Electrically Tunable Optical Nonlinearities in Graphene-Covered SiN

on a silicon nitride (SiN) waveguide covered with graphene which was gated ... or silicon nitride (SiN) waveguides.20,23–26 Both theoretical predict...
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Electrically Tunable Optical Nonlinearities in Graphene-Covered SiN Waveguides Characterized by Four-Wave Mixing Koen Alexander,*,†,‡ Nadja A. Savostianova,§ Sergey A. Mikhailov,§ Bart Kuyken,†,‡ and Dries Van Thourhout†,‡ †

Photonics Research Group, INTEC, Ghent University-IMEC, Ghent B-9000, Belgium Center for Nano-and Biophotonics (NB-Photonics), Ghent University, Ghent B-9000, Belgium § Institute of Physics, University of Augsburg, D-86135 Augsburg, Germany ‡

S Supporting Information *

ABSTRACT: Third order optical nonlinearities in graphene have been demonstrated to be large and have been predicted to be highly dependent on the Fermi energy of the graphene. This prediction suggests that graphene can be used to make systems with large and electrically tunable optical nonlinearities. In this work, we present what is to our knowledge the first experimental observation of this Fermi energy dependence of the optical nonlinearity. We have performed a degenerate four-wave mixing experiment on a silicon nitride (SiN) waveguide covered with graphene which was gated using a polymer electrolyte. We observe strong dependencies of the four-wave mixing conversion efficiency on the signal-pump detuning and Fermi energy, that is, the optical nonlinearity is indeed demonstrated to be electrically tunable. In the vicinity of the interband absorption edge (2|EF| ≈ ℏω), a peak value of the waveguide nonlinear −19 A m2V−3, is parameter of ≈6400 m−1W−1, corresponding to a graphene nonlinear sheet conductivity |σ(3) s | ≈ 4.3 × 10 measured. These results were qualitatively linked with theoretical calculations. Apart from providing a better understanding of the nonlinear optical response of graphene, these observations could pave the way toward the use of graphene for tunable nonlinear optics. KEYWORDS: graphene, gated graphene, integrated optics, nonlinear optics, four-wave mixing Graphene plasmonics is yet another emerging field,13 providing enhanced light−matter interaction from the mid-IR to the THz region.14,15 Moreover, graphene is expected to play a role in the bridging the THz gap, as sources,16 modulators17 and detectors18 in this scarcely researched frequency range have been demonstrated. The role of graphene for microwave applications is also being researched.19 In recent years, there has been increasing interest in the use of graphene for nonlinear optics. Third order optical nonlinearities allow for all-optical signal generation and processing,20 such as demultiplexing of signals at high speeds,21,22 alloptical logical gates,23 parametric gain,24 wavelength conversion,25 signal regeneration,26 and many others.20 Many of these experiments have been performed on CMOS compatible platforms, such as silicon (Si) or silicon nitride (SiN) waveguides.20,23−26 Both theoretical predictions27−32 and experimental studies33−37 have indicated that graphene has a very high third-order sheet conductivity σ(3) s , which leads to a strong nonlinear optical response. Monolayer graphene could

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raphene, an allotrope of carbon in which the atoms are arranged in a hexagonal two-dimensional lattice, has received large interest in a variety of fields, ranging from composites over energy applications to electronics. Also, in photonics and optoelectronics, graphene proves to be increasingly useful. Due to the conical, quasi-linear electronic dispersion relation, optical phenomena in weakly doped graphene are intrinsically broadband. For example, the optical absorption of graphene has been shown to be nearly constant over the visible and near-IR wavelength ranges.1,2 Photodetectors making use of graphene have been demonstrated on guided wave platforms, exploiting this inherent broadband absorption.3,4 Recently, Goossens et al. have demonstrated a graphene-CMOS image sensor array covering the 300−2000 nm wavelength range.5 Another asset of graphene is that its Fermi level can be readily changed by chemical doping or electrostatic gating, providing unprecedented tunability of its electromagnetic properties. In integrated optics this has already lead to the successful demonstration of broadband electro-optic amplitude modulators6,7 and phase modulators.8,9 Graphene also has been used as saturable absorber to obtain mode-locking in fiber lasers and vertical external-cavity surface-emitting lasers (VECSELs) with a variety of different wavelengths.10−12 © 2017 American Chemical Society

Special Issue: 2D Materials for Nanophotonics Received: May 31, 2017 Published: August 28, 2017 3039

