Abstract

Research on graphene has revealed its remarkable electro-optic properties, which promise to satisfy the needs of future electro-optic modulators. However, its ultrasmall thickness, compared with operating light wavelength, downplays its role in an optoelectronic device. The key to achieve efficient electro-optic modulation based on graphene is to enhance its interaction with light. To this end, some novel waveguides and platforms will be employed to enhance the interaction. Herein, we present our recent exploration of graphene electro-optic modulators based on graphene sandwiched in dielectric or plasmonic waveguides. With a suitable gate voltage, the dielectric constant of graphene can be tuned to be very small due to the effect of intraband electronic transition, resulting in “graphene-slot waveguides” and greatly enhanced absorption modes. Up to 3 dB modulation depth can be achieved within 800 nm long silicon waveguides, or 120 nm long plasmonic waveguides based on three-dimensional numerical simulations. They have the advantages of nanoscale footprints, small insertion loss, low power consumption, and potentially ultrahigh speed, as well as being CMOS-compatible.

© 2012 Optical Society of America

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2011

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, 64–67 (2011).
[CrossRef]

A. Vakil and N. Engheta, “Transformation optics using graphene,” Science 332, 1291–1294 (2011).
[CrossRef]

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

L. Alloatti, D. Korn, R. Palmer, D. Hillerkuss, J. Li, A. Barklund, R. Dinu, J. Wieland, M. Fournier, J. Fedeli, H. Yu, W. Bogaerts, P. Dumon, R. Baets, C. Koos, W. Freude, and J. Leuthold, “42.7 Gbit/s electro-optic modulator in silicon technology,” Opt. Express 19, 11841–11851 (2011).
[CrossRef]

2010

H.-W. Chen, Y. H. Kuo, and J. E. Bowers, “25  Gb/s hybrid silicon switch using a capacitively loaded traveling wave electrode,” Opt. Express 18, 1070–1075 (2010).
[CrossRef]

B. Guha, B. B. C. Kyotoku, and M. Lipson, “CMOS-compatible athermal silicon microring resonators,” Opt. Express 18, 3487–3493 (2010).
[CrossRef]

D. R. Andersen, “Graphene-based long-wave infrared TM surface plasmon modulator,” J. Opt. Soc. Am. B 27, 818–823 (2010).
[CrossRef]

W. Zhu, D. Neumayer, V. Perebeinos, and P. Avouris, “Silicon nitride gate dielectrics and band gap engineering in graphene layers,” Nano Lett. 10, 3572–3576 (2010).
[CrossRef]

G. T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photon. 4, 518–526 (2010).
[CrossRef]

Y. Rong, Y. Ge, Y. Huo, M. Fiorentino, M. R. T. Tan, T. I. Kamins, T. J. Ochalski, G. Huyet, and J. S. Harris, “Quantum-confined Stark effect in Ge/SiGe quantum wells on Si,” IEEE J. Sel. Top. Quantum Electron. 16, 85–92 (2010).
[CrossRef]

Y.-M. Lin, C. Dimitrakopoulos, K. A. Jenkins, D. B. Farmer, H.-Y. Chiu, A. Grill, and Ph. Avouris, “100-GHz transistors from wafer-scale epitaxial graphene,” Science 327, 662 (2010).
[CrossRef]

F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photon. 4, 611–622(2010).
[CrossRef]

2009

F. Xia, T. Mueller, Y.-M. Lin, A. Valdes-Garcia, and P. Avouris, “Ultrafast graphene photodetector,” Nat. Nanotechnol. 4, 839–843 (2009).
[CrossRef]

J. A. Dionne, K. Diest, L. A. Sweatlock, and H. A. Atwater, “PlasMOStor: A metal-oxide-Si field effect plasmonic modulator,” Nano Lett. 9, 897–902 (2009).
[CrossRef]

M. Breusing, C. Ropers, and T. Elsaesser, “Ultrafast carrier dynamics in graphite,” Phys. Rev. Lett. 102, 086809 (2009).
[CrossRef]

K. S. Kim, Y. Zhao, H. Jang, S. Y. Lee, J. M. Kim, K. S. Kim, J.-H. Ahn, P. Kim, J.-Y. Choi, and B. H. Hong, “Large-scale pattern growth of graphene films for stretchable transparent electrodes,” Nature 457, 706–710 (2009).
[CrossRef]

