y. Xu, W. Zhang, and A. E. Miroshnichenko, “Ideal Magnetic Dipole Scattering,” Phys. Rev. Lett. 118(17), 173901 (2017).
[Crossref] [PubMed]

Z.-J. Yang, R. Jiang, X. Zhuo, Y.-M. Xie, J. Wang, and H.-Q. Lin, “Dielectric nanoresonators for light manipulation,” Phys. Rep. 701, 1–50 (2017).
[Crossref]

M. Khorasaninejad and F. Capasso, “Metalenses: Versatile multifunctional photonic components,” Science 358(6367), 8100 (2017).
[Crossref] [PubMed]

S. Sun, Z. Zhou, C. Zhang, Y. Gao, Z. Duan, S. Xiao, and Q. Song, “All-Dielectric Full-Color Printing with TiO2Metasurfaces,” ACS Nano 11(5), 4445–4452 (2017).
[Crossref] [PubMed]

X. Zhu, W. Yan, U. Levy, N. A. Mortensen, and A. Kristensen, “Resonant laser printing of structural colors on high-index dielectric metasurfaces,” Sci. Adv. 3(5), e1602487 (2017).
[Crossref] [PubMed]

Z.-J. Yang, Q. Zhao, and J. He, “Boosting magnetic field enhancement with radiative couplings of magnetic modes in dielectric nanostructures,” Opt. Express 25(14), 15927–15937 (2017).
[Crossref] [PubMed]

S. V. Makarov, M. I. Petrov, U. Zywietz, V. Milichko, D. Zuev, N. Lopanitsyna, A. Kuksin, I. Mukhin, G. Zograf, E. Ubyivovk, D. A. Smirnova, S. Starikov, B. N. Chichkov, and Y. S. Kivshar, “Efficient Second-Harmonic Generation in Nanocrystalline Silicon Nanoparticles,” Nano Lett. 17(5), 3047–3053 (2017).
[Crossref] [PubMed]

T. Shibanuma, G. Grinblat, P. Albella, and S. A. Maier, “Efficient Third Harmonic Generation from Metal-Dielectric Hybrid Nanoantennas,” Nano Lett. 17(4), 2647–2651 (2017).
[Crossref] [PubMed]

I. Staude and J. Schilling, “Metamaterial-inspired silicon nanophotonics,” Nat. Photonics 11(5), 274–284 (2017).
[Crossref]

2016 (16)

W.-C. Zhai, T.-Z. Qiao, D.-J. Cai, W.-J. Wang, J.-D. Chen, Z.-H. Chen, and S.-D. Liu, “Anticrossing double Fano resonances generated in metallic/dielectric hybrid nanostructures using nonradiative anapole modes for enhanced nonlinear optical effects,” Opt. Express 24(24), 27858–27869 (2016).
[Crossref] [PubMed]

R. Guo, E. Rusak, I. Staude, J. Dominguez, M. Decker, C. Rockstuhl, I. Brener, D. N. Neshev, and Y. S. Kivshar, “Multipolar Coupling in Hybrid Metal–Dielectric Metasurfaces,” ACS Photonics 3(3), 349–353 (2016).
[Crossref]

M. Hentschel, B. Metzger, B. Knabe, K. Buse, and H. Giessen, “Linear and nonlinear optical properties of hybrid metallic-dielectric plasmonic nanoantennas,” Beilstein J. Nanotechnol. 7, 111–120 (2016).
[Crossref] [PubMed]

P. R. Wiecha, A. Arbouet, C. Girard, T. Baron, and V. Paillard, “Origin of second-harmonic generation from individual silicon nanowires,” Phys. Rev. B 93(12), 125421 (2016).
[Crossref]

S. Liu, M. B. Sinclair, S. Saravi, G. A. Keeler, Y. Yang, J. Reno, G. M. Peake, F. Setzpfandt, I. Staude, T. Pertsch, and I. Brener, “Resonantly Enhanced Second-Harmonic Generation Using III-V Semiconductor All-Dielectric Metasurfaces,” Nano Lett. 16(9), 5426–5432 (2016).
[Crossref] [PubMed]

A. I. Kuznetsov, A. E. Miroshnichenko, M. L. Brongersma, Y. S. Kivshar, and B. Luk’yanchuk, “Optically resonant dielectric nanostructures,” Science 354(6314), 2472 (2016).
[Crossref] [PubMed]

C. Ma, J. Yan, P. Liu, Y. Wei, and G. Yang, “Second harmonic generation from an individual all-dielectric nanoparticle: resonance enhancement versus particle geometry,” J. Mater. Chem. C Mater. Opt. Electron. Devices 4(25), 6063–6069 (2016).
[Crossref]

D. Smirnova and Y. S. Kivshar, “Multipolar nonlinear nanophotonics,” Optica 3(11), 1241–1255 (2016).
[Crossref]

A. S. Shorokhov, E. V. Melik-Gaykazyan, D. A. Smirnova, B. Hopkins, K. E. Chong, D.-Y. Choi, M. R. Shcherbakov, A. E. Miroshnichenko, D. N. Neshev, A. A. Fedyanin, and Y. S. Kivshar, “Multifold Enhancement of Third-Harmonic Generation in Dielectric Nanoparticles Driven by Magnetic Fano Resonances,” Nano Lett. 16(8), 4857–4861 (2016).
[Crossref] [PubMed]

