NANO LETTERS
Second Harmonic Generation from a Nanopatterned Isotropic Nonlinear Material
2006 Vol. 6, No. 5 1027-1030
Wenjun Fan,† Shuang Zhang,† N.-C. Panoiu,‡ A. Abdenour,† S. Krishna,† R. M. Osgood, Jr.,‡ K. J. Malloy,† and S. R. J. Brueck*,† Center for High Technology Materials and Electrical and Computer Engineering Department, UniVersity of New Mexico, Albuquerque, New Mexico 87106, and Department of Applied Physics and Applied Mathematics, Columbia UniVersity, New York, New York 10027 Received February 24, 2006; Revised Manuscript Received March 28, 2006
ABSTRACT Second harmonic generation (SHG) from a nanopatterned isotropic nonlinear material (GaAs) located inside the subwavelength gaps of a metallic coaxial array is demonstrated. The SHG results from the strong electromagnetic fields in the vicinity of the coaxial gaps; the signal strength is comparable to that from z-cut LiNbO3 even though the path length is much shorter (∼100 nm compared to 14 µm). Numerical simulations are in good agreement with the experimental data. The observation of a peak-wavelength blue shift between the SH spectrum and the linear transmission spectrum is explained.
Recently, the anomalously high optical transmission through arrays of subwavelength apertures in metal films has attracted significant attention.1,2 Much of the discussion has focused on the linear optical properties of these structures. We have shown recently3,4 that for the case of annular (coaxial) arrays the transmission can approach unity and is related to coupling between surface waves and the TE11 coaxial mode. In contrast, the nonlinear optical properties of these structures have attracted relatively less attention5,6 and previous reports have largely been confined to relatively weak quadrupole and higher order, interface related, nonlinear effects from metal/amorphous-dielectric structures that lack a dipoleallowed χ(2) nonlinearity. Models of the enhanced transmission predict strong electromagnetic field enhancements in the vicinity of the apertures7 and thus second-harmonic (SH) generation is expected to be a sensitive probe of the physics involved. Here, we demonstrate SH from a material with a large χ(2), GaAs, which fills the aperture gaps in a coaxial nanopatterned array in an Au film, and quantitatively compare the generated SH signals to those from a z-cut LiNbO3 standard. The SH signals from the coaxial arrays are only about an order-of-magnitude smaller than those from the LiNbO3 even though the interaction length is about a factor of 100 smaller, clearly demonstrating the impact of the field enhancement. A numerical calculation of the SH spectrum is in good agreement with the measurements. A * Corresponding author. E-mail:
[email protected]. † University of New Mexico. ‡ Columbia University. 10.1021/nl0604457 CCC: $33.50 Published on Web 04/18/2006
© 2006 American Chemical Society
small blue shift between the peak linear transmission (largest field enhancement) and the fundamental wavelength for peak SHG results from the 1/λ2 dependence of the SHG. Many isotropic semiconductors, point group 4h3m, have great potential as mid-infrared nonlinear optical materials. GaAs, for example, has a large χ(2), a broad transparency range, low optical absorption, high thermal conductivity and a high laser damage threshold. The maturity of GaAs growth and its widespread use in optoelectronic applications make it an excellent candidate for optical frequency mixing. However, its optical isotropy prevents birefringent phase matching, so it has found only limited practical application. Recently, epitaxially grown orientation-patterned GaAs8,9 has been developed to provide quasi-phase-matching for infrared nonlinear applications. The use of surface plasmons (SP) to enhance nonlinear processes such as Raman scattering and harmonic generation is well-known.10-12 We fabricated a subwavelength metallic coaxial array pattern on a (100) GaAs substrate. The GaAs was etched before the metal deposition so that a single-crystal GaAs annulus extended through the coaxial aperture. Thus, the GaAs is in the high-field region associated with the nanostructure. Because the SHG intensity depends on the fourth power of the fundamental fields, a large enhancement over a small volume is obtained. The second harmonic signal strength from the sample is comparable to that from a planar slab of unphasematched, z-cut LiNbO3. Because the patterned GaAs thickness is much shorter than the wavelengths (both fundamental and second harmonic) involved and also
