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Dynamically Tunable ElectromagneticallyInduced Transparency in Graphene-BasedCoupled Micro-ring ResonatorsVolume 9, Number 2, April 2017

Xuetong ZhouTian ZhangXiang YinLin Chen, Member, IEEEXun Li, Senior Member, IEEE

DOI: 10.1109/JPHOT.2017.26906841943-0655 © 2017 IEEE

IEEE Photonics Journal Dynamically Tunable Electromagnetically Induced

Dynamically Tunable ElectromagneticallyInduced Transparency in Graphene-Based

Coupled Micro-ring ResonatorsXuetong Zhou,1 Tian Zhang,1 Xiang Yin,1 Lin Chen,1 Member, IEEE,

and Xun Li,2 Senior Member, IEEE

1Wuhan National Laboratory for Optoelectronics, Huazhong University of Science andTechnology, Wuhan 430074, China

2Department of Electrical and Computer Engineering, McMaster University, Hamilton, ONL8S 4K1, Canada

DOI:10.1109/JPHOT.2017.26906841943-0655 C© 2017 IEEE. Translations and content mining are permitted for academic research only.

Personal use is also permitted, but republication/redistribution requires IEEE permission.See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

Manuscript received February 4, 2017; revised March 29, 2017; accepted March 31, 2017. Date ofpublication April 4, 2017; date of current version April 18, 2017. This work was supported in part bythe National Natural Science Foundation of China (501100001809) (11104093, 11474116, 11674118,and 61675074) and in part by the State Key Laboratory of Advanced Technology for Materials Syn-thesis and Processing (Wuhan University of Technology). Corresponding author: Lee Chen (e-mail:[email protected]).

Abstract: A dynamically tunable electromagnetically induced transparency (EIT) systemconsisting of two coupled micro-ring resonators, one of which is embedded with a graphenelayer, is proposed and numerically demonstrated. The effective refractive index of thegraphene-based micro-ring resonator can be significantly tuned by varying the gate volt-age applied on graphene, inducing significant modulation of the resonant wavelength of EITtransparency window over a wide spectral bandwidth. Typical tunability of the EIT resonanceis approximately 1.62 nm/V around 1550 nm, which is much better than that based on a na-noelectromechanical EIT system. Such a configuration implies the possibility of constructingvarious optical devices toward realization of photon pulse trapping, optical modulation, andfiltering on a chip.

Index Terms: Coupled resonators, electromagnetically induced transparency (EIT), inte-grated optics, resonance.

1. IntroductionThe electromagnetically induced transparency (EIT) effect, which is a spectrally narrow opticaltransmission window within a broad absorption spectrum, originates from the quantum interferenceof multiple excitation pathways through short and long-lived resonances [1]. The EIT effect in theatomic medium is formed by the coupling between different Zeeman levels [2]–[6]. Within thisspectral window, it is accompanied by dramatically slowed photons and enhanced nonlinearities,which offers the capability to manipulate light at a few-photon power level [7]. However, a significantlimitation to the use of the EIT effect is the limited material choices and stringent requirements forthe coherence of excitation pathways in atomic systems. In recent years, various optical structureshave been proposed to realize EIT-like phenomena in optical systems, promising great potentialapplications in optical routers, buffer memories, and optical signal processing. Typical examplesinclude coupled resonators [8], [9], metamaterials [10]–[13], photonic crystals [14], a hybrid system

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with dielectric waveguides and subwavelength gratings [15], [16], plasmonic resonator antennascoupled with a dielectric waveguide [17], and plasmonic resonator systems [18]. Generally, mostof these configurations can only enable light transparency at a fixed operating wavelength oncethe systems are fabricated, which will significantly limit practical applications. To implement activelycontrollable EIT-like resonance, several schemes have been proposed by using nonlinear materials[19], thermal tuning materials [20], [21], and nanoelectromechanical systems [22].

