Gate-Tunable Nonlinear Refraction and Absorption in Graphene

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Gate-Tunable Nonlinear Refraction and Absorption in Graphene-Covered Silicon Nitride Waveguides Koen Alexander, Nadja A. Savostianova, Sergey Mikhailov, Dries Van Thourhout, and Bart Kuyken ACS Photonics, Just Accepted Manuscript • DOI: 10.1021/acsphotonics.8b01132 • Publication Date (Web): 12 Nov 2018 Downloaded from http://pubs.acs.org on November 14, 2018

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Gate-Tunable Nonlinear Refraction and Absorption in Graphene-Covered Silicon Nitride Waveguides Koen Alexander,∗,†,‡ Nadja A. Savostianova,¶ Sergey A. Mikhailov,¶ Dries Van Thourhout,†,‡ and Bart Kuyken†,‡ † Photonics Research Group, INTEC Department, Ghent University-imec, Technologiepark-Zwijnaarde 15, B-9052 Zwijnaarde, Belgium ‡ Center for Nano- and Biophotonics (NB-Photonics), Ghent University, Technologiepark-Zwijnaarde 15, B-9052 Zwijnaarde, Belgium ¶ Institut f¨ ur Physik, Universität Augsburg, Universitätsstraße 1, D-86135 Augsburg, Germany E-mail: [email protected] Abstract The nonlinear optical properties of graphene have received significant interest in the past years. Especially third order nonlinear effects have been demonstrated to be large. Recently several groups have shown, through four-wave mixing (FWM) and third harmonic generation (THG) experiments, that the optical nonlinearity of graphene can be tuned through electrostatic gating. These effects are quantified by a strongly tun(3)

(3)

able |σs |, with σs

the complex third order conductivity. Here, by simultaneously

observing cross-phase and cross-amplitude modulation on a silicon nitride waveguide covered with gated graphene, we are able to confirm such strong tunability for these

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nonlinear effects as well. Moreover, we can separately quantify the real and imaginary (3)

parts of σs , which respectively represent nonlinear absorption and refraction. This unveils a tunability which is far more drastic than what could be observed through FWM or THG, including sign changes in both the nonlinear absorption and refraction. Our results are confirmed by a theoretical model for the optical nonlinearity of graphene. The ability to tailor the nonlinearity of graphene to this extent can lead to new opportunities, such as nanophotonic devices with electrically tunable nonlinear properties.

Keywords Graphene, Integrated Optics, Nonlinear Optics, Nonlinear refraction, Nonlinear absorption, Silicon nitride photonics Since the first exfoliation of single-layer graphene from graphite in 2004, 1 many extraordinary properties have been attributed to this material, as a consequence interest has surged in many fields of science and engineering. Also in photonics, an increasing number of potential applications of graphene are being explored. By combining graphene with integrated optics, its broadband absorption has already been exploited in photodetectors. 2–4 Making use of the efficient gate-tunability of the Fermi level, broadband electro-absorption modulators, 5,6 as well as phase modulators, 7,8 have been demonstrated. Plasmonics is yet another field in which graphene can play an important role, 9 as well as pulsed lasers, where graphene has been successfully used as a saturable absorber in a variety of mode-locked laser types. 10–13 The material has also found its way into THz photonics 14,15 and microwave applications. 16 In nonlinear optics, another important area of research, graphene has provoked strong interest as well. Several theoretical 17–22 and experimental 23–28 studies have attributed a strong nonlinear optical response to graphene, quantified by a large third order nonlinear surface (3)

conductivity σs . Third order nonlinear optical processes include four-wave mixing (FWM), the optical Kerr effect, third harmonic generation (THG), etc. Such processes can among oth2


