Optical Diode Action from Axially Asymmetric Nonlinearity in an All

Nov 13, 2013 - Action of an all-optical diode based on asymmetric nonlinear absorption. ..... It can also provide optical isolation to pulsed diode la...
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Letter pubs.acs.org/NanoLett

Optical Diode Action from Axially Asymmetric Nonlinearity in an AllCarbon Solid-State Device Benoy Anand,† Ramakrishna Podila,*,‡,§,∥ Kiran Lingam,§ S. R. Krishnan,†,# S. Siva Sankara Sai,† Reji Philip,⊥ and Apparao M. Rao*,‡,§,∥ †

Department of Physics, Sri Sathya Sai Institute of Higher Learning, Prashanti Nilayam, Andhra Pradesh, India 515134 Center for Optical Materials Science and Technology, §Department of Physics and Astronomy, and ∥Clemson Nanomaterials Center, Clemson University, Clemson, South Carolina 29634, United States ⊥ Light and Matter Physics Group, Raman Research Institute, Bangalore, India 560080 ‡

S Supporting Information *

ABSTRACT: Nanostructured carbons are posited to offer an alternative to silicon and lead to further miniaturization of photonic and electronic devices. Here, we report the experimental realization of the first all-carbon solid-state optical diode that is based on axially asymmetric nonlinear absorption in a thin saturable absorber (graphene) and a thin reverse saturable absorber (C60) arranged in tandem. This all-optical diode action is polarization independent and has no phase-matching constraints. The nonreciprocity factor of the device can be tuned by varying the number of graphene layers and the concentration or thickness of the C60 coating. This ultracompact graphene/C60 based optical diode is versatile with an inherently large bandwidth, chemical and thermal stability, and is poised for cost-effective large-scale integration with existing fabrication technologies. KEYWORDS: Optical diode, graphene, nonlinear absorption, nonreciprocity

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and optics, optical diodes that break the time-reversal symmetry in the propagation of light require novel nanoscale engineering to work around the intrinsic reciprocity in linear transmission, which is a consequence of the wave equation.4 Several optical diodes have been realized in the past using photonic crystals (PCs),5 second harmonic generators,6 magneto-optic effect,7 liquid crystal heterojunctions,8,9 opto-acoustic effect,10 absorbing multilayer systems,11 thermo-optic effect,12 or dynamically modulated ring resonator structures.13 Albeit conceptually elegant, these approaches face major challenges such as poor scalability, high cost, and a limited scope for device integration. Moreover, most of these devices operate only under specialized conditions (in electric/magnetic field or under phase matching conditions) or with a very narrow bandwidth, thus limiting their possible set of applications. Recently it was demonstrated that a steplike variation in the longitudinal nonlinear absorption (NLA) coefficient results in a nonreciprocal light transmission, or an optical diode action.14 Such optical diodes that are based on the axial asymmetry in nonlinearity are promising as they are passive, polarization independent, and function with minimal peripheral require-

n the past three decades, Si-based technologies have widely impacted electronics, communications, and many other applications. The ever-increasing demand for denser, faster, and power-efficient devices has sustained a continuous effort to miniaturize Si technology to such an extent that it is at the verge of its fundamental limit. This impending bottleneck has invigorated the search for alternative materials and technologies to replace Si technologies, and carbon-based nanomaterials such as carbon nanotubes and graphene are in vogue as building blocks for future electronic and photonic devices.1−3 While the present day carbon nanotechnology is well set to carry forward the scaling in size, a concomitant scaling in speed enforces the need for all-carbon photonic devices. Yet, carbonbased photonic technologies ostensibly lag their electronic congeners in development. A key element missing in the allcarbon offering of photonic devices is the optical diode, a fundamental element in any photonic logic circuit, which allows nonreciprocal transmission of light similar to current flow in an electronic p−n junction diode. Here, we demonstrate the experimental realization of the first all-carbon optical diode that is ready for scalable integration along with being inherently broadband in operation with no restrictions on polarization or phase-matching criteria. While devices such as filters, amplifiers, and wavelength converters are obvious from the physics-standpoint of materials © XXXX American Chemical Society