A. Reina, X. Jia, J. Ho, D. Nezich, H. Son, V. Bulovic, M. S. Dresselhaus, and J. Kong, “Large area, few-layer graphene films on arbitrary substrates by chemical vapor deposition,” Nano Lett. 9, 30–35 (2009).
[CrossRef]

J. Teng, P. Dumon, W. Bogaerts, H. Zhang, X. Jian, X. Han, M. Zhao, G. Morthier, and R. Baets, “Athermal silicon-on-insulator ring resonators by overlaying a polymer cladding on narrowed waveguides,” Opt. Express 17, 14627–14633 (2009).
[CrossRef]

2008

F. G. Della Corte, S. Rao, M. A. Nigro, F. Suriano, and C. Summonte, “Electro-optically induced absorption in α-Si:H/α-SiCN waveguiding multistacks,” Opt. Express 16, 7540–7550 (2008).
[CrossRef]

R. Yang, M. A. Abushagur, and Z. Lu, “Efficiently squeezing near infrared light into a 21 nm-by-24 nm nanospot,” Opt. Express 16, 20142 (2008).
[CrossRef]

A. B. Kuzmenko, E. van Heumen, F. Carbone, and D. van der Marel, “Universal optical conductance of graphite,” Phys. Rev. Lett. 100, 117401 (2008).
[CrossRef]

G. W. Hanson, “Dyadic Green’s functions and guided surface waves for a surface conductivity model of graphene,” J. Appl. Phys. 103, 064302 (2008).
[CrossRef]

R. Liu, Q. Cheng, T. Hand, J. J. Mock, T. Cui, S. A. Cummer, and D. R. Smith, “Experimental demonstration of electromagnetic tunneling through an epsilon-near-zero metamaterial at microwave frequencies,” Phys. Rev. Lett. 100, 023903 (2008).
[CrossRef]

J. Liu, M. Baels, A. Pomerene, S. Bernardis, R. Sun, J. Cheng, L. C. Kimerling, and J. Michel, “Waveguide-integrated, ultralow-energy GeSi electro-absorption modulators,” Nat. Photon. 2, 433–437 (2008).
[CrossRef]

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

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science 320, 1308 (2008).
[CrossRef]

X. Du, I. Skachko, A. Barker, and E. Y. Andrei, “Approaching ballistic transport in suspended graphene,” Nat. Nanotechnol. 3, 491–495 (2008).
[CrossRef]

A. A. Balandin, S. Ghosh, W. Bao, I. Calizo, D. Teweldebrhan, F. Miao, and C. N. Lau, “Superior thermal conductivity of single-layer graphene,” Nano Lett. 8, 902–907 (2008).
[CrossRef]

2007

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

M. G. Silveirinha and N. Engheta, “Theory of supercoupling, squeezing wave energy, and field confinement in narrow channels and tight bends using ε-near-zero metamaterials,” Phys. Rev. B 76, 245109 (2007).
[CrossRef]

V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, “Magneto-optical conductivity in graphene,” J. Phys., Condens. Matter 19, 026222 (2007).

Q. Xu, S. Manipatruni, B. Schmidt, J. Shakya, and M. Lipson, “12.5 Gbit/s carrier-injection-based silicon microring silicon modulators,” Opt. Express 15, 430–436 (2007).
[CrossRef]

2006

M. Silveirinha and N. Engheta, “Tunneling of electromagnetic energy through subwavelength channels and bends using ε-near-zero materials,” Phys. Rev. Lett. 97, 157403 (2006).
[CrossRef]

R. S. Jacobsen, K. N. Andersen, R. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature 441, 199–202 (2006).
[CrossRef]

2005

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature 435, 325–327 (2005).
[CrossRef]

Y.-H. Kuo, Y. Lee, Y. Ge, S. Ren, J. E. Roth, T. I. Kamins, D. A. B. Miller, and J. S. Harris, “Strong quantum-confined Stark effect in germanium quantum-well structures on silicon,” Nature 437, 1334–1336 (2005).
[CrossRef]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438, 197–200 (2005).
[CrossRef]

2004

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
[CrossRef]

