We measure third-harmonic generation (THG) from arrays of sub-wavelength metal apertures in transmission using fundamental input at 800 nm. Samples with different aperture spacings, sizes, and shapes are used. Strong angular dependence of THG is observed, with maxima located at incidence angles corresponding to extraordinary optical transmission (EOT) for the fundamental. We demonstrate an anomalous scaling of TH intensity with aperture size, where at different EOT peaks, the TH may either increase or decrease with aperture size. The aperture shape is also shown to have a strong effect on TH output.
©2009 Optical Society of America
Extraordinary optical transmission (EOT) through metal films modulated with a 2-D array of sub-wavelength apertures  was reported in 1998. It is now well established that upon the condition of EOT, intensity buildup within the apertures can occur [2, 3], motivating the study of nonlinear processes. Indeed, resonant enhancement of second-harmonic generation (SHG) by a factor of 104 has been demonstrated for a single sub-wavelength aperture surrounded by periodic annular corrugation . SHG has also been studied in arrays of sub-wavelength apertures of various shapes, using disordered [5, 6, 7] and periodic [6, 8, 10, 11] arrangements. The effect of the symmetry of the aperture has been shown , in that, at normal incidence, apertures with inversion symmetry produce much weaker SH than non-centrosymmetric apertures, while at off-normal incidence, SH can be produced with centrosymmetric apertures [6, 11, 7].
So far, nonlinear optical studies have been directed towards χ (2) effects, although multi-photon luminescence has been observed . Closely related are nonlinear optical studies using bow-tie antennae, where strong field enhancement is obtained within the feedgap . Recently, high-harmonic generation was demonstrated utilizing the strong field enhancement within the gaps of bow-tie antennae . Our focus is on third-harmonic generation (THG) in transmission from sub-wavelengthmetallic apertures arrayed in gold films, where the effects of aperture spacing, size, and shape on conversion are demonstrated.
2. Experimental methods
Arrangements of sub-wavelength apertures were produced in 100 nm thick gold films using electron beam lithography (EBL). Briefly, a 5 nm chromium or TiO2 adhesion layer was sputter deposited onto the quartz substrate, followed by 100 nm of gold and 20 nm of chromium. ZEP520A e-beam resist of about 300 nm thickness was spin coated. Following e-beam exposure, the upper chromium layer was dry etched with chlorine, and the e-beam resist removed. The chromium layer served as a hard mask for argon ion milling of the gold. A wet etch removed the upper chromium layer (and likely resulted in some undercut in the underlying chromium adhesion layer). For samples with TiO2 as the adhesion layer, we used reactive sputtering to produce the ~5 nm TiO2 layer by introducing O2 during the sputtering process; pure O2 was flowed through the chamber to fully oxidize the thin film before the chamber was pumped down to sputter the gold film.
The experimental setup is similar to that used previously , as shown in Fig. 1. A Ti:Sapphire laser is used at 800 nm wavelength and ~30 fs pulse duration. The setup allows the rotation of the sample with respect to the incident fundamental beam as well as rotation of the detector around the sample so that the radiation pattern can be measured in transmission. The detector is a blue-sensitized PMT (H5784-03) and two spectral filters are used to block the transmitted fundamental at 800 nm and minimize the influence of broadband background luminescence . The angular acceptance of light collection is roughly 1° through a slit of about 2 mm width. Lock-in detection is performed by modulating the 86 MHz pulse train at 2 kHz, and average incident power is 75 mW(measured after the chopper), except where noted.
One significant difference between SHG and THG is that THG does not have the symmetry limitations of SHG. This is observed in Fig. 2 which plots the fundamental transmission, second-harmonic (SH) output, and third-harmonic (TH) output versus incidence angle for a sample with Cr adhesion layer, and 885 nm spacing of round holes. Because of centro-symmetry of the sample at normal incidence, there can be no SH output [6, 7]. However, the χ (3) response always exists. As shown in Fig. 2, the TH output peaks with maxima in fundamental transmission, indicating that the greatest intensity enhancement within the aperture occurs near the transmission maxima, as expected.
Power scaling of the SH and TH signals are also shown in Fig. 2. The measured data points are plotted on a log-log scale and fit to a linear equation with slopes of 2.0 and 2.8, respectively, for SH and TH. From the measurements, it is clear that the samples can withstand average incident power levels where the TH signal is about the same as the maximum SH (under strong symmetry-breaking conditions), not correcting for differences in collection efficiency and PMT responsivity (taking these factors into account, SH is detected with about 4x greater efficiency than TH). Whether this holds for even higher harmonics is not known yet.