X. Zambrana-Puyalto and N. Bonod, “Tailoring the chirality of light emission with spherical Si-based antennas,” Nanoscale 8(19), 10441–10452 (2016).
[Crossref] [PubMed]

M. Decker and I. Staude, “Resonant dielectric nanostructures: a low-loss platform for functional nanophotonics,” J. Opt. 18(10), 103001 (2016).
[Crossref]

S. Jahani and Z. Jacob, “All-dielectric metamaterials,” Nat. Nanotechnol. 11(1), 23–36 (2016).
[Crossref] [PubMed]

W. Fan, B. Yan, Z. Wang, and L. Wu, “Three-dimensional all-dielectric metamaterial solid immersion lens for subwavelength imaging at visible frequencies,” Sci. Adv. 2(8), e1600901 (2016).
[Crossref] [PubMed]

N. Papasimakis, V. A. Fedotov, V. Savinov, T. A. Raybould, and N. I. Zheludev, “Electromagnetic toroidal excitations in matter and free space,” Nat. Mater. 15(3), 263–271 (2016).
[Crossref] [PubMed]

M. Cazzanelli and J. Schilling, “Second order optical nonlinearity in silicon by symmetry breaking,” Appl. Phys. Rev. 3(1), 011104 (2016).
[Crossref]

D. A. Zuev, S. V. Makarov, I. S. Mukhin, V. A. Milichko, S. V. Starikov, I. A. Morozov, I. I. Shishkin, A. E. Krasnok, and P. A. Belov, “Fabrication of hybrid nanostructures via nanoscale laser-induced reshaping for advanced light manipulation,” Adv. Mater. 28(16), 3087–3093 (2016).
[Crossref] [PubMed]

2015 (10)

J. Butet, P.-F. Brevet, and O. J. F. Martin, “Optical Second Harmonic Generation in Plasmonic Nanostructures: From Fundamental Principles to Advanced Applications,” ACS Nano 9(11), 10545–10562 (2015).
[Crossref] [PubMed]

W. Liu, J. Zhang, B. Lei, H. Hu, and A. E. Miroshnichenko, “Invisible nanowires with interfering electric and toroidal dipoles,” Opt. Lett. 40(10), 2293–2296 (2015).
[Crossref] [PubMed]

W. Liu, J. Zhang, and A. E. Miroshnichenko, “Toroidal dipole‐induced transparency in core–shell nanoparticles,” Laser Photonics Rev. 9(5), 564–570 (2015).
[Crossref]

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nat. Nanotechnol. 10(11), 937–943 (2015).
[Crossref] [PubMed]

M. Caldarola, P. Albella, E. Cortés, M. Rahmani, T. Roschuk, G. Grinblat, R. F. Oulton, A. V. Bragas, and S. A. Maier, “Non-plasmonic nanoantennas for surface enhanced spectroscopies with ultra-low heat conversion,” Nat. Commun. 6(1), 7915 (2015).
[Crossref] [PubMed]

R. M. Bakker, D. Permyakov, Y. F. Yu, D. Markovich, R. Paniagua-Domínguez, L. Gonzaga, A. Samusev, Y. Kivshar, B. Luk’yanchuk, and A. I. Kuznetsov, “Magnetic and electric hotspots with silicon nanodimers,” Nano Lett. 15(3), 2137–2142 (2015).
[Crossref] [PubMed]

Y. Yang, W. Wang, A. Boulesbaa, I. I. Kravchenko, D. P. Briggs, A. Puretzky, D. Geohegan, and J. Valentine, “Nonlinear Fano-Resonant Dielectric Metasurfaces,” Nano Lett. 15(11), 7388–7393 (2015).
[Crossref] [PubMed]

H. Hu, K. Wang, H. Long, W. Liu, B. Wang, and P. Lu, “Precise determination of the crystallographic orientations in single ZnS nanowires by second-harmonic generation microscopy,” Nano Lett. 15(5), 3351–3357 (2015).
[Crossref] [PubMed]

P. R. Wiecha, A. Arbouet, H. Kallel, P. Periwal, T. Baron, and V. Paillard, “Enhanced nonlinear optical response from individual silicon nanowires,” Phys. Rev. B 91(12), 121416 (2015).
[Crossref]

H. Wang, P. Liu, Y. Ke, Y. Su, L. Zhang, N. Xu, S. Deng, and H. Chen, “Janus Magneto-Electric Nanosphere Dimers Exhibiting Unidirectional Visible Light Scattering And Strong Electromagnetic Field Enhancement,” ACS Nano 9(1), 436–448 (2015).
[Crossref] [PubMed]

2014 (6)

