Letter pubs.acs.org/NanoLett
Metamaterials with Tailored Nonlinear Optical Response Hannu Husu,†,* Roope Siikanen,† Jouni Mak̈ italo,† Joonas Lehtolahti,‡ Janne Laukkanen,‡ Markku Kuittinen,‡ and Martti Kauranen*,† †
Department of Physics, Tampere University of Technology, P.O. Box 692, FI-33101 Tampere, Finland Department of Physics and Mathematics, University of Eastern Finland, P.O. Box 111, FI-80101 Joensuu, Finland
‡
S Supporting Information *
ABSTRACT: We demonstrate that the second-order nonlinear optical response of noncentrosymmetric metal nanoparticles (metamolecules) can be efficiently controlled by their mutual ordering in an array. Two samples with minor change in ordering have nonlinear responses differing by a factor of up to 50. The results arise from polarization-dependent plasmonic resonances modified by long-range coupling associated with metamolecular ordering. The approach opens new ways for tailoring the nonlinear responses of metamaterials and their tensorial properties. KEYWORDS: Metamaterials, plasmonics, diffraction, nonlinear optics
T
address the role of structural dimensions,20,23,24 resonance enhancement,20,25 defects,21 higher-multipole effects,22 and local-field effects26 in their nonlinear response. These shapes are strongly dichroic, that is, their resonances differ for two linear eigenpolarizations. This suggests that the orientational distribution of the metamolecules can be utilized to achieve resonance enhancement for the desired tensorial nonlinear responses. This approach, however, has not been pursued to date, mainly because the nonlinear responses of even the most basic samples have been influenced by defects.20−23,27,28 In this Letter, we demonstrate noncentrosymmetric metamolecules with improved sample quality, and control their second-order response by their ordering in an array. The response is shown to depend sensitively not only on the orientational distribution but also on long-range diffractive coupling associated with the details of metamolecular ordering.19 Significantly, two samples with a subtle difference in metamolecular ordering are found to have polarizationdependent nonlinear responses differing by a factor of up to 50. The orientational distribution and more detailed ordering therefore provide new opportunities for controlling the nonlinear optical response of metamaterials and their tensorial properties. The investigated samples, shown in Figure 1, were fabricated on a fused silica substrate using electron-beam lithography. The particles were arranged in a square array with a separation of 500 nm. A building block for the arrays was an L-shaped gold nanoparticle with 250 nm arm length and 100 nm arm width. The thickness of the particles was 20 nm and there was a thin adhesion layer of chromium between the substrate and gold. The particles were also covered with a 20 nm thick protective
he nonlinear optical response of a material depends on its molecular-scale constituents and their macroscopic ordering. The ordering is essential for second-order nonlinear response, which requires molecular and macroscopic noncentrosymmetry.1 In traditional molecular nonlinear optics, microscopic noncentrosymmetry is usually obtained by using polar molecules.2 For macroscopic noncentrosymmetry, the molecules are poled (aligned) in an electric field3 or by alloptical means.4 The nonlinear response can be further enhanced by molecular resonances and local-field effects. Because of weak intermolecular interactions, relatively simple Lorentz factors are traditionally used to account for the localfield effects.1,2 The macroscopic response is then obtained as an orientational average of the responses of individual molecules.2 The local-field effects, however, can play a more significant role in nanocomposite materials, enhancing their response beyond the constituents.5 Metamaterials are artificial materials whose optical properties arise from their geometry.6 They often consist of metal nanoparticles (metamolecules), whose plasmon resonances7 and local-field effects are intimately connected. The resonances depend on the size and shape of the particles and can be further modified by interparticle coupling, typically through near-field effects.8−12 The metamolecules are usually ordered in periodic arrays, where the main goal has been in structures with subwavelength periods in order to achieve the effective medium limit.13 Recent work, however, has shown that for wavelengthscale periods, the resonances and optical responses can be significantly modified by diffractive long-range coupling even when no propagating diffraction orders exist in free space.14−19 Several noncentrosymmetric metamolecular shapes have been introduced for second-order nonlinear optics, including L-shaped nanoparticles,20−22 U-shaped split-ring resonators,23−25 and T-shaped nanodimers.26 Such structures have been characterized by second-harmonic generation (SHG) to © 2012 American Chemical Society
Received: October 7, 2011 Revised: January 5, 2012 Published: January 10, 2012 673
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respectively). Sample A has broad features between 900 and 1400 nm and clear differences between the eigenpolarizations. On the other hand, Sample B has almost identical spectra for both polarizations and its resonances are significantly narrower than those of the Standard array. As discussed in detail in ref 19, these differences arise from diffractive long-range coupling between the metamolecules, because the unit cell dimensions depend on the detailed metamolecular ordering. The second-harmonic generation measurements were performed at normal incidence and in transmission using a femtosecond Nd/glass laser (wavelength 1060 nm, pulse length 200 fs, repetition rate 82 MHz, average power 150 mW). The SH signal was detected using a photomultiplier tube (PMT) combined with a photon counting unit. The initial polarization was cleaned with a high quality calcite polarizer and continuously rotated using a half-wave plate. Furthermore, the polarization of the detected SHG signal was chosen with an analyzer. Such polarization lineshapes provide valuable information as to whether the expected symmetry rules of the sample are fulfilled. To illuminate only the desired sample area we used a weakly focusing lens with a 30 cm focal length, resulting in a spot size of about 300 μm diameter. On the other hand, using a long focal length lens allows us to neglect the coupling of the incident light to the normal component of the sample. To ensure that the measured SH signal comes from the sample itself, we used a SH blocking filter before the sample and a fundamental blocking filter right after the sample. In addition, an interference filter was placed at the input of the PMT to decrease the background signal. We analyze our SHG experiments by the nonlinear response tensor (NRT)30 Ajkl, which relies on the polarization components of the incoming fundamental and outgoing SHG fields. NRT is essentially equivalent to the susceptibility of the sample in the effective-medium limit (Supporting Information). The intensity of the polarization component j of the SHG field is given by
Figure 1. (a) Dimensions of the L particles. (b−d) Layouts of the investigated samples and the coordinate systems. (e) Scanning electron microscope image of Sample B.