Received: June 2, 2013 Revised: October 21, 2013

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Figure 1. Action of an all-optical diode based on asymmetric nonlinear absorption. Light propagating through the diode encounters a steplike discontinuity in the nonlinearity that is achieved by employing an SA and RSA in tandem. The light green pulse at the output represents linearly transmitted pulse and the dark green one represents nonlinearly transmitted pulse. The factor for normalized transmittance is so chosen that the linear transmittance is set to unity in each case. In forward (reverse) bias configuration, light passes through the SA (RSA) layer prior to the RSA (SA) layer resulting in an increase (decrease) in the normalized transmission relative to linear transmission at high intensities. By simply changing the order of SA and RSA in the configuration, optical nonreciprocity can be achieved.

αI dI = − o I − βI 2 d z′ 1+ I

ments. The device organization is extremely simple as it does not have to satisfy structural periodicity or phase-matching conditions. It is well-known that time-reversal symmetry in third-order nonlinear optical materials leads to interesting reciprocal effects like phase conjugation.15 Intriguingly, the same third-order nonlinearity can be manipulated in such way that the time-reversal symmetry is broken, resulting in optical nonreciprocity. However, major drawbacks of such optical diodes14 include the use of solvents and thickness (∼4 mm). As-expected, the large footprint and liquid phase operation obviate large-scale integration (LSI) of this device into ultracompact spaces. Therefore, in view of LSI, it is highly desirable to develop solid-state optical diodes with a minimal footprint and working volume. To this end, we fabricated a solid-state all-carbon passive optical diode by employing a saturable absorber (graphene) and a reverse saturable absorber (C60) in tandem. In our optical diode, we used thin-films of C60 (∼5 nm) and graphene (∼2 nm) to achieve a moderate optical nonreciprocity factor (ratio of forward to backward transmission) of 4. Further, by varying the number of graphene layers and the thickness or concentration of C60 coating we demonstrated tunability of key nonlinear parameters that determine the nonreciprocity factor. Importantly, our optical diode is inexpensive for LSI and ultracompact with a potentially large bandwidth, chemical, and thermal stability. Device Model and Simulation. One of the simplest ways to achieve axial asymmetry is to introduce a jump discontinuity in nonlinearity along the direction of beam propagation. This can be realized by juxtaposing two materials of opposing NLA behavior adjacent to each other (see Figure 1), viz. a saturable absorber (SA) and a reverse saturable absorber (RSA). Both SA and RSA are a result of the dynamical interaction of these media with the incident laser pulses. In an SA, the excited state absorption cross section is lower than the ground state absorption cross section. Thus, the ground state absorption saturates with increasing input intensity, resulting in an increased light transmission. The generalized pulse propagation equation for a third order nonlinear absorber is given by

s

(1)

where I is the incident intensity and z′ is the propagation distance within the sample. αo, Is, and β are the linear absorption coefficient, saturation intensity, and two-photon absorption (2PA) coefficient, respectively. In the case of a SA (like graphene), the 2PA component in eq 1 is weak and the dominant effect comes from the saturable absorption component. On the other hand, for a RSA the absorption cross-section of the excited state is larger than that of the ground state. Thus the net light absorption increases with input intensity due to excited state transitions, resulting in an optical limiting (OL) response. Since the Is values of an RSA (like C60) are much higher than the incident intensity, the pulse propagation equation gets modified as16 dI = −αoI − βI 2 d z′

(2)

where β is the 2PA coefficient of RSA. We obtained the transmission characteristics of SA and RSA by numerically solving the pulse propagation eqs 1 and 2 (see Figure S1 in the Supporting Information). For the ease of identification in subsequent discussions, β for SA and RSA are denoted as βSA and βRSA, respectively. We model the diode action in this optical all-carbon device on the basis of eqs 1 and 2 with no assumptions a priori (see Supporting Information). This model demonstrates and captures the optical diode action using parameters that are determined entirely from the characteristics of the constituents, without the need to introduce free parameters.17 Physically, the optical diode action may be understood as follows. An SA or RSA, when considered individually, shows spatially reciprocal linear and nonlinear light transmission, that is, light transmission remains the same for opposite propagation directions through the material. However, the transmission characteristics become nonreciprocal for SA/RSA sandwich structures shown in Figure 1 due to the axial asymmetry in nonlinearity.14 Here, B

