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Controlling graphene plasmons with resonant metal antennas and spatial conductivity patterns

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Science  20 Jun 2014:
Vol. 344, Issue 6190, pp. 1369-1373
DOI: 10.1126/science.1253202

A controlled launch for plasmons

To create nanophotonic devices, engineers must combine large-scale optics with tiny nanoelectronics. Plasmons, the collective light-induced excitations of electrons at a metal's surface, can bridge that difference in size scales. Alonso-Gonzalez et al. placed structured gold “antennas” on top of a graphene layer to launch and propagate plasmonic excitations into the graphene. By carefully designing the antennas, the researchers could engineer the wavefronts of the plasmons and control the direction of propagation. This approach illustrates a versatile approach for the development of nanophotonics.

Science, this issue p. 1369

Abstract

Graphene plasmons promise unique possibilities for controlling light in nanoscale devices and for merging optics with electronics. We developed a versatile platform technology based on resonant optical antennas and conductivity patterns for launching and control of propagating graphene plasmons, an essential step for the development of graphene plasmonic circuits. We launched and focused infrared graphene plasmons with geometrically tailored antennas and observed how they refracted when passing through a two-dimensional conductivity pattern, here a prism-shaped bilayer. To that end, we directly mapped the graphene plasmon wavefronts by means of an imaging method that will be useful in testing future design concepts for nanoscale graphene plasmonic circuits and devices.

Surface plasmon polaritons—coupled excitations of photons and mobile charge carriers—in metals and doped semiconductors offer intriguing opportunities to control light in nanoscale devices (17). Plasmons provide both a strong local field enhancement and confinement, accompanied by an appreciable reduction of the wavelength relative to free-space radiation. However, plasmons in metals exhibit relatively strong losses and cannot be controlled by electrical fields. Consequently, novel plasmonic materials are being sought (8). Among them, doped graphene is advantageous because of its two-dimensional nature and high carrier mobility, supporting plasmons with an extreme confinement and a wavelength that can be strongly reduced relative to photons of the same frequency (914). More importantly, the carrier concentration in graphene can be tuned by electrical gating, opening exciting avenues for nanoscale electrical control of light (1521). The ultrashort graphene plasmon (GP) wavelengths, however, come at the expense of a large momentum mismatch with photonic modes of the same frequency (2225). Future graphene plasmonic circuits (15) will thus critically depend on converting incident light into propagating GPs, and on controlling their propagation and focusing to enhance light-matter interactions.

Figure 1 introduces the launching of GPs by metal antennas. The calculations (26) consider gold rods of length L acting as resonant dipole antennas. As shown in Fig. 1A, they provide strong near fields of opposite polarity at the rod extremities. For the fixed illumination wavelength λ0 = 10.20 μm, the near-field intensity enhancement factor f2 = (E/E0)2 indicates the fundamental dipolar antenna resonance at L = 2.9 μm, where E is the electric field averaged over the antenna surface and E0 is the incident electric field. The Fourier transform (FT) of Fig. 1A reveals antenna near fields with momentum increased by orders of magnitude relative to the incident wave vector k0 (Fig. 1C). When such an antenna is placed on graphene (assuming a Fermi energy EF = 0.44 eV and a carrier mobility μ = 1136 cm2 V–1 s–1), the high-momentum near-field components match the GP wave vector, thus exciting propagating GPs. Indeed, we observed an oscillating near-field distribution around the antenna on graphene (Fig. 1D). The distance between the field maxima of the same polarity (same color) yields the GP wavelength, λp = 380 nm, which is smaller than λ0 by a factor of 27 (24, 25). Accordingly, the FT of Fig. 1D yields a bright ring of diameter kp = 2π/λp = 27k0, corroborating propagating GPs (Fig. 1F). As expected, the excitation of GPs broadens and shifts the antenna resonance (black curve in Fig. 1E).

Fig. 1 Numerical study of launching propagating GPs with resonant dipole antennas at λ0 = 10.20 μm.

(A) Near-field distribution of a resonant antenna (length L = 2.9 μm, width w = 0.6 μm, height h = 40 nm) on a CaF2 substrate. (B) Near-field intensity enhancement factor f2 as a function of L. (C) Absolute value of the Fourier transform of the near field in (A). (D) Near-field distribution of a resonant antenna (L = 3.2 μm, w = 0.6 μm, h = 40 nm) on graphene on a CaF2 substrate. (E) Enhancement factor f2 and ηp as a function of L. (F) Absolute value of the Fourier transform of the near field in (D). The images in (A) and (D) show the real part of the near-field z-component 5 nm above the antenna surface, normalized to |E0|.