As one of the key components on silicon-on-insulator (SOI) platform, micro-ring resonators havebeen intensively investigated and demonstrated to enable construction of various optical devices,such as filters [23], polarization rotators [24], photonic logic gates [25], modulators [26], and sensors[27]. By utilization of two coupled micro-ring resonators, an EIT-like effect has been demonstratedand widely investigated due to their easy operation, engineering transparency window, and easyintegration on a chip [8], [28], [29]. Recent research on the EIT effect has moved towards construct-ing various coupled micro-ring resonators that have the capability of operating with a dynamicallytunable EIT transparency window via thermal, nonlinear, and carrier tuning [29]–[31].

Graphene, a single sheet of carbon atoms arranged in a two-dimensional honeycomb lattice,shows great promise for developing highly efficient optoelectronics devices due to its outstandingelectrical and optical properties [32], [33]. Graphene is unique because its conductivity can be dy-namically tuned by modulating the chemical potential via varying gate voltage or chemical doping[33]. Graphene is emerging as an attractive material for the development of high-performance opticaldevices, such as modulators, photodetectors, and polarizers [34]–[37]. Meanwhile, the unique char-acteristics of graphene have been intensively introduced to develop tunable micro-ring resonators[38], [39] and demonstrate actively controllable EIT-like effects [40]–[42]. By taking advantage ofdifferences in attenuation for the TM and TE modes when graphene is involved in a dielectricwaveguide, we have previously proposed and demonstrated a silicon waveguide polarizer as wellas a polarization beam splitter on SOI platform [37], [43]. However, to the best of our knowledge,little work has been devoted to exploring the utilization of graphene to construct coupled micro-ringresonators for controllable EIT transparency window on SOI platform. In this article, we propose anEIT-like system comprised of two coupled ring resonators, one of which is embedded with a sheetof graphene. Similar to the tunable EIT system in atomic-like medium where the EIT window canbe opened or closed by controlling the coupling field [2], here the present results show that EIT-liketransparency window is flexibly tuned by slightly adjusting the gate voltage applied on graphene.The designed EIT micro-ring resonator presents much larger tunability, even in comparison withthat based on a nanoelectromechanical system [22].

2. Tunable Micro-ring Resonator With Monolayer Graphene EmbeddedConsider a graphene-based tunable micro-ring resonator, shown in Fig. 1, which consists of agraphene-based micro-ring resonator and a bus waveguide, spaced with a gap d between them.The bus waveguide [see Fig. 1(c)] is a conventional silicon rib waveguide with a thin, centrallylocated hexagonal boron nitride (hBN) layer (t2 = 7 nm) sandwiched between an upper and lowersilicon layer. The micro-ring resonator [see Fig. 1(b)] has the same cross-section as the buswaveguide except that a monolayer graphene is embedded in the central region of the hBN layer.For the micro-ring resonator, a capacitor is formed as graphene/hBN/doped silicon configuration.Here the hBN layer is introduced to act as an insulator that allows graphene to maintain its highmobility because it is atomically flat and free of dangling bonds and charge traps [44]. The dopedsilicon layer is connected with one metallic electrode, and the graphene layer is extended toconnected the other metallic electrode. In this case, an applied voltage, as shown in Fig. 1 maytune the carrier density of graphene in real-time, and hence the chemical potential of graphene canbe flexibly changed [32], [35], [45]. The relationship between the chemical potential and gate voltagewill be discussed later in this section. It should be noted here, the influence of a metal electrodeon the modal field distributions of the dielectric waveguide can be effectively avoided by keepinga large distance between the metal electrode and micro-ring resonator in a practical situation.However, to prevent the graphene layer from dropping down and touching the doped silicon, the

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Fig. 1. (a) Schematic of a tunable micro-ring resonator with a sheet of graphene embedded. (b) Cross-sections for the micro-ring resonator with a sheet of graphene embedded (left panel) and the buswaveguide (right panel) in the regions bounded by the dashed lines in (a). The relative permittivity ofhBN layer is 3.92.