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Figure 2. Sample transmittance is simulated by numerically solving the appropriate pulse propagation equations (eqs 1 and 2) sequentially. Light transmission increases in the forward bias (solid lines) and reduces in the reverse bias (dotted lines) configuration, giving rise to an optical diode like function. The nonreciprocity factor can be tuned by adjusting the key sample parameters, viz., βRSA, Is, LT, and L (see text). Plot of nonreciprocal transmittance for (a) different βRSA values with βSA = 5 × 10−11 m/W, Is = 4.5 × 1011 W/m2 and LT = 0.0001, (b) different Is values with βSA = 5 × 10−11 m/W, βRSA = 1.5 × 10−8 m/W, and LT = 0.0001, (c) different LT values with βSA = 5 × 10−11 m/W, βRSA = 1.5 × 10−8 m/W, and Is = 4.5 × 1011 W/m2, and (d) different L values with βSA = 5 × 10−11 m/W, βRSA = 1.5 × 10−8 m/W, and Is = 4.5 × 1011 W/m2, and LT = 0.0001. The nonreciprocity factor can be as high as 100 as seen in (a).

Is; sample length, LSA), RSA (LT; nonlinear absorption coefficient, βRSA ; sample length, LRSA), or both. This is clearly demonstrated in our simulation results in Figure 2. For instance, the nonreciprocity factor can be increased by increasing the two-photon absorption coefficient (βRSA) of RSA as shown in Figure 2a; it can be as high as 100 for a value of βRSA = 8.1 × 10−8 m/W. The variation of the normalized transmittance for different values of Is, LT and sample length L are shown in Figure 2b−d, respectively. Thus, by carefully choosing the nonlinear parameters, nonreciprocal transmission characteristics can be tailored. Materials and Characterization. The bilayer graphene (BLG) and few-layer graphene (FLG) samples were grown on Cu substrates using a previously reported CVD technique.17 Briefly, Cu foils (1 cm ×1 cm) were placed in a 1 in. quartz tube furnace and heated to 1000 °C in 50 sccm of H2 and 450 sccm of Ar. Next, CH4 at different flow rates (2 sccm for BLG and 8 sccm for FLG) was introduced into the furnace for 20− 30 min and the samples were subsequently cooled to room temperature in flowing H2, Ar, and CH4. The graphene layers were transferred by spin coating 4% poly(methyl methacrylate) (PMMA) in anisole on to the Cu substrates at 4000 rpm followed by heat treatment for 5 min at 150 °C. The Cu foil was etched out from the graphene layer using Transene Inc., CE-100 etchant and was carefully washed in 10% HCl and deionized water for 10 min to remove any metal residue. Finally, the samples were transferred to 0.2 mm thick polished

the transmission becomes nonreciprocal above a threshold incident light intensity where optical nonlinearities of SA and RSA are prominent. In the forward bias (SA followed by RSA), light transmission initially increases above the linear transmittance while passing through the SA, followed by attenuation while passing through the RSA. If the SA effect is more prominent compared to RSA, then the overall response will be an increase in the light transmission (Figure 1). This is analogous to the behavior of a forward biased electronic diode, and the regime of linear transmission (lower input intensity) is comparable to the knee-voltage regime of the electronic diode. When the bias voltage exceeds knee voltage current flows through the diode; similarly, when the input light intensity exceeds a certain threshold level (which is strong enough to induce saturation in SA) the configuration allows increased light transmission in that direction. On the other hand, in the reverse bias configuration (RSA followed by SA) if the intensity of the light transmitted by the RSA is attenuated below the saturation intensity (Is) then it does not evoke a high transmittance in the SA. Consequently, the overall light transmission is reduced below the linear transmittance of the combined system at high input intensities, similar to the behavior of a reverse-biased electronic diode. Since the nonreciprocal light transmission arises from the axial asymmetry in the nonlinearity, the nonreciprocity factor may be varied by adjusting the linear and nonlinear optical parameters of SA (linear transmission, LT; saturation intensity, C