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Figure 1. (a) Band diagram of graphene. (b) Degenerate FWM energy diagram. (c) SEM image of the cross-section of a SiN waveguide. (d) Sketch of the gating scheme. (e) Optical microscope image of a set of waveguides. The extent of the graphene (under the contacts) is shown by the dashed lines. On top of this structure the polymer electrolyte is spin-coated (not in this image).

the coupling between the evanescent tail of the highly confined waveguide mode and the graphene over a relatively long length, significant light-matter interaction can be achieved. Studies of nonlinear effects in graphene-covered silicon waveguides and resonators have been published previously.38,40−42 However, an intrinsic disadvantage of using a silicon platform for the characterization of graphene nonlinearities is that silicon has a relatively strong nonlinear response itself. The real part of the nonlinear parameter of a typical Si waveguide is about γSi ≈ 300 m−1 W−1, as opposed to about γSiN ≈ 1.4 m−1 W−1 for a SiN waveguide,20 which is negligible compared to the nonlinear parameters of the graphene-covered waveguide measured in this work (γPL is the nonlinear phase shift acquired by a beam of power P over length L, see section S1 of the Supporting Information or ref 43). Using SiN, we can thus avoid any ambiguity about the origin of the strong nonlinear effects. Furthermore, we have achieved electrical tuning of the Fermi energy EF (gating) by using a polymer electrolyte.44 We have performed measurements for a varying signal-pump detuning and for a broad range of charge carrier densities and demonstrate, for the first time to our knowledge, a significant increase of the nonlinear response of graphene in the vicinity the interband absorption edge ℏω ≈ 2|EF|. Moreover, we demonstrate a good qualitative agreement with theoretical calculations.

be easily transferred to existing guided wave platforms, enhancing the nonlinear functionality. Despite the consensus that nonlinearities in graphene are strong, very different values of the corresponding material parameters have been reported (see, e.g., discussions in refs 29 and 37). Reasons for this can be found in the fact that in different experiments different nonlinear effects (harmonics generation, four-wave mixing, Kerr effect) are probed at different wavelengths in samples with different carrier densities and in different dielectric environments. Moreover, in experimental studies, pulses with vastly different durations and optical bandwidths have been used. All these factors can significantly influence the final result. Hence, a detailed quantitative study of the nonlinear response of graphene, at different frequencies and in samples with different electron densities, is imperative. Another important research direction is the search for interband resonances in the nonlinear response function of graphene. As was mentioned before, tunability of the electromagnetic properties through chemical doping or electrostatic gating is a strong asset of graphene, for nonlinear applications, this is expected to be no different. It has been theoretically predicted29−32 that the nonlinear parameters of graphene should have resonances at frequencies corresponding to the interband absorption edge, for example, at ℏω = 2|EF|/3 for third harmonic generation or at ℏω = 2|EF| for self-phase modulation (SPM; SPM in ungated graphene on a waveguide has been measured, e.g., in ref 38), and so on, where ω is the incident photon frequency and EF the Fermi energy. Figure 1a shows the band diagram of graphene, along with the photon energy. SPM, which scales as Im[σ(3) s ], has been predicted to peak at 2|EF| ≈ ℏω, after which it decreases sharply for further increasing |EF| (see, for example, Figure 3 in ref 39). The majority of experiments have been performed in weakly doped graphene at high frequencies (near-IR, visible), where ℏω ≫ 2|EF|. An experimental observation of the Fermi energy related resonances would not only be interesting for fundamental science, but also for nonlinear devices, since it would provide a way to control the nonlinear optical response of practical systems. In this work, we characterize the Fermi energy dependence of the third order nonlinear effects in graphene, tuning the graphene from intrinsic (2|EF| ≪ ℏω) to beyond the interband absorption edge (2|EF| > ℏω). We do this by means of fourwave mixing (FWM) in an integrated silicon nitride (SiN) waveguide, covered with a monolayer of graphene. Because of

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RESULTS AND DISCUSSION Theory of Four-Wave Mixing in Graphene-Covered Waveguides. Degenerate four-wave mixing (FWM) is a third order nonlinear optical process in which two pump photons at frequency ωp are converted into two photons at different frequencies, typically denoted as the signal ωs and idler ωi. Energy conservation dictates that ωs + ωi = 2ωp, which is schematically shown in Figure 1b. In a typical FWM experiment, both pump and signal waves are injected into the sample and the power conversion to the idler frequency is used to quantify the optical nonlinearities in the system. In the experiment discussed here, a pump at a fixed wavelength and a signal with variable wavelength are injected into a graphene-covered SiN waveguide. Under the used experimental conditions, one can prove that the conversion efficiency η, defined as the ratio of the idler power to the signal power at the output, is quadratically dependent on the nonlinear parameter γ of the waveguide (see section S1 in Supporting Information), 3040

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Figure 2. Setup used for the FWM experiments.