much shorter than the coherence length, no phase matching is required. Additionally as shown below, the longitudinal fields, perpendicular to the surface, identically zero for TEM propagation in bulk materials are the strongest fields in the vicinity of the nanostructured apertures and take advantage of the dipole-allowed GaAs χ14(2) tensor component. The sample was fabricated on double polished semiinsulating (100) GaAs. Using interference lithography (IL)13 and standard self-aligned semiconductor processing steps, a large area, 1.5 × 1.5 cm2, coaxial metallic aperture array was uniformly fabricated. The processing flow includes the following: (1) The GaAs substrate was covered by a sacrificial layer of SiNx, and a positive tone photoresist (PR) was applied; (2) IL was used to produce a post array on PR; (3) A 60-nm-thick layer of Cr was deposited on the patterned sample. After liftoff, a metallic etch mask was formed; (4) Reactive ion etching (RIE) was used to anisotropically etch the SiNx, followed by an anisotropic etch of GaAs by inductive coupled plasma (ICP) to generate the location for the central Au dots of the coaxial array; (5) RIE selective isotropic etching of the SiNx layer was then performed to generate an undercut that defines the gap of the coaxial structure; (6) Depositing and liftoff of the first Au layer (70 nm) to form the central coaxial regions, a thin Ti layer (5 nm) was used to improve the metal adhesion to the substrate; (7) Spinning a thick layer of photoresist on the sample and etching back to expose the remaining SiNx film while protecting the deposited Au; (8) Etching off the remaining SiNx with buffered oxide etcher, while leaving the photoresist filler; (9) Using the PR filler as etching mask, ICP etch GaAs in the field (outer webbing) region to the same depth as the center-GaAs hole; (9) Depositing and lifting off a second Au film to form the outer webbing around the central coaxial regions. The square-array pitch was 720 nm in orthogonal directions on the surface, with a coaxial inner radius of 114 nm and an outer radius of 199 nm (gap width 85 nm). The metal film was e-beam evaporated with a 5-nm Ti layer for adhesion followed by a 70-nm-thick Au layer. The height of GaAs annulus was 140 nm, so the GaAs extends above the metal film. A scanning electron microscope (SEM) image of the final structure is shown in Figure 1, along with a schematic of the structure cross-section. The linear transmission spectrum was recorded with a Fourier transform infrared (FTIR) spectrometer at normal incidence with an incoherent light source and is normalized to an air background (uncorrected for the large GaAs reflectivity). A peak transmission around 20% was observed at 3.23 µm for a GaAs open-area percentage of 16%. Figure 1 shows the linear transmission spectrum. Two dominant features are evident, an asymmetric peak at about 2.4 µm associated with the coupling into the metal-GaAs surface plasma wave and a broad, symmetric peak with larger peak transmission centered at 3.23 µm that is related to the cutoff of the TE11 coaxial mode. An IR-OPA, producing optical pulses with 200-fs duration and 15-nm bandwidth at a 1-kHz repetition rate, was used as the pump source for SHG. The unfocused laser output 1028
Figure 1. (a) Schematic cross section of structure showing GaAs annuli protruding through the Au film. (b) Top-down SEM of fabricated structure. (c) FTIR linear transmission spectrum (solid black line) and wavelength-dependent second harmonic signal spectrum (blue crosses). The structure around 4.3 µm is due to residual atmospheric CO2.