A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, “A high-speed silicon optical modulator based on a metal-oxide-semiconductor capacitor,” Nature 427, 615–618 (2004).
[CrossRef]

Q. Xu, V. R. Almeida, and M. Lipson, “Experimental demonstration of guiding and confining light in nanometer-size low-refractive-index material,” Opt. Lett. 29, 1626–1628 (2004).
[CrossRef]

2000

E. L. Wooten, K. M. Kissa, A. Yan, E. J. Murphy, D. A. Lafaw, P. F. Hallemeier, D. Maack, D. V. Attanasio, D. J. Fritz, G. J. McBrien, and D. E. Bossi, “A review of lithium niobate modulators for fiber-optic communication systems,” IEEE J. Sel. Top. Quantum Electron. 6, 69–82 (2000).
[CrossRef]

Abushagur, M. A.

Ahn, J.-H.

K. S. Kim, Y. Zhao, H. Jang, S. Y. Lee, J. M. Kim, K. S. Kim, J.-H. Ahn, P. Kim, J.-Y. Choi, and B. H. Hong, “Large-scale pattern growth of graphene films for stretchable transparent electrodes,” Nature 457, 706–710 (2009).
[CrossRef]

Alloatti, L.

Almeida, V. R.

Andersen, D. R.

Andersen, K. N.

R. S. Jacobsen, K. N. Andersen, R. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature 441, 199–202 (2006).
[CrossRef]

Andrei, E. Y.

X. Du, I. Skachko, A. Barker, and E. Y. Andrei, “Approaching ballistic transport in suspended graphene,” Nat. Nanotechnol. 3, 491–495 (2008).
[CrossRef]

Attanasio, D. V.

E. L. Wooten, K. M. Kissa, A. Yan, E. J. Murphy, D. A. Lafaw, P. F. Hallemeier, D. Maack, D. V. Attanasio, D. J. Fritz, G. J. McBrien, and D. E. Bossi, “A review of lithium niobate modulators for fiber-optic communication systems,” IEEE J. Sel. Top. Quantum Electron. 6, 69–82 (2000).
[CrossRef]

Atwater, H. A.

J. A. Dionne, K. Diest, L. A. Sweatlock, and H. A. Atwater, “PlasMOStor: A metal-oxide-Si field effect plasmonic modulator,” Nano Lett. 9, 897–902 (2009).
[CrossRef]

Avouris, P.

W. Zhu, D. Neumayer, V. Perebeinos, and P. Avouris, “Silicon nitride gate dielectrics and band gap engineering in graphene layers,” Nano Lett. 10, 3572–3576 (2010).
[CrossRef]

F. Xia, T. Mueller, Y.-M. Lin, A. Valdes-Garcia, and P. Avouris, “Ultrafast graphene photodetector,” Nat. Nanotechnol. 4, 839–843 (2009).
[CrossRef]

Avouris, Ph.

Y.-M. Lin, C. Dimitrakopoulos, K. A. Jenkins, D. B. Farmer, H.-Y. Chiu, A. Grill, and Ph. Avouris, “100-GHz transistors from wafer-scale epitaxial graphene,” Science 327, 662 (2010).
[CrossRef]

Baels, M.

J. Liu, M. Baels, A. Pomerene, S. Bernardis, R. Sun, J. Cheng, L. C. Kimerling, and J. Michel, “Waveguide-integrated, ultralow-energy GeSi electro-absorption modulators,” Nat. Photon. 2, 433–437 (2008).
[CrossRef]

Baets, R.

Balandin, A. A.

A. A. Balandin, S. Ghosh, W. Bao, I. Calizo, D. Teweldebrhan, F. Miao, and C. N. Lau, “Superior thermal conductivity of single-layer graphene,” Nano Lett. 8, 902–907 (2008).
[CrossRef]

Bao, W.

A. A. Balandin, S. Ghosh, W. Bao, I. Calizo, D. Teweldebrhan, F. Miao, and C. N. Lau, “Superior thermal conductivity of single-layer graphene,” Nano Lett. 8, 902–907 (2008).
[CrossRef]

Barker, A.