⎛ ⎞2 Pi(L) 2 ⎜ ωi ⎟ 2 η≡ ≈ |γ(ωi ; ωp , ωp , −ωs)| ⎜ ⎟ Pp(0)2 Leff Ps(L) ⎝ ωp ⎠

VGS − VD = sgn(E F) (1)

1 − e−αL

the effective length of the nonlinear section, Leff ≈ α process and α the linear waveguide loss. The effect of the phase mismatch is neglected since Lβ2Δω2 ≪ 1 in the presented experiment (L = 100 μm, Δω < 1013 rad/s and β2 of a SiN ∂ 2β

waveguide is on the order of 10−25 s2/m;20 here β2 ≡ ∂ω2 , with β(ω) the propagation constant of the optical mode). The nonlinear parameter γ of the waveguide is, to a good approximation, proportional to the nonlinear conductivity σ(3) s of graphene (see section S1 in Supporting Information), 3σs,(3) xxxx(ωi ; ωp , ωp , − ωs) 167 2p

∫G |e(ωp)

ℏ2vF2πC EDL

+

EF e

(3)

where e is the electron charge, vF ≈ 106 m/s the Fermi velocity, CEDL the electric double layer capacitance, and VD the Dirac voltage. Based on measurements of the optical loss and the graphene sheet resistance versus the gate voltage we estimated CEDL ≈ 1.8 × 10−2 F m−2 and VD ≈ 0.64 V, see section S2 in the Supporting Information. Figure 1e shows an optical microscope image of a set of contacted graphene-covered waveguides, prior to the deposition of the polymer electrolyte. The SiN waveguides can be seen, as well as the grating couplers used to couple to the optical fibers. The graphene is not visible, therefore its extent is shown by the dashed lines. Four-Wave Mixing Experiment. The setup used for the FWM experiment is shown in Figure 2. A pump laser (Syntune S7500, λp = 1550.18 nm) is amplified using an Erbium-doped fiber amplifier (EDFA), a tunable band-pass filter suppresses the Amplified Spontaneous Emission (ASE) of the EDFA. The signal is provided by a Santec Tunable Laser TSL-510. Pump and signal are coupled into the waveguide through a grating coupler. At the output a fiber Bragg grating (FBG) filters out the strong pump light and the signal and idler are visualized on an Anritsu MS9740A optical spectrum analyzer (OSA). Figure 3 summarizes the experimental results obtained for a set of 1600 nm wide waveguides. By measuring the transmission of a set of waveguides with varying graphene lengths, as well as the transmission as a function of the gate voltage VGS, the propagation loss as a function of VGS was extrapolated, Figure 3a. Note that the absorption drops sharply for negative voltages, indicating that the Fermi level of the graphene gets tuned beyond the interband absorption edge. In Figure 3b, some of the measured spectra for the FWM experiment are plotted (VGS = −0.5 V), the pump laser light is filtered out by the FBG. The conversion efficiency η can be read as the ratio between the idler (λi) and signal (λs) peak powers (we correct for variations in the transmission of the grating couplers with changing wavelength). The measured conversion efficiencies are plotted in Figure 3c, for a range of different voltages and signal wavelengths (λp = 1550.18 nm), with an estimated onchip pump power of Pp(0) = 10.5 dBm and a graphene length L = 100 μm. The FWM conversion efficiency is highly dependent on both detuning λs−λp and the applied voltage. Calculation of γ and σ(3) s . Using eqs 1 and 2, the magnitude of the nonlinear parameter γ(ωi;ωp,ωp,−ωs) and of the third order conductivity σ(3) s (ωi;ωp,ωp,−ωs) can be calculated. For the calculation of Leff the loss measurement in Figure 3a was used. The integral and power normalization constant 7p in eq 2 are calculated using a COMSOL Multiphysics model of the cross-section in Figure 1c. Figure 4a,b show the results of these conversions. The measured values for |γ| (|σ(3) s |) have a sharp resonance as a function of detuning and a broad asymmetric −1 resonance as a function of EF. |γ| (|σ(3) W−1 s |) is about 2800 m

where L is the length of the graphene-covered waveguide

γ(ωi ; ωp , ωp , − ωs) ≈ i

eE F2

× eẑ |4 dS

(2)