Double-angle scans for SHG and THG using the sample with Cr adhesion layer are shown in Fig. 3, where both the incidence and detection angles are varied. Again, the difference between the SHG and THG mechanisms is observed in that there is minimal SH under conditions of inversion symmetry (normal incidence and normal detection), other than a small two-photon luminescence background. The peaks in the detection scan correspond to coherent emissions from the apertures that satisfy the following momentum matching condition :
where n is the harmonic order, K is a reciprocal lattice vector with |K|=2π/Λ, Λ is the aperture spacing, m is the diffraction order, and k t represents a transverse light wave-vector. For a square lattice, and assuming that the optical wavevectors have only the x̂ transverse component (since the scans are performed along only one axis), Eq. (1) can be written
where γ is the detection angle and θ is the incidence angle. Therefore, the angular spacing between peaks in the TH measurements are narrower due to the shorter wavelength of emission (n=3). At detection angles that lie in-between these peaks, luminescence background can be observed. Since two- and three-photon luminescence are incoherent emissions, they produce broad angular spectra, which is clearly evident. Evidence that the luminescence emits from the apertures is given by the fact that the luminescence is strongest at the same incidence angles that the SH and TH peaks occur.
A practical issue not always addressed for plasmonic structures is the adhesion layer. Often-times, a thin layer of Cr is used to promote the adhesion of Au to a glass substrate. However, Cr is a highly lossy material, and can cause significant attenuation of SPP propagation at the metal/substrate interface [14, 15]. We performed subsequent TH measurements on samples with TiO2 adhesion layers, except where noted.
3.1. Effects of aperture spacing
Keeping the aperture size fixed at 250 nm, we investigated the effects of varying the spacing. The results are shown in Fig. 4 for both the transmission of the fundamental beam and emission at the TH wavelength. In these measurements, the sample was rotated with respect to the incident beam (varying θ) and detection was performed at the zeroth order transmission (γ=-θ).
Two effects of changing the aperture spacing are readily observable. First, there is a shift to higher incidence angles at which the transmission/TH output peak. Second, there is a clear increase in TH output for spacings of 885 nm and longer; note that this is repeatable across multiple measurements of these patterns. Even though the fundamental transmission peaks also increase with aperture spacing, the effect is not as dramatic.
3.2. Effects of aperture size
Keeping the aperture spacing fixed at about 885 nm, we investigated the effects of varying the aperture size. The results are shown in Fig. 5. Again, there are two effects which are immediately noticed. The first is that the transmission of the fundamental increases with increasing aperture size, which is expected; however, the second effect is unexpected. At the first two peaks in TH output (near 0° and 10°), TH decreases with aperture size, while at the third peak (near 30°), TH increases with aperture size; at the fourth peak, it decreases again. Individual apertures have cutoff frequencies, below which group velocity is minimized, resulting in increase in intra-aperture intensity [16, 10]. This simplification (neglecting effects due to periodicity) suggests an explanation for the behavior seen at 0°, 10°, and 50°, where the decreasing aperture size should result in increasing TH. However, this doesn’t explain the results at 30°, which is the subject of further investigation.
3.3. Effects of aperture shape
It is known that aperture shape can have a strong influence on SHG [10, 11, 7], due, in part, to symmetry breaking. Aperture shape also affects the conversion efficiency of THG, as shown in Fig. 6 for a sample with asymmetric aperture shape and Cr adhesion layer, where field enhancement is expected to be localized along the long edge of the apertures . In comparison to the results of a round aperture, an 8 times increase in TH is obtained. Optimization of the aperture shape may allow for even greater TH conversion to be obtained.
In conclusion, we have observed TH from arrays of sub-wavelength apertures. TH maxima are obtained at incidence angles corresponding to EOT of the fundamental, with signal strengths comparable to SH under symmetry-breaking conditions. There is a clear effect of lattice spacing and aperture size and shape on the TH signal, where an anomaly is observed in the scaling of TH with aperture size at different incidence angles corresponding to EOT.
We thank the reviewers for their useful comments. This research was sponsored by grant ECS 0622225 from the NSF and contractW911NF-07-1-0245 from the ARO.
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