Visible frequency magnetic activity in silver nanocluster metamaterial

Transcription

1 Visible frequency magnetic activity in silver nanocluster metamaterial Venkata Ananth Tamma, Jin-Hyoung Lee, Qi Wu, and Wounjhang Park* Department of Electrical, Computer, and Energy Engineering, University of Colorado, Boulder, Colorado , USA *Corresponding author: Received 3 August 2009; revised 30 September 2009; accepted 2 October 2009; posted 2 October 2009 (Doc. ID ); published 29 October 2009 We experimentally observe magnetic resonance in the visible frequency region from self-assembled silver nanocluster metamaterials. Extensive numerical modeling studies were conducted to find the optimal nanocluster dimensions. Self-assembly of silver nanoparticles coated with nanoscale silica coating was then performed on polymer templates fabricated by laser interference lithography. The nanoclusters supported magnetic resonance in the visible region, and the extracted effective permeability exhibited Lorentz-like resonance. The experimentally observed lowest value for the real part of permeability was The nanocluster metamaterial represents a practical metamaterial architecture that is compatible with the scalable bottom-up manufacturing process Optical Society of America OCIS codes: , , Introduction Metamaterial is a new class of artificial materials whose electromagnetic properties can be tuned by their structural parameters. Using metamaterials, novel optical properties generally unavailable in natural materials can be obtained. A prime example is metamaterial structures that exhibit a negative refractive index, which have been extensively studied in both the microwave and the optical regimes for their potential applications in, for example, subwavelength imaging [1]. Negative refractive index requires simultaneous control of both the dielectric permittivity (ε) and the magnetic permeability (μ). The general condition for the negative index is ε 0 jμjþμ 0 jεj < 0, where the prime indicates the real part [2]. While this condition can be met with only ε being negative, it is desirable to have both ε and μ negative because it tends to result in lower loss. More recently, metamaterial research has extended beyond the negative index and began exploring inhomogeneous index profiles for tailored optical properties. The effort has spawned a new field often /10/070A11-07$15.00/ Optical Society of America referred to as transformation optics, and the hallmark application is the cloak of invisibility [3,4]. In the transformation optics approach, an invisibility cloak is designed by a coordinate transformation that opens an electromagnetically inaccessible region in the transformed space. In general, one must be able to achieve extreme values of permittivity and permeability to realize this structure, and, therefore, many schemes have been proposed to mitigate these requirements. A notable example is the ground plane cloak that hides objects in front of a mirror plane [5]. This structure does not require extreme values for optical constants and has recently been experimentally demonstrated in both the microwave and the optical frequency regions [6 8]. Whether the application is a negative index or an invisibility cloak, the fundamental requirement for practical metamaterial structures is the ability to control the permittivity and permeability values as desired. In the optical regime, it is relatively straightforward to achieve a negative real part of permittivity because metals possess the real part of negative permittivity below their plasma frequencies. However, it is difficult to obtain negative real parts of permeability especially at optical wavelengths. Naturally, 1 March 2010 / Vol. 49, No. 7 / APPLIED OPTICS A11

2 achieving optical frequency magnetism has been the focus of metamaterial research. So far, the most successful structures in achieving negative real parts of permeability in the optical regime include a split-ring resonator [9], a fishnet structure [10 12], and a nanorod pair [13]. While these successes are highly promising, fabrication remains a major challenge. The above-mentioned structures are all fabricated by electron-beam or focused ion-beam lithography, and it is currently difficult to envision large-scale manufacture of these structures. An alternative approach, which utilizes the magnetic Mie resonance of a single dielectric cylinder to achieve the negative real part of permeability, has been proposed [14]. This concept has recently been extended to nanocluster metamaterial. In this architecture, the magnetic activity is achieved by using clusters of metal nanowires or nanoparticles that can support magnetic Mie resonance [15 18]. These magnetically active metal nanoclusters can be combined with thin metal films or metal shells to obtain a negative refractive index in the optical regime. This new metamaterial architecture is highly attractive because it can be fabricated by simple and scalable bottom-up fabrication techniques such as the selfassembly technique. We recently demonstrated a gold nanocluster metamaterial structure fabricated by template-directed self-assembly and observed collective plasmon resonance in the near-infrared region [19]. Here we report the experimental observation of magnetic resonance in the visible frequency region from the silver nanocluster metamaterial fabricated by template-directed self-assembly. 