Carbon Nanotubes in a Photonic Metamaterial

Giant nonlinearity of carbon nanotubes in a photonic metamaterial Andrey E. Nikolaenko,1 Francesco De Angelis,2 Stuart A. Boden,3 Nikitas Papasimakis,1 Peter Ashburn,3 Enzo Di Fabrizio,2 and Nikolay I. Zheludev1 1 Optoelectronics Research Centre, University of Southampton, Southampton SO17 1BJ, United Kingdom Italian Institute of Technology, 16163 Genova and the University of Magna Graecia, 88100 Catanzaro, Italy 3 School of Electronics and Computer Science, University of Southampton, Southampton SO17 1BJ, United Kingdom (Dated: December 3, 2009) arXiv:0912.0680v1 [physics.optics] 3 Dec 2009 2 Metamaterials, artificial media structured on the subwavelength scale offer a rich paradigm for developing unique photonic functionalities ranging from negative index of refraction and directionally asymmetric transmission to slowing light. Here we demonstrate that a combination of carbon nanotubes with a photonic metamaterial offers a new paradigm for the development of nonlinear media with exceptionally strong ultrafast nonlinear response invaluable in photonic applications. It is underpinned by strong coupling between weakly radiating Fano-type resonant plasmonic modes and the excitonic response of single-walled semiconductor carbon nanotubes. Using a ”combinatorial” approach to material discovery we show that the optical response of such a composite system can be tailored and optimized by metamaterial design. Carbon nanotubes (CNTs) are nearly ideal onedimensional systems, with diameter of only a few nanometers and length on the micron scale. Single walled CNTs rolled from a graphene sheet to create spiral arrangements of atoms along the tube are of particular interest to photonics. Such nanotubes are direct gap semiconductors with absorbtion spectra dominated by exciton lines [1]. Their possible technological uses include nanometre-scale light sources, photodetectors and photovoltaic devices. CNTs also possess unique nonlinear optical properties [2] as they exhibit high third-order susceptibility with sub-picosecond recovery time [3, 4] lending to applications in ultrafast lasers [5, 6, 7, 8, 9]. CNTs exhibit significant advantages over other materials as nonlinear media: they offer much simpler and cheaper fabrication than conventional semiconductor nonlinear optical components, they are robust and they can be easily integrated into optical-fibre and waveguide environments. The main source of optical nonlinearity in semiconductor CNTs is the saturation of the resonant exciton line. Combining CNTs as nonlinearity agents with metamaterial structures provides the opportunity to link the plasmonic resonances of metamaterials with the excitonic resonances of nanotubes. In fact, we demonstrate here that engaging the strong local fields in the vicinity of the metamaterial leads to an enhanced response of the nonlinear agent. For that matter selecting an appropriate metamaterial structure is crucially important. In our experiments we used a planar structure that belongs to the class of metamaterials supporting dark mode plasmonic excitations [10]. In such metamaterials weak coupling of the excitation mode to the free-space radiation modes creates narrow reflection, transmission and absorption resonances with asymmetric, Fano-like dispersion. The first example of such a metamaterial was a double-periodic array of metallic asymmetrically split ring wire resonators that has found numerous applications in cases where sharp spectral features are required [11, 12, 13, 14]. Here we used a structure complementary to the split ring wire metamaterial: a double periodic array of asymmetrically split ring slits in a metal film (see Fig. 1). The metamaterial structures were fabricated by focused ion beam milling through a 65 nm thick gold film evaporated on a 102 nm thick Si3 N 4 membrane. Gold film roughness of less than 5 nm was obtained with low pressure (10−8 mbar) thermal evaporation. On a single membrane we manufactured five metamaterial arrays with overall sizes 22 × 22 µm2 and different unit cell size D varying from to 731 nm to 839 nm. This allowed us to follow a combinatorial approach for materials discovery, where a rapid search for the optimal composition is achieved by parallel screening of a number of different but structurally related samples [15]. Here the spectral position of the plasmonic resonance λp depends on the size of the unit cell. The available range of metamaterial structures with different unit cell size D allowed the study of the linear and nonlinear response for varying spectral separation of the main excitonic resonance of CNTs at λ11 from the plasmonic resonance of the metamaterial at λp , providing thus control over δpe = λ11 −λp . For wavelengths longer than the unit cell such periodic nanostructures do not cause diffraction of infrared optical radiation. In the spectral range of the CNT excitonic absorption lines they are true metamaterials as far as their far-field electromagnetic properties are concerned and may be fully characterized by their absorption, transmission and reflection. Characteristic spectra of the metamaterial are presented on Fig. 2a for an array with D = 731 nm. Fig. 3d shows the dependence of the peak of the metamaterial plasmon absorption line λp on the unit cell size. The Au@Si3 N 4 metamaterial structures were functionalized with single walled semiconductor carbon nanotubes with a characteristic diameter of 1.4 nm. A thin layer of nanotubes was formed on the metamaterial sur- 2 FIG. 1: Carbon Nanotube Metamaterial imaged under a scanning helium ion microscope. The combinatorial sample consists of five different structurally related metamaterial designs with different unit cell sizes D and an empty area annotated as ”Si3 N 4 window” on the same substrate (a). The metamaterial structure is a two-dimensional nanoscale array of slits in a gold film supported on a silicon-nitride mebrane (b). Carbon nanotubes deposited on the surface of the metal nanostructure form a layer of ”nanoscale feutre” (c). Plates (d) and (e) show unit cells of the metamaterial before and after deposition of nanotubes. On plate (e) note the arrow pointing at a single nanotube crossing the slit. Plate (f) shows a milled slit manufactured to study the morphology of the structure, which is presented in plate (g). face by spraying a sonificated water suspension of nanotubes and heating to 100 0 C resulting in the rapid evaporation of the water component. When deposited on a bare Si3 N 4 membrane, the nanotube layer shows a characteristic absorption spectrum dominated by λ11 and λ22 excitonic lines, as presented in Fig. 3b. Figure 1 shows microscope images of the metamaterial before and after functionalization with CNTs. The images were taken with a scanning helium ion microscope. This novel imaging technique [16] is very well suited for imaging carbon nanotubes on metamaterials as it benefits from large depth of field, small interaction volume of ions with the medium and high contrast of the image ensuring excellent FIG. 2: Spectral response of the Carbon Nanotube Metamaterial: Transmission (T), Reflection (R) and Absorption (A) for a metamaterial array with a D = 731 nm unit cell size (a) and for the same metamaterial fuctionalized with CNTs (b). Note the red shift of the plasmon absorption resonance in the CNT-fuctionalized metamaterial. surface detail. CNTs seem to form a strongly interlinked network, a layer of ”nanoscale feutre” where individual nanotubes are bunched in thicker thread-like structures. On a few occasions single nanotubes bridging the gaps of the metal nanostructure are also seen (see Fig. 1e). We investigated the morphology of the carbon nanotube metamaterial by observing its cross-section in a trench cut through the sample by a focused ion beam (Fig. 1f). For this matter, a section of the sample was covered by a thin protective layer of tungsten. The layer of carbon nanotubes had a thickness between 20 nm and 70 nm across the sample as can be seen on Fig. 1g. It creates negligible scattering at optical frequencies as it is structured at a deep sub-wavelength scale. We observed substantial changes in the metamaterial’s optical properties resulting from the CNT functionalization. All resonance features exhibited an anticipated ”red shift” ∆ = λ∗p − λp of the plasmon resonance resulting from the reduction of the plasmon frequency due to the presence of the highly polarizable carbon nanotubes (compare Fig. 2a and Fig. 2b). After functionalization the metamaterial’s reflection decreased, whereas the spectrum of absorption accrued a background associated with the interband and exciton transition in the 3 on the sample of only about 2.4 mW. The spectra of the nonlinear response are presented on Fig. 4. Here the nonlinear response is normalized to the fluence level of 40 µJ/cm2 across the entire spectrum. At resonance the light induced transmitted intensity variation of the carbon nanotube metamaterial is about 10 percent. In good agreement with previous works [8, 9], we detected a much weaker nonlinear response of CNTs on the unstructured dielectric substrate (Fig. 4a). FIG. 3: Electronic Density of States (DOS) in a semiconductor single walled carbon nanotube (a); Plasmonic absorption resonance in a metamaterial without CNTs and excitonic resonances in a CNT film on a silicon nitride substrate (b); calculated color coded field map showing the total magnitude of the electric field of the