H. Aouani, M. Rahmani, M. Navarro-Cía, and S. A. Maier, “Third-harmonic-upconversion enhancement from a single semiconductor nanoparticle coupled to a plasmonic antenna,” Nat. Nanotechnol. 9(4), 290–294 (2014).
[Crossref] [PubMed]

M. R. Shcherbakov, D. N. Neshev, B. Hopkins, A. S. Shorokhov, I. Staude, E. V. Melik-Gaykazyan, M. Decker, A. A. Ezhov, A. E. Miroshnichenko, I. Brener, A. A. Fedyanin, and Y. S. Kivshar, “Enhanced third-harmonic generation in silicon nanoparticles driven by magnetic response,” Nano Lett. 14(11), 6488–6492 (2014).
[Crossref] [PubMed]

R. Sanatinia, S. Anand, and M. Swillo, “Modal Engineering of Second-Harmonic Generation in Single GaP Nanopillars,” Nano Lett. 14(9), 5376–5381 (2014).
[Crossref] [PubMed]

D. Lin, P. Fan, E. Hasman, and M. L. Brongersma, “Dielectric gradient metasurface optical elements,” Science 345(6194), 298–302 (2014).
[Crossref] [PubMed]

M. L. Brongersma, Y. Cui, and S. Fan, “Light management for photovoltaics using high-index nanostructures,” Nat. Mater. 13(5), 451–460 (2014).
[Crossref] [PubMed]

F. Priolo, T. Gregorkiewicz, M. Galli, and T. F. Krauss, “Silicon nanostructures for photonics and photovoltaics,” Nat. Nanotechnol. 9(1), 19–32 (2014).
[Crossref] [PubMed]

2013 (2)

Z.-J. Yang, Q.-Q. Wang, and H.-Q. Lin, “Tunable two types of Fano resonances in metal–dielectric core–shell nanoparticle clusters,” Appl. Phys. Lett. 103(11), 111115 (2013).
[Crossref]

P. Moitra, Y. Yang, Z. Anderson, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “Realization of an all-dielectric zero-index optical metamaterial,” Nat. Photonics 7(10), 791–795 (2013).
[Crossref]

2012 (1)

W. Liu, A. E. Miroshnichenko, D. N. Neshev, and Y. S. Kivshar, “Broadband Unidirectional Scattering by Magneto-Electric Core-Shell Nanoparticles,” ACS Nano 6(6), 5489–5497 (2012).
[Crossref] [PubMed]

2011 (1)

2010 (1)

J. Leuthold, C. Koos, and W. Freude, “Nonlinear silicon photonics,” Nat. Photonics 4(8), 535–544 (2010).
[Crossref]

2005 (1)

B. Liu and H. C. Zeng, “Symmetric and asymmetric Ostwald ripening in the fabrication of homogeneous core-shell semiconductors,” Small 1(5), 566–571 (2005).
[Crossref] [PubMed]

2004 (1)

2001 (1)

M. Falasconi, L. C. Andreani, A. M. Malvezzi, M. Patrini, V. Mulloni, and L. Pavesi, “Bulk and surface contributions to second-order susceptibility in crystalline and porous silicon by second-harmonic generation,” Surf. Sci. 481(1-3), 105–112 (2001).
[Crossref]

1986 (1)

P. Guyot-Sionnest, W. Chen, and Y. R. Shen, “General considerations on optical second-harmonic generation from surfaces and interfaces,” Phys. Rev. B Condens. Matter 33(12), 8254–8263 (1986).
[Crossref] [PubMed]

Aizpurua, J.

Albella, P.

T. Shibanuma, G. Grinblat, P. Albella, and S. A. Maier, “Efficient Third Harmonic Generation from Metal-Dielectric Hybrid Nanoantennas,” Nano Lett. 17(4), 2647–2651 (2017).
[Crossref] [PubMed]

M. Caldarola, P. Albella, E. Cortés, M. Rahmani, T. Roschuk, G. Grinblat, R. F. Oulton, A. V. Bragas, and S. A. Maier, “Non-plasmonic nanoantennas for surface enhanced spectroscopies with ultra-low heat conversion,” Nat. Commun. 6(1), 7915 (2015).
[Crossref] [PubMed]

Anand, S.

R. Sanatinia, S. Anand, and M. Swillo, “Modal Engineering of Second-Harmonic Generation in Single GaP Nanopillars,” Nano Lett. 14(9), 5376–5381 (2014).
[Crossref] [PubMed]

Anderson, Z.

P. Moitra, Y. Yang, Z. Anderson, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “Realization of an all-dielectric zero-index optical metamaterial,” Nat. Photonics 7(10), 791–795 (2013).
[Crossref]

Andreani, L. C.

M. Falasconi, L. C. Andreani, A. M. Malvezzi, M. Patrini, V. Mulloni, and L. Pavesi, “Bulk and surface contributions to second-order susceptibility in crystalline and porous silicon by second-harmonic generation,” Surf. Sci. 481(1-3), 105–112 (2001).
[Crossref]

Aouani, H.