distance between them should be properly selected. For future experimental implementation of themicro-ring resonator, first, we can prepare six shadow masks for the doped silicon substrate, twohalf micro-ring resonators, bus waveguide, and two metal electrodes. By properly arranging theorder of the six masks, choosing the deposition methods, and transferring the graphene layersfrom the copper foil, the presented micro-ring resonator might be fabricated. It’s well-known thatthe resonant wavelength of a micro-ring resonator is determined by the effective mode index of theresonator once its structural parameters are fixed. In the present scheme, it is highly anticipatedthat the resonant wavelength of the graphene-based micro-ring resonator can be modulated byvarying the effective mode index via tuning the gate voltage.

The optical response of graphene is characterized by its surface conductivity, σg , which can beretrieved by the Kubo formula [32]

σg = ie2kB T

π�2(ω + iτ−1

)[

μc

kB T+ 2 ln

(exp

(− μc

kB T

)+ 1

)]

+ ie2

4π�ln

[2 |μc| − �

(ω + iτ−1

)

2 |μc| + �(ω + iτ−1

)

]

(1)

where kB is the Boltzmann constant, � is the reduced Planck constant, λ is the wavelength (angularfrequency ω), T is temperature, μc is the chemical potential, and τ is the momentum relaxation,respectively. In this work, we have chosen T = 300 K, and τ = 0.5 ps for the calculation. It isapparent that graphene’s surface conductivity is closely related to the chemical potential. Originatingfrom the fact that carbon atoms of graphene merely distribute periodically in the horizontal plane, asheet of graphene is commonly regarded as highly anisotropic material, i.e., the in-plane permittivity(ε||) can be tuned by the chemical potential, whereas the out-of-plane permittivity (ε⊥) is keptconstant at 2.5 [46]. By treating the graphene monolayer as an ultra-thin film, ε‖ can be written as[33]

ε|| = 1 + iσgη0

k0(2)

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Fig. 2. (a) Surface conductivity σg and (b) in-plane equivalent permittivity ε|| of graphene as a functionof chemical potential μc at 1550 nm.

where is the physical thickness of graphene ( =0.34 nm), η0 is the impedance of air (≈ 377 ),and k0 is the wavenumber (= 2π/λ) in vacuum. The surface conductivity σg and in-planepermittivity of graphene ε‖ as a function of μc at 1550 nm are shown in Fig. 2. It can be seenthat σg varies sharply around μc = 0.4 eV, leading to a significant change for ε|| accordingly. For ascheme shown in Fig. 1, the chemical potential of graphene can be determined by the gate voltageapplied on the graphene layer [35]

μc = �VF

√π

ε0εh

dh e

∣∣Vg − VD i r ac∣∣ (3)

where VF = 106 m/s is the Fermi velocity, ε0 is the permittivity of the vacuum, εh is the relativepermittivity of hBN, and dh ( = t2/2) is the thickness of the insulator (hBN) between the graphenemonolayer and doped silicon layer. |Vg − VD i r ac| can also be seen as the applied gate voltage Vg

since VD i r ac is closed to zero [see Fig. 1].Considering that a sheet of graphene is inserted into a dielectric waveguide, the dominant electric

field, Ey, of the TM mode is much unaffected since a sheet of graphene is ultra-thin and its out-of-plane permittivity (ε⊥) is kept constant at 2.5. Meanwhile, the field intensity, Ez, of TM mode isextremely weak since graphene is located in the center of the dielectric waveguide in our case [47],[48], hence the influence of embedded graphene on the modal field distribution of the TM mode couldbe negligible. As for the TE mode, both the field intensity of Ex, and Ez are significant and parallelto the graphene sheet. Consequently, the TE mode will feel the variation of ε‖ significantly. Then,with a monolayer graphene involved in the micro-ring resonator [shown in Fig. 1], it is supposed tohave a much larger influence on the modal characteristics of the TE mode than on those of the TMmode. In other words, for the purpose of achieving the largest tunability of the resonant wavelength,the TE mode should be selected for the design of the micro-ring resonator. Fig. 3 clearly indicatesthat the effective refractive index of the TE mode [Real(neff)] undergoes very significant changesaround μc = 0.4 eV. It is monotonically reduced from 2.119 to 2.102 when μc undergoes a changefrom 0.4 to 0.8 eV. In addition to having a large effective mode-index tunability, the loss coefficient,represented by the imaginary part of the effective mode index [Imag(neff)], is kept at very low levelsif μc> 0.4 eV. To summarize, a sheet of graphene is highly expected to enable large resonantwavelength tunability as well as high transmission for the micro-ring resonator.

