Nanostructured Plasmonic Medium for Terahertz Bandwidth AllOptical ...

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Oct 24, 2011 - M. Ren , J.-Y. Ou , Dr. E. Plum , J. Zhang , Dr. K. F. MacDonald , ... Mengxin Ren , Baohua Jia , Jun-Yu Ou , Eric Plum , * Jianfa Zhang , Kevin F. MacDonald , ... linear responses in gold. b) Scanning electron microscopy (SEM) ...
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Nanostructured Plasmonic Medium for Terahertz Bandwidth All-Optical Switching Mengxin Ren, Baohua Jia, Jun-Yu Ou, Eric Plum,* Jianfa Zhang, Kevin F. MacDonald, Andrey E. Nikolaenko, Jingjun Xu, Min Gu, and Nikolay I. Zheludev* Photonics has the potential for processing information at unprecedented speeds and accommodates massively parallel data processing algorithms. To compete against electronics, photonic switches must allow for dense integration and surpass the gigahertz performance of electronic components. This requires a nonlinear switching medium with an as-yet unavailable ultrafast giant nonlinear response. Here, we show that a suitable switching material can be engineered by harnessing the nanoscale confinement of light and the nonlinearity of metal. Using a nanostructured gold film, we demonstrate resonant switching, the performance of which is at least one order of magnitude faster and stronger than designed materials reported so far.[1–4] It exceeds electronic component speeds by a factor of a thousand and achieves control of light with light in a film only 50 nm thick at an average light power level of only a few milliwatts, thus providing a ground-breaking solution for all-optical data processing. Research on the optical nonlinearities of metal surfaces, films, and nanoparticles[5–9] and in particular studies of degenerate cubic nonlinearities responsible for light’s self-action, nonlinear absorption, pulse reshaping and self-modulation, limiting, saturable absorption, frequency degenerate four-wave mixing, and pump–probe effects have attracted tremendous attention over several decades.[10–16] They revealed a range of response mechanisms, from the transient smearing of the electron energy distribution and multiphoton transitions to temperature, spin, and phonon-mediated processes.[17–19] It is now well-understood that the nonlinear properties of metal films and nanoparticles dramatically depend on film roughness and morphology and nanoparticle size distribution and shape.[20–24] What we report here is distinctively different from this body of prior work: we demonstrate a new strategy for achieving an

extremely fast engineered optical nonlinearity through nanoscale periodic sub-wavelength patterning of thin metal films. This leads to a resonant, orders of magnitude enhancement of the cubic nonlinear response of the metal. The frequency at which this enhancement occurs may be controlled by varying the design of the metamaterial and, in a certain frequency range, the nanostructuring can reverse the sign of the nonlinearity. To achieve an even faster nonlinear response than the picosecond or sub-picosecond response of hybrid metamaterials, wherein the relaxation time depends on the exciton dynamics[3] or thermalization of hot electrons in metals[4] or semiconductors,[1,2] we harness the much faster nonlinearity of the direct two-photon absorption process. Nanostructured gold is used to illustrate the concept: the dominant mechanism of gold’s cubic nonlinearity is the socalled “Fermi-smearing” process in which light absorption at a frequency ωp leads to a non-equilibrium redistribution of electrons near the Fermi level (EF). When probed at ωs, this Fermismearing has most impact on transitions between the d-band states lying ΔE = 2.4 eV[25,26] below the Fermi level to states above the Fermi level, as illustrated in Figure 1a. Fermi-smearing

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Population created by pump sp-conduction ~ps Band

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d-Band Fermi-smearing b

DOI: 10.1002/adma.201103162

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M. Ren, J.-Y. Ou, Dr. E. Plum, J. Zhang, Dr. K. F. MacDonald, Dr. A. E. Nikolaenko, Prof. N. I. Zheludev Optoelectronics Research Centre and Centre for Photonic Metamaterials University of Southampton SO17 1BJ, UK E-mail: [email protected]; [email protected] M. Ren, Prof. J. Xu Key Laboratory of Weak Light Nonlinear Photonics Nankai University Tianjin 300457, China Dr. B. Jia, Prof. M. Gu Center for Micro-Photonics and CUDOS Swinburne University of Technology Victoria 3122, Australia

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355 nm x Figure 1. Metamaterial with giant plasmon-mediated femtosecond nonlinearity. a) Comparison between Fermi smearing and two-photon nonlinear responses in gold. b) Scanning electron microscopy (SEM) image of the nanostructured gold film. c) Detail of a single meta-molecule.

