Abstract

In this paper we report TE-mode phase modulation obtained by inducing a capacitive charge on graphene layers embedded in the core of a waveguide. There is a biasing regime in which graphene absorption is negligible but large index variations can be achieved with a voltage–length product as small as VπLπ0.07Vcm for straight waveguides and VπLπ0.0024Vcm for 12 μm radius microring resonators. This phase modulation device uniquely enables a small signal amplitude <1V with a micrometer-sized footprint for compatibility with CMOS circuit integration. Examples of phase-induced changes are computed for straight waveguides and for microring resonators, showing the possibility of implementing several optoelectronic functionalities as modulators, tunable filters, and switches.

© 2014 Chinese Laser Press

Full Article  |  PDF Article
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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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2013 (2)

2012 (3)

2011 (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, 64–67 (2011).
[Crossref]

2010 (1)

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

2008 (4)

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

L. A. Falkovski, “Optical properties of graphene,” J. Phys.: Conf. Ser. 129, 012004 (2008).
[Crossref]

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

T. Stauber, N. M. R. Peres, and A. K. Geim, “Optical conductivity of graphene in the visible region of the spectrum,” Phys. Rev. B 78, 085432 (2008).
[Crossref]

2007 (3)

L. A. Falkovsky and S. S. Pershoguba, “Optical far-infrared properties of a graphene monolayer and multilayer,” Phys. Rev. B 76, 153410 (2007).
[Crossref]

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

L. Zhang, J.-Y. Yang, M. Song, Y. Li, B. Zhang, R. G. Beausoleil, and A. E. Willner, “Microring-based modulation and demodulation of DPSK signal,” Opt. Express 15, 11564–11569 (2007).
[Crossref]

2002 (1)

A. Yariv, “Critical coupling and its control in optical waveguide–ring resonator systems,” IEEE Photon. Technol. Lett. 14, 483–485 (2002).
[Crossref]

Beals, M.

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

Beausoleil, R. G.

Bernardis, S.

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

Boscolo, S.

Capobianco, A. D.

Chattin, B.

B. Milivojevic, C. Raabe, A. Shastri, M. Webster, P. Metz, S. Sunder, B. Chattin, S. Wiese, B. Dama, and K. Shastri, “112 Gb/s DP-QPSK transmission over 2427  km SSMF using small size silicon photonics IQ modulator and low power CMOS driver,” in Optical Fiber Conference (Optical Society of America, 2013), paper OTh1D.1.

Cheng, J.

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

Dama, B.

B. Milivojevic, C. Raabe, A. Shastri, M. Webster, P. Metz, S. Sunder, B. Chattin, S. Wiese, B. Dama, and K. Shastri, “112 Gb/s DP-QPSK transmission over 2427  km SSMF using small size silicon photonics IQ modulator and low power CMOS driver,” in Optical Fiber Conference (Optical Society of America, 2013), paper OTh1D.1.

De Angelis, C.

Falkovski, L. A.

L. A. Falkovski, “Optical properties of graphene,” J. Phys.: Conf. Ser. 129, 012004 (2008).
[Crossref]

Falkovsky, L. A.

L. A. Falkovsky and S. S. Pershoguba, “Optical far-infrared properties of a graphene monolayer and multilayer,” Phys. Rev. B 76, 153410 (2007).
[Crossref]

Gardes, F. Y.

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

Geim, A. K.

T. Stauber, N. M. R. Peres, and A. K. Geim, “Optical conductivity of graphene in the visible region of the spectrum,” Phys. Rev. B 78, 085432 (2008).
[Crossref]

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

Geng, B.

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]

Hanson, G. W.

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

Hao, R.

Hu, T.

Jiang, X.

Jin, Y.

Ju, L.

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]

Kimerling, L. C.

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

Kogelnik, H.

H. Kogelnik, “Theory of dielectric waveguide,” in Integrated Optics, T. Tamir, ed. (Springer-Verlag, 1985), Chap. 2.

Li, X.