where e(ωp)∥ is the electric field component tangential to the graphene sheet at the pump frequency, êz is the unit vector along the propagation direction and 7p is the power normalization constant of the optical mode. For a small signal-pump detuning, ωp ≈ ωs ≈ ωi, the theory published in refs 30 and 31 predicts a vanishing FWM response beyond the interband absorption edge, 2|EF| > ℏωp, in analogy with self-phase modulation described before. However, as opposed to SPM, a sharp peak at 2|EF| ≈ ℏωp is not predicted. This is because the FWM response scales as the absolute value (3) of the third order conductivity, |σ(3) s |, in which Re[σs ] typically (3) dominates Im[σs ], as can be clearly seen from eqs 1 and 2. Sample Preparation. A set of straight waveguides was patterned in a 330 nm thick SiN layer deposited by low pressure chemical vapor deposition (LPCVD) on top of a 3 μm burried oxide layer on a silicon handle wafer. The sample was then covered with LPCVD oxide and planarized using a combination of chemical mechanical polishing, reactive ion etching and wet etching. Subsequently, a graphene layer grown with chemical vapor deposition (CVD) was transferred to the samples by Graphenea and patterned using photolithography and oxygen plasma etching so that different waveguides were covered with different lengths of graphene. Metallic contacts (Ti/Au; ≈5/300 nm) were applied at both sides of each waveguide, with a spacing of 12 μm. Figure 1c shows a SEM image of the waveguide cross-section, note that ≈80 nm of oxide is left on the waveguide. Finally the structures were covered with a polymer electrolyte consisting of LiClO4 and poly(ethylene oxide) (PEO) in a weight ratio of 0.1:1. Figure 1d shows a sketch of the cross-section (not to scale). The gate voltage VGS can be used to gate the graphene layer.44 The dependence of EF on VGS can be approximated by the following formula:44,45 3041

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independent. However, under these assumptions, the theory does not predict the measured increase of σ(3) s with increasing |EF| (see the solid line in Figure S5 in the Supporting Information). To get a better correspondence between theory and experiment, we can however assume that Γ(E) is a function of the electron energy. Both theoretical (e.g., ref 46) and experimental (e.g., ref 47) studies indicate that the relaxation rate Γ(E) ∝ |E|−α is a power-law function of energy E, at |E| ≳ E0, with α being determined by the scattering mechanism. According to theory, α = 1 for impurity scattering and E0 is related to the density of impurities.46 Experimental data confirmed the power-law dependence of Γ(E) but showed a slightly smaller value of α, 0.5 ≲ α ≲ 1 (see the inset in Figure 2 in ref 47). To be able to use a formula for Γ(E) at all energies including the limit E → 0 we adopt the model Γ(E) =

Γ0 (1 + E2 /E02)α /2

(4)

which has a correct asymptote Γ(E) ∝ |E|−α at large energies |E| ≫ E0 and gives a constant relaxation rate at E → 0; the quantities Γ0, E0 and α in eq 4 are treated as fitting parameters. In addition, to take into account the effects of nonzero temperatures, we can use the formula (the frequency arguments are omitted for clarity):30

Figure 3. (a) Waveguide loss as a function of gating voltage. (b) Examples of the optical spectra (VGS = −0.5 V). The pump peak (1550.18 nm) is filtered out by the FBG. The signal peaks can be seen on the left and the corresponding idler peaks on the right. Graphene section length: 100 μm. (c) Conversion efficiency η as a function of VGS and detuning λs−λp.

σs,(3) αβγδ(E F , Γ0, E0 , α , T ) =

(2 × 10−19 Am2/V3) at small |EF| (for minimum detuning) and about 6400 m−1 W−1(4.3 × 10−19 Am2/V3) at its absolute peak. Comparison with Theory. We can compare these experimental results with a slightly modified version of the theory published in refs 30 and 31. In these papers, analytical expressions for the third order conductivity (3) σs,αβγδ (ω1+ω2+ω3;ω1,ω2,ω3,EF,Γ) were derived at T = 0, where the relaxation rate Γ was assumed to be energy-

1 4T

+∞

∫−∞

σs,(3) αβγδ(E F′ , Γ0, E0 , α , T = 0)

(

cosh2

EF − EF′ 2T

)

dE F′

(5)