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leads to a very strong cubic optical nonlinearity and nonlinear absorption (β ≈ 10−5 m W−1) peaking at a wavelength of about 516 nm.[7,8] However, this nonlinearity is relatively slow as it depends on the thermalization of the hot electron ensemble, which occurs over a period of several picoseconds.[8] To engineer a much faster nonlinear medium, we engage the less efficient but “instantaneous” nonlinear process of direct non-resonant two-photon absorption between the d and sp states of the metal (see Figure 1a). Direct two-photon absorption takes place without a real intermediate level as there are no empty states in the Fermi sea. It occurs through a virtual state when the energy of two incident photons is combined to bridge a gap that cannot be bridged by individual photons: h¯ ωp + h¯ ωs > E . When characterized in a pump–probe experiment, the direct two-photon absorption nonlinearity has a very fast response time because it requires both the pump ωp and the probe ωs photons to be present simultaneously, and no slow decay carrier recombination is involved.[27] In fact the uncertainty principle prescribes a finite lifetime for the virtual level, and thus a finite nonlinearity response time of order h¯ /δ E < 1 fs, where δ E ≈ 12 E is the energy difference between the virtual level and the nearest real state.[28] Even with this limitation, this is an extremely fast degenerate cubic optical nonlinearity giving rise to a nonlinear absorption coefficient of order 10−8 m W−1. To enhance the efficiency of the direct two-photon nonlinearity even further we use resonant plasmon-mediated local field enhancement: a gold layer is structured with a metamaterial pattern, as shown in Figure 1b,c to support a plasmonic closed mode (Fano-like) excitation,[29] which has been previously discussed in detail.[30] This pattern is chosen for its small resonant mode volume ≈10−3 λ3 (where λ is wavelength) located mostly within the grooves of the structure, leading to a very high field concentration at the edges of the grooves (see inset of Figure 2c). A metamaterial with a lattice parameter of 425 nm provides a plasmonic resonance at λ = 890 nm where the nonlinear response of gold is dominated by direct two-photon absorption. The nanostructure consists of a periodic array of asymmetric split ring slits cut through a 50 nm thick gold film thermally evaporated on a fused quartz substrate. The 100 μm × 100 μm metamaterial pattern was manufactured by focused ion beam milling. Its transmission, reflection, and absorption spectra are presented in Figure 2a. The metamaterial shows an incredibly strong and fast nonlinear response. This was first studied using an open aperture Z-scan technique[31] based on a femtosecond frequency tunable Ti:saphire laser (pulse duration 115 fs, repetition rate 80 MHz). The film’s transmission was recorded while scanning the sample through the 6 μm focus of the laser beam, which was polarized perpendicular to the split in the metamaterial ring resonators (the y-direction as defined in Figure 1b). These measurements (Figure 3a) were performed at wavelengths in the proximity of the metamaterial’s plasmonic absorption line around λ = 890 nm. The nonlinearity of the film is clearly seen at an average laser power level of only a few milliwatts, which corresponds to a peak pulse intensity at the focus of a few GW cm−2. The spectral dependence of the nonlinear change in transmissivity for both structured and unstructured gold films recorded at a pulse peak intensity of 2.3 GW cm−2 is presented

Figure 2. Metamaterial linear and nonlinear optical properties. a) Linear absorption, transmission, and reflection spectra of the metamaterial near its plasmonic resonance. Light is polarized in the y-direction as defined in Figure 1b. b) Nonlinear transmission change ΔT/Tlinear at an illumination pulse peak intensity of 2.3 GW cm−2 for the metamaterial and an unstructured gold reference film. c) The metamaterial’s experimentally measured and theoretically evaluated effective two-photon ˜ compared to that of an unstructured gold absorption coefficient β film β (multiplied 50×). The shaded area shows the frequency range of absorption saturation. The inset shows a numerically simulated map of the electric field magnitude 10 nm below the gold surface at a wavelength of 890 nm.

in Figure 2b. While the 50 nm thick unstructured gold film shows only very small changes of transmissivity at this intensity, the structured metamaterial film exhibits a much more pronounced response: a sharp decrease of transmissivity is seen at the resonance, while at longer wavelengths, in the range from λ = 920 nm to λ = 980 nm (the shaded area in Figure 2b) transmissivity increases. The effects of two-photon absorption and nonlinear bleaching on the light intensity I within a nonlinear medium are con= α I + β I 2 + ..., ventionally described by the expression − dI dz where z is the propagation distance and α and β are, respectively, the linear and nonlinear absorption coefficients. In the present case, values of α and β can be derived[31] from absorption and Z-scan measurements if one reasonably assumes that higher-order processes are insignificant and considers the nanostructured gold film as an effectively continuous medium, the latter being justified because a metamaterial with periodic sub-wavelength patterning does not diffract or scatter light at