The transmission spectrum of the graphene-based micro-ring resonator as a function of lightwavelength for different μc is shown in Fig. 4(a). It is clearly seen that the resonant wavelengthis strongly dependent on μc. The resonant wavelength shifts from 1550.45 to 1549.6 nm with μc

varying from 0.42 to 0.45 eV, corresponding to a gate voltage change from 2.085 to 2.394 V. Wehave noted in a recent study on an optical modulator consisting of a graphene/graphene capacitorintegrated along a ring resonator that the resonant wavelength can be significantly tuned over a widerange of gate voltage applied on graphene [49]. The numerical result agrees with the experimentalresult very well. It should be noted that, in our case the resonant wavelength can be varied within amuch larger range if a wider range of μc is used. In addition, it can be highly anticipated to effectivelyenlarge the adjusting range of the effective mode index by embedding more graphene layers into

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Fig. 3. Calculated effective refractive indices of the graphene-based micro-ring resonator as a functionof chemical potential μc and the applied voltage Vg . (Inset) Electric filed intensity distribution |E|2 for theTE mode at 1550 nm with μc = 0.42 eV. The simulation work is conducted by an eigenmode solverwith a commercial software Lumerical MODE Solutions. In the simulation, the thickness of the dopedsilicon layer [denoted in Fig. 1(c)] is t1 = 20 nm, and the width and height of the graphene-basedmicro-ring resonator is W = 400 nm and H = 200 nm, respectively.

Fig. 4. (a) Transmission spectrum of the graphene-based micro-ring resonator as a function of light wave-length for different μc . (Inset) Electric field distribution |E| at the resonant wavelength of 1550.45 nm withμc = 0.42 eV. (b) Resonant wavelength versus μc and Vg . Finite difference time domain method is usedto accurately retrieve the transmission spectrum. Perfect matched layers are used in the boundaries toabsorb light that reaches the boundaries, and the maximum mesh size in the x-, y- and z-direction is 5,10, and 25 nm, respectively. Two mesh grids are used to denote the thickness of the graphene sheet(0.34 nm). In the simulation, the radius of the graphene-based micro-ring resonator is R2 = 15 μm.The gap between the bus waveguide and the micro-ring resonator is d = 150 nm.

the dielectric waveguide [46]. Defining the tunability as the shift of the resonant peak wavelengthper applied voltage, the estimated tunability can be up to 2.75 nm/V. This value is much largerthan that for tunable silicon micro-ring resonators based on the electro-optic effect, for which themaximum tunability is 0.02 nm/V [50]–[52].

3. Tunable Electromagnetically Induced Transparency in Graphene-BasedCoupled Micro-ring ResonatorsThe EIT-like effect in coupled micro-ring resonators is resulting from the destructive interferencebetween the bright and dark resonators [9], [28], [29]. Generally, the bright and dark resonators

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Fig. 5. Schematic of the proposed graphene-based coupled micro-ring resonators. The gap betweenthe small micro-ring resonator and the bus waveguide is d1, and the gap between the two micro-ringresonators is d2.