To analyze how efficiently GPs are excited, we calculated the quantity ηp = Pp/(I0Aant) (red curve in Fig. 1E), where Pp is the power transferred into graphene, I0 is the illuminating intensity, and Aant is the geometrical antenna cross section. The value of ηp provides a good estimate for the cross section of exciting GPs relative to the antenna’s geometrical cross section (26). It clearly follows the antenna’s resonance. Relative to nonresonant antennas [e.g., with a quadratic cross section (600 nm × 600 nm)], the efficiency on resonance is enhanced by a factor of 28. The resonant near-field enhancement around the antenna is thus the source for strong GP excitation.

Intriguingly, we observed plane GP wavefronts parallel to the antenna axis, in contrast to metal surface plasmon polaritons launched by dipole antennas (Fig. 1D) (27). We explain these plane wavefronts by the weak diffraction of the GPs, which results from their short wavelength relative to the antenna length. The antenna can thus be considered as an extended plasmon source with a length of several GP wavelengths.

For an experimental demonstration, we fabricated gold rods on chemical vapor deposition–grown graphene transferred onto a 5-nm-thick SiO2 layer on a CaF2 substrate (26). We imaged the near-field distribution with a scattering-type scanning near-field microscope using a dielectric Si tip (Fig. 2A). The tip and sample were illuminated with s-polarized light (electric field E0) parallel to the antenna axis, thus efficiently exciting the antenna. While scanning the sample, the real part of the p-polarized tip-scattered light, Re(Es,p), is recorded simultaneously with topography (26). On metal plasmonic antennas, such an imaging scheme yields the vertical near-field component, Re(Ez) (28). This scheme also allows for mapping the vertical near field of the GP wavefronts launched by the antenna. This represents a fundamental difference from earlier experiments (24, 25) in which a metal tip was used to both excite and detect GPs, yielding complex images of plasmon interference.

Fig. 2 Verification of an antenna-based GP launcher.

(A) Illustration of the experiment. (B) Topography image of an off- and on-resonance dipole antenna (left and right, respectively). (C and D) Experimental and (E and F) calculated images illustrating the real part of the vertical near-field component of the antennas shown in (B) for λ0 = 11.06 μm and 10.20 μm, respectively. (G) Experimental and (H) calculated near-field profiles along the dashed black lines in (C) and (D) and in (E) and (F), respectively. Data in (C) to (H) are normalized to the near-field signals at the left antenna extremity. (I) Experimental (symbols) and calculated (solid line) GP wavelength λp as a function of λ0. Error bars denote SD of the averaged GP wavelengths obtained form adjacent near-field profiles.

Figure 2B shows the topography of two Au antennas on graphene being strongly off resonance (left) and near resonance (right). Near-field images at λ0 = 11.06 μm and λ0 = 10.20 μm (Fig. 2, C and D) verify the dipolar mode on the right antenna. We also observed short-range spatial near-field oscillations around this antenna. Their period is about 400 nm, matching the GP wavelength at mid-infrared frequencies (24, 25). Our experimental observations agree well with numerical simulations (Fig. 2, E and F) assuming EF = 0.44 eV and μ = 1136 cm2 V–1 s–1. These values, used in all the calculations throughout this work, are consistent with our earlier experiments in which similarly grown graphene was used (24, 26). Because of the relatively low mobility, the field oscillations decay within a few plasmon wavelengths. For quantitative comparison, we show in Fig. 2, G and H, the experimental and calculated near-field profiles, Re(Es,p) and Re(Ez), along the dashed black lines indicated in Fig. 2, C and D, and Fig. 2, E and F, respectively. We found excellent agreement, particularly for the oscillation periods and relative field strengths.

Figure 2I depicts the plasmon wavelength λp extracted from near-field images taken at different illumination wavelengths λ0. Good agreement with the calculations is found, confirming the GP origin of the near-field oscillations. Note that the experimental images directly reveal the plasmon wavefronts and wavelength λp [the latter given by the distance between two consecutive field maxima of the same polarity (color)], rather than local density of states (LDOS) maps and λp/2 as observed in (24, 25).