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ers be used for parametric gain, 29 wavelength conversion, 30,31 frequency comb generation, 32 supercontinuum generation, 33 all-optical signal processing 34,35 and signal regeneration. 36 In earlier experimental publications, 23–26 strongly varying values of the nonlinear material parameters have been reported. This can partly be explained by the observation that (3)

the third order surface conductivity σs (ωj + ωk + ωl ; ωj , ωk , ωl ) function strongly depends on its frequency arguments. 27 In Reference 27, it was shown that the FWM efficiency can drop by an order of magnitude when changing the pump-signal detuning over only a couple of nanometers. This in strong contrast to many other platforms, such as single mode fiber (SMF), 37 silicon or silicon nitride waveguides, 38,39 or III-V semiconductors, 40 where the bulk nonlinear susceptibility χ(3) can be assumed to be frequency-independent under most circumstances. Secondly, it has been shown experimentally that taking only the third order nonlinearity in graphene into account is not always suitable, as also higher order nonlinearities become significant at intensities on the order of 1012 Wm−2 and higher. 41 Many experimental works in literature assume the third order nonlinearity to be the only one of relevance without further ado, whilst using pulsed lasers that typically exceed these inten(3)

sities. A third possible reason for the large spread in reported σs

values for graphene, is

its very strong dependence on the carrier density. 27,28,42 Hence it comes to no surprise that measuring different nonlinear phenomena, typically observed using different optical intensities and wavelengths, on samples of varying quality and doping level, results in different measured nonlinear parameters. (3)

This variability, especially the strong dependence of σs

on the Fermi level EF , has re-

ceived considerable attention recently. The Fermi level of graphene can be relatively easily tuned using a gate voltage. Several recent studies have demonstrated that this can be used to actively tailor the strength of various nonlinear processes. 27,28,42 This could enable the design of devices with strongly tunable nonlinear properties. In earlier work, we performed a degenerate FWM experiment on integrated silicon nitride waveguides covered with gated (3)

graphene. 27 We showed that the FWM conversion efficiency and the corresponding |σs | 3


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increase significantly in the vicinity of 2|EF | = h ¯ ωp , with ωp the pump frequency. 27 More recently, Fermi energy dependence of the THG efficiency has been demonstrated independently by two research groups, 28,42 both reporting a tunability of almost two orders of magnitude. A disadvantage of using FWM (or THG) to study the nonlinear properties of graphene, (3)

(3)

is that the response only depends on the magnitude of the nonlinear conductivity |σs |. σs

is however a complex parameter, its real part expresses power dependent changes in the optical absorption, whereas its imaginary part expresses changes in optical refraction. For (3)

many applications, such as all-optical signal processing, full knowledge of σs is imperative. In this work, gate-tunable graphene integrated on a silicon nitride waveguide was used to perform a simultaneous measurement of cross-amplitude and cross-phase modulation (XAM/XPM) between a relatively strong pump and a weaker probe. An advantage of using silicon nitride waveguides is the relatively weak nonlinear response of the silicon nitride itself. The nonlinear parameter γ of a typical silicon nitride waveguide without graphene is about three orders of magnitude smaller than the ones measured for graphene-covered waveguides. 27,39 As a consequence the silicon nitride response can be considered negligible. The measurements in this work have been done in a relatively low-power regime (Ppump ≈ 10 mW, corresponding to local intensities on the order of ≈ 1010 W m−2 ), this assures that the third order nonlinear effect is dominant. For the first time to our knowledge, we could extract the full complex value of the waveguide nonlinear parameter γ, and a corresponding (3)

estimate of σs , as a function of Fermi level/gate voltage and pump-probe detuning. These measurements show a very strong dependence of both nonlinear refraction and absorption on these parameters. Moreover, we are able to model the observed dependencies using a simple phenomenological model. Such a model can provide an initial tool for the design of devices with tunable optical nonlinearities.

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Results and Discussion Sample Fabrication and Characterization (a)

Ti/Au

Grating Coupler SiN Waveguide

(b)

L

Graphene

Graphene pattern

SiN 500 nm

100 μm

(d)

SiOx

SiOx

(c) Graphene SiOx SiOx

330 nm SiN

1400 nm

500 nm

(e)

VGS

SiN Polymer Electrolyte Graphene

Ti/Au

SiN SiOx

Figure 1: (a) Optical microscope image of the sample, the graphene is not visible, though its extent (partly under the contacts) is shown by the dashed lines. The gap between the electrodes is 12 μm. (b) Cross-section of a typical waveguide, with the fundamental quasiTE mode. (c) SEM image of the SiN waveguide cross-section. (d) Conceptual sketch of the gating scheme. (e) Measurement of the waveguide propagation loss (blue circles/left axis) and the resistance per unit length over the graphene sheet (red diamonds, right axis), measured for a waveguide with L = 800 μm. The top axis shows the estimated Fermi energy EF for a given gate voltage VGS .