Fig. 6. (a) Transmission spectrum of the tunable graphene-based micro-ring resonators. (b) Peakwavelength of EIT transparency window versus μc and Vg . (c)–(e) Distributions of the electric field |E|corresponding to (c), (d) the two transmission dips, and (e) the transmission peak with μc = 0.42 eV.In the simulation, the geometrical parameters are chosen as d1 = 150 nm, d2 = 150 nm, and R1 =5 μm, while the other parameters are the same as those in Fig. 4.

have the same resonant wavelength, around which the bright mode can be excited by couplingwith the bus waveguide directly, while the dark resonator is not allowed to directly interact with thebus waveguide but can be excited through the near-field coupling with the bright resonator. Withproper design of the structural parameters, the bright resonator usually possesses a low qualityfactor (Q), whereas the dark resonator has a high Q. The schematic illustration of the tunablegraphene-based coupled micro-ring resonator is shown in Fig. 5. The small micro-ring resonator isdirectly coupled with the bus waveguide, acting as the bright resonator, while the large one with asheet of graphene involved does not interact with the bus waveguide directly, serving as the darkresonator. Consequently, the destructive interference between the two micro-ring resonators leads

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to the EIT effect. Choosing a bending radius 5 μm for the small micro-ring resonator, the resonantwavelength (1549.6 nm) almost coincides with that of the graphene-based one, and the Q value iskept at a relatively low level (smaller than that associated with graphene).

The peak wavelength of the transparency window is primarily determined by the resonant wave-length of the dark resonator [53], [54]. By varying μc to tune the resonant wavelength of the darkresonator, we are able to dynamically tune the EIT transparency window. Fig. 6(a) shows the sim-ulated transmission spectrum with μc changing from 0.42 to 0.45 eV with a step of 0.01 eV. Apronounced EIT-like transmission is clearly observed for each chemical potential. Here, it is worthnoting that the EIT peak has a very high transmission (>90%) due to the low absorption loss fromgraphene when μc > 0.4 eV. More interestingly, the peak wavelength of EIT-like transmission can bedynamically tuned by altering μc to shift to a shorter wavelength while increasing μc [see Fig. 6(b)].As the wavelength is tuned to the dips in transmission [see Fig. 6(c) and (d)], very weak lightintensity is observed in the output port. However, by tuning the wavelength to make the micro-ringresonator work at the transparency window, light can be transmitted through the output port almostentirely [see Fig. 6(e)]. With μc tuned from 0.42 to 0.45 eV, (associated with the gate voltage from2.085 to 2.394 V) the peak wavelength of the EIT resonance shifts from 1550.25 to 1549.75 nm[see Fig. 6(b)]. The tunability of the EIT resonance is approximately 1.62 nm/V, which is significantlylarger than that based on a nanoelectromechanical system with a tunability of 0.06 nm/V [22].

4. ConclusionIn summary, we have proposed a tunable EIT-like system consisting of two coupled micro-ringresonators, one of which is embedded with a monolayer graphene sheet. The simulation resultsshow that the resonant wavelength of the EIT transparency window can be flexibly tuned by varyingthe gate voltage applied on graphene. The estimated tunability of the EIT resonance is approximately1.62 nm/V, which is significantly larger than that based on a nanoelectromechanical system with atunability of 0.06 nm/V [22]. Additionally, the EIT peak can be kept with a very high transmissiondue to the low absorption loss from graphene. It should be noted that such a configuration offersthe extra dimension of the effective refractive index tunability of the micro-ring resonator by tuningthe chemical potential via varying the gate voltage, which enables the designed EIT system tooperate with variable output power. Finally, under the tunability of graphene’s chemical potential, itcan be highly expected that the coupled micro-ring resonators have less wavelength dependenceand larger fabrication tolerance as opposed to those associated with previous EIT systems [8],[28]–[31].

AcknowledgmentThe authors wish to thank the anonymous reviewers for their valuable suggestions.

References[1] K.-J. Boller, A. Imamoglu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev.

