1. Introduction

The enhanced optical transmission (greater than the simple geometrical open area fraction) through sub-wavelength hole arrays implies corresponding enhanced electromagnetic fields in the vicinity of the apertures [1–5], which in turn can be used to enhance nonlinear optical interactions. In this work, we investigated the linear transmission and the second-harmonic generation (SHG) for a subwavelength metallic GaAs-filled hole array on a GaAs substrate. The second harmonic intensity, proportional to the fourth power of the fundamental electric fields, is strongly enhanced in this nanophotonic structure. Additionally, for propagation along the the GaAs (100) axis, the symmetry of the second-order nonlinearity tensor requires a longitudinal electric field, which is identically zero for bulk propagation but is enhanced over the incident fields in the near fields around the holes. Since the patterned GaAs thickness is much shorter than both the fundamental and second harmonic wavelengths involved, and thus much shorter than the coherence length, no phase matching is needed to generate the SH signal from this very thin sample structure. Recently, similar experiments from a 2D coaxial array, which exhibits much larger transmission [6, 7], but weaker SHG, have been reported [8]. This suggests that optimization of the transmission and of the SHG is a complex issue. Reference samples of subwavelength metallic air hole arrays on GaAs and Si were fabricated and characterized to verify that the SH signal observed was due to the GaAs second-order susceptibility, not to higher-order, interface related, nonlinear effects as has been the case for previous studies of metal film hole arrays on amorphous substrates [9, 10].

2. Fabrication, measurement and analysis

Interferometric lithography [11] (IL) was used to fabricate periodic array samples. All of the samples reported here were uniformly fabricated over >1.0×1.0 cm² areas on double-polished, semi-insulating substrates. The processing flow is described here: 1) The GaAs substrate was covered with a 20-nm thick layer of PMMA by spin coating, this layer serves as a sacrificial lift-off dissolution layer in the final processing step. An anti-reflective coating (ARC) layer, for i-line lithography was then spun on to minimize reflection of the IL beams; Finally, a 500-nm thick negative-tone photoresist (Futurrex NR7-500P) was applied; 2) IL at a wavelength of 355 nm, 3^rd harmonic of a YAG:Nd³⁺ laser, was used to expose periodic holes (879-nm pitch for all samples discussed herein) in the photoresist; 3) A 60-nm thick layer of Cr was deposited on the developed sample; after lift-off, the remaining Cr dots formed a metal etch-mask on top of the ARC layer; 4) An O₂ plasma reactive-ion-etch was used to anisotropically etch through the ARC and PMMA layers, followed by an anisotropic inductive coupled plasma (ICP) etch into the GaAs substrate to generate the GaAs post arrays (GaAs post height ~110 nm); 5) A thin Ti layer (5 nm), used to improve the metal adhesion to the GaAs, and a thicker Au layer (65 nm) were deposited. After deposition, a lift-off step using the sacrificial PMMA layer removed the Au on top of the GaAs posts to give the completed structure. A scanning electron micrograph (SEM) picture of the final structure was shown in Fig. 1, along with a schematic cross section view.

The linear transmission spectrum, shown in Fig. 1, was recorded with a Fourier-transform infrared (FTIR) spectrometer at normal incidence with an incoherent light source, and was normalized to an air transmission background. A peak transmission through these subwavelength holes of around 8% was observed at 3180 nm for the (1,0) GaAs/Au surface plasmons (SP), only slightly less than the expected transmission through the same size effective apertures on an unpatterned sample (the hole radius is 214 nm; fractional opening area 18.5%; GaAs transmission ~51%; so the transmission ascribed to effective apertures of the same size would be 9.4%).

 

Fig. 1. FTIR linear transmission spectrum of the hole array sample. 8% transmission observed at 3180 nm corresponding to (1,0) Au/GaAs SP peak. SEM picture of metallic hole-array sample with GaAs posts and a schematic drawing of cross-section view were shown as insets.

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An IR-OPA producing optical pulses with 200-fs duration and 15-nm bandwidth at 1 kHz repetition rate at a fundamental wavelength near the 3.2 µm SPW transmission peak was used for the SHG experiments. The unfocused laser beam with a diameter of ~1.0 mm passes through a chopper and a long-pass filter with a cut-off at 2.5 µm, then is incident normally onto the unpatterned side of the sample. The transmitted light, which contains both the fundamental pump wavelength and the frequency-doubled SH radiation, passes through a 2.0-µm short-pass filter, goes to a monochromator and an InGaAs fW photoreceiver connected to a lock-in amplifier.

We compared the normal incidence SH conversion between the GaAs-filled metallic hole array sample and a z-cut LiNbO₃ sample at a fundamental pump wavelength of 3180 nm, as shown in Fig. 2. The SHG radiation intensity for both samples scales as the square of the fundamental intensity as expected. After correcting for the difference of the reflection of the fundamental pump intensity in the front surface and that of the SH intensity in the back patterned surface as well as also the available SH signal generation area (only 18.5% of the sample area is GaAs), the SH signal from the GaAs-filled metallic hole array sample is about 45% as intense as that from the z-cut LiNbO₃.