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The dramatic increase in the efficiency of two-photon absorption can be explained as a consequence of local field enhancement in the metamaterial. Indeed, following ref. [33] and assuming that the complex cubic susceptibility of gold is dominated by its imaginary part,[7,23] the metamaterial’s effective two-photon absorption coefficient β˜ resulting from local field enhancement can be calculated from the measured twophoton absorption coefficient of unstructured gold β and the knowledge of the local field distribution in the metamaterial E˜ as follows:   2  E˜ 2  E˜  dv n2 β˜ = Re β (1) n˜ 2 E 2 | E | 2 V˜

Figure 3. Giant ultrafast nonlinearity of a plasmonic metamaterial. a) Z-scan traces taken at an average laser power level of 3 mW (data points) with corresponding analytical fits (lines) for a selection of characteristic wavelengths near the metamaterial’s plasmonic resonance. b) Time-resolved pump–probe scans showing nonlinear absorption and bleaching dynamics for the metamaterial alongside a reference secondharmonic autocorrelation envelope for the pulses.

normal incidence. We believe that the metal is the dominant source of nonlinearity here rather than the supporting substrate. Indeed, the nonlinearity of fused quartz is several orders of magnitude smaller than that of gold.[32] As illustrated in Figure 2c, the two-photon absorption coefficient β of the continuous gold film (shown 50× enlarged) exhibits monotonic dispersion in the wavelength range between 800 and 1000 nm. In contrast, the nonlinearity of the nanostructured gold film has a dramatic resonance at λ = 890 nm (coinciding with a linear absorption peak) where its nonlinearity reaches β = 7.7 × 10−6 m W−1. This is a 300 times enhancement in nonlinearity over the level for unstructured gold at the same wavelength. Intriguingly, in the wavelength range between 920 nm and 980 nm the nanostructured film shows absorption saturation (bleaching) instead of the nonlinear absorption characteristic of unstructured gold. This absorption saturation corresponds to negative values of β, reaching –9.0 × 10−7 m W−1 at 930 nm.

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where V˜ is the gold volume of a single meta-molecule, n˜ is the metamaterial’s effective refractive index, n is the refractive index of bulk gold, and E is the electric field of the incident wave as it would be distributed in an unstructured gold layer. We evaluated the integral in Equation (1) numerically using a full 3D Maxwell solver to calculate the electric field distribution E˜ in the metamaterial. n˜ was also retrieved from these calculations using the S-parameter method.[34] As Figure 2c shows, the field enhancement model describes all characteristic features of the metamaterial’s two-photon absorption spectral dispersion, including the resonant enhancement of nonlinear absorption and nonlinear bleaching (absorption saturation) at longer wavelengths. This bleaching effect is described by negative values of β˜ and may be traced to a pecular phase relation between E and E˜ in the asymmetric split ring metamaterial pattern that produces negative values of the field enhancement factor (similar nonlinearity sign reversal is also found in gold nanoparticle colloids and thin films[7,11]). The temporal dynamics of the metamaterial’s nonlinear response were studied by non-collinear (15°) degenerate pump– probe transient spectroscopy with pulses spatially overlapped at a ≈30 μm diameter focal spot. The pump and probe beams had fluences of ≈70 μJ cm−2 and ≈1.6 μJ cm−2, respectively, and both were y-polarized, perpendicular to the split in the metamaterial rings, as in the Z-scan experiment. Measurements of pump-induced nonlinear absorption and bleaching revealed no asymmetric temporal dynamics (Figure 3b) indicating that the nonlinear response time is substantially shorter than the 115 fs duration of the pump and probe pulses. Although the underlying two-photon absorption nonlinearity is extremely fast and controlled by the sub-femtosecond lifetime of the virtual state, the resonant nonlinearity enhancement must take a toll on the speed of the metamaterial’s nonlinear response: if the two-photon nonlinearity is enhanced by a resonant plasmonic response with a spectral width δν = 2.7 × 1013 s−1, the uncertainty argument δτ × δν ≥ 1 dictates that its relaxation time will be limited to δτ = 1/δν ≈ 40 fs, which still is a very fast response that cannot be resolved with 115 fs optical pulses. The resonant enhancement of the gold film’s third order nonlinearity resulting from nanostructuring is a narrow-band effect. However, the spectral localization of this engineered resonance can be controlled by adjusting the metamaterial design, for instance by simply varying the dimensions of the