layer of evaporated quartz. The sample areas were 1 mm × 1 mm. The linear properties of the samples were characterized by measuring their extinction spectra, which takes into account both absorption and scattering, and is quantified by the optical density log10(1/transmittance). Measurements were performed at normal incidence using a fiber coupled broadband halogen bulb as a light source and the spectra were recorded using two spectrometers, Avantes AvaSpec-2048 for the visible and Avantes NIR256 for the near-infrared, to cover a broad spectral range from 400 to 1700 nm. The linear polarization state was controlled using a calcite polarizer. In the Standard array, all metamolecules are oriented the same way (Figure 1b). The L shape determines the eigenpolarizations along its symmetry axis (y) and perpendicular to it (x). The extinction spectra of the sample (Figure 2a) show two distinct resonances, for y polarization at 1004 nm and for x polarization at 1512 nm. The additional peaks at 700 nm are related to the line width of the metamolecules.29 Note that the sample is designed to have a resonance close to the laser wavelength (1060 nm) used in the SHG experiments. Note also that the period of the Standard array, 500 nm, is subwavelength for this resonance. The response of the Standard array thus provides a reference that is a close approximation for the properties of the individual particles. In Samples A and B, the mutual arrangement of the metamolecules is modified (Figures 1c,d). Both have the same orientational distribution, but there is a minor difference in the ordering of the metamolecules. The symmetry group of both samples, however, is the same and determines the coordinate axes (u, v) for these samples. Despite their similarity, Samples A and B have completely different extinction spectra (Figure 2 panels b and c,
Ij(2ω) = |A jkk Ek2(ω) + A jll El2(ω) + 2A jkl Ek (ω)El(ω)|2
(1)
where, depending on the coordinate system, the indices j,k,l can be either x,y or u,v. Only in-plane tensor components are taken into account as the measurements are performed at normal incidence. Furthermore, certain tensor components are forbidden due to symmetry of the structures (Supporting Information) and only the components shown in Table 1 are nonvanishing. Polarization-dependent measurements were used to address the tensorial properties of the response. The results for the
Figure 2. The extinction spectra of (a) Standard array, (b) Sample A and (c) Sample B for the eigenpolarizations of the structures. Insets show the sample layout. 674
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have two different orientations of the metamolecules. The NRT components in the new u,v-coordinate system are obtained from the equation2
Table 1. Symmetry-Allowed NRT Tensor Components and Their Relative Magnitudes Obtained from the Fitting to the Measured Dataa xxy
yxx
yyy
Standard
0.13 uuv
0.42 vuu
1 vvv
prediction Sample A Sample B
0.21 0.14 0.97
0.60 0.40 1.10
0.41 0.36 0.94
A mno =
1 2
∑
∑ A jkl cos(j , m)cos(k , n)cos(l , o)
orientations j , k , l
(2)
where m,n,o are either u or v and j,k,l are either x or y. The cosine factors project the original NRT components into the new coordinates. Because of symmetry, the predicted tensor components with odd number of u are zero. The predicted allowed components (Table 1) show that the nonlinear response should now be more equally distributed over different tensor components. The measured and predicted SHG intensities as a function of the linear input polarization angle for Samples A and B are shown in Figure 4. The lineshapes for both samples are similar due to their similar symmetry and also similar to the predicted ones. Nevertheless there are remarkable differences in the signal levels. Sample A underperforms the prediction for any polarization combination, being close to the prediction only for v-polarized fundamental light and v-polarized detection. On the other hand, Sample B is consistently above the prediction, and the responses of Samples A and B differ by a remarkable factor of 50 for u-polarized SHG. Another interesting feature is that Sample B exhibits strong SHG responses for several polarization combinations, whereas the Standard array has only one favorable configuration. Equation 1 was fitted to the measured data for Samples A and B by again neglecting the forbidden tensor components (Supporting Information). The magnitudes of the fitted components are shown in Table 1. The measured differences in the various signal levels shown in Figure 4 depend on the second power of the ratio of the magnitudes of the respective tensor components shown in Table 1. The remarkable differences between Samples A and B can be qualitatively understood on the basis of their extinction spectra (Figure 2). The nonlinear response depends both on the resonance width and its location with respect to the laser wavelength. All the resonances affecting the nonlinear response are quite close to the laser wavelength, and thus we focus on the widths of the resonances (for more detailed analysis, see Supporting Information). For Sample A, the measured component vuu is less than expected, because of the broad resonance for u polarization (Figure 2b). The resonance for v polarization is more complicated, but the width of its main
a
The prediction is obtained as the orientational average of the individual metamolecules from the Standard sample.