The sample design and fabrication is identical to the devices presented in Reference 27. Figure 1 summarizes the waveguide design. In a CMOS pilot line, a set of straight waveguides of varying widths was patterned into a 330 nm thick layer of LPCVD (low-pressure chemical vapor deposition) silicon nitride (SiN) on a ≈ 3 μm thick buried oxide (BOX) layer, on a silicon handle wafer. Subsequently, the chips were covered with ≈ 1 μm of LPCVD oxide and planarized using a combination of wet HF etching and reactive ion etching (RIE). A monolayer of graphene grown with chemical vapor deposition (CVD) was transferred to the waveguides by Graphenea S.A. and subsequently patterned through oxygen plasma etching. After the graphene patterning, metallic (Ti/Au ≈ 5/500 nm) contacts were applied on both sides of each waveguide. Finally, the chips are covered with a polymer electrolyte (LiClO4

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and poly(ethylene oxide) in a weight ratio of 0.1:1), to enable gating of the graphene. 27,43,44 Figure 1a shows a top-view image of the chip after fabrication, prior to the electrolyte deposition. The waveguides can be clearly distinguished, as well as the grating couplers used to couple the light in and out of the chip. The graphene itself cannot be seen on this image, but its extent is shown by the dashed lines. Different waveguides are covered with graphene sections of different lengths, enabling cut-back loss measurements. On Figure 1b the waveguide cross-section with the corresponding fundamental quasi-TE mode (used in the experiments) is shown. Figure 1c shows a SEM image of the cross-section. It is clear that the oxide was slightly overetched, resulting in slight trenches along the waveguide. The approximate position of the graphene is shown by the dashed black line. Figure 1d shows a conceptual sketch of the cross-section. The dependence of the graphene’s Fermi energy EF on the gate voltage VGS can be approximated by: 27,43,44

VGS − VD = sgn(EF )

EF eEF2 + , 2 2 e h ¯ vF πCEDL

(1)

with e, vF ≈ 106 m/s, CEDL and VD respectively the electron charge, Fermi velocity, electric double layer capacitance and Dirac voltage. Using measurements of the graphene resistance and the waveguide propagation loss α versus gate voltage (Figure 1e), we estimate CEDL ≈ 1.82 · 10−2 F m−2 and VD ≈ 0.6 V, see Supporting Information. The estimated EF values are shown on the top axis of Figure 1e.

Experimental Results Cross-Amplitude/Cross-Phase Modulation Measurement In guided-wave optics, third order nonlinear processes are quantified by the nonlinear waveguide parameter γ, 37 which is effectively a weighted average of the third order nonlinear susceptibilities χ(3) of the materials constituting the waveguide. 38 In the experiment discussed here, a modulated pump with a fixed wavelength (λpump ; ωpump ), 6


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(a) Pump Laser

VNA

EDFA Modulator

Filter

50/50

2

1

3

4

90/10

V GS

| S21 | | S31 |

− 100 0

1

− 100

VGS =0 V; Im  < 0 VGS =-0.9 V; Im  > 0

0 2 Ω /2 π (GHz)

4

PD4

− 80

2

| S41 | (dB)

S31 S21

( π rad)

− 50

| Im  |

SMF

(d) 3

|S | lim 31 Ω 0 | S 21 |

EDFA

90

FBG

(c)

(b)

PD3 10

PD2

Graphene Waveguides

Probe Laser

| Sij | (dB)

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0

0.2

0.1 Ω /2 π (GHz)

− 120

0.3

VGS =0 V VGS =-0.6 V Fit

0

5

10 Ω /2 π (GHz)