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and FLG (shown by the peaks in Figure 3) is known to arise from ultrafast carrier dynamics and Pauli blocking of the excited carriers. When excited by intense laser pulses, a nonequilibrium carrier population (electrons in the conduction band and holes in the valence band) is generated by intraband as well as interband one-photon absorption (1PA) and 2PA processes.21 The initial narrow carrier distribution (almost a Dirac-delta distribution) broadens via inelastic and elastic carrier−carrier scattering, and thermalizes into a Fermi−Dirac distribution with a temperature much higher than the lattice temperature within ∼10−150 fs.21 These hot electrons cool down by interband carrier-phonon scattering in a time scale of few picoseconds and eventually reach a thermal equilibrium with the lattice.21,22 In the presence of trap states, the carrier decay can be delayed up to ∼100 ps to 1 ns.23 Once a steady state is reached between excited carriers and carriers relaxing to initial states, further absorption of photons within the pulse width is restricted as two photoexcited carriers cannot occupy the same state due to the Pauli’s exclusion principle (Pauli blocking).21 In our recent work, we had shown that the saturation depth is sensitive to the in-plane crystallite size (La) in the case of CVD grown polycrystalline graphene.17 The saturation carrier density (N) can be approximated as N = αIτ/ℏω where α is the linear absorption coefficient, I is the input intensity, τ is the recombination time, ℏ is the Dirac’s constant, and ω is the excitation frequency.24 Therefore, for a fixed excitation saturation carrier density (and hence Is) depends only on the carrier recombination time, which is sensitive to the defect density in the lattice. In fact, ultrafast carrier dynamics studies done on epitaxial graphene by Dawlaty et al. show that τ decreases with increase in crystal disorder (or a decrease in La).22 Therefore the higher saturation/modulation depth (lower Is) of FLG (300%) compared to BLG (250%) seen in Figure 3 can be attributed to the increase in disorder with layer stacking which influences the saturation carrier density. The Is values determined from these measurements for FLG and BLG are 3.5 × 1011 and 5 × 1011 W/m2 (which correspond to saturation fluence values, Fs of 1.75 × 103 and 2.5 × 103 J/m2), respectively. Implementation and Results. Upon the basis of our simulation results, we fabricated an optical diode by coating 5 nm thick C60 film and BLG (∼2 nm)/FLG (∼5 nm) on opposite sides of a 200 μm thick polished quartz sheets. The forward and reverse bias transmission characteristics of this optical diode for incident pulse energy of 5 μJ (energy density or fluence of 102−103 J/m2) are shown in Figure 4a,b. The transmission is reciprocal for FLG/C60 (BLG/C60) for incident peak intensities less than 7.7 × 1010 W/m2 (1.1 × 1011 W/m2). Beyond this intensity, the nonlinearity in graphene and C60 films becomes sufficiently strong to induce spatially nonreciprocal transmission. We achieved a nonreciprocity factor of 4.2 (6.2 dB) for FLG/C60 (βSA = 5 × 10−11 m/W, βRSA = 1.3 × 10−8 m/W and Is = 4.9 × 1011 W/m2) while BLG/C60 (βSA = 4.9 × 10−11 m/W, βRSA = 1.2 × 10−8 m/W and Is = 6 × 1011 W/ m2) exhibited a nonreciprocity factor of 3.1 (4.9 dB). The fit curves in Figure 4 are a result of simulating the device action based on the model detailed earlier. It is noteworthy that the model describes the device in its entirety using experimentally determined quantities, input intensity, sample thickness, SA and RSA coefficients, and beam-size, within measurement errors. Thus, no free-parameters were required in this physical device model that has excellent agreement with the measurements. The higher nonreciprocity factor obtained with FLG/C60