beam with a diameter of 1.0 mm passed through a chopper and a long-pass filter with a cutoff at 2.5 µm, and was directed at normal incidence onto the unpatterned side of the sample. The transmitted light, which contained both the fundamental pump wavelength and the SH radiation, passed through a short-pass filter with a cutoff at 2.0 µm and a monochromator and was detected with an InGaAs photoreceiver using a lock-in amplifier. To quantify the conversion efficiency, we compared the normal incidence SH signal from the nanopatterned coaxial GaAs sample with that from a z-cut LiNbO3 wafer at a fundamental pump wavelength of 3.23 µm, as shown in Figure 2. The SHG radiation intensity for both samples scales as the square of the fundamental intensity. The SH signal for the z-cut LiNbO3 is about 72 times larger than that from the nanopatterned GaAs sample. After factoring in the difference of the reflection of the fundamental pump intensity in the front surface [RLNO(ω) ≈ 13% and RGaAs(ω) ≈ 29%] and that of the SH intensity in the back patterned surface [RLNO(2ω) ≈ 14% and RGaAs(2ω) ≈ 29%] as well as the available SH signal generation area (only 16% of the sample area is not covered by metal), the ratio of the signals is reduced to 9.4, that is, the GaAs SHG signal is 0.11 times as intense as that from the z-cut LiNbO3. The second-order nonlinear coefficients calculated using Miller’s rule are d14 ≈ 87 pm/V (χ(2) ) 2d) for GaAs and d31 ≈ 4 pm/V for Nano Lett., Vol. 6, No. 5, 2006
Figure 2. SH intensity versus fundamental intensity for z-cut LiNbO3 and coaxial patterned GaAs at a fundamental wavelength of 3.23 µm. The curves labeled “corrected” are adjusted for Fresnel reflectivities and the GaAs open area.
LiNbO3 at this wavelength.14 However, the spatial extent of the nonlinear generation is only ∼140 nm for the nanopatterned GaAs compared with a coherence length of ∼14 µm for LiNbO3 at this wavelength.15 Two control samples, one a gold 2D hole array on Si with pitch of 879 nm and hole radius of 213 nm, giving a Si/Au SP transmission peak of 1.3% at 3.114 µm, and the other an unpatterned double-polished GaAs substrate were measured as well. With a fixed fundamental pump light intensity, we varied the fundamental pump wavelengths in the vicinity of the Si/Au SP resonance. No SH signal was observed from the sample on the Si substrate within our experimental noise floor. Because Si has an inversion-symmetric crystal structure, only surface SH is expected; this observation indicates that the metal structure is not contributing significantly to the observed SHG. Similarly, no SH signal was seen on the
unpatterned GaAs (100) sample. No SHG response from this surface at normal incidence is expected as a result of the GaAs SHG selection rules. Both observations verify that the SH signal observed on the coaxial GaAs sample is due to field enhancement and direction effects associated with the coaxial layer. Note that this relatively strong signal did not require phase matching and, in fact, the 140-nm-thick layer is much thinner than the optical coherence length, which is of micrometer order. The wavelength dependence of the SHG 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 by the cross symbols in Figure 1. For a fundamental wavelength near the transmission peak, the patterned GaAs sample generates a strong SH signal. As the fundamental wavelength is detuned from the linear transmission peak position, the corresponding SHG intensity drops at a much faster rate than the linear transmission, reflecting the expected nonlinear response. The peak wavelength for the SH signal is about 20 nm shorter than the linear transmission peak. The wavelength-dependent response of the components in the optical path of the SH wave was eliminated by calibrating the detected signal with that from a standard blackbody radiation source. Transfer matrix numerical simulations of linear transmission and SHG were carried out. A square coaxial unit cell with the same open area as the annular experimental geometry was used to obtain faster convergence. Figure 3 shows the electrical field components in the plane of the metal/air interface at 3.23 µm for incident light polarized in the x direction. The fields are very small at the metal surface, as expected. The in-plane fields in the gap region are roughly
Figure 3. Field plot for the coax unit cell at the metal/air interface for an x-polarized incident field. The simulation was carried out for a square coaxial case keeping the same open area as the annular experimental geometry to obtain convergence with a smaller number of diffraction orders. Nano Lett., Vol. 6, No. 5, 2006
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Figure 4. Numerical simulations (transfer matrix) of the linear transmission and SHG spectra.