We also fabricated and imaged much shorter antennas (left structure in Fig. 2, B to F) being strongly off resonance with the incident wavelength. Owing to the weak field enhancement, we did not observe GPs around them (Fig. 2, C and D). For the same reason, some asperities remaining from the lithography process do not launch GPs. This result proves that GPs are launched by the resonant antenna near fields and not by the tip.

Resonant antennas can be simultaneously used for engineering the GP wavefronts, as we demonstrated with the use of concave and convex antenna extremities. While the convex extremity launches diverging GPs (Fig. 3, A to C; same data as shown in Fig. 2, A, C, and E), the concave extremity launches converging GPs (Fig. 3, D to F), yielding a focus at a distance of about 400 nm, as discerned by the change of the wavefront curvature (green lines in Fig. 3D).

Fig. 3 Wavefront engineering of GPs.

(A and D) Topography, (B and E) experimental near-field images Re(Es,p), and (C and F) calculated near-field images Re(Ez) of a convex and a concave antenna extremity, respectively (λ0 = 11.06 μm). The green lines in the topography images illustrate the GP wavefronts. (G) Illustration of GP focusing with a concave antenna extremity. (H and I) Experimental and calculated near-field intensity (red curves) along the white dashed lines in (E) and (F), respectively. The dark gray curves show the experimental and calculated near-field intensity along the black dashed lines in (B) and (C), respectively. All curves and near-field images are normalized to their maximum in the lower left corners of (E) and (F).

The concave extremity represents a 2D lens for focusing GPs (Fig. 3G). The focal length f is determined by the cavity radius, which nominally is 400 nm, and thus agrees well with the focus position observed in Fig. 3E. To analyze the focus, we plot in Fig. 3, H and I, the experimental and calculated near-field intensities, |Es,p|2 and |Ez|2, along the white dashed lines in Fig. 3, E and F, respectively (red curves). The dashed lines trace the field at a constant distance of 400 nm around the antenna extremity. We observed a strongly localized intensity at the focus position (position 2 in Fig. 3, E and F), which is enhanced by a factor of about 6 relative to positions 1 and 3. The plasmon focus yields an intensity enhancement by a factor of ~3 with respect to the convex antenna extremity (dark gray curves in Fig. 3, H and I).

The GP focus is determined by the numerical aperture (NA) of the concave extremity and the GP wavelength, analogous to diffraction-limited optics. Generally, the full width at half maximum (FWHM) of a focus size at wavelength λ can be estimated by FWHM ≈ λ/(2NA), where NA = sin(α). With α = 70° (from Fig. 3D) and λp = 436 nm, we calculate FWHM = 232 nm, which agrees well with FWHM = 235 nm in the experimental near-field profile (Fig. 3H) and FWHM = 216 nm in the calculated (Fig. 3I) near-field profile (red curves), respectively. Note that the focus size can be tailored by varying the NA. In Fig. 2C, where the opening angle α of the cavity and thus the numerical aperture are smaller (α = 29°, NA = 0.485), we measure a larger FWHM = 458 nm (fig. S2), in agreement with the expected FWHM = 450 nm (26).

Both the launching of GPs by antennas and wavefront mapping offer unique possibilities for studying fundamental and applied aspects of graphene plasmonics. In Fig. 4 we demonstrate that the propagation direction of GPs can be controlled by 2D refractive elements based on spatial conductivity patterns, as recently proposed (15). Our experiment is illustrated in Fig. 4A. A resonant gold antenna is illuminated with field E0 parallel to the antenna axis. The antenna fields launch GPs propagating perpendicular to the antenna, which are refracted at a prism structure where the Fermi energy and thus the GP wavelength are locally modified.

Fig. 4 Refraction of GPs at a graphene bilayer prism.

(A) Illustration of our experiment and Snell’s law of refraction. (B) Topography image of a graphene bilayer prism next to a resonant Au antenna. (C) Height profile along the dashed line in Fig. 3B. (D) Near-field image, Re(Es,p), recorded simultaneously with the topography shown in (B). (E) Near-field profiles taken at the positions marked by black and green arrows in (D). (F) Analysis of the GP wavefronts. Image extracted from Fig. 4D. (G) Calculated near-field image, Re(Ez). (H) Near-field profiles taken at the positions marked by black and green arrows in (G). All near-field data are shown in arbitrary units.