2. Metamaterial Design and Numerical Modeling The structure we aim to fabricate is a 1D array of trenches filled with silver nanoparticles schematically shown in Fig. 1. The entire structure can be viewed as a 1D grating made up of silver nanoclusters. The geometric parameters of the structure are chosen such that the feature sizes of this structure are sufficiently small for the red region of the visible wavelengths at which we aimed to operate. In comparison with the 2D array of circular disk clusters reported previously, this 1D structure is capable of producing a larger magnetic resonance. The price to pay is the structure is now anisotropic and the optical properties are strongly dependent on the incident polarization. The magnetic mode is excited Fig. 1. (Color online) Schematic of the 1D silver nanocluster metamaterial. The circles represent the silica-coated silver nanoparticles: p, periodicity; w, width of the trenches; h, height of the trenches. when illuminated by transverse-magnetic [(TM) field along the nanocluster lines] polarized light. The induced magnetic moment subsequently gives rise to resonance in effective magnetic permeability. When the magnetic resonance is strong enough, the real part of permeability can become negative. Since the magnetic resonance supported by the nanocluster is essentially a collective plasmon resonance of silver nanoparticles and the plasmon resonance of individual silver nanoparticles is located at around 380 nm for the diameters of 19 and 24 nm used in this work, the resultant magnetic resonance occurs in the visible frequency region, as shown below. We note that the current design of nanocluster metamamterial is anisotropic and the effective permeability discussed here refers to the permeability tensor component that corresponds to the direction along the nanocluster lines. We also note that nanocluster metamaterial can be made isotropic by using isotropic nanoclusters as was done in Ref. [19]. The optical properties of the structure were modeled by using the commercial finite-element solver COMSOL (Burlington, Massachusetts). Experimental values of the dielectric constant of silver obtained from [20] were used for the calculations. The silver nanoparticle cluster was treated as a homogeneous effective medium with effective permeability and permittivity calculated using the extended Maxwell- Garnett theory. Such an approximation is valid in this case because the particle diameters are much smaller than the operating wavelength range of nm. To justify the use of the extended Maxwell-Garnett effective medium theory, rigorous photonic band structure calculations were performed using the multiple scattering method [21]. Figures 2(a) 2(c) show the band structures obtained by the multiple scattering calculations for silver fill fractions of f ¼ 0:1, 0.3, and 0.5, respectively. Also plotted in Figs. 2(a) 2(c) are the dispersion curves obtained from the extended Maxwell-Garnett theory. In Figs. 2(d) 2(f), the effective permittivity calculated by the extended Maxwell- Garnett effective medium theory is plotted for the same fill fractions. Because of the constraints in our multiple scattering code, for both band structure calculations we used the Drude model for the silver dielectric function with plasma frequency and damping parameters of 2: and 4: Hz, respectively. Note that we used the experimental values for the silver dielectric function taken from Ref. [20] for all the other simulation results presented here. Overall the agreement between the photonic band structure calculated by the multiple scattering theory and the effective medium theory is good. The photonic bandgap opens in the region in which the real part of permittivity is negative. The two photonic band structures diverge slightly from each other near the band edge, which is expected as described in [22]. It should be noted that the effective medium theory provides the correct dispersion curve for wavelengths greater than 600 nm, which is the region in which the magnetic resonance is observed A12 APPLIED OPTICS / Vol. 49, No. 7 / 1 March 2010