15

20

Figure 2: (a) Setup used in the experiment. VNA: Vector Network Analyzer, EDFA: Erbium Doped Fiber Amplifier, FBG: Fiber Bragg Grating, SMF: Single Mode Fiber, PD: Highspeed Photodiode. Pump wavelength λpump = 1550.18 nm. (b-d) Examples of S-parameter measurements used to estimate the nonlinear optical parameter γ of the waveguide, λprobe = 1551 nm. (b) Trace of |S21 | and |S31 | for VGS = 0 V. The ratio |S31 |/|S21 | can be used to estimate |Im(γ)|. (c) Trace of 6 (S31 /S21 ) used to estimate the sign of Im(γ), for two different gate voltages. (d) Traces of |S41 | for two different gate voltages. The dashed lines show the corresponding sinusoidal fits (∝ |sin (β2 LSMF Ω2 /2 + 6 γ)|), used to estimate 6 γ. and a weaker probe of variable wavelength (λprobe ; ωprobe ) are injected into a graphenecovered SiN waveguide. Through the nonlinear interactions with the pump, the probe will acquire both amplitude and phase modulation. The nonlinear parameter γ governing this process in the graphene-covered SiN waveguide is, to good approximation (see Supporting Information), γ(ωprobe ; ωprobe , ωpump , −ωpump ) ≈ (3)

3σs, xxxx (ωprobe ; ωprobe , ωpump , −ωpump ) i 16P 2

Z G

(2) 4

|ek × ˆ ez | d` ,

where ek is the electrical field component of the optical mode tangential to the graphene sheet, ˆ ez is the unit vector in the propagation direction and P is the power normalization constant of the mode.

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The measurement methodology was partly based on Wathen et al. 45 and the experimental setup is shown in Figure 2a. The pump laser (λpump =1550.18 nm) is modulated using a vector network analyzer (VNA), combined with a weaker CW probe of tunable wavelength λprobe and coupled into the graphene-covered waveguide. The modulation frequencies (< 20 GHz) are well below the ones related to the slowest carrier relaxation times in graphene, 46 so we can assume a quasi-CW regime. The probe field acquires a respective nonlinear phase change and amplitude modulation of 2Re(γ)Ppump Leff and exp(−2Im(γ)Ppump Leff ) (see Eq. (S12) in the Supporting Information), where the effective length Leff = (1 − e−αL )/α. Crossamplitude and cross-phase modulation are thus quantified by Im(γ) and Re(γ), respectively. After the chip, pump and probe are separated by a circulator and a fiber Bragg grating (FBG) (reflects λpump , transmits λprobe ). The pump and a fraction of the probe are sent to port 2 and 3 of the VNA, respectively, the S-parameters measured on these ports, S21 and S31 , are proportional to the amplitude modulation of both pump and probe. We can show that (see Supporting Information): RPD3 T3 |S31 | ≈4 |Im(γ)|Leff Pprobe (0), Ω→0 |S21 | RPD2 T2 lim

(3)

where Ω is the (radial) modulation frequency, T2 and T3 are the total power transmission of the pump and probe between the waveguide section and the photodiode, RPD2 and RPD3 are the responsivities of the respective photodiodes and Pprobe (0) is the probe power at the input of the waveguide section. Such a measurement is shown on Figure 2b, for a graphene-covered waveguide with VGS = 0 V and λprobe = 1551 nm. The optical receivers at ports 2 and 3 have a bandwidth limited to 1.8 GHz. Furthermore, it can be shown that (see Supporting Information),    0 if Im(γ) < 0 6 6 lim ( S31 − S21 ) = , Ω→0  π if Im(γ) > 0

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(4)

