Abstract

We demonstrate that enhanced linear absorption coefficient (LAC) of in-plane monolayer graphene is determined by the optical transmission spectra of a graphene layer coated symmetrically coupled add-drop silicon microring resonator (SC-ADSMR), of which the value is around 0.23 dB/µm. In contrast to the traditional cut-back method, the measured results aren’t dependent on the coupling efficiency between the fiber tip and the waveguide. Moreover, precisely evaluation of graphene layer coated silicon microring resonator (SMR) is crucial for future optoelectronic devices with compact footprint and low power consumption.

© 2016 Optical Society of America

1. Introduction

Graphene is a two-dimensional material [1,2], which exhibits remarkable optoelectronic characteristics, such as ultrahigh carrier mobility at room temperature [3], ultra-broadband absorption [4], controllable band-gap transition [5], and giant Kerr coefficient [6]. Graphene has been integrated on photonic integrated circuits (PICs) in which the hexagonal carbon sheet is evanescently coupled to the waveguide, leading to unprecedented optical performances [7–10].

Recently, graphene resting on silicon-on-insulator (SOI) platform offers great potential for optoelectronic devices. Broadband optical modulators [11], mode locked laser [12] and high-responsivity photodetectors [13, 14] have all been demonstrated utilizing graphene-silicon hybrid waveguides (GSHWs). However, these non-resonant structures adopting straight waveguides require large-area graphene, which range from several tens to several hundred micrometers, to obtain sufficient optical absorption, resulting in large footprint and high power consumption. Owing to its intrinsic field enhancement (FE), silicon microring resonators (SMRs) [15] can strengthen the light-matter interaction, which is promising in reduction of footprint and power consumption by the GSHWs. Thus, monolithic integration of graphene on SMRs offer great opportunities in resonant cavity enhanced photonic devices [16], which is beneficial to photodetectors [17], optical modulators [18] and mode-locked lasers [12].

The fundamental feature in GSHWs is the optical absorption property of graphene [18]. Consequently, precisely evaluation of linear absorption coefficients (LACs) would be an important task in optimizing optical performances of the proposed GSHWs. Even though the LACs of GSHWs have been measured ranging from 0.03 dB/µm to 0.2 dB/µm for TE mode [19, 20] while 0.05 dB/µm to 0.33 dB/µm for TM mode [21, 22], the unique absorption properties in this configuration are still to be fully characterized, theoretically or experimentally, as mentioned in [23]. In previous reports, the LACs of GSHWs were generally obtained through a cut-back method [9, 10]. However this method is subject to several problems, for instance,

  • (i). The coupling efficiencies between the fiber tips and the waveguides as well as waveguide end facets maintain non-uniformity. Moreover, fiber-to-waveguide coupling losses are often comparable to or even much higher than the propagation losses in the waveguides [20, 22], leading to high uncertainties in loss measurements, as stated in [24].
  • (ii). The measured losses in these straight hybrid waveguides deviate from linear fit when the lengths of the transferred graphene are beyond 500 µm because of coverage problems, which is a fairly common situation [9].
  • (iii). This widely used method could not be directly applied to the measurement of resonant-enhanced optical absorption, which has not been measured and fully understood in the literature.

In this paper, we present a comprehensive method to determine the enhanced LAC of in-plane monolayer graphene on a microring resonator, on which graphene with only several micrometers in length is used. Commercially available monolayer graphene grown by chemical vapor deposition (CVD) is transferred onto the fabricated symmetrical add-drop SMR. The monolayer graphene patterning is accomplished by an electron beam lithography (EBL) process following by a “lift-off” process. Simulation results based on Finite Element Method (FEM) show that enhanced optical absorptions of monolayer graphene on our resonator are two times larger than those of monolayer graphene on silicon straight waveguide, which is in accordance with our experimental measurements. The enhanced absorption of in-plane monolayer graphene is wavelength-independent in the telecommunication band, which could be explained by the unique band structure of monolayer graphene [1,2]. More importantly, enhanced optical absorption with equally wavelength spacing can be potentially applied in resonance-enhanced photodetectors for chip-scale wavelength-division multiplexed optical interconnects.

2. Experimental details

A symmetrically coupled add-drop silicon microring resonator (SC-ADSMR) consisting of a SMR and dual stripe waveguides working as through and drop ports is fabricated. The SMR has a width of W = 500 nm, a height of H = 220 nm and a radius of R = 15 µm, which is fabricated on a SOI wafer with a buried oxide (BOX) layer of 3 µm using EBL and inductively coupled plasmon (ICP) etching. The stripe waveguides are laterally coupled with the SMR and both of them have the same dimensions. The corresponding gaps between the stripes and SMR are 125 nm and 117 nm respectively. The nearly identical gaps show that the fabricated add-drop silicon microring resonator is symmetrically coupled.

Figure 1 illustrates the monolayer graphene transfer and SC-ADSMR device fabrication processes. The CVD monolayer graphene is grown on both sides of a copper foil (Cu) in a first step. A 200-nm thick poly (methyl methacrylate) (PMMA) (Allresist, AR-P 672.045) film is spin-coated onto the upper surface of layered backside graphene/Cu/monolayer graphene to protect monolayer graphene from damage in a second step. The sample consisting of layered backside graphene/Cu/monolayer graphene/PMMA is floated on marble's etchant with 15 grams of copper(II) sulfate pentahydrate (CuSO4·5H2O), 50 ml of deionized water (DI), and 50 ml of concentrated hydrochloric acid (HCl). The backside graphene is totally removed after 2-min of chemical etching. Then the Cu/monolayer graphene/PMMA sample is floated on DI for about 3 minutes to remove the chemical impurities. Another marble’s etchant with the same chemical recipe is applied for removing the Cu beneath monolayer graphene. The etching time is about 1.5 hours. The remained sample consisting of a layered monolayer graphene/PMMA is last rinsed in DI, leaving it ready for transferring. We employ the following processes to transfer monolayer graphene to a specific region of the SC-ADSMR by ripping out the abundant monolayer graphene: a 450-nm thick PMMA film is spin-coated onto the SOI wafer containing fabricated SC-ADSMR device and a specific region with a 45 degree sector area is patterned using EBL, followed by developing and fixing of the PMMA photoresist. In the time, the prepared monolayer graphene/PMMA sample is transferred onto the chip followed by drying with a mild nitrogen blow. Subsequently, a “lift-off” process is introduced to form the monolayer graphene coated SC-ADSMR device. The whole chip is baked at 180°C for 15 minutes. The PMMA is then dissolved in hot acetone for about 1 hour. The removal of PMMA also results in cutting-away of monolayer graphene resting on the 450-nm thick PMMA, which is similar to a lift-off [22, 25] process. Finally, the chip is rinsed with isopropyl alcohol (IPA) for further cleaning and then dried again by a mild nitrogen blow. A scanning electron micrograph (SEM) picture of the monolayer graphene coated SC-ADSMR device with partial part of the stripe waveguides is shown in Fig. 2(a), where secondary-electron contrast is obtained. The possible reason for imaging contrast lies in different secondary-electron-generation efficiencies of silicon, silicon oxide and monolayer graphene. At the boundary of patterned monolayer graphene, the random roughness of monolayer graphene is large due to the coarse-controlled “lift-off” process.

 figure: Fig. 1

Fig. 1 The processes of monolayer graphene preparation and SC-ADSMR device fabrication.

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 figure: Fig. 2

Fig. 2 (a) SEM image of the SC-ADSMR covered with patterned monolayer graphene (top view). Close-up view of the two coupling regions are also shown. (b) Zoom-in SEM images of the local monolayer graphene covered area in (a), showing that monolayer graphene uniformly clings to the silicon waveguide. Here X is the radial length of side-monolayer-graphene and W is the width of waveguide. (c) Photonic crystal grating coupler used for coupling light into and out of the SC-ADSMR device.

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The detailed SEM picture of our fabricated GSHW is shown in Fig. 2(b), in which the patterned top-monolayer-graphene rests on the surface of the waveguide and side-monolayer-graphene extends to the surface of BOX layer, forming a trapezoid configuration. According to our measurements, the radial length of side-monolayer-graphene is estimated as X = 200 nm. Figure 2(c) shows the photonic crystal grating coupler, which is optimized for TE mode coupling exhibiting an insertion loss of 7.5 dB per facet.