H. Aouani, M. Rahmani, M. Navarro-Cía, and S. A. Maier, “Third-harmonic-upconversion enhancement from a single semiconductor nanoparticle coupled to a plasmonic antenna,” Nat. Nanotechnol. 9(4), 290–294 (2014).
[Crossref] [PubMed]

Arbabi, A.

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nat. Nanotechnol. 10(11), 937–943 (2015).
[Crossref] [PubMed]

Arbouet, A.

P. R. Wiecha, A. Arbouet, C. Girard, T. Baron, and V. Paillard, “Origin of second-harmonic generation from individual silicon nanowires,” Phys. Rev. B 93(12), 125421 (2016).
[Crossref]

P. R. Wiecha, A. Arbouet, H. Kallel, P. Periwal, T. Baron, and V. Paillard, “Enhanced nonlinear optical response from individual silicon nanowires,” Phys. Rev. B 91(12), 121416 (2015).
[Crossref]

Bagheri, M.

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nat. Nanotechnol. 10(11), 937–943 (2015).
[Crossref] [PubMed]

Bakker, R. M.

R. M. Bakker, D. Permyakov, Y. F. Yu, D. Markovich, R. Paniagua-Domínguez, L. Gonzaga, A. Samusev, Y. Kivshar, B. Luk’yanchuk, and A. I. Kuznetsov, “Magnetic and electric hotspots with silicon nanodimers,” Nano Lett. 15(3), 2137–2142 (2015).
[Crossref] [PubMed]

Baron, T.

P. R. Wiecha, A. Arbouet, C. Girard, T. Baron, and V. Paillard, “Origin of second-harmonic generation from individual silicon nanowires,” Phys. Rev. B 93(12), 125421 (2016).
[Crossref]

P. R. Wiecha, A. Arbouet, H. Kallel, P. Periwal, T. Baron, and V. Paillard, “Enhanced nonlinear optical response from individual silicon nanowires,” Phys. Rev. B 91(12), 121416 (2015).
[Crossref]

Belov, P. A.

D. A. Zuev, S. V. Makarov, I. S. Mukhin, V. A. Milichko, S. V. Starikov, I. A. Morozov, I. I. Shishkin, A. E. Krasnok, and P. A. Belov, “Fabrication of hybrid nanostructures via nanoscale laser-induced reshaping for advanced light manipulation,” Adv. Mater. 28(16), 3087–3093 (2016).
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Bonod, N.

X. Zambrana-Puyalto and N. Bonod, “Tailoring the chirality of light emission with spherical Si-based antennas,” Nanoscale 8(19), 10441–10452 (2016).
[Crossref] [PubMed]

Boulesbaa, A.

Y. Yang, W. Wang, A. Boulesbaa, I. I. Kravchenko, D. P. Briggs, A. Puretzky, D. Geohegan, and J. Valentine, “Nonlinear Fano-Resonant Dielectric Metasurfaces,” Nano Lett. 15(11), 7388–7393 (2015).
[Crossref] [PubMed]

Bragas, A. V.

M. Caldarola, P. Albella, E. Cortés, M. Rahmani, T. Roschuk, G. Grinblat, R. F. Oulton, A. V. Bragas, and S. A. Maier, “Non-plasmonic nanoantennas for surface enhanced spectroscopies with ultra-low heat conversion,” Nat. Commun. 6(1), 7915 (2015).
[Crossref] [PubMed]

Brener, I.

S. Liu, M. B. Sinclair, S. Saravi, G. A. Keeler, Y. Yang, J. Reno, G. M. Peake, F. Setzpfandt, I. Staude, T. Pertsch, and I. Brener, “Resonantly Enhanced Second-Harmonic Generation Using III-V Semiconductor All-Dielectric Metasurfaces,” Nano Lett. 16(9), 5426–5432 (2016).
[Crossref] [PubMed]

R. Guo, E. Rusak, I. Staude, J. Dominguez, M. Decker, C. Rockstuhl, I. Brener, D. N. Neshev, and Y. S. Kivshar, “Multipolar Coupling in Hybrid Metal–Dielectric Metasurfaces,” ACS Photonics 3(3), 349–353 (2016).
[Crossref]

M. R. Shcherbakov, D. N. Neshev, B. Hopkins, A. S. Shorokhov, I. Staude, E. V. Melik-Gaykazyan, M. Decker, A. A. Ezhov, A. E. Miroshnichenko, I. Brener, A. A. Fedyanin, and Y. S. Kivshar, “Enhanced third-harmonic generation in silicon nanoparticles driven by magnetic response,” Nano Lett. 14(11), 6488–6492 (2014).
[Crossref] [PubMed]

Brevet, P.-F.

J. Butet, P.-F. Brevet, and O. J. F. Martin, “Optical Second Harmonic Generation in Plasmonic Nanostructures: From Fundamental Principles to Advanced Applications,” ACS Nano 9(11), 10545–10562 (2015).
[Crossref] [PubMed]

Briggs, D. P.