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meaning that, in the case of absorption saturation (Im(γ) < 0), the pump and probe powers will oscillate in phase, in the case of the reverse effect (Im(γ) > 0), their powers will oscillate out of phase. The blue circles on Figure 2c show this phase difference for the measurement shown in Figure 2b, the linear fit shows that limΩ→0 (6 S31 − 6 S21 ) ≈ 0, indicating saturable absorption. A measurement for a different gate voltage (VGS = −0.9 V) is plotted in red, this time the phase difference converges to π, indicating that the opposite to saturable absorption, an increase of absorption with power, occurs for certain gating voltages. The remaining probe power is passed through ≈ 50 km of single mode fiber (SMF), and detected with a high-speed photodiode connected to port 4 of the VNA. In the Supporting Information, we show that, β2 LSMF Ω2 + 6 γ , |S41 | ∝ sin 2

(5)

with LSMF and β2 respectively the length and the group-velocity dispersion of the SMF. Hence a sinusoidal fit of the |S41 |-measurement, in combination with the knowledge of |Im(γ)| and sgn(Im(γ)) acquired using respectively equations (3) and (4), can be used to fully characterize the nonlinear parameter γ. As an example, Figure 2d shows two of these measurements, accompanied by the sinusoidal fits. In brief, through equations (3)-(5) we can estimate the complex value of γ. In practice, the fibers used to couple light into the chip also cause non-negligible crossphase modulation. This contribution is corrected for in the measurements presented below, as is described in the Supporting Information. (3)

Measured Values for γ and σs

Figure 3 shows a summary of the measurement results obtained on one of the waveguides (L = 50 μm, waveguide width = 1400 nm). In Figure 3(a,b), the measured values for (3)

Im(γ) and Re(γ) are plotted. The right-hand axes show the corresponding Re(σs ) and

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Figure 3: Experimental results. The waveguide width and height are respectively 1400 nm and 330 nm, the graphene length 50 μm, λpump =1550.18 nm. (a) and (b), Im(γ) and Re(γ) as function of VGS , respectively, for different probe wavelengths λprobe (see legend). The top axes show the estimated Fermi energy corresponding to the gate voltage, the right-hand axes (3) (3) show the corresponding Re(σs ) and Im(σs ). The grey dashed lines show the simulated results for λprobe = λpump . (c) and (d), Im(γ) and Re(γ) as a function of λprobe , respectively, for different gate voltages VGS (see legend). The right hand axes show the corresponding (3) (3) Re(σs ) and Im(σs ) and the top axes the corresponding probe-pump detuning in radial frequency. (3)

Im(σs ), the conversion was done through equation (2). On the top axes, the estimated (3)

Fermi energies are plotted. It is clear from these measurements that γ (σs ) is very Fermi energy-dependent, and that both its real and imaginary part show strong resonance-like features around |EF | ≈ h ¯ ωpump /2. At lower doping levels (|EF | h ¯ ωpump /2), the negative (3)

sign of Im(γ) (Re(σs )) corresponds to saturable absorption, a well-known phenomenon in graphene. 10–12 However, in the vicinity of |EF | ≈ h ¯ ωpump /2, the opposite effect is observed.

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(3)

The measured Re(γ) (∝ −Im(σs )) is positive for low doping, but becomes strongly negative around |EF | ≈ h ¯ ωpump /2, after which it decays to zero. In Figs. 3(c, d), these parameters are plotted as a function of λprobe , for different gating voltages VGS . γ is relatively insensitive to pump-probe detuning, apart from a small resonant feature around λprobe ≈ λpump .

Comparison with Theory (3)

To explain the observed behavior of σs , we devised a simple phenomenological model, the details of which are described in the Supporting Section S4. A short overview is given here. We assume the electron/hole distribution to be described by the Fermi-Dirac distribution,

f (E, µ, T ) =

1 , 1 + exp E−µ kB T

(6)

with a chemical potential µ and the temperature T which can depend on the illumination intensity. The values of µ and T can be calculated by enforcing two conditions. Firstly, we assume electroneutrality,

nh (µ, T ) − ne (µ, T ) = −

sgn(EF )EF2 , π(¯ hvF )2

(7)

where nh and ne are respectively the hole and electron densities. Secondly, we assume that the energy absorbed by the graphene relaxes to the environment with a phenomenological energy relaxation time τ , E(µ, T ) − E(µ0 , T0 ) 1 = Re{σs,(1)xx (ωpump , µ, T )}|Exωpump |2 , τ 2