Adopting the experimental setup in Fig. 3(a), the SC-ADSMR is characterized by an amplified spontaneous emission (ASE) light source (Amonics, AEDFA-300-B-FA) ranging from 1535 nm to 1565 nm. The normalized transmission spectra of through port before and after monolayer graphene transfer (noted as woGr and wGr respectively) are recorded by an optical spectrum analyzer (OSA, YOKOGAWA AQ6370), which is shown in Fig. 3(b). It shows that the resonator before and after monolayer graphene transfer have a mean free spectral range (FSR) of FSR = 5.74 nm. The significant reduction of extinction ratio and broadening of the resonances in Fig. 3(b) are the result of increased propagation loss (absorption) induced by monolayer graphene. The red shift of resonances is probably a result of the change in the mode effective refractive index induced after transfer of the graphene.

 figure: Fig. 3

Fig. 3 (a) Experimental setup for characterizing the LAC of in-plane graphene. (b) Optical transmission spectra of the SC-ADSMR device before and after monolayer graphene transfer (noted as woGr and wGr respectively). (c) Raman spectra measured in the graphene-covered region (red) and in the area where graphene is lifted off (blue).

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The explicit characterization of monolayer graphene is obtained by Raman spectrum. In Fig. 3(c), we have measured Raman spectrum of the graphene layer coated SC-ADSMR device using a spectrometer with high resolution (LabRAM HR800, France, Jobin Yvon). The blue curve represents Raman spectrum of the area where graphene is lifted off and we see that the typical Raman peaks are missing. The red curve shows a G peak (~1586 cm−1) with a full width at half maximum (FWHM) of ~18 cm−1 and a 2D peak (~2700 cm−1), with a 2D-to-G peak intensity ratio of about 1.2, implying that the transferred graphene is a monolayer and the corresponding chemical potential is around 0.2 eV [26]. Moreover, a weak D peak is also found at ~1350 cm−1, indicating the transferred monolayer graphene is of high quality. We have also measured the Raman spectra in some other regions. The results turn out to be similar to the Raman spectra presented in Fig. 3(c).

3. Experimental Results

We have adopted an analytical model proposed by Shijun Xiao et al. [24] to characterize the propagation loss in our monolayer graphene covered SC-ADSMR device. In Fig. 4, schematic diagram of the model is presented. κt2,κd2 are coefficients representing the fraction of optical power coupled into and out of the SMR through input and drop port respectively. κp2 is the fraction of optical power losses per round-trip in the SMR due to intrinsic losses mainly resulting from graphene absorption and roughness induced scattering. In our case, κt=κd is satisfied and the optical response of through port is given as [24]:

Tthrough(λ)=(λλ0)2+(FSR4π)2(κp2)2(λλ0)2+(FWHMt2)2.
where Tthrough(λ) is the power transmission of through port, FWHMt is the FWHM of the optical transmission spectrum at the through port and λ0 is the resonant wavelength. When the input wavelength is at resonance (λ = λ0), Tthrough(λ) has a minimal value of γt satisfying:
ERt(dB)=10log10(γt).
with ERt and γt the extinction ratio and minimal power transmission at the through port respectively. The coefficients κt,κd and κp are described as:
κp2=2πFWHMtγtFSR,
κt2=κd2=πFWHMt(1γt)FSR,
The loss per round-trip in the resonator is determined by:
α(dB/round)=10log10(1κp2).
Also, the Q factor, Finesse and FE of the SC-ADSMR are summarized as [15,27]:

 figure: Fig. 4

Fig. 4 Scheme of the SC-ADSMR with patterned monolayer graphene

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Q=λ0FWHMt,
Finesse=FSRFWHMt=2πκt2+κd2+κp2,
FE=Finesseπ.

In the proposed device, an eighth part of the resonator is covered with monolayer graphene. The total losses of SMR coated with monolayer graphene include the linear absorption (LA) of in-plane monolayer graphene and LA of silicon waveguide. Assuming graphene “lift off” process does not induce extra LA in the silicon waveguide, the LAC of silicon waveguide and GSHW can be written as:

LACsilicon=αwoGr2πR,
LACGSHW=(αwGrαwoGr(1n))2πnR.
where αwoGr and αwGr correspond to the loss per round-trip before and after graphene transfer respectively, n = 1/8 corresponds to the fractional coverage length of monolayer graphene. Thus, the LAC of in-plane monolayer graphene on the silicon microring resonator is expressed as:

LACGr_resonator=LACGSHWLACsilicon.

Table 1 shows detailed experimental results before and after graphene transfer, including the resonant wavelengths, the corresponding extinction ratio and FWHM of transmission spectra. By using the analytical method mentioned above, the enhanced LAC of in-plane monolayer graphene in our case is nearly identical, of which the mean value is ~0.23 dB/µm.

Tables Icon

Table 1. Parameters for LAC deduction before and after graphene transfer.

Given the fact that in most previously published works [21, 28–30] the LACs of monolayer graphene on silicon waveguides have a typical value of ~0.1 dB/µm, which are one time smaller than the LACs in our case. The difference can be explained by the field enhancement in our SC-ADSMR device which lies in enhancement in the interaction of light with graphene through coupling resonant modes within the silicon microring resonator [31]. To fully understand this discrepancy, we introduce FE parameter and the sidewall loss in the next section to simulate the propagation loss of our fabricated device.

4. Simulation Model and Discussion

Most widely used method for simulating graphene in literature is the equivalent bulk medium approach, in which graphene is modeled as a bulk-material layer of finite thickness [9]. However, the simulation results with this approach are strongly dependent on the simulated grid size and the thickness of monolayer graphene, which leads to inefficient calculation. Hence, we model the atomic-thick layer as a conductive surface in a commercial software (COMSOL Multiphysics) according to its fundamental optical properties and boundary conditions, which has been approved valid and more efficient [23, 32].

Graphene can be treated electromagnetically by its surface dynamic conductivity in a complex form consisting of interband and intraband contributions [33]:

σ(ω,μc,τ,T)=σintra(ω,μc,τ,T)+σinter(ω,μc,τ,T).
The intraband contribution can be evaluated as:
σintra(ω,μc,τ,T)=ie2kBTπ2(ω+iτ1)[|μc|kBT+2In(exp(|μc|kBT)+1)].
For ħω and |μc|kBT, the interband contribution is expressed as:
σinter(ω,μc,τ,T)=ie24πIn[2|μc|(ω+iτ1)2|μc|+(ω+iτ1)].
where e is the electron charge, kB is the Boltzmann constant, ħ is the reduced Planck’s constant, ω is the angular frequency of incident light, T is the temperature, μc is the chemical potential and τ is the momentum relaxation of carriers in monolayer graphene. Adopting an incident wavelength of λs = 1550 nm, a temperature of T = 300 K and a momentum relaxation of τ = 12 fs [34], σ (ω, μc, τ, T) is numerically calculated and plotted as a function of graphene’s chemical potential in Fig. 5.

 figure: Fig. 5

Fig. 5 Surface dynamic conductivity of monolayer graphene as a function of its chemical potential

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The optical linear absorption of graphene is directly determined by the real part of its surface dynamic conductivity shown in Fig. 5. Thus Eqs. (12), (13) and (14) are implemented in COMSOL Multiphysics and the enhanced LAC of in-plane monolayer graphene in our SC-ADSMR device is modelled with a 2D configuration illustrated in Fig. 6(a), in which the graphene locates on top of the silicon waveguide and attaches to the BOX layer at an angle of φ with respect to the side wall of silicon waveguide. According to our estimation through SEM picture (section 2), X has a value of ~200 nm in experiment. The corresponding surface current density of monolayer graphene in Fig. 6(a) is expressed as [23, 32]:

J//=σ(ω,μc,τ,T)(FEE//),
J=0.
where subscript // and denote the field component that is tangential and normal to the graphene sheet, respectively, E is the electrical field and J is the surface current density of monolayer graphene. Equation (15) given by Ohm’s law is critical, in which the FE of silicon microring resonator is taken into consideration, because the enhanced optical absorption of graphene-on-resonator mainly origins from the localized electrical field in our resonator. FE is deliberately solved via Eqs. (7) and (8) and presented in Table 1 (section 3). Because electric fields perpendicular to the surface of silicon microring have no interaction with monolayer graphene, the corresponding surface current density in the perpendicular direction could be set as zero as written in Eq. (16). In the simulation, a mesh size of 1 nm is chosen for monolayer graphene and a chemical potential of ~0.2 eV is confirmed by the Raman spectrum, which is also identical to the reported values of PMMA-transferred monolayer graphene [20]. With these parameters, the complex effective refractive index of GSHW in Fig. 6(a) is calculated in COMSOL Multiphysics. Then, the LAC of in-plane monolayer graphene in the proposed structure is obtained through [9]:
α(dB/μm)=2k0neff,imag×4.343×106.
where k0 is the vacuum wave number, subscript imag denotes the imaginary part of modal effective index and 4.343 × 10−6 is the constant for converting from m−1 to dB/µm. Figure 6(b) shows that the enhanced LAC of in-plane monolayer graphene in our case has an average value of ~0.20 dB/µm in simulation, which agrees well with the experimental results (~0.23 dB/µm).

 figure: Fig. 6

Fig. 6 (a) Cross section of the simulated GSHW. (b) Experimental and simulated LAC of in-plane monolayer graphene as a function of the five resonant wavelengths of our SC-ADSMR device. In this simulation, the FEs of the SC-ADSMR and side-monolayer-graphene which is clung to the waveguide have both been taken into consideration. Here, λ1 = 1537.94 nm, λ2 = 1543.62 nm, λ3 = 1549.34 nm, λ4 = 1555.10 nm and λ5 = 1560.90 nm represent the five resonant wavelengths of our SC-ADSMR device after graphene transfer process.

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The parameter of X is estimated through SEM picture from top view (section 2), which possibly leads to inaccuracy of optical absorption. In order to verify our theoretical model with experimental results, we further simulated the enhanced LAC of in-plane monolayer graphene for quasi TE mode based on our SC-ADSMR device with a varying X parameter. By fixing FE to an average value of ~2.10, x, y and z component of electric field at the incident wavelength of 1550 nm is shown in Fig. 7(a). Mesh grids of our device are also presented, in which the densest grids indicate where monolayer graphene is located. In the top of Fig. 7(a), the x-component of electric field of the GSHW is evanescently coupled with top-monolayer-graphene and side-monolayer-graphene. In the middle of Fig. 7(a), y-component of electric field of the GSHW can’t contribute to the optical absorption owing to Eq. (16). Interestingly, the z-component of electric field in GSHW strongly interacts with the side-monolayer-graphene, which is often neglected in the literature [19, 20]. Following the electric fields distribution in Fig. 7(a), the LAC of GSHW is plotted as a function of parameter X in Fig. 7(b). For fundamental quasi TE mode in our case, LA of GSHW origins from both the side-monolayer-graphene and top-monolayer-graphene. With the parameter of X = 200 nm, the optical absorption by top-monolayer-graphene is ~0.15 dB/µm, while the corresponding contribution by side-monolayer-graphene is ~0.05 dB/µm, which can’t be neglected in resonant configuration. With increased parameter of X (X>200 nm), the coupling between electric field of GSHW and side-monolayer-graphene becomes weaker, resulting in small variation of optical absorption (~0.01 dB/μm). It is worth noting that when X>100 nm, the fluctuation of our simulated LACs will never exceed ± 0.01 dB/µm compared to the simulated result at X = 200 nm, which indicate that the experimental results fit well with the simulation.

 figure: Fig. 7

Fig. 7 (a) The x, y and z components of electrical field in the GSHW. Here the mesh grids are also shown. (b) The LAC of GSHW in Fig. 6(a) with a varying parameter of X. The inset shows typical fundamental quasi TE mode profile of simulated GSHW at 1550 nm. Other parameters for this simulation are also shown in the box above.

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The simulation results (~0.20 dB/µm) are slightly lower than the experimental ones (~0.23 dB/µm). The small discrepancy is attributed to the following facts:

  • (i). The “lift-off” procedures cause wrapping of graphene at the edges which lead to light scattering when light enters the waveguide section covered with graphene.
  • (ii). The surface roughness of silicon waveguide or Cu residues also introduce extra loss.

Furthermore, we also estimate the absorption case for TM mode, which is illustrated in Fig. 8.

 figure: Fig. 8

Fig. 8 Simulated waveguide loss for TM mode as a function of parameter X.

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The absorption of TM mode is larger than that of TE mode when X>10 nm. This is attributed to tangential component of the localized electric field.

5. Conclusion

We propose a comprehensive way towards direct determination of the LACs of in-plane monolayer graphene integrated with a SC-ADSMR device, which does not depend on the coupling efficiencies between the fiber tips and the waveguides as well as the waveguide end facets. A SC-ADSMR with patterned monolayer graphene is designed and fabricated, in which the universal enhanced LAC of in-plane monolayer graphene over a large wavelength range is proportional to the field enhancement in SMR. Our work provides an efficient method to evaluate the linear optical performances of high-performance graphene-comprising waveguides leading to compact-footprint and low-power-consumption PICs.

Funding

National Basic Research Program of China (Grant No. 2012CB922103 and 2013CB933303); National Scientific Founding of China (Grant No. 60806016 and 61177049).

Acknowledgments

We thank all the engineers in the Center of Micro-Fabrication and Characterization (CMCF) of Wuhan National Laboratory for Optoelectronics (WNLO) for the support in device fabrication.

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30. I. F. Crowe, N. Clark, S. Hussein, B. Towlson, E. Whittaker, M. M. Milosevic, F. Y. Gardes, G. Z. Mashanovich, M. P. Halsall, and A. Vijayaraghaven, “Determination of the quasi-TE mode (in-plane) graphene linear absorption coefficient via integration with silicon-on-insulator racetrack cavity resonators,” Opt. Express 22(15), 18625–18632 (2014). [CrossRef]   [PubMed]  

31. X. Gan, K. F. Mak, Y. Gao, Y. You, F. Hatami, J. Hone, T. F. Heinz, and D. Englund, “Strong enhancement of light-matter interaction in graphene coupled to a photonic crystal nanocavity,” Nano Lett. 12(11), 5626–5631 (2012). [CrossRef]   [PubMed]  

32. D. Chatzidimitriou, A. Pitilakis, and E. E. Kriezis, “Rigorous calculation of nonlinear parameters in graphene-comprising waveguides,” J. Appl. Phys. 118(2), 023105 (2015). [CrossRef]  

33. P.-Y. Chen and A. Alù, “Atomically thin surface cloak using graphene monolayers,” ACS Nano 5(7), 5855–5863 (2011). [CrossRef]   [PubMed]  

34. V. Sorianello, M. Midrio, and M. Romagnoli, “Design optimization of single and double layer Graphene phase modulators in SOI,” Opt. Express 23(5), 6478–6490 (2015). [CrossRef]   [PubMed]  

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  26. A. Das, S. Pisana, B. Chakraborty, S. Piscanec, S. K. Saha, U. V. Waghmare, K. S. Novoselov, H. R. Krishnamurthy, A. K. Geim, A. C. Ferrari, and A. K. Sood, “Monitoring dopants by Raman scattering in an electrochemically top-gated graphene transistor,” Nat. Nanotechnol. 3(4), 210–215 (2008).
    [Crossref] [PubMed]
  27. V. Van, T. Ibrahim, P. Absil, F. Johnson, R. Grover, and P.-T. Ho, “Optical signal processing using nonlinear semiconductor microring resonators,” IEEE J. Sel. Top. Quantum Electron. 8(3), 705–713 (2002).
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    [Crossref] [PubMed]
  31. X. Gan, K. F. Mak, Y. Gao, Y. You, F. Hatami, J. Hone, T. F. Heinz, and D. Englund, “Strong enhancement of light-matter interaction in graphene coupled to a photonic crystal nanocavity,” Nano Lett. 12(11), 5626–5631 (2012).
    [Crossref] [PubMed]
  32. D. Chatzidimitriou, A. Pitilakis, and E. E. Kriezis, “Rigorous calculation of nonlinear parameters in graphene-comprising waveguides,” J. Appl. Phys. 118(2), 023105 (2015).
    [Crossref]
  33. P.-Y. Chen and A. Alù, “Atomically thin surface cloak using graphene monolayers,” ACS Nano 5(7), 5855–5863 (2011).
    [Crossref] [PubMed]
  34. V. Sorianello, M. Midrio, and M. Romagnoli, “Design optimization of single and double layer Graphene phase modulators in SOI,” Opt. Express 23(5), 6478–6490 (2015).
    [Crossref] [PubMed]

