Second harmonic generation from plasmonic nanoantennas is investigated numerically using a surface integral formulation for the calculation of both the fundamental and the second harmonic electric field. The comparison between a realistic and an idealized gold nanoantenna shows that second harmonic generation is extremely sensitive to asymmetry in the nanostructure shape even in cases where the linear response is barely modified. Interestingly, minute geometry asymmetry and surface roughness are clearly revealed by far-field analysis, demonstrating that second harmonic generation is a promising tool for the sensitive optical characterization of plasmonic nanostructures. Furthermore, defects located where the linear field is strong (e.g., in the antenna gap) do not necessarily have the strongest impact on the second harmonic signal. KEYWORDS: Plasmonics, nonlinear optics, surface integral formulation, realistic nanostructures Furthermore, the coupling between several substructures is a convenient way to control SPR properties.2,3 In particular, bringing two nanostructures in close proximity results in an enhancement by several orders of magnitude of the electric field in the hot spot. This geometry is called a nanoantenna, or an optical antenna, since it represents the optical analogous of microwave and radiowave antennas.4−6 The electromagnetic properties of nanoantennas can be tuned by modifying their geometric parameters (length, shape, and gap dimension) and tailored for specific applications.7 For instance, optical antennas have been designed for studying quantum systems at the single emitter level, Optical antennas are also promising for the observation of nonlinear optical effects that require a high electric field such as that observed in the hot spots.19 Several studies have reported the observation of multiphoton excited luminescence, 20−22 second harmonic generation (SHG), 23,24 third harmonic generation, 25,26 high harmonic generation, 27 and four-wave mixing, 28 as well as ultrafast spectroscopy. 29,30 Recently, a new approach has been proposed to enhance nonlinear conversion in nanoantennas, using structures that are resonant at the several wavelengths involved in the frequency conversion.
31−33Among the different nonlinear parametric optical processes, SHG is the simplest one and has the advantage of being sensitive to the symmetry of the plasmonic nanostructures as well as their spatial arrangement. 34−40 Contrary to the other nonlinear optical processes, it was observed that SHG can be significantly suppressed in centrosymmetric gaps, although the fundamental electric field is strongly enhanced. 41 On the other hand, efficient SHG is observed in asymmetric gaps, such as the one formed in noncentrosymmetric T-shaped gold dimers.42 A clear insight into the impact of the nanoantenna shape on their SHG properties, particularly in the far-field, is therefore required to guide further the development of SHG from nanoantennas for practical applications like nonlinear plasmonics sensing.
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