(8) ω

where E(µ, T ) = Ee (µ, T ) + Eh (µ, T ) is the energy of the electron and hole gases and Ex pump is (1)

the in-plane electric field component of the pump wave. The linear conductivity σs, xx (ω, µ, T ) and the electron/hole distribution (equation (6)) can be directly related. 47–49 By solving this set of equations, we can now calculate the linear complex conductivity 11


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(1)

σs as a function of the pump field. The third order conductivity can then be calculated by taking a first order (linear) approximation of this relationship (see Supporting Information), (1)

σs,(3)xxxx (ωprobe ; ωprobe , ωpump , −ωpump ) =

2 ∂σs, xx (ωprobe ) . ω 3 ∂|Ex pump |2

(9)

Using this simple model we calculated the third order conductivity for the estimated range of Fermi energies used for the experiments. The results are plotted as grey dashed lines on Figs. 3(a,b), for λprobe = λpump . The simple model clearly follows the same trends as the measurement. In the Supporting Information, more extensive simulations of σ (3) , both as a function of Fermi energy and probe wavelength, are given. Over a wavelength range of several tens of nanometers, our model captures the trends seen in the measurements, however over a bandwidth of ≈ 5 nm (≈ 0.6 THz), there is a deviation between measurement and model. We believe this difference is due to a slight deviation between the assumed FermiDirac carrier distribution (equation (6)), and the actual carrier distribution, due to spectral hole burning around energy levels (±¯hωpump /2).

Conclusions and Future Prospects Through direct observation of cross-phase and cross-amplitude modulation, we have performed a simultaneous measurement of both the nonlinear phase and amplitude response of a graphene-covered integrated waveguide. By using a polymer electrolyte we were able to tune the Fermi level of the graphene. Our results show that both the nonlinear refraction (3)

of graphene (quantified by the imaginary part of its nonlinear conductivity Im(σs )), as (3)

well as its nonlinear absorption (quantified by Re(σs )) are vastly dependent on the Fermi level of the graphene. A strong gate-voltage dependence of the four-wave mixing response, (3)

∝ |σs |, had been shown before, 27 however the results in this work unveil even more complex (3)

(3)

dependencies, including sign changes and strong resonances in both Im(σs ) and Re(σs ) in the vicinity of the absorption edge |EF | = h ¯ ωpump /2. Good agreement was obtained with a 12


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simple phenomenological theoretical model. Both the real part and the imaginary part of the nonlinear waveguide parameter γ can exceed 5000 m−1 W−1 and can be tuned to a large extent. |Re(γ)| is more than 3 orders of magnitude larger than for a standard SiN waveguide. 39 Compared to silicon waveguides, 38 the improvement is roughly one order of magnitude. Moreover, silicon suffers from two-photon absorption, effectively limiting the maximum optical power in the waveguide. As we show here graphene also exhibits nonlinear absorption, though of the opposite sign for most Fermi energies, this means that at higher pump powers the effective interaction length will increase, rather than decrease. An initial theoretical study taking into account the interplay between these effects has been done in Reference 50, we however believe that further theoretical and experimental work is necessary. A commonly used figure of merit for nonlinear waveguides is FOM =

Reγ 51 . 4πImγ

For the

case of Imγ > 0, the maximum phase shift which can be obtained by self-phase modulation is |∆φmax | = 2π · FOM. 51 For the waveguides presented here, with Imγ < 0, one cannot use this figure of merit. Higher powers will cause absorption saturation and hence the interaction length will increase. On the other hand recent experiments have shown that not only the absorption, but also the nonlinear response of the waveguides can saturate. 41 Due to these complex dependencies further experiments are necessary to assess what limits the nonlinear phase-shift in graphene-covered waveguides. Numerical calculations taking into account the power dependency of both absorption and nonlinear parameter can also provide more insight. The phenomenological model introduced in this work can provide a valuable starting point. The combination of electrostatic tunability of both the nonlinear refraction and nonlinear absorption of graphene-covered waveguides indicates that such waveguides can for example be used for all-optical signal processing, where the tunability could be used for fine-tuning of the devices. Note that current experiments were performed on waveguides with a rather large cross-section, and that the graphene was located in the evanescent field. By tailoring the waveguide cross-section and going to more confined structures, the figure of merit γ/α

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can still be significantly increased. Further investigations need to be done to see how the conclusions in this paper hold for much higher pump powers, where, as mentioned in the introduction, the material nonlinearity can most likely not be described by a simple third-order model. Another avenue is to assess whether other gate-tunable third order nonlinear effects in graphene, most notably third harmonic generation, can be harnessed on our platform.