Y. Yang, W. Wang, A. Boulesbaa, I. I. Kravchenko, D. P. Briggs, A. Puretzky, D. Geohegan, and J. Valentine, “Nonlinear Fano-Resonant Dielectric Metasurfaces,” Nano Lett. 15(11), 7388–7393 (2015).
[Crossref] [PubMed]

P. Moitra, Y. Yang, Z. Anderson, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “Realization of an all-dielectric zero-index optical metamaterial,” Nat. Photonics 7(10), 791–795 (2013).
[Crossref]

Brongersma, M. L.

A. I. Kuznetsov, A. E. Miroshnichenko, M. L. Brongersma, Y. S. Kivshar, and B. Luk’yanchuk, “Optically resonant dielectric nanostructures,” Science 354(6314), 2472 (2016).
[Crossref] [PubMed]

D. Lin, P. Fan, E. Hasman, and M. L. Brongersma, “Dielectric gradient metasurface optical elements,” Science 345(6194), 298–302 (2014).
[Crossref] [PubMed]

M. L. Brongersma, Y. Cui, and S. Fan, “Light management for photovoltaics using high-index nanostructures,” Nat. Mater. 13(5), 451–460 (2014).
[Crossref] [PubMed]

Buse, K.

M. Hentschel, B. Metzger, B. Knabe, K. Buse, and H. Giessen, “Linear and nonlinear optical properties of hybrid metallic-dielectric plasmonic nanoantennas,” Beilstein J. Nanotechnol. 7, 111–120 (2016).
[Crossref] [PubMed]

Butet, J.

J. Butet, P.-F. Brevet, and O. J. F. Martin, “Optical Second Harmonic Generation in Plasmonic Nanostructures: From Fundamental Principles to Advanced Applications,” ACS Nano 9(11), 10545–10562 (2015).
[Crossref] [PubMed]

Cai, D.-J.

Caldarola, M.

M. Caldarola, P. Albella, E. Cortés, M. Rahmani, T. Roschuk, G. Grinblat, R. F. Oulton, A. V. Bragas, and S. A. Maier, “Non-plasmonic nanoantennas for surface enhanced spectroscopies with ultra-low heat conversion,” Nat. Commun. 6(1), 7915 (2015).
[Crossref] [PubMed]

Capasso, F.

M. Khorasaninejad and F. Capasso, “Metalenses: Versatile multifunctional photonic components,” Science 358(6367), 8100 (2017).
[Crossref] [PubMed]

Cazzanelli, M.

M. Cazzanelli and J. Schilling, “Second order optical nonlinearity in silicon by symmetry breaking,” Appl. Phys. Rev. 3(1), 011104 (2016).
[Crossref]

Chantada, L.

Chen, H.

H. Wang, P. Liu, Y. Ke, Y. Su, L. Zhang, N. Xu, S. Deng, and H. Chen, “Janus Magneto-Electric Nanosphere Dimers Exhibiting Unidirectional Visible Light Scattering And Strong Electromagnetic Field Enhancement,” ACS Nano 9(1), 436–448 (2015).
[Crossref] [PubMed]

Chen, J.-D.

Chen, W.

P. Guyot-Sionnest, W. Chen, and Y. R. Shen, “General considerations on optical second-harmonic generation from surfaces and interfaces,” Phys. Rev. B Condens. Matter 33(12), 8254–8263 (1986).
[Crossref] [PubMed]

Chen, Z.-H.

Chichkov, B. N.

S. V. Makarov, M. I. Petrov, U. Zywietz, V. Milichko, D. Zuev, N. Lopanitsyna, A. Kuksin, I. Mukhin, G. Zograf, E. Ubyivovk, D. A. Smirnova, S. Starikov, B. N. Chichkov, and Y. S. Kivshar, “Efficient Second-Harmonic Generation in Nanocrystalline Silicon Nanoparticles,” Nano Lett. 17(5), 3047–3053 (2017).
[Crossref] [PubMed]

Choi, D.-Y.

A. S. Shorokhov, E. V. Melik-Gaykazyan, D. A. Smirnova, B. Hopkins, K. E. Chong, D.-Y. Choi, M. R. Shcherbakov, A. E. Miroshnichenko, D. N. Neshev, A. A. Fedyanin, and Y. S. Kivshar, “Multifold Enhancement of Third-Harmonic Generation in Dielectric Nanoparticles Driven by Magnetic Fano Resonances,” Nano Lett. 16(8), 4857–4861 (2016).
[Crossref] [PubMed]

Chong, K. E.

A. S. Shorokhov, E. V. Melik-Gaykazyan, D. A. Smirnova, B. Hopkins, K. E. Chong, D.-Y. Choi, M. R. Shcherbakov, A. E. Miroshnichenko, D. N. Neshev, A. A. Fedyanin, and Y. S. Kivshar, “Multifold Enhancement of Third-Harmonic Generation in Dielectric Nanoparticles Driven by Magnetic Fano Resonances,” Nano Lett. 16(8), 4857–4861 (2016).
[Crossref] [PubMed]

Cortés, E.

M. Caldarola, P. Albella, E. Cortés, M. Rahmani, T. Roschuk, G. Grinblat, R. F. Oulton, A. V. Bragas, and S. A. Maier, “Non-plasmonic nanoantennas for surface enhanced spectroscopies with ultra-low heat conversion,” Nat. Commun. 6(1), 7915 (2015).
[Crossref] [PubMed]

Cui, Y.

