Apex-enhanced second-harmonic generation by using double-hole arrays in a gold film

The enhancement of second harmonic generation (SHG) from arrays of subwavelength double holes in a gold film is studied. Each overlapping double hole, which is created in a straightforward manner by approaching two individual holes, has apexes that are responsible for nanoscale focusing of the electric field. A 14 times enhancement of SHG is measured when compared to the circular hole shape. The angular dependence of the SHG is explained by momentum matching and by symmetry breaking required for SHG. By varying the periodicity of the arrays, the Bragg resonances are tuned and modify the SHG signal. The SHG is shown to be enhanced by a resonance at the second harmonic wavelength. The local enhancement of the electric field presented in this work shows that the double-hole structure is a good candidate for applications such as surface-enhanced Raman spectroscopy and nonlinear optics.

Figure 1

Scanning electron microscope image for a double-hole array with a spacing of $d=195\mathrm{nm}$ and a periodicity $l=750\mathrm{nm}$. $x$ and $y$ polarizations are shown with arrows.

Figure 2

Linear transmission spectra for different hole spacings, $d$, (0, 195, and $250\mathrm{nm}$). The measurements are normalized to the spectrum of the incident beam.

Figure 3

FDTD calculation of natural logarithm of electric field from double-hole structure with apexes for a $750\mathrm{nm}$ periodicity with an incident beam polarized along (a) the $y$ direction and (b) the $x$ direction. The colormap is the same for both figures.

Figure 4

Angle-dependent SHG measurements as a function of center-to-center hole spacing. $d=0\mathrm{nm}$ corresponds to a circular shape while the $d=250\mathrm{nm}$ consists in two holes separated by a gap of $50\mathrm{nm}$. The array periodicity was $750\mathrm{nm}$.

Figure 5

Linear transmission spectra for different periodicities, $l$, (430, 490, 580, and $750\mathrm{nm}$).

Figure 6

Periodicity dependence of SHG for a 10° angle of incidence.

Figure 7

Angle-dependent SHG measurements for two arrays: $l=430\mathrm{nm}$ and $l=750\mathrm{nm}$.

Figure 8

Linear transmission measurements for $l=430\mathrm{nm}$ with two angles of incidence: 0° and 15°. The measurements are normalized by the incident beam.