3 retrieved from the complex transmission and reflection coefficients by the standard retrieval method [23]. The calculated transmission, reflection, and absorption spectra of the 1D silver nanocluster metamaterial are shown in Fig. 3. The volume fraction of silver nanoparticles was 0.5 and the periodicity, width, and height of the nanoclusters were 280, 140, and 120 nm, respectively. Three absorption peaks are observed at 580, 609, and 727 nm. The transmission spectrum exhibits dips at similar positions at 576, 616, and 696 nm. The lowest-order resonance at 696 nm corresponds to the ground state magnetic resonance whereas the two higher-order resonances are electric in nature. This is clearly seen by the magnetic field pattern calculated at the resonance wavelength. As shown in Figs. 3(d) and 3(e), the magnetic field is strongly concentrated at the center of the nanocluster and the electric field forms a circulating loop, which is a signature of magnetic-dipolelike resonance. This magnetic resonance consequently results in resonant behavior in the effective permeability. The effective permittivity and permeability of 1D silver nanocluster metamaterial calculated from the complex transmission and reflection coefficients are shown in Figs. 3(b) and 3(c), respectively. The calculated effective permeability exhibits a Lorentz type behavior centered at 728 nm, which coincides with the absorption peak position. The permeability reaches a minimum value of 1:2 at 700 nm. The extracted permittivity also exhibits a Lorentz type resonance at 618 nm corresponding to the higher-order electric resonance. These effective parameters are valid for normal incidence. We performed further calculations on the silver nanocluster metamaterial structure for oblique incident angles. It was found Fig. 2. (Color online) (a), (b), (c) Plots of the dispersion curves obtained from multiple scattering (M.Scat) and extended Maxwell- Garnett effective medium theory (EMT) for silver fill fractions of f ¼ 0:1, 0., and 0.5 respectively. (d), (e), (f) Plots of the real and imaginary parts of the effective permittivity calculated by the extended Maxwell-Garnett effective medium for silver fill fractions of f ¼ 0:1, 0.3, and 0.5 respectively. in our structure. This confirms the validity of the effective medium theory in this work. We also note that the extended Maxwell-Garnett theory generally does not satisfy the Wiener scaling law as pointed out in Ref [23]. Our analysis showed that, for the particle radius of 10 nm and operating wavelength of nm, the extended Maxwell-Garnett formula gives almost the same result as the Maxwell-Garnett theory, indicating that our effective medium theory obeys the scaling law. We calculated the steady-state field distribution across the nanocluster metamaterial structure with COMSOL, and the effective parameters can then be Fig. 3. (Color online) (a) Calculated transmission (T), reflection (R), and absorption (A) for the 1D silver nanocluster metamaterial with parameters of p ¼ 280 nm, w ¼ 140 nm, h ¼ 120 nm and volume fill fraction of silver of 0.50 for TM polarized incident light. (b) Real and imaginary parts of the effective permittivity (ε 1, ε 2 ) for the structure with parameters given in (a). (c) Real and imaginary parts of the effective permeability (μ 1, μ 2 ) for the structure with parameters given in (a). (d) Magnetic field pattern of the lowest-order Mie resonance at 700 nm. (e) Electric field pattern inside the cluster at 700 nm. 1 March 2010 / Vol. 49, No. 7 / APPLIED OPTICS A13

4 that the effective parameters extracted for normal incidence remain valid for incident angles of up to at least 30 deg. At 45 deg, the transmittance spectrum calculated for the nanocluster metamatetrial showed a shift of approximately 30 nm relative to the effective medium result. 3. Metamaterial Fabrication and Experimental Results To fabricate the nanocluster metamaterial structure we developed a template-directed self-assembly technique. Briefly, the template with a 1D array of trenches was fabricated by laser (325 nm He Cd laser) interference lithography using negative photoresist (SU-8) on a glass substrate. Periodicity (p) and width (w) of the trenches can be controlled by adjusting the incident angles of the two interfering laser beams and the UV exposure time while the thickness of the spin-coated SU-8 determines the height (h) of the trench. A scanning electron micrograph (SEM) of the 1D pattern with p ¼ 280 nm, w ¼ 128 nm, and h ¼ 100 nm is shown in Fig. 4(a). When the templates are ready, silver nanoparticles with diameters that vary between 19 and 24 nm were synthesized using the polyol process [24]. The polydispersity of the nanoparticle size distribution is typically 15% or less. The nanoparticles are then coated with a thin silica layer (typically 2 nm) by the modified Stöber method [25,26]. The silica coating is required to ensure insulating gaps between nanoparticles inside the cluster. This is a crucial