2016 (3)

2015 (6)

C. C. Evans, C. Liu, and J. Suntivich, “Low-loss titanium dioxide waveguides and resonators using a dielectric lift-off fabrication process,” Opt. Express 23(9), 11160–11169 (2015).
[Crossref] [PubMed]

C. Horvath, D. Bachman, G. Mi, and V. Van, “Fabrication and characterization of edge-conformed graphene-silicon waveguides,” IEEE Photonics Technol. Lett. 27(6), 585–587 (2015).
[Crossref]

M. Ji, H. Cai, L. Deng, Y. Huang, Q. Huang, J. Xia, Z. Li, J. Yu, and Y. Wang, “Enhanced parametric frequency conversion in a compact silicon-graphene microring resonator,” Opt. Express 23(14), 18679–18685 (2015).
[Crossref] [PubMed]

D. Chatzidimitriou, A. Pitilakis, and E. E. Kriezis, “Rigorous calculation of nonlinear parameters in graphene-comprising waveguides,” J. Appl. Phys. 118(2), 023105 (2015).
[Crossref]

V. Sorianello, M. Midrio, and M. Romagnoli, “Design optimization of single and double layer Graphene phase modulators in SOI,” Opt. Express 23(5), 6478–6490 (2015).
[Crossref] [PubMed]

Y. Ding, X. Zhu, S. Xiao, H. Hu, L. H. Frandsen, N. A. Mortensen, and K. Yvind, “Effective electro-optical modulation with high extinction ratio by a graphene-silicon microring resonator,” Nano Lett. 15(7), 4393–4400 (2015).
[Crossref] [PubMed]

2014 (5)

L. Yu, J. Zheng, Y. Xu, D. Dai, and S. He, “Local and nonlocal optically induced transparency effects in graphene-silicon hybrid nanophotonic integrated circuits,” ACS Nano 8(11), 11386–11393 (2014).
[Crossref] [PubMed]

M. Mohsin, D. Schall, M. Otto, A. Noculak, D. Neumaier, and H. Kurz, “Graphene based low insertion loss electro-absorption modulator on SOI waveguide,” Opt. Express 22(12), 15292–15297 (2014).
[Crossref] [PubMed]

R. Kou, S. Tanabe, T. Tsuchizawa, T. Yamamoto, H. Hibino, H. Nakajima, and K. Yamada, “Influence of graphene on quality factor variation in a silicon ring resonator,” Appl. Phys. Lett. 104(9), 091122 (2014).
[Crossref]

T. Gu, H. Zhou, J. F. McMillan, N. Petrone, A. van der Zande, J. C. Hone, M. Yu, G.-Q. Lo, D.-L. Kwong, and C. W. Wong, “Coherent four-wave mixing on hybrid graphene-silicon photonic crystals,” IEEE J. Sel. Top. Quantum Electron. 20(1), 7500106 (2014).
[Crossref]

I. F. Crowe, N. Clark, S. Hussein, B. Towlson, E. Whittaker, M. M. Milosevic, F. Y. Gardes, G. Z. Mashanovich, M. P. Halsall, and A. Vijayaraghaven, “Determination of the quasi-TE mode (in-plane) graphene linear absorption coefficient via integration with silicon-on-insulator racetrack cavity resonators,” Opt. Express 22(15), 18625–18632 (2014).
[Crossref] [PubMed]

2013 (3)

R. Kou, S. Tanabe, T. Tsuchizawa, K. Warabi, S. Suzuki, H. Hibino, H. Nakajima, and K. Yamada, “Characterization of optical absorption and polarization dependence of single-layer graphene integrated on a silicon wire waveguide,” Jpn. J. Appl. Phys. 52(6R), 060203 (2013).
[Crossref]

A. Pospischil, M. Humer, M. M. Furchi, D. Bachmann, R. Guider, T. Fromherz, and T. Mueller, “CMOS-compatible graphene photodetector covering all optical communication bands,” Nat. Photonics 7(11), 892–896 (2013).
[Crossref]

X. Gan, R.-J. Shiue, Y. Gao, I. Meric, T. F. Heinz, K. Shepard, J. Hone, S. Assefa, and D. Englund, “Chip-integrated ultrafast graphene photodetector with high responsivity,” Nat. Photonics 7(11), 883–887 (2013).
[Crossref]

2012 (4)

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. K. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photonics Rev. 6(1), 47–73 (2012).
[Crossref]

T. Gu, N. Petrone, J. F. McMillan, A. van der Zande, M. Yu, G. Q. Lo, D. L. Kwong, J. Hone, and C. W. Wong, “Regenerative oscillation and four-wave mixing in graphene optoelectronics,” Nat. Photonics 6(8), 554–559 (2012).
[Crossref]

H. Li, Y. Anugrah, S. J. Koester, and M. Li, “Optical absorption in graphene integrated on silicon waveguides,” Appl. Phys. Lett. 101(11), 111110 (2012).
[Crossref] [PubMed]

X. Gan, K. F. Mak, Y. Gao, Y. You, F. Hatami, J. Hone, T. F. Heinz, and D. Englund, “Strong enhancement of light-matter interaction in graphene coupled to a photonic crystal nanocavity,” Nano Lett. 12(11), 5626–5631 (2012).
[Crossref] [PubMed]

2011 (3)

P.-Y. Chen and A. Alù, “Atomically thin surface cloak using graphene monolayers,” ACS Nano 5(7), 5855–5863 (2011).
[Crossref] [PubMed]

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[Crossref] [PubMed]

Q. Bao, H. Zhang, B. Wang, Z. Ni, C. Lim, Y. Wang, D. Tang, and K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics 5(7), 411–415 (2011).
[Crossref]

2009 (2)

A. K. Geim, “Graphene: status and prospects,” Science 324(5934), 1530–1534 (2009).
[Crossref] [PubMed]

Y. M. Lin, K. A. Jenkins, A. Valdes-Garcia, J. P. Small, D. B. Farmer, and P. Avouris, “Operation of graphene transistors at gigahertz frequencies,” Nano Lett. 9(1), 422–426 (2009).
[Crossref] [PubMed]

2008 (2)

F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, “Gate-variable optical transitions in graphene,” Science 320(5873), 206–209 (2008).
[Crossref] [PubMed]

A. Das, S. Pisana, B. Chakraborty, S. Piscanec, S. K. Saha, U. V. Waghmare, K. S. Novoselov, H. R. Krishnamurthy, A. K. Geim, A. C. Ferrari, and A. K. Sood, “Monitoring dopants by Raman scattering in an electrochemically top-gated graphene transistor,” Nat. Nanotechnol. 3(4), 210–215 (2008).
[Crossref] [PubMed]

2007 (2)

2002 (1)

V. Van, T. Ibrahim, P. Absil, F. Johnson, R. Grover, and P.-T. Ho, “Optical signal processing using nonlinear semiconductor microring resonators,” IEEE J. Sel. Top. Quantum Electron. 8(3), 705–713 (2002).
[Crossref]

1995 (1)

M. S. Ünlü and S. Strite, “Resonant cavity enhanced photonic devices,” J. Appl. Phys. 78(2), 607–639 (1995).
[Crossref]

Absil, P.

V. Van, T. Ibrahim, P. Absil, F. Johnson, R. Grover, and P.-T. Ho, “Optical signal processing using nonlinear semiconductor microring resonators,” IEEE J. Sel. Top. Quantum Electron. 8(3), 705–713 (2002).
[Crossref]

Alù, A.

P.-Y. Chen and A. Alù, “Atomically thin surface cloak using graphene monolayers,” ACS Nano 5(7), 5855–5863 (2011).
[Crossref] [PubMed]

Anugrah, Y.

H. Li, Y. Anugrah, S. J. Koester, and M. Li, “Optical absorption in graphene integrated on silicon waveguides,” Appl. Phys. Lett. 101(11), 111110 (2012).
[Crossref] [PubMed]

Assefa, S.

X. Gan, R.-J. Shiue, Y. Gao, I. Meric, T. F. Heinz, K. Shepard, J. Hone, S. Assefa, and D. Englund, “Chip-integrated ultrafast graphene photodetector with high responsivity,” Nat. Photonics 7(11), 883–887 (2013).
[Crossref]

Avouris, P.