Figure 4c,d show thus obtained theoretical dependencies of the a b s o l u t e v al u e o f t h e t h i r d o r de r c o n d u c t i v i t y |σ(3) s,xxxx(ωi;ωp,ωp,−ωs)| on the Fermi energy and the detuning λs−λp. The parameters ℏΓ0 = 2.5 meV, E0 = 250 meV, and α = 0.8 have been chosen so that good qualitative agreement was obtained with the experimental plots shown in Figure 4a,b. One

Figure 4. (a, b) Measured nonlinear parameter |γ(ωi;ωp,ωp,−ωs)|/graphene nonlinear conductivity |σ(3) s (ωi;ωp,ωp,−ωs)|. As a function of gate voltage/Fermi energy for different values of detuning λs−λp (a). As a function of detuning for different values of the gate voltage (b). (c, d) Calculated values of |σ(3) s (ωi;ωp,ωp,−ωs)|, as a function of Fermi energy for different wavelength detunings (c) and as a function of detuning for a range of Fermi energies (d). 3042

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can see that the theory indeed describes the most important features of the FWM response: a narrow resonance as a function of λs−λp and a broad strongly asymmetric shape as a function of EF; the inflection point at EF ≈ −0.4 eV corresponds to ℏωp ≈ 2|EF|. Quantitatively, the theory predicts about 1 order of magnitude larger response than was experimentally observed (this contrasts to a number of previous publications, where the measured nonlinear response was claimed to be larger than the theoretically calculated one, see discussions in refs 29, 30, and 39). This discrepancy should be subject to further investigation. Experimental errors could have an influence, such as an overestimated pump power Pp(0) or effective length Leff, errors on the exact dimensions of the waveguide cross-section, etc. Inhomogeneities in the doping level of the graphene might also have an influence, effectively creating inhomogeneous broadening of the measured response in the |EF| direction and diminishing the height of the peak. Finally, the difference could partly be due to imperfections in the graphene which the theory might fail to fully take into account.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Koen Alexander: 0000-0002-5048-749X Sergey A. Mikhailov: 0000-0003-0880-3249 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank Prof. Daniel Neumaier and Dr. Muhammad Mohsin for useful discussions and for providing the polymer electrolyte. We also thank Dr. Owen Marshall for giving useful advice. The work has received funding from the European Union’s Horizon 2020 research and innovation program GrapheneCore1 under Grant Agreement No. 696656. K.A. is funded by FWO Flanders.

CONCLUSION In conclusion, we have performed a degenerate four-wave mixing experiment on a graphene-covered SiN waveguide. A polymer electrolyte enabled us to gate the graphene over a relatively large window. The experiment shows that the nonlinear conductivity of graphene has a sharp resonance as a function of signal-pump detuning, also a broad asymmetric resonance shape in the vicinity of the absorption edge 2|EF| = ℏωp is observed. Qualitative agreement was obtained between these experimental data and an adapted version of previously published theory,30,31 in which we introduced an energydependent relaxation rate Γ(E). From an application perspective, it is important to note that the measured nonlinear parameter of the waveguide |γ| is tunable by applying a gate voltage. Hence, we have demonstrated that graphene can be integrated in a guided wave platform to be used as a building block for electrically tunable nonlinear optics. For the optimal gate voltage, |γ| surpasses ≈2000 m−1 W−1 over the full measured bandwidth of 20 nm, with peak values over ≈6000 m−1 W−1. This is more than 3 orders of magnitude larger than the nonlinear parameter of a standard SiN waveguide. The most obvious trade-off is the strongly increased linear absorption (more than 2 orders of magnitude, though this absorption is also tunable with voltage). Applications such as electrically controlled all-optical signal processing, wavelength conversion, and so on, can be envisaged. The feasibility of such applications requires further research, such as experiments that quantify not only the magnitude, but also the phase of γ, experiments to test how the material behaves over larger bandwidths and at higher optical powers, optimizations of the waveguide cross-section, and so on. Changing the gating method, such as a graphene−graphene capacitor in ref 7, could provide more robust tunability, at orders of magnitude higher speeds. The quantitative gap between theoretical and experimental results is another issue that needs further investigation.

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Extended theory of third order nonlinear optical interaction between a set of monochromatic waves in a graphene-covered waveguide, with focus on the degenerate four-wave mixing case discussed in this work and the derivation of eqs 1 and 2 (section S1). More information on the use of the polymer electrolyte and the procedure to estimate the relation between gate voltage VGS and Fermi energy EF (section S2). More information on the theoretical calculation of σ(3) s (section S3; PDF).

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsphotonics.7b00559. 3043

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DOI: 10.1021/acsphotonics.7b00559 ACS Photonics 2017, 4, 3039−3044