requirement because, when the nanoparticles are touching, the nanocluster simply behaves like a metal line, completely losing its magnetic properties. Template-directed self-assembly was then performed. In this process, a confinement cell is first placed on the 1D patterned template Fig. 4. (Color online) (a) SEM picture of the 1D pattern in SU-8 with parameters of p ¼ 280 nm, w ¼ 128 nm, and h ¼ 100 nm. (b) SEM picture of self-assembled 1D pattern with parameters of p ¼ 280 nm, w ¼ 140 nm, and h ¼ 120 nm with silver nanoparticles of 12 nm radius and 2 nm coating. (c) SEM picture with higher resolution of the self-assembled pattern with parameters given in (c). (d) SEM picture of a self-assembled 1D pattern with parameters of p ¼ 280 nm, w ¼ 120 nm, and h ¼ 140 nm with silver nanoparticles of 12 nm radius and an 2 nm coating. and the colloidal solution of silica-coated silver nanoparticles is injected and slowly dried. The capillary force then drives the nanoparticles into the trenches, forming lines of nanoclusters. To prevent the undesired nanoparticle deposition outside the trenches, the template is treated with reactive ion etching. This process creates a surface charge on the SU-8 pattern and the electrostatic repulsive force between the SU-8 surface and the silver nanoparticles reduces the particle deposition on the SU-8 surface. The SEM images of the self-assembled structures are shown in Figs. 4(b) 4(d). It can be seen clearly that the self-assembly process produced highly ordered 1D nanoclusters with virtually no particle deposition outside the trenches. Also, the cluster formation was uniform and the fluctuation in nanoparticle packing was minimal. The nanocluster width variation, measured by the ratio of average nanocluster width to their standard deviation, was found to be 9.1% and 11.7% for the samples shown in Figs. 4(b) 4(d), respectively. The self-assembled 1D silver nanocluster metamaterials were optically characterized by using a microscope-coupled fiber spectrometer. The sample was illuminated by normally incident light from a halogen lamp source and the reflection and transmission spectra were recorded. For polarization control, a linear polarizer was placed between the light source and the sample. Figures 5(a) and 5(b) show the transmittance, reflectance, and absorptance spectra for the nanocluster metamaterial selfassembled on the template shown in Fig. 4(a) for the TM and TE polarizations, respectively. The silver nanoparticle diameter was 19 nm with a 2 nm silica coating. The polarization dependence is distinct. For TM polarization (electric field perpendicular to nanocluster lines) we observed a transmission tip at 710 nm with a shoulder feature at around 630 nm. While significantly broadened, the positions of these features are in good agreement with the theoretically calculated wavelengths of magnetic and electric resonances. The broadening is partially due to the inhomogeneity of the nanoclusters, which exhibited fluctuations in widths of 10%. Also, the nanocluster dimensions were not optimal in this sample and, as shown later, some adjustments in nanocluster dimensions produced more pronounced transmission dips. In contrast, the transmittance, reflectance, and absorption spectra for TE polarization (electric field along the direction of nanocluster lines) did not show any features. This is expected from the effective medium theory which predicts that the 1D nanocluster metamaterial would simply behave as a dispersive dielectric material with no resonance for TE excitation. This result further confirms that the TM spectra suggest the observation of magnetic and electric resonance predicted from numerical modeling. To quantitatively estimate the effective permeability, we fitted the experimentally observed transmittance spectrum by adjusting the loss parameter of silver. In nanostructures, it is often observed A14 APPLIED OPTICS / Vol. 49, No. 7 / 1 March 2010

5 Fig. 6. (Color online) (a) Comparison of experimental and fitted transmittance (T) and reflectance (R) data for structures with parameters of p ¼ 280 nm, w ¼ 140 nm, and h ¼ 120 nm. Silver nanoparticle of 20 nm diameter and an 4 nm silica coating thickness for TM polarized incident light. (b) Extracted real and imaginary parts of the effective permeability (μ 1, μ 2 ) for the structure and parameters described in (a). Fig. 5. (Color online) Measured transmittance (%), reflectance (%), and absorption (%) spectra for the nanocluster metamaterial self-assembled on the template shown in Fig. 4(a): (a) TM polarization and (b) TE polarization. that the losses become higher than in bulk. This method of fitting the experimentally observed optical spectrum using adjustable loss parameters has been used previously for other types of metamaterial [27]. Figures 6(a) and 6(b) show the fitted