Y. M. Lin, K. A. Jenkins, A. Valdes-Garcia, J. P. Small, D. B. Farmer, and P. Avouris, “Operation of graphene transistors at gigahertz frequencies,” Nano Lett. 9(1), 422–426 (2009).
[Crossref] [PubMed]

Bachman, D.

C. Horvath, D. Bachman, G. Mi, and V. Van, “Fabrication and characterization of edge-conformed graphene-silicon waveguides,” IEEE Photonics Technol. Lett. 27(6), 585–587 (2015).
[Crossref]

Bachmann, D.

A. Pospischil, M. Humer, M. M. Furchi, D. Bachmann, R. Guider, T. Fromherz, and T. Mueller, “CMOS-compatible graphene photodetector covering all optical communication bands,” Nat. Photonics 7(11), 892–896 (2013).
[Crossref]

Baets, R.

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. K. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photonics Rev. 6(1), 47–73 (2012).
[Crossref]

Bao, Q.

Q. Bao, H. Zhang, B. Wang, Z. Ni, C. Lim, Y. Wang, D. Tang, and K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics 5(7), 411–415 (2011).
[Crossref]

Bienstman, P.

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. K. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photonics Rev. 6(1), 47–73 (2012).
[Crossref]

Bogaerts, W.

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. K. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photonics Rev. 6(1), 47–73 (2012).
[Crossref]

Cai, H.

Chakraborty, B.

A. Das, S. Pisana, B. Chakraborty, S. Piscanec, S. K. Saha, U. V. Waghmare, K. S. Novoselov, H. R. Krishnamurthy, A. K. Geim, A. C. Ferrari, and A. K. Sood, “Monitoring dopants by Raman scattering in an electrochemically top-gated graphene transistor,” Nat. Nanotechnol. 3(4), 210–215 (2008).
[Crossref] [PubMed]

Chatzidimitriou, D.

D. Chatzidimitriou, A. Pitilakis, and E. E. Kriezis, “Rigorous calculation of nonlinear parameters in graphene-comprising waveguides,” J. Appl. Phys. 118(2), 023105 (2015).
[Crossref]

Chen, P.-Y.

P.-Y. Chen and A. Alù, “Atomically thin surface cloak using graphene monolayers,” ACS Nano 5(7), 5855–5863 (2011).
[Crossref] [PubMed]

Claes, T.

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. K. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photonics Rev. 6(1), 47–73 (2012).
[Crossref]

Clark, N.

Crommie, M.

F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, “Gate-variable optical transitions in graphene,” Science 320(5873), 206–209 (2008).
[Crossref] [PubMed]

Crowe, I. F.

Dai, D.

L. Yu, J. Zheng, Y. Xu, D. Dai, and S. He, “Local and nonlocal optically induced transparency effects in graphene-silicon hybrid nanophotonic integrated circuits,” ACS Nano 8(11), 11386–11393 (2014).
[Crossref] [PubMed]

Das, A.

A. Das, S. Pisana, B. Chakraborty, S. Piscanec, S. K. Saha, U. V. Waghmare, K. S. Novoselov, H. R. Krishnamurthy, A. K. Geim, A. C. Ferrari, and A. K. Sood, “Monitoring dopants by Raman scattering in an electrochemically top-gated graphene transistor,” Nat. Nanotechnol. 3(4), 210–215 (2008).
[Crossref] [PubMed]

De Heyn, P.

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. K. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photonics Rev. 6(1), 47–73 (2012).
[Crossref]

De Vos, K.

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. K. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photonics Rev. 6(1), 47–73 (2012).
[Crossref]

Deng, L.

Ding, Y.

Y. Ding, X. Zhu, S. Xiao, H. Hu, L. H. Frandsen, N. A. Mortensen, and K. Yvind, “Effective electro-optical modulation with high extinction ratio by a graphene-silicon microring resonator,” Nano Lett. 15(7), 4393–4400 (2015).
[Crossref] [PubMed]

Dumon, P.

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. K. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photonics Rev. 6(1), 47–73 (2012).
[Crossref]

Englund, D.

X. Gan, R.-J. Shiue, Y. Gao, I. Meric, T. F. Heinz, K. Shepard, J. Hone, S. Assefa, and D. Englund, “Chip-integrated ultrafast graphene photodetector with high responsivity,” Nat. Photonics 7(11), 883–887 (2013).
[Crossref]

X. Gan, K. F. Mak, Y. Gao, Y. You, F. Hatami, J. Hone, T. F. Heinz, and D. Englund, “Strong enhancement of light-matter interaction in graphene coupled to a photonic crystal nanocavity,” Nano Lett. 12(11), 5626–5631 (2012).
[Crossref] [PubMed]

Evans, C. C.

Farmer, D. B.

Y. M. Lin, K. A. Jenkins, A. Valdes-Garcia, J. P. Small, D. B. Farmer, and P. Avouris, “Operation of graphene transistors at gigahertz frequencies,” Nano Lett. 9(1), 422–426 (2009).
[Crossref] [PubMed]

Feng, G.

H. Zhou, T. Gu, J. F. McMillan, M. Yu, G. Lo, D.-L. Kwong, G. Feng, S. Zhou, and C. W. Wong, “Enhanced photoresponsivity in graphene-silicon slow-light photonic crystal waveguides,” Appl. Phys. Lett. 108(11), 111106 (2016).
[Crossref]

Ferrari, A. C.

A. Das, S. Pisana, B. Chakraborty, S. Piscanec, S. K. Saha, U. V. Waghmare, K. S. Novoselov, H. R. Krishnamurthy, A. K. Geim, A. C. Ferrari, and A. K. Sood, “Monitoring dopants by Raman scattering in an electrochemically top-gated graphene transistor,” Nat. Nanotechnol. 3(4), 210–215 (2008).
[Crossref] [PubMed]

Frandsen, L. H.

Y. Ding, X. Zhu, S. Xiao, H. Hu, L. H. Frandsen, N. A. Mortensen, and K. Yvind, “Effective electro-optical modulation with high extinction ratio by a graphene-silicon microring resonator,” Nano Lett. 15(7), 4393–4400 (2015).
[Crossref] [PubMed]

Fromherz, T.

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X. Gan, K. F. Mak, Y. Gao, Y. You, F. Hatami, J. Hone, T. F. Heinz, and D. Englund, “Strong enhancement of light-matter interaction in graphene coupled to a photonic crystal nanocavity,” Nano Lett. 12(11), 5626–5631 (2012).
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Lim, C.

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M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
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T. Gu, N. Petrone, J. F. McMillan, A. van der Zande, M. Yu, G. Q. Lo, D. L. Kwong, J. Hone, and C. W. Wong, “Regenerative oscillation and four-wave mixing in graphene optoelectronics,” Nat. Photonics 6(8), 554–559 (2012).
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T. Gu, H. Zhou, J. F. McMillan, N. Petrone, A. van der Zande, J. C. Hone, M. Yu, G.-Q. Lo, D.-L. Kwong, and C. W. Wong, “Coherent four-wave mixing on hybrid graphene-silicon photonic crystals,” IEEE J. Sel. Top. Quantum Electron. 20(1), 7500106 (2014).
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X. Gan, R.-J. Shiue, Y. Gao, I. Meric, T. F. Heinz, K. Shepard, J. Hone, S. Assefa, and D. Englund, “Chip-integrated ultrafast graphene photodetector with high responsivity,” Nat. Photonics 7(11), 883–887 (2013).
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C. Horvath, D. Bachman, G. Mi, and V. Van, “Fabrication and characterization of edge-conformed graphene-silicon waveguides,” IEEE Photonics Technol. Lett. 27(6), 585–587 (2015).
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D. Chatzidimitriou, A. Pitilakis, and E. E. Kriezis, “Rigorous calculation of nonlinear parameters in graphene-comprising waveguides,” J. Appl. Phys. 118(2), 023105 (2015).
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X. Gan, R.-J. Shiue, Y. Gao, I. Meric, T. F. Heinz, K. Shepard, J. Hone, S. Assefa, and D. Englund, “Chip-integrated ultrafast graphene photodetector with high responsivity,” Nat. Photonics 7(11), 883–887 (2013).
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X. Gan, R.-J. Shiue, Y. Gao, I. Meric, T. F. Heinz, K. Shepard, J. Hone, S. Assefa, and D. Englund, “Chip-integrated ultrafast graphene photodetector with high responsivity,” Nat. Photonics 7(11), 883–887 (2013).
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Y. M. Lin, K. A. Jenkins, A. Valdes-Garcia, J. P. Small, D. B. Farmer, and P. Avouris, “Operation of graphene transistors at gigahertz frequencies,” Nano Lett. 9(1), 422–426 (2009).
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A. Das, S. Pisana, B. Chakraborty, S. Piscanec, S. K. Saha, U. V. Waghmare, K. S. Novoselov, H. R. Krishnamurthy, A. K. Geim, A. C. Ferrari, and A. K. Sood, “Monitoring dopants by Raman scattering in an electrochemically top-gated graphene transistor,” Nat. Nanotechnol. 3(4), 210–215 (2008).
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R. Kou, S. Tanabe, T. Tsuchizawa, T. Yamamoto, H. Hibino, H. Nakajima, and K. Yamada, “Influence of graphene on quality factor variation in a silicon ring resonator,” Appl. Phys. Lett. 104(9), 091122 (2014).
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[Crossref] [PubMed]

Ünlü, M. S.