M. L. Brongersma, Y. Cui, and S. Fan, “Light management for photovoltaics using high-index nanostructures,” Nat. Mater. 13(5), 451–460 (2014).
[Crossref] [PubMed]

Dadap, J. I.

Decker, M.

R. Guo, E. Rusak, I. Staude, J. Dominguez, M. Decker, C. Rockstuhl, I. Brener, D. N. Neshev, and Y. S. Kivshar, “Multipolar Coupling in Hybrid Metal–Dielectric Metasurfaces,” ACS Photonics 3(3), 349–353 (2016).
[Crossref]

M. Decker and I. Staude, “Resonant dielectric nanostructures: a low-loss platform for functional nanophotonics,” J. Opt. 18(10), 103001 (2016).
[Crossref]

M. R. Shcherbakov, D. N. Neshev, B. Hopkins, A. S. Shorokhov, I. Staude, E. V. Melik-Gaykazyan, M. Decker, A. A. Ezhov, A. E. Miroshnichenko, I. Brener, A. A. Fedyanin, and Y. S. Kivshar, “Enhanced third-harmonic generation in silicon nanoparticles driven by magnetic response,” Nano Lett. 14(11), 6488–6492 (2014).
[Crossref] [PubMed]

Deng, S.

H. Wang, P. Liu, Y. Ke, Y. Su, L. Zhang, N. Xu, S. Deng, and H. Chen, “Janus Magneto-Electric Nanosphere Dimers Exhibiting Unidirectional Visible Light Scattering And Strong Electromagnetic Field Enhancement,” ACS Nano 9(1), 436–448 (2015).
[Crossref] [PubMed]

Dominguez, J.

R. Guo, E. Rusak, I. Staude, J. Dominguez, M. Decker, C. Rockstuhl, I. Brener, D. N. Neshev, and Y. S. Kivshar, “Multipolar Coupling in Hybrid Metal–Dielectric Metasurfaces,” ACS Photonics 3(3), 349–353 (2016).
[Crossref]

Duan, Z.

S. Sun, Z. Zhou, C. Zhang, Y. Gao, Z. Duan, S. Xiao, and Q. Song, “All-Dielectric Full-Color Printing with TiO2Metasurfaces,” ACS Nano 11(5), 4445–4452 (2017).
[Crossref] [PubMed]

Ezhov, A. A.

M. R. Shcherbakov, D. N. Neshev, B. Hopkins, A. S. Shorokhov, I. Staude, E. V. Melik-Gaykazyan, M. Decker, A. A. Ezhov, A. E. Miroshnichenko, I. Brener, A. A. Fedyanin, and Y. S. Kivshar, “Enhanced third-harmonic generation in silicon nanoparticles driven by magnetic response,” Nano Lett. 14(11), 6488–6492 (2014).
[Crossref] [PubMed]

Falasconi, M.

M. Falasconi, L. C. Andreani, A. M. Malvezzi, M. Patrini, V. Mulloni, and L. Pavesi, “Bulk and surface contributions to second-order susceptibility in crystalline and porous silicon by second-harmonic generation,” Surf. Sci. 481(1-3), 105–112 (2001).
[Crossref]

Fan, P.

D. Lin, P. Fan, E. Hasman, and M. L. Brongersma, “Dielectric gradient metasurface optical elements,” Science 345(6194), 298–302 (2014).
[Crossref] [PubMed]

Fan, S.

M. L. Brongersma, Y. Cui, and S. Fan, “Light management for photovoltaics using high-index nanostructures,” Nat. Mater. 13(5), 451–460 (2014).
[Crossref] [PubMed]

Fan, W.

W. Fan, B. Yan, Z. Wang, and L. Wu, “Three-dimensional all-dielectric metamaterial solid immersion lens for subwavelength imaging at visible frequencies,” Sci. Adv. 2(8), e1600901 (2016).
[Crossref] [PubMed]

Faraon, A.

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nat. Nanotechnol. 10(11), 937–943 (2015).
[Crossref] [PubMed]

Fedotov, V. A.

N. Papasimakis, V. A. Fedotov, V. Savinov, T. A. Raybould, and N. I. Zheludev, “Electromagnetic toroidal excitations in matter and free space,” Nat. Mater. 15(3), 263–271 (2016).
[Crossref] [PubMed]

Fedyanin, A. A.

A. S. Shorokhov, E. V. Melik-Gaykazyan, D. A. Smirnova, B. Hopkins, K. E. Chong, D.-Y. Choi, M. R. Shcherbakov, A. E. Miroshnichenko, D. N. Neshev, A. A. Fedyanin, and Y. S. Kivshar, “Multifold Enhancement of Third-Harmonic Generation in Dielectric Nanoparticles Driven by Magnetic Fano Resonances,” Nano Lett. 16(8), 4857–4861 (2016).
[Crossref] [PubMed]

M. R. Shcherbakov, D. N. Neshev, B. Hopkins, A. S. Shorokhov, I. Staude, E. V. Melik-Gaykazyan, M. Decker, A. A. Ezhov, A. E. Miroshnichenko, I. Brener, A. A. Fedyanin, and Y. S. Kivshar, “Enhanced third-harmonic generation in silicon nanoparticles driven by magnetic response,” Nano Lett. 14(11), 6488–6492 (2014).
[Crossref] [PubMed]

Feng, T.