transmittance, reflectance, and absorption spectra and the extracted effective permeability for 1D silver nanocluster metamaterial with parameters of 280 nm periodicity, 140 nm width, 120 nm height, 20 nm diameter of the silver nanoparticle, and an ~4 nm coating thickness. Because of the roughness of the self-assembled nanocluster surface, there are slight errors in fitting the reflectance curve. The extracted effective permeability exhibits a Lorentz-like behavior with a resonance at 680 nm. The adjustable loss parameter resulted in some distortion of the effective permeability curves. The minimum value of the real part of permeability was approximately This can be reduced further by optimizing the nanocluster design as described below. The optimization process to find the best geometric parameters for the structure was done such that we obtain the minimum value possible for the real part of the permeability. The parameters that influence the optimization process include the periodicity, width, and height of the trench, and the volume fraction of silver in the structure. Calculations were performed using COMSOL over a wide range of parameters. It was found that the optimum height for the trench was 120 nm and the optimum width of the trench was half of the periodicity. The magnetic resonance becomes stronger for a higher volume fraction of silver. The volume fraction is controlled by the silver nanoparticle diameter and silica coating thickness. The silver volume fraction can be increased by increasing the silver nanoparticle diameter. However, when the particle size is too large, the self-assembly is compromised, leading to a highly nonuniform filling of trenches. So practically, the highest volume fraction achievable was Based on these findings, we fabricated new templates and self-assembled nanoclusters with 24 nm silver nanoparticles coated with 2 nm silica layers. Figure 7 shows optical spectra of two nanocluster metamaterials with p ¼ 280 nm for TM polarized incident light. In Fig. 7(a), by increasing the height of the nanocluster we were able to obtain a transmission dip as low as 11.4%. However, the larger volume of nanocluster along the light propagation direction resulted in higher absorption and significant broadening of the spectrum. It was not possible to distinguish the two separate features of magnetic and electric resonance, although the asymmetric shape of he spectrum suggested their presence. In Fig. 7(b) the height was reduced to 120 nm and the width was increased to exactly half of the periodicity. This sample showed the lowest transmission dip of 7.3% at 665 nm. Using the same fitting process used for Fig. 6(b), we found that the observed transmission dip corresponded to the real part of permeability value as low as We are currently in the process of further optimizing the nanocluster quality to 1 March 2010 / Vol. 49, No. 7 / APPLIED OPTICS A15

6 Fig. 7. (Color online) (a) Experimentally measured transmission (T), reflection (R), and absorption (A) of the 1D silver nanocluster metamaterial with parameters of p ¼ 280 nm, w ¼ 120 nm, and h ¼ 140 nm. Silver nanoparticle of 24 nm diameter and an 2 nm silica coating thickness for TM polarized incident light. (b) Experimentally measured transmission (T), reflection (R), and absorption (A) of the 1D silver nanocluster metamaterial with parameters of p ¼ 280 nm, w ¼ 140 nm, and h ¼ 120 nm, Silver nanoparticle of 24 nm diameter and an 2 nm silica coating thickness for TM polarized incident light. experimentally observe the negative real part of permeability in the visible. 4. Summary We reported a 1D silver nanocluster metamaterial that exhibits magnetic activity in the visible frequency region. This metamaterial exhibits magnetic resonance that is due to the coupled plasmon resonance of metal nanoparticles assembled into a finitesized nanocluster. The nanoclusters are fabricated by the template-directed self-assembly process, which is a bottom-up, scalable manufacturing process. The geometric design of the nanoclusters was carefully optimized by extensive numerical simulations to obtain the strongest magnetic resonance in the visible. Also, the fabrication processes were optimized to produce highly uniform and densely packed nanoclusters. The fabricated nanoclusters exhibited a uniform filling of templates with variations in their widths of 10%. Optical spectra of the nanocluster metamaterials exhibited strong dips in transmission and peaks in absorption in the red spectrum that are due to the excitation of magnetic resonance supported by the nanoclusters. The lowest value of the real part of the effective permeability experimentally observed was Further optimization of the fabrication process is expected to produce a negative real part of permeability. 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