Figure 3. Normalized SHG intensity as function of the linear input polarization angle measured from x direction for Standard array and for x and y output polarizations. Circles are measured data and lines fits to the data. Inset shows the sample layout.
Standard array as a function of the linear polarization of the fundamental field are shown in Figure 3 for x- and y-polarized SHG signals. Equation 1 was fitted to the data by assuming the symmetry forbidden components to be zero. An excellent fit is obtained, showing that the forbidden components play no significant role in the response (Supporting Information). The sample quality is thus sufficient that the particles can indeed be used as building blocks for more sophisticated nonlinear structures. The magnitudes of the fitted components are shown in Table 1. The response is dominated by the component Ayyy, which is near-resonant for the fundamental frequency. This component is therefore normalized to unity and all the other components in the table are normalized to it. The NRT components for the Standard array can be used to predict the response of the modified Samples A and B based on the orientational average over all metamolecules.2 Both samples
Figure 4. The normalized SHG intensity as a function of the linear input polarization angle measured from u direction for (a) Sample A and (b) Sample B. Circles are measured data and solid lines fits to the measured points. Dashed lines are the predicted responses calculated by the orientational average of the responses of individual particles. Note that the dashed lines are the same in both plots but the vertical scale is different. Insets illustrate the layout of the particles. 675
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feature is close to the width of the corresponding resonance for the Standard array, which agrees with the almost equal predicted and measured responses. For Sample B, the resonances for both polarizations are very narrow and the linear response is almost perfectly isotropic (Figure 2c). The original y-polarized resonance of the Standard array is thus equally distributed between the u and v polarizations of Sample B, allowing significant resonance enhancement for both fundamental polarizations. This leads to almost equal values for all the allowed tensor components, which are all significantly enhanced compared to the prediction. The enhancement is particularly strong for the component uuv with an enhancement factor of about 5 compared to the predicted response, or even more striking factor of 7 when compared to Sample A. We emphasize that these comparisons are based on the tensor components. For the SHG signal intensities, the enhancement factors are squared, which leads to the impressive factor of about 50 between the uuv components of Samples A and B. The effect of the different resonance characteristics of the samples to their nonlinear responses can also be understood through differences in the local fields in the structures. In general, the local fields for Sample B are more favorable for the second-order response than those of the Sample A (Supporting Information). It is instructive to compare the present results to traditional molecular nonlinear optics, where intermolecular interactions are usually relatively weak and the local-field effects can be described by the Lorentz-type factors. In consequence, the macroscopic response is usually well described by the orientational average of the molecular responses. In the present metamolecular case, however, the properties of the sample are dominated by the long-range coupling between the particles. In the linear response, this gives rise to very different resonance characteristics of the samples. Furthermore, the nonlinear response depends strongly on the linear properties of the sample near the fundamental wavelength, as demonstrated by Niesler et al.25 Thus, in the present case, the orientational distribution and the detailed metamolecular ordering play key roles in determining the coupling. The ordering and intermolecular coupling can therefore not be considered independently and the overall response depends on the collective properties of the sample. In conclusion, we have introduced a new concept for controlling the nonlinear optical response of metamaterials. The concept relies on diffractive long-range coupling between the particles, which is sensitive to the detailed ordering of the particles in the array. Our results show that even small differences in metamolecular ordering can lead to large differences in the nonlinear response. The results also show that with proper care and understanding metamolecular concepts combined with long-range coupling provide unprecedented tools for optimizing the nonlinear responses of metamaterials and their tensor properties for future nanophotonics applications.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected];
[email protected].
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ACKNOWLEDGMENTS We acknowledge funding from the Academy of Finland (114913, 134980). H.H. and J.M. acknowledge support from the Graduate School of Tampere University of Technology.
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ASSOCIATED CONTENT
S Supporting Information *
Description of the nonlinear response tensor, more details regarding the sample quality and forbidden tensor components, detailed analysis of resonance factors, analysis of the results based on the local electric field distributions, and supporting references. This material is available free of charge via the Internet at http://pubs.acs.org. 676
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(30) Canfield, B. K.; Kujala, S.; Jefimovs, K.; Svirko, Y.; Turunen, J.; Kauranen, M. J. Opt. A: Pure Appl. Opt. 2006, 8, S278−S284.
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