M. S. Ünlü and S. Strite, “Resonant cavity enhanced photonic devices,” J. Appl. Phys. 78(2), 607–639 (1995).
[Crossref]

Valdes-Garcia, A.

Y. M. Lin, K. A. Jenkins, A. Valdes-Garcia, J. P. Small, D. B. Farmer, and P. Avouris, “Operation of graphene transistors at gigahertz frequencies,” Nano Lett. 9(1), 422–426 (2009).
[Crossref] [PubMed]

Van, V.

C. Horvath, D. Bachman, G. Mi, and V. Van, “Fabrication and characterization of edge-conformed graphene-silicon waveguides,” IEEE Photonics Technol. Lett. 27(6), 585–587 (2015).
[Crossref]

V. Van, T. Ibrahim, P. Absil, F. Johnson, R. Grover, and P.-T. Ho, “Optical signal processing using nonlinear semiconductor microring resonators,” IEEE J. Sel. Top. Quantum Electron. 8(3), 705–713 (2002).
[Crossref]

van der Zande, A.

T. Gu, H. Zhou, J. F. McMillan, N. Petrone, A. van der Zande, J. C. Hone, M. Yu, G.-Q. Lo, D.-L. Kwong, and C. W. Wong, “Coherent four-wave mixing on hybrid graphene-silicon photonic crystals,” IEEE J. Sel. Top. Quantum Electron. 20(1), 7500106 (2014).
[Crossref]

T. Gu, N. Petrone, J. F. McMillan, A. van der Zande, M. Yu, G. Q. Lo, D. L. Kwong, J. Hone, and C. W. Wong, “Regenerative oscillation and four-wave mixing in graphene optoelectronics,” Nat. Photonics 6(8), 554–559 (2012).
[Crossref]

Van Thourhout, D.

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. K. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photonics Rev. 6(1), 47–73 (2012).
[Crossref]

Van Vaerenbergh, T.

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. K. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photonics Rev. 6(1), 47–73 (2012).
[Crossref]

Vijayaraghaven, A.

Waghmare, U. V.

A. Das, S. Pisana, B. Chakraborty, S. Piscanec, S. K. Saha, U. V. Waghmare, K. S. Novoselov, H. R. Krishnamurthy, A. K. Geim, A. C. Ferrari, and A. K. Sood, “Monitoring dopants by Raman scattering in an electrochemically top-gated graphene transistor,” Nat. Nanotechnol. 3(4), 210–215 (2008).
[Crossref] [PubMed]

Wang, A.

Wang, B.

Q. Bao, H. Zhang, B. Wang, Z. Ni, C. Lim, Y. Wang, D. Tang, and K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics 5(7), 411–415 (2011).
[Crossref]

Wang, F.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[Crossref] [PubMed]

F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, “Gate-variable optical transitions in graphene,” Science 320(5873), 206–209 (2008).
[Crossref] [PubMed]

Wang, J.

Wang, Y.

Warabi, K.

R. Kou, S. Tanabe, T. Tsuchizawa, K. Warabi, S. Suzuki, H. Hibino, H. Nakajima, and K. Yamada, “Characterization of optical absorption and polarization dependence of single-layer graphene integrated on a silicon wire waveguide,” Jpn. J. Appl. Phys. 52(6R), 060203 (2013).
[Crossref]

Whittaker, E.

Wong, C. W.

H. Zhou, T. Gu, J. F. McMillan, M. Yu, G. Lo, D.-L. Kwong, G. Feng, S. Zhou, and C. W. Wong, “Enhanced photoresponsivity in graphene-silicon slow-light photonic crystal waveguides,” Appl. Phys. Lett. 108(11), 111106 (2016).
[Crossref]

T. Gu, H. Zhou, J. F. McMillan, N. Petrone, A. van der Zande, J. C. Hone, M. Yu, G.-Q. Lo, D.-L. Kwong, and C. W. Wong, “Coherent four-wave mixing on hybrid graphene-silicon photonic crystals,” IEEE J. Sel. Top. Quantum Electron. 20(1), 7500106 (2014).
[Crossref]

T. Gu, N. Petrone, J. F. McMillan, A. van der Zande, M. Yu, G. Q. Lo, D. L. Kwong, J. Hone, and C. W. Wong, “Regenerative oscillation and four-wave mixing in graphene optoelectronics,” Nat. Photonics 6(8), 554–559 (2012).
[Crossref]

Xia, J.

Xiao, S.

Y. Ding, X. Zhu, S. Xiao, H. Hu, L. H. Frandsen, N. A. Mortensen, and K. Yvind, “Effective electro-optical modulation with high extinction ratio by a graphene-silicon microring resonator,” Nano Lett. 15(7), 4393–4400 (2015).
[Crossref] [PubMed]

S. Xiao, M. H. Khan, H. Shen, and M. Qi, “Modeling and measurement of losses in silicon-on-insulator resonators and bends,” Opt. Express 15(17), 10553–10561 (2007).
[Crossref] [PubMed]

Xu, Y.

L. Yu, J. Zheng, Y. Xu, D. Dai, and S. He, “Local and nonlocal optically induced transparency effects in graphene-silicon hybrid nanophotonic integrated circuits,” ACS Nano 8(11), 11386–11393 (2014).
[Crossref] [PubMed]

Yamada, K.

R. Kou, S. Tanabe, T. Tsuchizawa, T. Yamamoto, H. Hibino, H. Nakajima, and K. Yamada, “Influence of graphene on quality factor variation in a silicon ring resonator,” Appl. Phys. Lett. 104(9), 091122 (2014).
[Crossref]

R. Kou, S. Tanabe, T. Tsuchizawa, K. Warabi, S. Suzuki, H. Hibino, H. Nakajima, and K. Yamada, “Characterization of optical absorption and polarization dependence of single-layer graphene integrated on a silicon wire waveguide,” Jpn. J. Appl. Phys. 52(6R), 060203 (2013).
[Crossref]

Yamamoto, T.

R. Kou, S. Tanabe, T. Tsuchizawa, T. Yamamoto, H. Hibino, H. Nakajima, and K. Yamada, “Influence of graphene on quality factor variation in a silicon ring resonator,” Appl. Phys. Lett. 104(9), 091122 (2014).
[Crossref]

Yamashita, S.

Yin, X.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[Crossref] [PubMed]

You, Y.

X. Gan, K. F. Mak, Y. Gao, Y. You, F. Hatami, J. Hone, T. F. Heinz, and D. Englund, “Strong enhancement of light-matter interaction in graphene coupled to a photonic crystal nanocavity,” Nano Lett. 12(11), 5626–5631 (2012).
[Crossref] [PubMed]

Yu, J.

Yu, L.

L. Yu, J. Zheng, Y. Xu, D. Dai, and S. He, “Local and nonlocal optically induced transparency effects in graphene-silicon hybrid nanophotonic integrated circuits,” ACS Nano 8(11), 11386–11393 (2014).
[Crossref] [PubMed]

Yu, M.