quartz sheets precoated on with 5 nm thick C60 layer on one side and annealed at 450 °C in Ar (300 sccm) and H2 (700 sccm) for 2 h to remove the residual PMMA. A detailed characterization of as-grown and transferred graphene samples is provided in the Supporting Information. The C60 film was grown directly on quartz sheets using a home-built physical vapor deposition system.18 Z-Scan Measurements. In order to characterize the saturable and reverse-saturable absorption in these materials, we employed the open aperture Z-scan technique used for measuring the absorptive nonlinearity of materials. Here, 5 ns, 532 nm Gaussian pulses obtained from an externally triggered Q-switched frequency-doubled Nd:YAG laser operating at 0.25 Hz are initially split into two beams by a beam splitter. The reflected beam was directly measured by a pyroelectric detector (RjP-735, Laser probe Inc.) to monitor pulse-to-pulse energy variations, if any, during the experiment. The transmitted beam was measured by a similar detector after it passed through a converging lens and the sample. A lens (f = 10.5 cm) focused the beam, and from repeated knife-edge measurements, the beam radius at the focal point was determined to be ∼20 μm corresponding to a Rayleigh range of ∼2.4 mm, is much larger than the thickness of the samples used (∼10 nm). This enables us to apply the “thin sample approximation” of Z-scan theory.19 The sample is mounted on a linear translation stage and scanned along the beam axis near the focal region of the lens so that it is subjected to a gradual input intensity/fluence variation. With z = 0 being the position of the laser beam focus, the sample is scanned between two extremes −z to +z over a span of 30 mm. The sample transmission was measured as a function of sample position during these scans in steps of 200 μm, and a position versus normalized transmittance curve (Z-scan curve) is deduced. The nonlinear coefficients for saturable and reverse saturable absorption are calculated from these curves using numerical fitting of the data to standard nonlinear transmission equations detailed in the previous section. Figure 3 shows the individual Z-scan curves for FLG, BLG, and C60 films used in this study fitted with eqs 1 and 2, respectively. The C60 film shows OL behavior arising due to the excited state absorption from the triplet state (sequential absorption of two photons) mediated by intersystem crossing.20 The prominent absorption saturation observed in BLG

Figure 3. Open aperture Z-scan curves of BLG and FLG showing saturable absorption and C60 showing reverse saturable absorption. Solid lines represent theoretical fits to the Z-scan data. Samples are excited with 5 ns laser pulses at 532 nm. The measured sample transmittance is normalized to the linear transmittance and plotted. D

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Figure 4. Transmission characteristics of the all-carbon optical diode. Light transmission in forward bias (purple square) and reverse bias (gray circle) configurations of (a) FLG/C60 with LT = 0.4, βSA = 5 × 10−11 m/W, βRSA = 1.3 × 10−8 m/W, and Is = 4.9 × 1011 W/m2, and (b) BLG/C60 with LT = 0.45, βSA = 4.9 × 10−11 m/W, βRSA = 1.2 × 10−8 m/W, and Is = 6 × 1011 W/m2. The nonreciprocity factors for FLG/C60 and BLG/C60 are 4.2 and 3.1, respectively. Solid lines are theoretical fits to the experimental data obtained by numerically simulating the sample transmittance. Nonreciprocity can be further increased by optimizing the nonlinear parameters of graphene and C60.

NLA features associated with the present optical diode allow us to control and achieve nonreciprocity factor possibly as high as 15−20 dB (cf. Figure 2). In addition to diode action, this configuration can equally well serve as an alignment-free compact optical isolator for pulsed laser systems with wide angular acceptance. Thus, this nanodevice is a potential alternative to the conventionally used larger Faraday isolators; especially in the case of highly compact fiber-based pulsed lasers. It can also provide optical isolation to pulsed diode lasers in ultracompact set-ups, which are very sensitive to back reflections. In summary, we have demonstrated the first all-carbon alloptical diode by utilizing the axial asymmetry in optical nonlinearity in a graphene/C60 sandwich structure initiating the realization of this key component in all-carbon photonics. In this broadband solid-state device which is not limited by resonance matching requirements and has intrinsic polarization independence, for a sample thickness of ∼10 nm, we have demonstrated a moderate nonreciprocity factor of ∼4. Detailed numerical simulations revealed that the key nonlinear parameters that determine the nonreciprocity factor can be precisely tuned by varying the number of graphene layers and the thickness or concentration of C60 coating that makes our optical diode highly attractive for LSI.