X. Du, I. Skachko, A. Barker, and E. Y. Andrei, “Approaching ballistic transport in suspended graphene,” Nat. Nanotechnol. 3, 491–495 (2008).
[CrossRef]

Barklund, A.

Bergman, K.

B. G. Lee, A. Biberman, J. Chan, and K. Bergman, “High-performance modulator and switches for silicon photonic networks-on-chip,” IEEE J. Sel. Top. Quantum Electron. 16, 6–22 (2010).
[CrossRef]

Bernardis, S.

J. Liu, M. Baels, A. Pomerene, S. Bernardis, R. Sun, J. Cheng, L. C. Kimerling, and J. Michel, “Waveguide-integrated, ultralow-energy GeSi electro-absorption modulators,” Nat. Photon. 2, 433–437 (2008).
[CrossRef]

Biberman, A.

B. G. Lee, A. Biberman, J. Chan, and K. Bergman, “High-performance modulator and switches for silicon photonic networks-on-chip,” IEEE J. Sel. Top. Quantum Electron. 16, 6–22 (2010).
[CrossRef]

Bjarklev, A.

R. S. Jacobsen, K. N. Andersen, R. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature 441, 199–202 (2006).
[CrossRef]

Blake, P.

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science 320, 1308 (2008).
[CrossRef]

Bogaerts, W.

Bonaccorso, F.

F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photon. 4, 611–622(2010).
[CrossRef]

Booth, T. J.

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science 320, 1308 (2008).
[CrossRef]

Borel, R. I.

R. S. Jacobsen, K. N. Andersen, R. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature 441, 199–202 (2006).
[CrossRef]

Bossi, D. E.

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Figures (5)

Fig. 1.
Fig. 1.

(a) Real part and (b) imaginary part of the graphene conductivity as a function of chemical potential and wavelength (T=300K) based on the Kubo formula. (c) The graphene conductivity (real part and imaginary part), by interband transition and intraband transition, as the function of chemical potential at λ0=1550nm. (d) The effective dielectric constant (real part, imaginary part, and magnitude) as the function of chemical potential at λ0=1550nm. (e) The illustration of a 2D “graphene-slot waveguide” with a 10 nm thick Si3N4 buffer layer on each side of graphene. (f) The plots of the transverse electric field magnitude across the waveguide at μc=0 and μc=μt, respectively.

Fig. 2.
Fig. 2.

The transverse electric field profiles, effective indices, and propagation loss for different graphene-slot waveguides at μc=0 and μc=μt, respectively: (a) in a dielectric waveguide (Si waveguide is 450 nm wide and 150 nm thick for each layer); (b) in a dielectric strip waveguide (strip Si waveguide is 450 nm wide and 150 nm thick for each layer); (c) in a metal-insulator-metal waveguide (waveguide is 200 nm wide); (d) in a metal strip waveguide (strip metal is 200 nm wide); (e), (f) in photonic-plasmonic hybrid waveguides [waveguide is 400 nm wide in (e) and 200 nm wide in (f), Si layer is 130 nm thick for both structures]. The refractive indices of Si, Si3N4, and SiO2 are assumed to be 3.47, 1.98, and 1.44, respectively.

Fig. 3.
Fig. 3.

(a) The illustration of a graphene EO modulator based on a silicon waveguide. (b), (c) The 3D simulation of light propagation between a silicon waveguide and the EO modulator at μc=0 and μc=μt, respectively. (d) The illustration of a graphene EO modulator based on a metal strip plasmonic waveguide. (e), (f) The 3D simulation of light propagation between a metal strip plasmonic waveguide and the EO modulator at μc=0 and μc=μt, respectively.

Fig. 4.
Fig. 4.

The attenuation of graphene-slot waveguides as a function of working wavelength at μc=0 and μc=μt, respectively: (a) in a silicon waveguide; (b) in a metal strip waveguide. The attenuation of graphene-slot waveguides as a function of chemical potential and gate voltage at λ0=1550nm: (c) in a silicon waveguide (450 nm wide and 150 nm thick for each layer); (d) in a metal strip plasmonic waveguide (strip metal is 200 nm wide).

Fig. 5.
Fig. 5.

The illustration of nanoscale graphene modulators containing direct graphene-semiconductor contacts based on (a) dielectric strip waveguide, and (b) metal strip waveguide.

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