H. Zhou, T. Gu, J. F. McMillan, M. Yu, G. Lo, D.-L. Kwong, G. Feng, S. Zhou, and C. W. Wong, “Enhanced photoresponsivity in graphene-silicon slow-light photonic crystal waveguides,” Appl. Phys. Lett. 108(11), 111106 (2016).
[Crossref]

T. Gu, H. Zhou, J. F. McMillan, N. Petrone, A. van der Zande, J. C. Hone, M. Yu, G.-Q. Lo, D.-L. Kwong, and C. W. Wong, “Coherent four-wave mixing on hybrid graphene-silicon photonic crystals,” IEEE J. Sel. Top. Quantum Electron. 20(1), 7500106 (2014).
[Crossref]

T. Gu, N. Petrone, J. F. McMillan, A. van der Zande, M. Yu, G. Q. Lo, D. L. Kwong, J. Hone, and C. W. Wong, “Regenerative oscillation and four-wave mixing in graphene optoelectronics,” Nat. Photonics 6(8), 554–559 (2012).
[Crossref]

Yvind, K.

Y. Ding, X. Zhu, S. Xiao, H. Hu, L. H. Frandsen, N. A. Mortensen, and K. Yvind, “Effective electro-optical modulation with high extinction ratio by a graphene-silicon microring resonator,” Nano Lett. 15(7), 4393–4400 (2015).
[Crossref] [PubMed]

Zentgraf, T.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[Crossref] [PubMed]

Zettl, A.

F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, “Gate-variable optical transitions in graphene,” Science 320(5873), 206–209 (2008).
[Crossref] [PubMed]

Zhang, H.

Q. Bao, H. Zhang, B. Wang, Z. Ni, C. Lim, Y. Wang, D. Tang, and K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics 5(7), 411–415 (2011).
[Crossref]

Zhang, X.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[Crossref] [PubMed]

Zhang, Y.

F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, “Gate-variable optical transitions in graphene,” Science 320(5873), 206–209 (2008).
[Crossref] [PubMed]

Zheng, J.

L. Yu, J. Zheng, Y. Xu, D. Dai, and S. He, “Local and nonlocal optically induced transparency effects in graphene-silicon hybrid nanophotonic integrated circuits,” ACS Nano 8(11), 11386–11393 (2014).
[Crossref] [PubMed]

Zhou, H.

H. Zhou, T. Gu, J. F. McMillan, M. Yu, G. Lo, D.-L. Kwong, G. Feng, S. Zhou, and C. W. Wong, “Enhanced photoresponsivity in graphene-silicon slow-light photonic crystal waveguides,” Appl. Phys. Lett. 108(11), 111106 (2016).
[Crossref]

T. Gu, H. Zhou, J. F. McMillan, N. Petrone, A. van der Zande, J. C. Hone, M. Yu, G.-Q. Lo, D.-L. Kwong, and C. W. Wong, “Coherent four-wave mixing on hybrid graphene-silicon photonic crystals,” IEEE J. Sel. Top. Quantum Electron. 20(1), 7500106 (2014).
[Crossref]

Zhou, S.

H. Zhou, T. Gu, J. F. McMillan, M. Yu, G. Lo, D.-L. Kwong, G. Feng, S. Zhou, and C. W. Wong, “Enhanced photoresponsivity in graphene-silicon slow-light photonic crystal waveguides,” Appl. Phys. Lett. 108(11), 111106 (2016).
[Crossref]

Zhu, L.

Zhu, X.

Y. Ding, X. Zhu, S. Xiao, H. Hu, L. H. Frandsen, N. A. Mortensen, and K. Yvind, “Effective electro-optical modulation with high extinction ratio by a graphene-silicon microring resonator,” Nano Lett. 15(7), 4393–4400 (2015).
[Crossref] [PubMed]

ACS Nano (2)

L. Yu, J. Zheng, Y. Xu, D. Dai, and S. He, “Local and nonlocal optically induced transparency effects in graphene-silicon hybrid nanophotonic integrated circuits,” ACS Nano 8(11), 11386–11393 (2014).
[Crossref] [PubMed]

P.-Y. Chen and A. Alù, “Atomically thin surface cloak using graphene monolayers,” ACS Nano 5(7), 5855–5863 (2011).
[Crossref] [PubMed]

Appl. Phys. Lett. (3)

H. Li, Y. Anugrah, S. J. Koester, and M. Li, “Optical absorption in graphene integrated on silicon waveguides,” Appl. Phys. Lett. 101(11), 111110 (2012).
[Crossref] [PubMed]

R. Kou, S. Tanabe, T. Tsuchizawa, T. Yamamoto, H. Hibino, H. Nakajima, and K. Yamada, “Influence of graphene on quality factor variation in a silicon ring resonator,” Appl. Phys. Lett. 104(9), 091122 (2014).
[Crossref]

H. Zhou, T. Gu, J. F. McMillan, M. Yu, G. Lo, D.-L. Kwong, G. Feng, S. Zhou, and C. W. Wong, “Enhanced photoresponsivity in graphene-silicon slow-light photonic crystal waveguides,” Appl. Phys. Lett. 108(11), 111106 (2016).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (2)

T. Gu, H. Zhou, J. F. McMillan, N. Petrone, A. van der Zande, J. C. Hone, M. Yu, G.-Q. Lo, D.-L. Kwong, and C. W. Wong, “Coherent four-wave mixing on hybrid graphene-silicon photonic crystals,” IEEE J. Sel. Top. Quantum Electron. 20(1), 7500106 (2014).
[Crossref]

V. Van, T. Ibrahim, P. Absil, F. Johnson, R. Grover, and P.-T. Ho, “Optical signal processing using nonlinear semiconductor microring resonators,” IEEE J. Sel. Top. Quantum Electron. 8(3), 705–713 (2002).
[Crossref]

IEEE Photonics Technol. Lett. (1)

C. Horvath, D. Bachman, G. Mi, and V. Van, “Fabrication and characterization of edge-conformed graphene-silicon waveguides,” IEEE Photonics Technol. Lett. 27(6), 585–587 (2015).
[Crossref]

J. Appl. Phys. (2)

M. S. Ünlü and S. Strite, “Resonant cavity enhanced photonic devices,” J. Appl. Phys. 78(2), 607–639 (1995).
[Crossref]

D. Chatzidimitriou, A. Pitilakis, and E. E. Kriezis, “Rigorous calculation of nonlinear parameters in graphene-comprising waveguides,” J. Appl. Phys. 118(2), 023105 (2015).
[Crossref]

Jpn. J. Appl. Phys. (1)

R. Kou, S. Tanabe, T. Tsuchizawa, K. Warabi, S. Suzuki, H. Hibino, H. Nakajima, and K. Yamada, “Characterization of optical absorption and polarization dependence of single-layer graphene integrated on a silicon wire waveguide,” Jpn. J. Appl. Phys. 52(6R), 060203 (2013).
[Crossref]

Laser Photonics Rev. (1)

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. K. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photonics Rev. 6(1), 47–73 (2012).
[Crossref]

Nano Lett. (3)

Y. Ding, X. Zhu, S. Xiao, H. Hu, L. H. Frandsen, N. A. Mortensen, and K. Yvind, “Effective electro-optical modulation with high extinction ratio by a graphene-silicon microring resonator,” Nano Lett. 15(7), 4393–4400 (2015).
[Crossref] [PubMed]

Y. M. Lin, K. A. Jenkins, A. Valdes-Garcia, J. P. Small, D. B. Farmer, and P. Avouris, “Operation of graphene transistors at gigahertz frequencies,” Nano Lett. 9(1), 422–426 (2009).
[Crossref] [PubMed]

X. Gan, K. F. Mak, Y. Gao, Y. You, F. Hatami, J. Hone, T. F. Heinz, and D. Englund, “Strong enhancement of light-matter interaction in graphene coupled to a photonic crystal nanocavity,” Nano Lett. 12(11), 5626–5631 (2012).
[Crossref] [PubMed]

Nat. Mater. (1)

A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6(3), 183–191 (2007).
[Crossref] [PubMed]

Nat. Nanotechnol. (1)

A. Das, S. Pisana, B. Chakraborty, S. Piscanec, S. K. Saha, U. V. Waghmare, K. S. Novoselov, H. R. Krishnamurthy, A. K. Geim, A. C. Ferrari, and A. K. Sood, “Monitoring dopants by Raman scattering in an electrochemically top-gated graphene transistor,” Nat. Nanotechnol. 3(4), 210–215 (2008).
[Crossref] [PubMed]

Nat. Photonics (4)