Lett., vol. 66, pp. 2593–2596, 1991.[2] Y. Du et al., “Controlling four-wave mixing and six-wave mixing in a multi-zeeman-sublevel atomic system with electro-

magnetically induced transparency,” Phys. Rev. A, vol. 79, Jun. 25, 2009, Art. no. 063839.[3] Y. Zhang, U. Khadka, B. Anderson, and M. Xiao, “Temporal and spatial interference between four-wave mixing and

six-wave mixing channels,” Phys. Rev. Lett., vol. 102, Jan. 7, 2009, Art. no. 013601.[4] Y. Zhang et al., “Four-wave mixing dipole soliton in laser-induced atomic gratings,” Phys. Rev. Lett., vol. 106, Mar.

4, 2011, Art. no. 093904.[5] Y. Zhang et al., “Photonic floquet topological insulators in atomic ensembles,” Laser Photon. Rev., vol. 9, pp. 331–338,

May 2015.[6] C. Li et al., “Controlled correlation and squeezing in Pr3+:Y2SiO5 to yield correlated light beams,” Phys. Rev. Appl.,

vol. 7, Jan. 30, 2017, Art. no. 014023.[7] S. E. Harris, J. Field, and A. Imamoglu, “Nonlinear optical processes using electromagnetically induced transparency,”

Phys. Rev. Lett., vol. 64, pp. 1107–1110, 1990.

Vol. 9, No. 2, April 2017 6600609


[8] Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. Fan, and M. Lipson, “Experimental realization of an on-chip all-opticalanalogue to electromagnetically induced transparency,” Phys. Rev. Lett., vol. 96, Mar. 31, 2006, Art. no. 123901.

[9] D. D. Smith, H. Chang, K. A. Fuller, A. Rosenberger, and R. W. Boyd, “Coupled-resonator-induced transparency,” Phys.Rev. A, vol. 69, Jun. 2004, Art. no. 063804.

[10] S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev.Lett., vol. 101, Jul. 25, 2008, Art. no. 047401.

[11] N. Liu et al., “Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit,” NatureMater., vol. 8, pp. 758–762, Sep. 2009.

[12] Y. Yang, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “All-dielectric metasurface analogue of electromagneticallyinduced transparency,” Nature Commun., vol. 5, Dec. 2014, Art. no. 5753.

[13] M. Wan, Y. Song, L. Zhang, and F. Zhou, “Broadband plasmon-induced transparency in terahertz metamaterials viaconstructive interference of electric and magnetic couplings,” Opt. Exp., vol. 23, pp. 27361–27368, Oct. 19, 2015.

[14] X. Yang, M. Yu, D.-L. Kwong, and C. W. Wong, “All-optical analog to electromagnetically induced transparency inmultiple coupled photonic crystal cavities,” Phys. Rev. Lett., vol. 102, May 1, 2009, Art. no. 173902.

[15] J. Zhang, W. Bai, L. Cai, Y. Xu, G. Song, and Q. Gan, “Observation of ultra-narrow band plasmon induced transparencybased on large-area hybrid plasmon-waveguide systems,” Appl. Phys. Lett., vol. 99, Oct. 31, 2011, Art. no. 181120.

[16] S.-G. Lee, S.-Y. Jung, H.-S. Kim, S. Lee, and J.-M. Park, “Electromagnetically induced transparency based on guided-mode resonances,” Opt. Lett., vol. 40, pp. 4241–4244, Sep. 15, 2015.

[17] R. D. Kekatpure, E. S. Barnard, W. Cai, and M. L. Brongersma, “Phase-coupled plasmon-induced transparency,” Phys.Rev. Lett., vol. 104, Jun. 17, 2010, Art. no. 243902.

[18] H. Lu, X. Liu, D. Mao, Y. Gong, and G. Wang, “Induced transparency in nanoscale plasmonic resonator systems,” Opt.Lett., vol. 36, pp. 3233–3235, Aug. 15, 2011.