compared to BLG/C 60 is the consequence of higher modulation depth of FLG films. Even though some of the previously reported optical diodes possess nonreciprocity values in the range 20−25 dB,7,10,12 they are limited either by incompatibility (especially in the case of magneto-optic materials whose integration with scalable complementary metal−oxide−semiconductor (CMOS) photonic platforms is indeed challenging),7 complexity in fabrication processes,10 narrow bandwidth or by stringent resonance matching requirements.12 The choice of appropriate all-carbon materials in the device we present here overcomes all of these limitations concomitantly owing to the unique properties of these constituents, as reasoned below. Graphene exhibits universal absorbance in the near-infraredto-visible spectral range owing to its linear energy dispersion near the Dirac point.25 Consequently its saturable absorption is tunable over this broad spectral range.26 Similarly, the electronic structure of C60 allows substantial excited state absorption in the entire visible spectral range.20 Thus, optical diode action over a broad wavelength range can be realized by using graphene and C60 arranged in tandem. Another key advantage of the present device geometry is its ultracompactness. The SA and RSA media are each only ∼2−5 nm and ∼5 nm thick respectively, making it attractive for highly integrated photonic information processing chips. Also, these nanocarbons are well-known for their long-term chemical and temperature stability and are much superior to those of their counterparts.27,28 Finally, all key parameters that determine the optical nonreciprocity (described in Figure 2) can be controlled during device fabrication which makes our optical diode properties predictable, tunable, and inexpensive to manufacture or print using scalable processes such as R2R manufacturing onto flexible polymer substrates.29 Furthermore, we previously demonstrated that the key nonlinear optical parameters of graphene, required to control the optical diode action, may be tuned using layer stacking and the generation of in-plane defects.17 Indeed, we found that a reduction in the in-plane coherence length (or average defect-to-defect distance) and increase in number of layers can result in a decrease in Is, thereby increasing the modulation depth. Similarly the limiting depth of C60 coating (determined by β) can be increased by increasing its concentration or thickness. Such realistic tunable

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ASSOCIATED CONTENT

S Supporting Information *

The following details are presented: (1) numerical simulation, and (2) graphene characterization. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. Present Address #

IBM-Semiconductor R&D Center, Bangalore, India 560045.

Notes

The authors declare no competing financial interests. E

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ACKNOWLEDGMENTS B.A. and S.S.S.S. are grateful to Sri Sathya Sai Baba, the founder chancellor of SSSIHL, for the continuous support and lab facilities. B.A. acknowledges UGC, Government of India for a senior research fellowship (SRF). A.M.R. acknowledges support from the National Science Foundation, Division of Civil, Mechanical and Manufacturing Innovation (CMMI; Grant1246800).

