Hybrid graphene plasmonic waveguide geometry

The most straightforward HGPWM geometry modulated by the Pauli blocking effect (Fig. 1a) is based on the classical SPP configuration and is shown in Fig. 1b, top inset, where the gold strip (yellow colour), which supports the SPP propagation and serves as a backgate, is covered by a hexagonal boron-nitride (hBN) flake (purple colour), acting as a dielectric spacer and atomically smooth substrate for graphene, and a graphene flake (black colour). However, the SPP mode in such a waveguide configuration is, away from the surface plasmon resonance in the visible, only weakly bound to the metal surface and features primarily transverse electromagnetic fields, which do not excite currents in graphene, while in-plane fields (which do interact with the graphene in-plane conductivity) are negligibly small in the infrared29. Hence, the classical HGPWM configuration, producing only very weak graphene-related absorption (Supplementary Discussion 1A) and promising thereby only very weak modulation by gating, can hardly be used in practice. Attempting to enhance in-plane field components in the graphene layer, we introduced a nanostructured (corrugated) part of the plasmonic waveguide (Methods) so as to produce longitudinal near fields generated by the SPP mode propagating along the corrugated part of waveguide (see middle inset of Fig. 1b). It is however clear that the expected enhancement of in-plane field components is quite limited as the metal surface corrugation has to be shallow to not introduce significant additional propagation losses by scattering. Finally, we decided to make use of the wedge SPP mode supported by the edge of planar section of the waveguide30,31 (see bottom inset of Fig. 1b,c). This mode, in addition to enhanced in-graphene-plane fields near the edge of the strip that should result in higher modulation depth induced by graphene gating (Supplementary Discussions 1 and 5 and Supplementary Fig. 4), has superior field confinement characteristics, which is essential when considering potential applications to the surface plasmon circuitry. Figure 1d provides a general outline of modulation experiments: a non-transparent gold grating couples light into a plasmon-propagating mode that can be affected by gated graphene placed on the top of dielectric spacer and then running plasmons are decoupled into light through the transparent grating. Such configuration allows one to decrease the crosstalk between input and output lights, see Methods.

Figure 1: Principle of hybrid graphene plasmonic waveguide modulators. (a) Optical Pauli blocking expressed in terms of graphene relative conductivity. (b) Sketches of three types of plasmonic modes under investigation—flat, corrugated and wedge plasmons. White arrows indicate approximate direction of electric field. (c) 3D rendering of the experiment with the wedge plasmon mode. (d) The schematic of experiment where non-transparent grating couples light into plasmon modes (flat, corrugated or wedge), which can be affected by gated graphene, black layer, placed on the top of dielectric spacer (a flake of boron nitride, purple layer) and then be decoupled into light through the transparent grating. Full size image

All three studied plasmon–polariton modes—flat plasmons (FPs), corrugated plasmons (CPs) and wedge plasmons (WPs)—can be excited by moving the incident light beam to different parts of the coupler (Fig. 2a). An optical micrograph of one of our devices studied in this work is shown in Fig. 2b along with outlines demonstrating positions of hBN and graphene flakes. We have checked operation of plasmonic waveguides in both transmission and leakage radiation32,33 modes. Leakage radiation detection of plasmonic propagating modes for wedge and FPs are shown in Fig. 2c. Figure 2c confirms that the plasmonic modes were successfully excited and propagated along the waveguide. For completeness, Fig. 2d provides a scanning electron microscope micrograph of an area marked in Fig. 2b by the blue dashed box where the semitransparent decoupler and a part of the nanostructured area of the waveguide are shown. As preliminary experiments, we performed AFM studies of our samples to find thickness of hBN crystals (which turned out to be ∼50–70 nm, see Supplementary Fig. 1 and Supplementary Discussion 2) and hence to deduce the gating voltage necessary to induce optical Pauli blocking at the telecom wavelength (∼10–16 V). We also measured dc graphene resistance as a function of gating voltage in flat and corrugated regions of the waveguide with an idea to evaluate the position of the charge neutrality point (CNP) in graphene (V CNP ∼0 V), see Supplementary Fig. 2 and Supplementary Discussion 3. Alternatively, the CNP has been evaluated from Raman measurements described in Supplementary Fig. 3 and Supplementary Discussion 4.