Associated Content Supporting Information Supporting information available:

Theory of third order nonlinear optical interactions between a set of monochromatic waves in a graphenecovered waveguide, with focus on cross-modulation (Section S1). More elaborate discussion on the crossmodulation experiment using a long dispersive fiber and a vector network analyzer (Section S2). More information on the use of the polymer electrolyte and the procedure to estimate the relation between gate (3)

voltage VGS and Fermi energy EF (Section S3). More information on the theoretical calculations of σs (Section S4).

This material is available free of charge via the Internet at http://pubs.acs.org

Author Information Corresponding Author *Email: [email protected]

Acknowledgements The authors acknowledge Prof. Daniel Neumaier and Dr. Muhammad Mohsin for providing the polymer electrolyte and to Stéphane Clemmen for his overseeing role in the SiN chip

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fabrication and Liesbet Van Landschoot for operating the electron microscope. The work has been funded by the European Unions Horizon 2020 research and innovation program Graphene Core 2 under Grant Agreement No. 785219. K.A. is funded by FWO Flanders.

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For Table of Contents Use Only Manuscript Title Gate-Tunable Nonlinear Refraction and Absorption in Graphene-Covered Silicon Nitride Waveguides

Authors Koen Alexander, Nadja A. Savostianova, Sergey A. Mikhailov, Dries Van Thourhout, Bart Kuyken

Table of Contents Graphic

Graphene SiOx SiOx

330 nm SiN

1400 nm

500 nm

This work discusses a detailed measurement of the third order nonlinear response of a graphene-covered silicon nitride waveguide. Enabling us to quantify both the real and imaginary part of the third order nonlinear conductivity of graphene. These measurements are performed over a range of experimental parameters (gating voltage, pump-probe wavelength detuning) and are compared with a simple phenomenological model. The scanning electron microscope image in the table of contents graphic is a cross-section of the waveguide. The graph is the measurement of one of the nonlinear parameters, for different probe wavelengths and as a function of gate voltage.

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(a) Page 23 of 25

Grating Coupler 1 SiN Waveguide 2

Ti/Au

(b) ACS Photonics

L Graphene pattern

SiN 500 nm

100 μm

3 (d) 4 5 SiN 6 Polymer Electrolyte 7 8 Graphene 9 10 SiN 11 SiOx 12

Graphene

VGS

Ti/Au

SiOx

SiOx

(e)


(c) Graphene SiOx SiOx

330 nm SiN

1400 nm

500 nm

(a)

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Pump Laser

EDFA Modulator

Filter

50/50

Probe Laser

1

2

3

Page 24 of 25 4

90/10

| S21 | | S31 |

2 1 0 ACS Paragon

2 Ω /2 π (GHz)

4

PD4

− 80 | S41 | (dB)

( π rad)

Ω

| Im  |

SMF

(d) 3

| S 31 | 0 | S 21 |

EDFA

90

FBG

(c)

lim

PD3 10

PD2

Graphene Waveguides

V GS

S31 S21

| Sij | (dB)

1 2 3 4 5 6 7 (b) 8 9 10 11− 50 12 13 14 − 100 15 16 0 17

VNA

0

VGS =0 V; Im  < 0 Plus Environment VGS =-0.9 V; Im  > 0

0.2 0.1 Ω /2 π (GHz)

0.3

− 100

− 120

VGS =0 V VGS =-0.6 V Fit

0

5

10 Ω /2 π (GHz)

15

20

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Gate-Tunable Nonlinear Refraction and Absorption in Graphene

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