T. Feng, Y. Xu, W. Zhang, and A. E. Miroshnichenko, “Ideal Magnetic Dipole Scattering,” Phys. Rev. Lett. 118(17), 173901 (2017).
[Crossref] [PubMed]

Freude, W.

J. Leuthold, C. Koos, and W. Freude, “Nonlinear silicon photonics,” Nat. Photonics 4(8), 535–544 (2010).
[Crossref]

Froufe-Pérez, L. S.

Galli, M.

F. Priolo, T. Gregorkiewicz, M. Galli, and T. F. Krauss, “Silicon nanostructures for photonics and photovoltaics,” Nat. Nanotechnol. 9(1), 19–32 (2014).
[Crossref] [PubMed]

Gao, Y.

S. Sun, Z. Zhou, C. Zhang, Y. Gao, Z. Duan, S. Xiao, and Q. Song, “All-Dielectric Full-Color Printing with TiO2Metasurfaces,” ACS Nano 11(5), 4445–4452 (2017).
[Crossref] [PubMed]

García-Etxarri, A.

Geohegan, D.

Y. Yang, W. Wang, A. Boulesbaa, I. I. Kravchenko, D. P. Briggs, A. Puretzky, D. Geohegan, and J. Valentine, “Nonlinear Fano-Resonant Dielectric Metasurfaces,” Nano Lett. 15(11), 7388–7393 (2015).
[Crossref] [PubMed]

Giessen, H.

M. Hentschel, B. Metzger, B. Knabe, K. Buse, and H. Giessen, “Linear and nonlinear optical properties of hybrid metallic-dielectric plasmonic nanoantennas,” Beilstein J. Nanotechnol. 7, 111–120 (2016).
[Crossref] [PubMed]

Girard, C.

P. R. Wiecha, A. Arbouet, C. Girard, T. Baron, and V. Paillard, “Origin of second-harmonic generation from individual silicon nanowires,” Phys. Rev. B 93(12), 125421 (2016).
[Crossref]

Gómez-Medina, R.

Gonzaga, L.

R. M. Bakker, D. Permyakov, Y. F. Yu, D. Markovich, R. Paniagua-Domínguez, L. Gonzaga, A. Samusev, Y. Kivshar, B. Luk’yanchuk, and A. I. Kuznetsov, “Magnetic and electric hotspots with silicon nanodimers,” Nano Lett. 15(3), 2137–2142 (2015).
[Crossref] [PubMed]

Gregorkiewicz, T.

F. Priolo, T. Gregorkiewicz, M. Galli, and T. F. Krauss, “Silicon nanostructures for photonics and photovoltaics,” Nat. Nanotechnol. 9(1), 19–32 (2014).
[Crossref] [PubMed]

Grinblat, G.

T. Shibanuma, G. Grinblat, P. Albella, and S. A. Maier, “Efficient Third Harmonic Generation from Metal-Dielectric Hybrid Nanoantennas,” Nano Lett. 17(4), 2647–2651 (2017).
[Crossref] [PubMed]

M. Caldarola, P. Albella, E. Cortés, M. Rahmani, T. Roschuk, G. Grinblat, R. F. Oulton, A. V. Bragas, and S. A. Maier, “Non-plasmonic nanoantennas for surface enhanced spectroscopies with ultra-low heat conversion,” Nat. Commun. 6(1), 7915 (2015).
[Crossref] [PubMed]

Guo, R.

R. Guo, E. Rusak, I. Staude, J. Dominguez, M. Decker, C. Rockstuhl, I. Brener, D. N. Neshev, and Y. S. Kivshar, “Multipolar Coupling in Hybrid Metal–Dielectric Metasurfaces,” ACS Photonics 3(3), 349–353 (2016).
[Crossref]

Guyot-Sionnest, P.

P. Guyot-Sionnest, W. Chen, and Y. R. Shen, “General considerations on optical second-harmonic generation from surfaces and interfaces,” Phys. Rev. B Condens. Matter 33(12), 8254–8263 (1986).
[Crossref] [PubMed]

Hasman, E.

D. Lin, P. Fan, E. Hasman, and M. L. Brongersma, “Dielectric gradient metasurface optical elements,” Science 345(6194), 298–302 (2014).
[Crossref] [PubMed]

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Zhai, W.-C.

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S. Sun, Z. Zhou, C. Zhang, Y. Gao, Z. Duan, S. Xiao, and Q. Song, “All-Dielectric Full-Color Printing with TiO2Metasurfaces,” ACS Nano 11(5), 4445–4452 (2017).
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Zhu, X.