light wave in the immediate proximity of the metamaterial plane at the plasmonic resonance λp (c); and the dependence of the metamaterial absorption resonance spectral position on the unit cell size before and after functionalization with CNTs (d). nanotubes. Additional losses introduced by the CNTs damped the metamaterial plasmonic resonance, hence its quality factor decreased. Hidden in the stronger spectral features of the metal nanostructure, the λ11 excitonic line is not identifiable on the absorption spectrum of the functionalized metamaterial. The red-shifted positions of the trapped mode resonance in the metamaterial-CNT system are presented in Fig. 3d for different sizes of the unit cell D. The nonlinear response of the metamaterial was investigated with a broadband ultrafast super-continuum fiber source generating a continuous train of pulses with a repetition rate of 20 MHz. The source was equipped with a computer-controllable, tunable, 10 nm bandwidth, spectral filter. The sample was placed at the focal point of a dispersion-free reflective parabolic concentrator to achieve a spot size of about 20 µm in diameter (full width at half maximum). Through the nature of the super-continuum generation process the pulse duration was a function of wavelength and within the investigated spectral interval varied from a few ps to a few hundred femtoseconds; thus it is instructive to present results of nonlinearity measurements in terms of fluence of the light excitation. The measurements (see Fig. 4b) were taken by increasing fluence from about 3 µJ/cm2 to the level of 40 µJ/cm2 corresponding to the average power level FIG. 4: Light-induced change of transmission of the CNTfunctionalized metamaterial for different unit cell sizes (a). Light-induced transmission change for different levels of intensity for a CNT-functionalized metamaterial with unit cell size D = 839 nm (b). The nonlinear response of CNTs on a silicon nitride membrane (magnified by a factor of 10) is shown for comparison on panel (b) and also on panel (a) (without magnification). The nonlinear response of the metamaterial has a complex frequency dispersion that could be decomposed on two main components derived from the analysis of the response in structures with different unit cell sizes. The first component that is practically independent of the unit cell size is relevant to the bleaching of the carbon nanotube excitonic resonance. Here increase of the light intensity leads to an increase of transmission. On Fig. 4b this component of the response is illustrated by a dashed bell-shaped line with amplitude A1 that is centered at the CNT’s exciton absorbtion peak at 1950 nm and has a width of about 310 nm. This bleaching response is superimposed to a much sharper ”negative” peak of reduced transmission. For a metamaterial with D = 839 nm this peak, indicated as A2 , has a width of about 120 nm. We argue that this ”negative” component is linked to the reduced damping of the plasmon mode through excitonplasmon coupling. Indeed under strong resonant coupling, the lower excitonic damping results in the plasmon absorption peak becoming more intense and partially recovering the low transmission levels characteristic of the ”CNT-free” metamaterial. This interpretation is very well supported by the fact that the negative peak migrates towards higher frequencies in structures with a smaller unit cell size, i.e. with the reduction of the plasmon resonant wavelength. This mechanism will be 4 illustrated below using a classical oscillator model. However, as the nonlinear effect here has a transient nature, and also involves nonlinear refraction, it takes the form of dynamic resonance pulling, where the apparent resonance frequency of the ”negative” response is somewhere in between the excitonic line position and the plasmonic resonance in the structure. When the plasmon and exciton resonances nearly coincide, as in the case presented in Fig. 4b, the ”negative” effect is most pronounced. Here the nonlinear response may be compared with that of CNTs deposited on a bare Si3 N 4 membrane: one can see that the CNT’s response on the unstructured substrate (peak A3 ) is about 12 times smaller than the overall ”negative” response of the CNTs on the metamaterial (peak A2 ). One can also argue that the positive response on the CNTs (peak A3 ) is a factor of 13 smaller than that of the positive component of the CNT’s response in the metamaterial (peak A1 ) while the overall negative response (peak A1 plus peak A2 ) is a factor of 25 smaller than that of the CNTs alone. From a slightly different prospective, the enhanced non-linear response of the composite metamaterial-carbon nanotube system is due to the resonant increase of the