[19] Z. Chai, X. Hu, Y. Zhu, F. Zhang, H. Yang, and Q. Gong, “Low-power and ultrafast all-optical tunable plasmon-inducedtransparency in plasmonic nanostructures,” Appl. Phys. Lett., vol. 102, May 20, 2013, Art. no. 201119.

[20] J. Pan et al., “Tuning the coherent interaction in an on-chip photonic-crystal waveguide-resonator system,” Appl. Phys.Lett., vol. 97, Sep. 6, 2010, Art. no. 101102.

[21] H. Liu, G. Ren, Y. Gao, Y. Lian, Y. Qi, and S. Jian, “Tunable subwavelength terahertz plasmon-induced transparency inthe InSb slot waveguide side-coupled with two stub resonators,” Appl. Opt., vol. 54, pp. 3918–3924, May 1, 2015.

[22] P. Shi and G. Zhou, “Tuning all-optical analog to electromagnetically induced transparency in nanobeam cavities usingnanoelectromechanical system,” Sci. Rep., vol. 5, Sep. 29, 2015, Art. no. 14379.

[23] J. Hryniewicz, P. Absil, B. Little, R. Wilson, and P.-T. Ho, “Higher order filter response in coupled microring resonators,”IEEE Photon. Technol. Lett., vol. 12, no. 3, pp. 320–322, Mar. 2000.

[24] B. E. Little and S. T. Chu, “Theory of polarization rotation and conversion in vertically coupled microresonators,” IEEEPhoton. Technol. Lett., vol. 12, no. 4, pp. 401–403, Apr. 2000.

[25] T. Ibrahim, K. Amarnath, L. Kuo, R. Grover, V. Van, and P.-T. Ho, “Photonic logic NOR gate based on two symmetricmicroring resonators,” Opt. Lett., vol. 29, pp. 2779–2781, Dec. 1, 2004.

[26] Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature, vol. 435,pp. 325–327, May 19, 2005.

[27] K. H. Kim and X. Fan, “Surface sensitive microfluidic optomechanical ring resonator sensors,” Appl. Phys. Lett., vol. 105,Nov. 10, 2014, Art. no. 191101.

[28] K. Totsuka, N. Kobayashi, and M. Tomita, “Slow light in coupled-resonator-induced transparency,” Phys. Rev. Lett.,vol. 98, May 25, 2007, Art. no. 213904.

[29] C. Zheng et al., “Controllable optical analog to electromagnetically induced transparency in coupled high-Q microtoroidcavities,” Opt. Exp., vol. 20, pp. 18319–18325, Jul. 30, 2012.

[30] Q. Xu, P. Dong, and M. Lipson, “Breaking the delay-bandwidth limit in a photonic structure,” Nature Phys., vol. 3,pp. 406–410, Jun. 2007.

[31] J. Scheuer, A. A. Sukhorukov, and Y. S. Kivshar, “All-optical switching of dark states in nonlinear coupled microringresonators,” Opt. Lett., vol. 35, pp. 3712–3714, 2010.

[32] P.-Y. Chen and A. Alu, “Atomically thin surface cloak using graphene monolayers,” ACS Nano, vol. 5, pp. 5855–5863,Jul. 2011.

[33] A. Vakil and N. Engheta, “Transformation optics using graphene,” Science, vol. 332, pp. 1291–1294, Jun. 10, 2011.[34] T. Mueller, F. Xia, and P. Avouris, “Graphene photodetectors for high-speed optical communications,” Nature Photon.,

vol. 4, pp. 297–301, May 2010.[35] M. Liu et al., “A graphene-based broadband optical modulator,” Nature, vol. 474, pp. 64–67, Jun. 2, 2011.[36] Q. Bao et al., “Broadband graphene polarizer,” Nature Photon., vol. 5, pp. 411–415, Jul. 2011.[37] X. Yin, T. Zhang, L. Chen, and X. Li, “Ultra-compact TE-pass polarizer with graphene multilayer embedded in a silicon

slot waveguide,” Opt. Lett., vol. 40, pp. 1733–1736, Apr. 15, 2015.[38] W. Du, E.-P. Li, and R. Hao, “Tunability analysis of a graphene-embedded ring modulator,” IEEE Photon. Technol. Lett.,

vol. 26, no. 20, pp. 2008–2011, Oct. 15, 2014.[39] Y. Ding et al., “Effective electro-optical modulation with high extinction ratio by a graphene-silicon microring resonator,”