Q. Bao, H. Zhang, B. Wang, Z. Ni, C. Lim, Y. Wang, D. Tang, and K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics 5(7), 411–415 (2011).
[Crossref]

T. Gu, N. Petrone, J. F. McMillan, A. van der Zande, M. Yu, G. Q. Lo, D. L. Kwong, J. Hone, and C. W. Wong, “Regenerative oscillation and four-wave mixing in graphene optoelectronics,” Nat. Photonics 6(8), 554–559 (2012).
[Crossref]

A. Pospischil, M. Humer, M. M. Furchi, D. Bachmann, R. Guider, T. Fromherz, and T. Mueller, “CMOS-compatible graphene photodetector covering all optical communication bands,” Nat. Photonics 7(11), 892–896 (2013).
[Crossref]

X. Gan, R.-J. Shiue, Y. Gao, I. Meric, T. F. Heinz, K. Shepard, J. Hone, S. Assefa, and D. Englund, “Chip-integrated ultrafast graphene photodetector with high responsivity,” Nat. Photonics 7(11), 883–887 (2013).
[Crossref]

Nature (1)

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[Crossref] [PubMed]

Opt. Express (8)

M. Ji, H. Cai, L. Deng, Y. Huang, Q. Huang, J. Xia, Z. Li, J. Yu, and Y. Wang, “Enhanced parametric frequency conversion in a compact silicon-graphene microring resonator,” Opt. Express 23(14), 18679–18685 (2015).
[Crossref] [PubMed]

X. Hu, Y. Long, M. Ji, A. Wang, L. Zhu, Z. Ruan, Y. Wang, and J. Wang, “Graphene-silicon microring resonator enhanced all-optical up and down wavelength conversion of QPSK signal,” Opt. Express 24(7), 7168–7177 (2016).
[Crossref] [PubMed]

M. Mohsin, D. Schall, M. Otto, A. Noculak, D. Neumaier, and H. Kurz, “Graphene based low insertion loss electro-absorption modulator on SOI waveguide,” Opt. Express 22(12), 15292–15297 (2014).
[Crossref] [PubMed]

I. F. Crowe, N. Clark, S. Hussein, B. Towlson, E. Whittaker, M. M. Milosevic, F. Y. Gardes, G. Z. Mashanovich, M. P. Halsall, and A. Vijayaraghaven, “Determination of the quasi-TE mode (in-plane) graphene linear absorption coefficient via integration with silicon-on-insulator racetrack cavity resonators,” Opt. Express 22(15), 18625–18632 (2014).
[Crossref] [PubMed]

G. Kovacevic and S. Yamashita, “Waveguide design parameters impact on absorption in graphene coated silicon photonic integrated circuits,” Opt. Express 24(4), 3584–3591 (2016).
[Crossref] [PubMed]

S. Xiao, M. H. Khan, H. Shen, and M. Qi, “Modeling and measurement of losses in silicon-on-insulator resonators and bends,” Opt. Express 15(17), 10553–10561 (2007).
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C. C. Evans, C. Liu, and J. Suntivich, “Low-loss titanium dioxide waveguides and resonators using a dielectric lift-off fabrication process,” Opt. Express 23(9), 11160–11169 (2015).
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V. Sorianello, M. Midrio, and M. Romagnoli, “Design optimization of single and double layer Graphene phase modulators in SOI,” Opt. Express 23(5), 6478–6490 (2015).
[Crossref] [PubMed]

Science (2)

F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, “Gate-variable optical transitions in graphene,” Science 320(5873), 206–209 (2008).
[Crossref] [PubMed]

A. K. Geim, “Graphene: status and prospects,” Science 324(5934), 1530–1534 (2009).
[Crossref] [PubMed]

Other (2)

C. Y. Wong, Z. Cheng, Z. Shi, Y. M. Chen, K. Xu, and H. K. Tsang, “Mode-locked fiber laser using graphene on silicon waveguide,” in Proceedings of 10th International Conference on Group IV Photonics (GFP) (IEEE 2013), pp. 35–36.
[Crossref]

L. Yu, Y. Xu, Y. Shi, and D. Dai, “Linear and nonlinear optical absorption of on-chip silicon-on-insulator nanowires with graphene,” in Proceedings of Asia Communications and Photonics Conference (Optical Society of America, 2012), pp. AS1B–3.
[Crossref]

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Figures (8)

Fig. 1
Fig. 1 The processes of monolayer graphene preparation and SC-ADSMR device fabrication.
Fig. 2
Fig. 2 (a) SEM image of the SC-ADSMR covered with patterned monolayer graphene (top view). Close-up view of the two coupling regions are also shown. (b) Zoom-in SEM images of the local monolayer graphene covered area in (a), showing that monolayer graphene uniformly clings to the silicon waveguide. Here X is the radial length of side-monolayer-graphene and W is the width of waveguide. (c) Photonic crystal grating coupler used for coupling light into and out of the SC-ADSMR device.
Fig. 3
Fig. 3 (a) Experimental setup for characterizing the LAC of in-plane graphene. (b) Optical transmission spectra of the SC-ADSMR device before and after monolayer graphene transfer (noted as woGr and wGr respectively). (c) Raman spectra measured in the graphene-covered region (red) and in the area where graphene is lifted off (blue).
Fig. 4
Fig. 4 Scheme of the SC-ADSMR with patterned monolayer graphene
Fig. 5
Fig. 5 Surface dynamic conductivity of monolayer graphene as a function of its chemical potential
Fig. 6
Fig. 6 (a) Cross section of the simulated GSHW. (b) Experimental and simulated LAC of in-plane monolayer graphene as a function of the five resonant wavelengths of our SC-ADSMR device. In this simulation, the FEs of the SC-ADSMR and side-monolayer-graphene which is clung to the waveguide have both been taken into consideration. Here, λ1 = 1537.94 nm, λ2 = 1543.62 nm, λ3 = 1549.34 nm, λ4 = 1555.10 nm and λ5 = 1560.90 nm represent the five resonant wavelengths of our SC-ADSMR device after graphene transfer process.
Fig. 7
Fig. 7 (a) The x, y and z components of electrical field in the GSHW. Here the mesh grids are also shown. (b) The LAC of GSHW in Fig. 6(a) with a varying parameter of X. The inset shows typical fundamental quasi TE mode profile of simulated GSHW at 1550 nm. Other parameters for this simulation are also shown in the box above.
Fig. 8
Fig. 8 Simulated waveguide loss for TM mode as a function of parameter X.

Tables (1)

Tables Icon

Table 1 Parameters for LAC deduction before and after graphene transfer.

Equations (17)

Equations on this page are rendered with MathJax. Learn more.

T t h r o u g h ( λ ) = ( λ λ 0 ) 2 + ( F S R 4 π ) 2 ( κ p 2 ) 2 ( λ λ 0 ) 2 + ( F W H M t 2 ) 2 .
E R t ( d B ) = 10 log 10 ( γ t ) .
κ p 2 = 2 π F W H M t γ t F S R ,
κ t 2 = κ d 2 = π F W H M t ( 1 γ t ) F S R ,
α ( d B / r o u n d ) = 10 log 10 ( 1 κ p 2 ) .
Q = λ 0 F W H M t ,
F i n e s s e = F S R F W H M t = 2 π κ t 2 + κ d 2 + κ p 2 ,
F E = F i n e s s e π .
L A C s i l i c o n = α w o G r 2 π R ,
L A C G S H W = ( α w G r α w o G r ( 1 n ) ) 2 π n R .
L A C G r _ r e s o n a t o r = L A C G S H W L A C s i l i c o n .
σ ( ω , μ c , τ , T ) = σ int r a ( ω , μ c , τ , T ) + σ int e r ( ω , μ c , τ , T ) .
σ int r a ( ω , μ c , τ , T ) = i e 2 k B T π 2 ( ω + i τ 1 ) [ | μ c | k B T + 2 I n ( exp ( | μ c | k B T ) + 1 ) ] .
σ int e r ( ω , μ c , τ , T ) = i e 2 4 π I n [ 2 | μ c | ( ω + i τ 1 ) 2 | μ c | + ( ω + i τ 1 ) ] .
J // = σ ( ω , μ c , τ , T ) ( F E E // ) ,
J = 0.
α ( d B / μ m ) = 2 k 0 n e f f , i m a g × 4.343 × 10 6 .

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