Figure 2: Plasmon modes of hybrid graphene plasmonic waveguide modulators. (a) The schematics of a studied plasmonic waveguide. The red, green and blue arrows represent WP mode, FP mode and CP mode, respectively. (b) The optical micrograph of a typical hybrid graphene plasmonic modulator studied in this work. The red, green and blue arrows represent WP, FP and CP modes, respectively. An area enclosed by green dotted line represents hBN. An area enclosed by dotted brown line represents graphene. Scale bar, 50 μm. (c) Leakage radiation detection of wedge, upper panel, and flat, lower panel, plasmon-propagating modes. The wedge mode is given in both raw and Fourier filtered images. (d) A scanning electron micrograph of an area shown in b by the dotted box that shows corrugated waveguide and the semitransparent decoupling grating. Full size image

Modulation of plasmonic waveguides by graphene gating

Here we describe the main results of our experiments. The plasmonic waveguides were excited using telecom laser providing ∼3 mW of power at wavelength λ=1.5 μm. We measured the dynamic response of our modulators by applying an offset square-wave voltage to the back gate with peak-to-peak amplitude and dc component . Figure 3 shows the modulation-depth characteristics both as a function of and . Comparing the modulation depth of FP and CP modes (Fig. 3a), one can see that the modulation effect is substantially stronger for CP: the CP mode gives around an eightfold increase in modulation depth compared with FP (for large ). Here is set to 7.6 and 6 V for the measurements of the FP and CP mode modulation depths, respectively. For both FP and CP we see an approximately symmetrical increase in modulation depth with , which we attribute to being the positions of the CNP (for the FP mode this is V CNP ≈2.7 V; for the CP mode this is V CNP ≈0.9 V). For other samples the modulation for FP modes compared with CP modes was even less pronounced (see Supplementary Fig. 5 and Supplementary Discussion 6). A drastic improvement in the modulation depth is expected from the increased interaction of graphene with electric field of the CP mode. Indeed, the longitudinal component of the electric field of FP is rather weak, whereas the presence of corrugations creates strong local longitudinal fields near ridges (see the sketch of the mode on Fig. 1b and, for example, ref. 34).

Figure 3: Operation of hybrid graphene plasmonic waveguide modulators. (a) Modulated AC transmission of the waveguide expressed in dB μm−1 as a function of gating voltage for the flat, green data points, and the corrugated, blue data points, plasmon modes. The peak-to-peak amplitude of AC modulation was 7.6 and 6 V for FP and CP modes, respectively, the frequency 6 Hz. The filled and empty data points represent two different devices. The inset shows the position where the plasmonic modes were measured. (b) Modulated AC transmission of the waveguide expressed in dB μm−1 as a function of gating voltage for the wedge, red data points, and the corrugated, blue data points, plasmon modes. The amplitude of AC modulation was 6 V, the frequency 6 Hz. Notice the 10-fold increase of the modulation signal for wedge mode. The filled and empty data points represent two different devices. The inset shows the position where the plasmonic modes were measured. (c) Theoretical fit to the experimental data for the wedge mode modulation as a function of gating obtained for the following parameters: peak-to-peak modulation amplitude 6 V, frequency 6 Hz. (d) Modulated AC transmission of the waveguide expressed in dB μm−1 as a function of AC peak-to-peak amplitude for the wedge plasmon mode, red data points, and theoretical fit to the experimental data. The dc offset was 6 V, the frequency 6 Hz. Error bars were estimated as a noise level in the absence of AC modulation and were combined with random errors whenever repeated measurements were performed. Full size image