X. Zhu, W. Yan, U. Levy, N. A. Mortensen, and A. Kristensen, “Resonant laser printing of structural colors on high-index dielectric metasurfaces,” Sci. Adv. 3(5), e1602487 (2017).
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Zhuo, X.

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ACS Nano (4)

H. Wang, P. Liu, Y. Ke, Y. Su, L. Zhang, N. Xu, S. Deng, and H. Chen, “Janus Magneto-Electric Nanosphere Dimers Exhibiting Unidirectional Visible Light Scattering And Strong Electromagnetic Field Enhancement,” ACS Nano 9(1), 436–448 (2015).
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Front. Phys. (1)

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Nanoscale (1)

X. Zambrana-Puyalto and N. Bonod, “Tailoring the chirality of light emission with spherical Si-based antennas,” Nanoscale 8(19), 10441–10452 (2016).
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Nat. Commun. (1)

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Figures (5)

Fig. 1
Fig. 1 Linear optical responses. (a) Schematic of a core–shell nanostructure. The origin of the coordinate system is located at the center of the structure. (b) Extinction spectra of a core–shell structure, an Au sphere and an individual Si shell. The radius of the Au core is 50 nm. The outer radius of the Si shell is 73 nm. (c) Absorption and scattering spectra of the core–shell structure. The absorption of the individual Si shell and Au core are also shown (dashed lines). (d) Electric field enhancement of the core–shell structure on the y-z plane at λ = 800 nm. (e) Magnetic field enhancement of the core–shell structure on the x-z plane at λ = 800 nm. (f) Electric field enhancement of the individual Si nanoshell on the y-z plane at λ = 800 nm.
Fig. 2
Fig. 2 The SHG near field and far field properties of the core-shell structure and a solid Si sphere at λ = 400 nm. The radius of the solid Si sphere is 103 nm. The SH near fields (Log(|E(2ω)|/|E0|)) for core-shell (a), individual shell (b), core-shell with only χ Au ,   ( 2 ) source (c) and solid sphere (d). The SH far field Efar(2ω) for core-shell (e), individual shell (f), core-shell with only χ Au ,   ( 2 ) source (g) and solid sphere (h).
Fig. 3
Fig. 3 (a) The Efar(2ω) distributions on the y-z plane of the core–shell structure, which are calculated based on different nonlinear source terms. The angle 0 corresponds to the + y-axis direction. The results for the χ | | | | ( 2 ) , σ, γ have been multiplied by 5, respectively, for clearer demonstration. (b) The Efar(2ω) calculated with only the χ ( 2 ) source on the outer (black) and inner surface (red) of the core–shell structure. The results are shown on the same plane as that in (a). (c) The same contents as that in (b) for the individual Si nanoshell. The result of the inner surface has been multiplied by 10 for clearer demonstration.
Fig. 4
Fig. 4 (a) The maximal Efar(2ω) of the core–shell structure as a function of fundamental wavelength. The size of the structure is the same as above. The insets show the E(ω) / E0 at λ = 700 and 900 nm. The color bar for them is the same. (b) The resonant maximal Efar(2ω) of the core–shell structures with varying inner radius. The resonance for each case is kept at λ = 800 nm. The insets show the E(ω) / E0 of Rin = 45 and 55 nm.
Fig. 5
Fig. 5 SHG of nonconcentric core-shell nanostructures. (a) Schematic of a nonconcentric core-shell nanostructure excited by a plane wave. The size of the Au core and Si shell are the same as that in Fig. 1. (b) Absorption, scattering and extinction spectra of the core–shell structure. (c) Electric field enhancement of the core-shell structure on the y-z plane at λ = 820 nm. The distance between the centers of the core and shell is 15 nm. (d) The 3D Efar(2ω) distribution for the core-shell at λ = 410 nm. The distance between the centers of the core and shell is 15 nm. (e) The maximal SH far field as a function of the distance between the centers of the core and shell. The resonance wavelengths for the distances 0, 5, 10, 15 and 20 nm are λ = 400, 400, 405, 410, 410 nm, respectively, which are slightly different.

Equations (4)

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P s u r f ( 2 ω ) = P surf ( 2 ω ) + P bulk ( 2 ω ) ,
P surf ( 2 ω ) = ε 0 χ s ( 2 ) : E ( ω ) ( r ) E ( ω ) ( r ) δ ( r r s ) ,
P bulk ( 2 ω ) = ε 0 [ β E ( ω ) ( E ( ω ) ) + γ ( E ( ω ) E ( ω ) ) + δ ( E ( ω ) ) E ( ω ) ] ,
P surf ( 2 ω ) = ε 0 δ ( r r s ) [ χ ( 2 ) ( E r ( ω ) ) 2 r ^ + χ | | | | ( 2 ) ( E θ ( ω ) ) 2 r ^ + χ | | | | ( 2 ) ( E φ ( ω ) ) 2 r ^ + 2 χ | | | | ( 2 ) E r ( ω ) E θ ( ω ) + θ ^ + 2 χ | | | | ( 2 ) E r ( ω ) E φ ( ω ) φ ^ ] ,

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