The SH signal from the GaAs-filled metallic hole array sample shows higher nonlinear conversion (only 2.3 times less than that of z-cut LiNbO₃), compared to the ratio of 9.4 between the metallic coaxial array with GaAs gap and z-cut LiNbO₃ [8] over the similar wavelength range, even though simulation shows that the field inside the coaxial gap is much stronger than that inside the hole [12]. Also the peak linear transmission is much larger for the annular sample, 30% vs. 8%, so we would have expected much larger SHG signal from the annular array sample. The explanation is that the SH signal we detect is a volume integral over the field components of E_x,y E_z of the fundamental wave for patterned GaAs, since only P_x and P_y polarization radiation can couple to far-field radiation and the d matrix for GaAs only has three terms, d₁₄=d₂₅=d₃₆ requiring a z-directed field for propagation along the (100) GaAs crystal axis.

where the thickness of the nonlinear region is ≪l_coherence.

Although the field components in the coaxial sample are larger than those in the hole sample, the integrated volume over the field component E_y,x and E_z products overlap and the volume of GaAs where the enhanced field exists are larger for the hole sample. The result is that the SH signal we observed is stronger in hole array sample, even though the linear transmission is much higher in the coaxial sample [6, 7].

 

Fig. 2. SH intensity versus fundamental intensity for z-cut LiNbO₃ and hole array filled with GaAs at fundamental wavelength of 3180 nm. The curves labeled “corrected” are adjusted for Fresnel reflectivities and the GaAs open area. The red dots curve, which will be discussed later, is the SH intensity versus fundamental intensity for metallic air hole array on GaAs at fundamental wavelength of 3060 nm.

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The wavelength dependence of the SHG light of the sample was measured. The wavelength of the collected radiation was recorded from the monochromator to be equal to half that of the fundamental pump light, as shown in Fig. 3. The cross symbols are SH signals and the solid line is a portion of the linear transmission curve. Near the peak wavelength of the transmission, the patterned GaAs sample generates strong SH signal. As the fundamental pump wavelength moves away from the peak position, the corresponding SHG intensity drops at a much faster rate than the linear transmission reflecting the expected nonlinear response. In order to eliminate the wavelength dependent response from the components, namely short pass filter, monochromator and the detector, on the optical path of the SH wave, their response has been obtained by comparing the detected signal from a standard blackbody radiation source through these components.

The SH signal peaks at a wavelength about 30 nm shorter than the linear transmission peak, which is similar to what we observed from the metallic coaxial array filled with GaAs and can be explained with the simple point dipole theory [8]. Since the size of the hole unit cell region is much smaller than the SH wavelength, we can assume that each open GaAs region acts as a point dipole, that is, we neglect retardation effects across the aperture. The SH intensity radiated by the planar sheet of point dipoles shows that the SH peak should be shifted toward lower wavelengths because of the 1/λ ² factor (I(2ω)∝|p⃗(2ω)|²/λ ²) in the SHG intensity.

 

Fig. 3. Wavelength dependence of the SHG for metallic hole array filled with GaAs.

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We also measured the SHG from hole-array samples with air holes at the same pitch on both GaAs and Si substrates, the SEM pictures and linear transmission spectra are shown in Fig. 4. Since the refractive indices of the Si and GaAs are similar across this wavelength range, very similar transmission curves are obtained. The various peaks are associated with coupling into the Au-semiconductor surface plasmons.

At normal incidence, we observed a weak SH signal from the air hole sample on a GaAs substrate, about 10 times smaller than that of holes filled with GaAs, the intensity dependent data is shown in Fig. 2. Even without GaAs inside the opening hole area, SH is still generated by the GaAs below the aperture due to the fringing fields of the array. With the same fundamental pump light intensity, we varied the fundamental pump light wavelengths around the (1,0) Si/Au SP resonance at 3114 nm, no SH signal was observed from the sample on a Si substrate. Within the limits set by the present fundamental pump intensity and the detection signal to noise ratio, no SH signals from the metal are detected, all the SH signals observed are from the dipole-allowed second-order nonlinear susceptibility of the GaAs, since Si with an inversion-symmetric crystal structure does not have a bulk second-order nonlinear coefficient.

 

Fig.4. . FTIR linear transmission spectra of metallic hole array samples with air holes on GaAs and Si substrates. SEM pictures of metallic hole array samples with air holes on GaAs (left) and Si (right) substrates.

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3. Conclusions

In conclusion, we have demonstrated a strong SHG signal from nanoscale patterned GaAs without phase matching. The overall signal strength is comparable to that of z-cut, unphase-matched LiNbO₃. This holds out the possibility of useful SHG intensities without the need for phase-matching, which could have strong implications for signal processing functionality in the near- and mid-infrared spectral regions.