Nano Lett., vol. 15, pp. 4393–4400, Jul. 2015.[40] M. Amin, M. Farhat, and H. Bagci, “A dynamically reconfigurable Fano metamaterial through graphene tuning for

switching and sensing applications,” Sci. Rep., vol. 3, Jul. 1, 2013, Art. no. 2105.[41] H. Cheng, S. Chen, P. Yu, X. Duan, B. Xie, and J. Tian, “Dynamically tunable plasmonically induced transparency in

periodically patterned graphene nanostrips,” Appl. Phys. Lett., vol. 103, Nov. 11, 2013, Art. no. 203112.[42] X. Shi et al., “Plasmonic analog of electromagnetically induced transparency in nanostructure graphene,” Opt. Exp.,

vol. 21, pp. 28438–28443, Nov. 18, 2013.[43] T. Zhang, X. Yin, L. Chen, and X. Li, “Ultra-compact polarization beam splitter utilizing a graphene-based asymmetrical

directional coupler,” Opt. Lett., vol. 41, pp. 356–359, Jan. 15, 2016.

Vol. 9, No. 2, April 2017 6600609


[44] C. R. Dean et al., “Boron nitride substrates for high-quality graphene electronics,” Nature Nanotechnol., vol. 5,pp. 722–726, Oct. 2010.

[45] K. Kim, J.-Y. Choi, T. Kim, S.-H. Cho, and H.-J. Chung, “A role for graphene in silicon-based semiconductor devices,”Nature, vol. 479, pp. 338–344, Nov. 17, 2011.

[46] R. Hao, W. Du, H. Chen, X. Jin, L. Yang, and E. Li, “Ultra-compact optical modulator by graphene inducedelectro-refraction effect,” Appl. Phys. Lett., vol. 103, Aug. 5, 2013, Art. no. 061116.

[47] R. E. P. de Oliveira and C. J. S. de Matos, “Graphene based waveguide polarizers: In-depth physical analysis andrelevant parameters,” Sci. Rep., vol. 5, Nov. 19, 2015, Art. no. 16949.

[48] G. Kovacevic and S. Yamashita, “Waveguide design parameters impact on absorption in graphene coated siliconphotonic integrated circuits,” Opt. Exp., vol. 24, pp. 3584–3591, Feb. 22, 2016.

[49] C. T. Phare, Y.-H. D. Lee, J. Cardenas, and M. Lipson, “Graphene electro-optic modulator with 30 GHz bandwidth,”Nature Photon., vol. 9, pp. 511–514, Aug. 2015.

[50] P. Dong et al., “Low Vpp, ultralow-energy, compact, high-speed silicon electro-optic modulator,” Opt. Exp., vol. 17,pp. 22484–22490, Dec. 7, 2009.

[51] P. Dong et al., “Wavelength-tunable silicon microring modulator,” Opt. Exp., vol. 18, pp. 10941–10946, May 24, 2010.[52] M. Gould et al., “Silicon-polymer hybrid slot waveguide ring-resonator modulator,” Opt. Exp., vol. 19, pp. 3952–3961,

Feb. 28, 2011.[53] G. Lai et al., “Double plasmonic nanodisks design for electromagnetically induced transparency and slow light,” Opt.

Exp., vol. 23, pp. 6554–6561, Mar. 9, 2015.[54] L. Wang, W. Li, and X. Jiang, “Tunable control of electromagnetically induced transparency analogue in a compact

graphene-based waveguide,” Opt. Lett., vol. 40, pp. 2325–2328, May 15, 2015.

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