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REFERENCES

(1) Bonaccorso, F.; Sun, Z.; Hasan, T.; Ferrari, A. C. Nat. Photonics 2010, 4, 611−622. (2) Bandaru, P. R.; Daraio, C.; Jin, S.; Rao, A. M. Nat. Mater. 2005, 4, 663−666. (3) Avouris, P. Acc. Chem. Res. 2002, 35, 1026−1034. (4) Trzeciecki, M.; Hübner, W. Phys. Rev. B 2000, 62, 13888−13891. (5) Mingaleev, S. F.; Kivshar, Y. S. J. Opt. Soc. Am. B 2002, 19, 2241− 2249. (6) Trevino-Palacios, C. G.; Stegeman, G. I.; Baldi, P. Opt. Lett. 1996, 21, 1442−1444. (7) Bi, L.; Hu, j.; Jiang, P.; Kim, D. H.; Dionne, G. F.; Kimerling, L. C.; Ross, C. A. Nat. Photonics 2011, 5, 758−762. (8) Chen, J.-Y.; Chen, L.-W. Opt. Express 2006, 14, 10733−10739. (9) Hwang, J.; Song, M. H.; Park, B.; Nishimura, S.; Toyooka, T.; Wu, J. W.; Takanishi, Y.; Ishikawa, K.; Takezoe, H. Nat. Mater. 2005, 4, 383−387. (10) Kang, M. S.; Butsch, A.; Russell, P. S. J. Nat. Photonics 2011, 5, 549−553. (11) Gevorgyan, A. H. Tech. Phys. 2002, 47, 1008−1013. (12) Fan, L.; Wang, J.; Varghese, L. T.; Shen, H.; Niu, B.; Xuan, Y.; Weiner, A. M.; Qi, M. Science 2012, 335, 447−450. (13) Yu, Z.; Fan, S. Nat. Photonics 2009, 3, 91−94. (14) Philip, R.; Anija, M.; Yelleswarapu, C. S.; Rao, D. V. G. L. N. Appl. Phys. Lett. 2007, 91, 141118. (15) Jain, R. K.; Lind, R. C. J. Opt. Soc. Am. 1983, 73, 647−653. (16) Sutherland, R. L. Handbook of Nonlinear Optics; Marcel Dekker Inc.: New York, 1996. (17) Podila, R.; Anand, B.; Spear, J. T.; Puneet, P.; Philip, R.; Sai, S. S. S.; Rao, A. M. Nanoscale 2012, 4, 1770−1775. (18) Rao, A. M.; Zhou, P.; Wang, K-A; Hager, G. T.; Holden, J. M.; Wang, Y.; Lee, W.-T.; Bi, X-X; Ecklund, P. C.; Cornett, D. S. Science 1993, 259, 955−957. (19) Sheik-Bahae, M.; Said, A. A.; Wei, T. -H.; Hagan, D. J.; Van Stryland, E. W. IEEE J. Quantum Electron. 1990, 26, 760−769. (20) Couris, S.; Koudoumas, E.; Rutht, A. A.; Leach, S. J. Phys. B: At. Mol. Opt. Phys. 1995, 28, 4537−4554. (21) Yang, H.; Feng, X.; Wang, Q.; Huang, H.; Chen, W.; Wee, A. T. S.; Ji, W. Nano Lett. 2011, 11, 2622−2627. (22) Dawlaty, J. M.; Shivaraman, S.; Chandrashekhar, Mvs.; Rana, F.; Spencer, M. G. Appl. Phys. Lett. 2008, 92, 042116. (23) Lim, G.-K.; Chen, Z.-L.; Clark, J.; Goh, R. G. S.; Ng, W.-H.; Tan, H.-W.; Friend, R. H.; Ho, P. K. H.; Chua, L.-L. Nat. Photonics 2011, 5, 554−560. (24) Bao, Q.; Zhang, H.; Wang, Y.; Ni, Z.; Yan, Y.; Shen, Z. X.; Loh, K. P.; Tang, D. Y. Adv. Funct. Mater. 2009, 19, 3077−3083. (25) Nair, R. R.; Blake, P.; Grigorenko, A. N.; Novoselov, K. S.; Booth, T. J.; Stauber, T.; Peres, N. M. R.; Geim, A. K. Science 2008, 320, 1308. (26) Wang, F.; Zhang, Y.; Tian, C.; Girit, C.; Zettl, A.; Crommie, M.; Shen, Y. R. Science 2008, 320, 206−209. (27) Lee, C.; Wei, X.; Kysar, J. W.; Hone, J. Science 2008, 321, 385− 388. (28) Gao, D.; Helander, M. G.; Wang, Z.-B.; Puzzo, D. P.; Greiner, M. T.; Lu, Z.-H. Adv. Mater. 2010, 22, 5404−5408. (29) Bae, S.; Kim, H.; Lee, Y.; Xu, X.; Park, J.-S.; Zheng, Y.; Balakrishnan, J.; Lei, T.; Kim, H. R.; Song, Y. I.; Kim, Y.-J.; Kim, K. S.; Ö zyilmaz, B.; Ahn, J. H.; Hong, B. H.; Iijima, S. Nat. Nanotechnol. 2010, 5, 574−578. F

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