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Figure 4. Controlling nonlinearity of plasmonic metamaterial by pattern design. Theoretically predicted spectral dependence of the two-photon ˜ as a function of the unit cell size. The slit width absorption coefficient β of the pattern is kept constant at 35 nm in all cases. The horizontal grey dashed line corresponds to the experimental unit cell size.

meta-molecule. This is illustrated by Figure 4, which shows, based on Equation (1), how the nonlinear response will depend on the size of the metamaterial unit cell. At the long wavelength end of the range shown here the plasmonic local field enhancement factor remains strong but the underlying value of the unstructured gold nonlinearity decreases rapidly as the combined energy of the two photons approaches the 2.4 eV edge of the interband transitions between the d and sp states. At the plasmonic resonance the two-photon absorption coefficient β˜ is about 7.7 × 10−6 m W−1, corresponding to a thirdorder nonlinear susceptibility of 1.5 × 10−15 m2 V−2. We believe this to be the largest ultrafast frequency degenerate cubic optical nonlinearity observed to date with a relaxation time of less than 100 fs. For example, it is seven orders of magnitude stronger than the two-photon absorption nonlinearity of the classic nonlinear reference medium CS2.[35] To assess practical and data processing applications it is instructive to compare the resonance switching performance of the gold nanostructured metamaterial with other recently developed engineered nonlinear metamaterials in terms of modulation depth, speed of response, and required excitation fluence. The gold metamaterial reported here shows 40% transmission modulation with a response time considerably shorter than 100 fs (estimated to be 40 fs) at an excitation fluence of 270 μJ cm−2. In comparison: a metamaterial exploiting the nonlinearity of α-silicon[1] at a similar 300 μJ cm−2 excitation level shows a somewhat smaller level of response (30%) and crucially a response time (>750 fs) at least seven times slower. Another, exploiting that of carbon nanotubes,[3] offers ≈10% modulation at lower fluence (40 μJ cm−2), again with a relatively slow response time (estimated ≈600 fs). Finally, a recently reported plasmonic nanorod metamaterial[4] exhibits a large response (up to 80%) but one that is at least one order of magnitude slower and requires fluences that are more than one order of magnitude higher (a few mJ cm−2). In semiconductor saturable absorber mirrors (SESAMs), a popular medium for laser mode-locking, a relatively low saturation fluence (≈10 μJ cm−2) may be achieved by

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Figure 5. Optical limiting and absorption saturation. Average power of light transmitted through the nanostructure Pout against the average incident power Pin normalized by the low-intensity (linear) transmission. The dashed line corresponds to a strictly linear response; sublinear curves plotted for wavelengths of 880, 890, and 900 nm show regimes of optical limiting; a hyper-linear dependence at 930 nm shows the regime of absorption saturation (bleaching).

changing dopants or adjusting parameters of the nanostructure fabrication process but it is difficult to simultaneously achieve a femtosecond-timescale response as inevitable interband trapping and recombination processes limit the response time to the pico- to nanosecond range.[36] Potential applications of the gold metamaterial nonlinearity may be evaluated from Figure 5. It shows promise for ultrafast optical limiting and all-optical switching with sub-100 fs response times: such a nonlinearity could bring nanophotonic and plasmonic data processing comfortably into the >10 THz bit rate domain. Moreover, as has been demonstrated, nanostructuring can also bring about saturable absorption, which may be used for mode-locking of femtosecond lasers. In the metamaterial studied here the resonant insertion loss is about –7.5 dB. However, we envisage that this can be reduced by optimizing the design and using other less lossy plasmonic metals as the metamaterial framework. Silver in particular, with its larger 4 eV interband transition energy[26] corresponding to a two-photon absorption edge of about 620 nm, could be used across the visible part of the spectrum. In conclusion, we have found that the third order optical nonlinearity of metal films can be greatly enhanced and that its sign can be controlled by metamaterial nanostructuring. Such films offer applications in ultrafast optical limiters, saturable absorbers, and terahertz bandwidth all-optical gates.

Acknowledgements This work was supported by The Leverhulme Trust, The Royal Society (London), the UK Engineering and Physical Sciences Research Council (programme grant EP/G060363/1), the Australian Research Council (the Centres of Excellence programme, Laureate Fellowship grant FL100100099), and the P. R. China (‘111 Project’ grant B07013 and ‘973

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Program’ grant 2007CB307002). B.J. conducted research during her visit to Southampton, which was sponsored by the Australian Research Council APD grant DP0987006. Received: August 17, 2011 Published online: October 24, 2011

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