In the experiment, the prism consists of a graphene bilayer (26), which is outlined by a dashed black line in the topography image (Fig. 4B). Its height is 0.8 nm (Fig. 4C). In the near-field image (Fig. 4D), Re(Es,p), we observed horizontal GP wavefronts above both the left side and the end of the right side of the antenna (wavelength λp,2), as in Figs. 2 and 3. Inside the prism, we found an increased plasmon wavelength, λp,1 = 1.4 λp,2 (Fig. 4E). We explain it by a locally increased conductivity. Note that the conductivity, and thus the wavelength λp, scales with the Drude weight D (29). For stacks of decoupled graphene layers (where interlayer hopping of electrons is neglected), the Drude weight scales as D ~ nG1/2l (29), where nG is the carrier density per layer and l is the number of layers. Assuming that the carriers are equally distributed between the layers (30), we obtain nG = n/l, and subsequently D ~ n1/2l1/2, where n is the total carrier density equal to that of the monolayer graphene. For a bilayer, the conductivity is thus 1.41 larger than in a monolayer, yielding λp,1p,2 = D = 1.41, in agreement with our experimental finding.

Outside the left prism boundary, the wavefronts are tilted by 24°. For the propagation directions we found α1 = 50° and α2 = 26°, yielding sin(α1)/sin(α2) = 1.75 (Fig. 4F). Our findings, λp,1p,2 > 1 and sin(α1)/sin(α2) > 1, demonstrate that GPs qualitatively follow the most fundamental law of refraction, Snell’s law:Embedded ImageEmbedded Image (1)In Fig. 4G we corroborate the GP refraction with a numerical calculation, assuming EF,2 = 0.44 eV for the graphene monolayer (as in Figs. 2 and 3). For the bilayer, we increased the conductivity to match the experimental wavelength ratio, λp,1 = 1.4λp (Fig. 4H). We measured α1 = 50° and α2 = 30°, yielding sin(α1)/sin(α2) = 1.53, qualitatively following Snell’s law (Eq. 1). The quantitative discrepancy found in both experiment and theory [i.e., sin(α1)/sin(α2) > λp,1p,2] is attributed to the strong GP damping. In strongly absorbing media, Snell’s law deviates from its simple form (Eq. 1), as fronts of constant amplitude and phase may exhibit different diffraction angles (31), which is not considered in our analysis. Although further studies are required for a better quantitative understanding, our results demonstrate that GP propagation can be controlled by refraction. In the future, local gating of graphene could open exciting avenues for electrically tunable refractive elements, such as for steering of GPs.

Launching and control of propagating GPs by resonant metal antennas and spatial conductivity patterns could lead to various applications, including GP focusing into gated graphene waveguides, resonators, modulators, or plasmon interferometers for communication and sensing. Through the use of improved doping strategies and carrier mobility in graphene, we expect GPs to propagate over distances of many wavelengths at mid-infrared, near-infrared, and telecommunication wavelengths. Resonant antenna devices might also be used for converting the GPs into far-field radiation, which would enable a purely optical readout of graphene plasmonic circuits or wireless on-chip communication between them.

Supplementary Materials

www.sciencemag.org/content/344/6190/1369/suppl/DC1

Materials and Methods

Figs. S1 and S2

References (3235)

References and Notes

  1. See supplementary materials on Science Online.
  2. Acknowledgments: We thank P. S. Carney, A. Kuzmenko, I. Nechaev, and F. Guinea for stimulating discussions. Supported by the European Union through ERC starting grants (TERATOMO, SPINTROS and CarbonLight), NMP (HINTS and Grafol), Marie Curie Career Integration Grants (ITAMOSCINOM and GRANOP); the European Commission under Graphene Flagship (contract no. CNECT-ICT-604391); the Spanish Ministry of Economy and Competitiveness (National Projects MAT2012-36580 and MAT2012-37638) and from the Basque Government (Project PI2011-1). F.K. acknowledges support from the Fundacio Cellex Barcelona. R.H. is co-founder of Neaspec GmbH, a company producing scattering-type scanning near-field optical microscope systems such as the one used in this study. All other authors declare no competing financial interests.
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