plasmon fields in the vicinity of the slits in the metal film through which light penetrates the metamaterial. This is illustrated in Figs. 3c, where we present the results of full three-dimensional Maxwell calculations of the electric field magnitude just above the metamaterial surface. At the plasmon resonance λp the field just above the split-ring slits is up to 20 times stronger than the electric field of the incident wave, ensuring a strongly intensity-dependent response. The main features of the mechanism underlying the nonlinear optical response of the coupled plasmonexciton system in the carbon nanotube metamaterial can be understood in terms of a simple mechanical model consisting of coupled Hooke oscillators (mass on elastic spring) driven by an external harmonic force F (see Fig. 5a) [17]. Here the plasmon resonance is represented by the harmonic oscillation of two masses, M1 and M2 , elastically coupled through a third mass, M3 . The oscillators represent excitations in the Π-shaped and straight slit of the unit cell of the metamaterial and hence have different masses, while friction Γ stands for the plasmonic losses. The mass M3 linking the two oscillators is also damped to account for the radiation losses γr . At the plasmonic dark-mode resonance the larger masses oscillate with opposite phases leaving the middle mass still. Hence radiation losses are at minimum (since the mass M3 does not move), all the energy is stored in high-amplitude oscillations of the large masses M1 and M2 leading to a sharp absorption peak associated with friction Γ as seen in the corresponding dissipation spectrum of Fig. 5b. To account for the carbon nanotube layer we introduce two additional nonlinear oscillators containing masses M4 and M5 . They are responsible for the formation of the exciton absorption line (see Fig. 5b). The saturation of the FIG. 5: (a) Illustrative model of the carbon nanotube metamaterial and the plasmon-exciton nonlinearity. The metamaterial’s plasmon response is represented by harmonic oscillators with masses M1 and M2 linked to mass M3 . The carbon nanotube’s excitonic response is represented by the nonlinear oscillators M4 and M5 . Plate (b) separately shows the linear dissipation losses of the uncoupled plasmon (red line) and exciton (blue line) systems. Plate (c) shows the dissipation losses of the linked plasmon-exciton system at different levels of excitation. Note that the higher excitation level leads to an increase in the overall losses in spite of bleaching of the exciton absorption. excitonic absorption in the carbon nanotubes is introduced assuming that the oscillators are subject to nonlinear dissipation (β). The plasmon-exciton coupling is represented by elastic springs of constant Kc . The model reproduces all the essential features observed in the nonlinear response of the carbon nanotube metamaterial: When measured separately, the plasmon resonance appears at a frequency slightly higher then the carbon nanotube excitonic resonance and is sharper (see Fig. 5b). For a small amplitude of the driving force F , corresponding to low light intensity, the dark mode resonance experiences strong damping as a result of the plasmonexciton coupling. For a high level of excitation, corresponding to high levels of light intensity, the excitonic absorption saturates and hence the plasmonic peak, now subject to lower losses, partially recovers, increasing in amplitude and becoming narrower (see Fig. 5b). This illustrates our experimental observation that in the strong exciton-plasmon coupling regime (small δpe ) the trans- 5 mission through a metamaterial sample becomes lower at higher levels of excitation in spite of bleaching of the exciton absorption (compare with Fig. 4b). In summary we have demonstrated that single walled semiconductor carbon nanotubes can be used as a very efficient agent of nonlinearity in metallic metamaterial structures. Exciton-plasmon coupling and strong resonant local fields of the metamaterial create an ultrafast nonlinear response that is at least an order of magnitude stronger than that of a bare CNT film. Importantly, the metamaterial environment allows to spectrally tailor the nonlinear response and even reverse the sign of optical nonlinearity. We argue that carbon nanotubes on metamaterials promise to offer performance that is robust, stable and free from permanent bleaching. Indeed, the resonance nonlinear properties of the suggested composite metamaterial can be easily tuned throughout the near-IR (including technologically important wavelengths such as 1.06 µm and 1.55 µm) by employing carbon nanotubes of different diameter and appropriately scaling the metamaterial. 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