comparable (∼3 or 4×) to the incident field while the outof-plane, z-directed fields are ∼10× larger. The symmetry properties of the GaAs crystal point group require that the radiating SH polarization components are Px ) 2χ14(2)EyEz and Py ) 2χ(2) 14 ExEz so the high-intensity z-directed fields play a large role in the observed SH signal. The source polarization Pi (2ω) ) χ(2) ijk (2ω;ω,ω) Ej (ω) Ek(ω)
(1)
at the SH was computed and integrated over the domain occupied by GaAs to find the corresponding induced electric dipole b p per lattice cell. Because the size of this coax unit cell region is much smaller than the SH wavelength, we assume that this these sources act as point dipoles, that is, we neglect retardation effects across the coaxial aperture. With this assumption, the SH intensity radiated by the planar sheet of point dipoles was extracted. This point dipole theory shows that indeed the SH peak should be shifted toward lower wavelengths because I(2ω) ∝ |p b|2/λ2
(2)
The induced point dipole intensity is a maximum at exactly half the wavelength of the linear transmission peak, but because of the 1/λ2 factor, the overall SH peak is shifted to a shorter wavelength. The simulation shows a 31-nm peak wavelength shift compared to the measured 20-nm shift, and
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both linear transmission and SH spectra are in good qualitative agreement with the experimental data as shown in Figure 4. Previously, a similar peak wavelength blue shift between the SH spectrum and the linear transmission spectrum was observed but not explained.6 Experiments on 2D metallic hole-array samples filled with GaAs posts show similar results, with somewhat larger SH signals, possibly reflecting the larger open area of the hole arrays. This approach can be generalized for use with most nonlinear materials because no phase matching is needed to realize significant optical frequency conversion. Potentially, combining optoelectronic devices and nanophotonic optical frequency conversion without the need for phase matching could lead to integrated functionalities for optical signal processing, much as rf and microwave mixers are readily available and important systems components at longer wavelengths. Acknowledgment. This work was supported by the U.S. Army Research Office under the MURI program in Deep Subwavelength Optical Nanolithography and by DARPA under the University Photonics Research Center program. R.M.O.,Jr. and N.-C.P. also acknowledge support from the U.S. Air Force under Contract FA9550-05-C-0047. References (1) Ebbesen, T. W.; Lezec, H. J.; Ghaemi, H. F.; Thio, T.; Wolff, P. A. Nature 1998, 391, 667. (2) Barnes, W. L.; Murray, W. A.; Dintinger, J.; Devaux, E.; Ebbesen, T. W. Phys. ReV. Lett. 2004, 92, 107401. (3) Fan, W.; Zhang, S.; Minhas, B.; Malloy, K. J.; Brueck, S. R. J. Phys. ReV. Lett. 2005, 94, 033902. (4) Fan, W.; Zhang, S.; Malloy, K. J.; Brueck, S. R. J. Opt. Express 2005, 13, 4406. (5) Nahata, A.; Linke, R. A.; Ishi, T.; Ohashi, K. Opt. Lett. 2003, 28, 423. (6) Airola, M.; Liu, Y.; Blair, S. J. Opt. A: Pure Appl. Opt. 2005, 7, S118. (7) Baida, F. I.; Van Labeke, D. Opt. Commun. 2002, 209, 17. (8) Fejer, M. M.; Magel, G. A.; Jundt, D. H.; Byer, R. L. IEEE J. Quantum Electron. 1992, 28, 2631. (9) Eyres, L. A.; Tourreau, P. J.; Pinguet, T. J.; Ebert, C. B.; Harris, J. S.; Fejer, M. M.; Becouarn, L.; Gerard, B.; Lallier, E. Appl. Phys. Lett. 2001, 79, 904. (10) Jeanmaire, D. L.; Van Duyne, R. P. J. Electroanal. Chem. 1977, 84, 1. (11) Coutaz, J. L.; Neviere, M.; Pic, E.; Reinisch, R. Phys. ReV. B 1985, 32, 2227. (12) Tsang, T. Y. Opt. Lett. 1996, 21, 245. (13) Brueck, S. R. J. Proc. IEEE 2005, 93, 1704. (14) Shoji, I.; Kondo, T.; Kitamoto, A.; Shirane, M.; Ito, R. J. Opt. Soc. Am. B 1997, 14, 2268. (15) Edwards, G. J.; Lawrence, M. A. Opt. Quantum Electron. 1984, 16, 373.
NL0604457
Nano Lett., Vol. 6, No. 5, 2006