Li, Y.

Liu, J.

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

Liu, M.

M. Liu, X. Yin, and X. Zhang, “Double-layer graphene optical modulator,” Nano Lett. 12, 1482–1485 (2012).
[Crossref]

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]

Locatelli, A.

Mashanovich, G.

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

Metz, P.

B. Milivojevic, C. Raabe, A. Shastri, M. Webster, P. Metz, S. Sunder, B. Chattin, S. Wiese, B. Dama, and K. Shastri, “112 Gb/s DP-QPSK transmission over 2427  km SSMF using small size silicon photonics IQ modulator and low power CMOS driver,” in Optical Fiber Conference (Optical Society of America, 2013), paper OTh1D.1.

Michels, J.

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

Midrio, M.

Milivojevic, B.

B. Milivojevic, C. Raabe, A. Shastri, M. Webster, P. Metz, S. Sunder, B. Chattin, S. Wiese, B. Dama, and K. Shastri, “112 Gb/s DP-QPSK transmission over 2427  km SSMF using small size silicon photonics IQ modulator and low power CMOS driver,” in Optical Fiber Conference (Optical Society of America, 2013), paper OTh1D.1.

Moresco, M.

Novoselov, K. S.

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

Peres, N. M. R.

T. Stauber, N. M. R. Peres, and A. K. Geim, “Optical conductivity of graphene in the visible region of the spectrum,” Phys. Rev. B 78, 085432 (2008).
[Crossref]

Pershoguba, S. S.

L. A. Falkovsky and S. S. Pershoguba, “Optical far-infrared properties of a graphene monolayer and multilayer,” Phys. Rev. B 76, 153410 (2007).
[Crossref]

Pomerene, A.

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

Qiu, C.

Raabe, C.

B. Milivojevic, C. Raabe, A. Shastri, M. Webster, P. Metz, S. Sunder, B. Chattin, S. Wiese, B. Dama, and K. Shastri, “112 Gb/s DP-QPSK transmission over 2427  km SSMF using small size silicon photonics IQ modulator and low power CMOS driver,” in Optical Fiber Conference (Optical Society of America, 2013), paper OTh1D.1.

Reed, G. T.

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

G. T. Reed, Silicon Photonics (Wiley, 2008).

Romagnoli, M.

Shastri, A.

B. Milivojevic, C. Raabe, A. Shastri, M. Webster, P. Metz, S. Sunder, B. Chattin, S. Wiese, B. Dama, and K. Shastri, “112 Gb/s DP-QPSK transmission over 2427  km SSMF using small size silicon photonics IQ modulator and low power CMOS driver,” in Optical Fiber Conference (Optical Society of America, 2013), paper OTh1D.1.

Shastri, K.

B. Milivojevic, C. Raabe, A. Shastri, M. Webster, P. Metz, S. Sunder, B. Chattin, S. Wiese, B. Dama, and K. Shastri, “112 Gb/s DP-QPSK transmission over 2427  km SSMF using small size silicon photonics IQ modulator and low power CMOS driver,” in Optical Fiber Conference (Optical Society of America, 2013), paper OTh1D.1.

Song, M.

Stauber, T.

T. Stauber, N. M. R. Peres, and A. K. Geim, “Optical conductivity of graphene in the visible region of the spectrum,” Phys. Rev. B 78, 085432 (2008).
[Crossref]

Sun, R.

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

Sunder, S.

B. Milivojevic, C. Raabe, A. Shastri, M. Webster, P. Metz, S. Sunder, B. Chattin, S. Wiese, B. Dama, and K. Shastri, “112 Gb/s DP-QPSK transmission over 2427  km SSMF using small size silicon photonics IQ modulator and low power CMOS driver,” in Optical Fiber Conference (Optical Society of America, 2013), paper OTh1D.1.

Tao Chu, Z.

Thomson, D. J.

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

Ulin-Avila, E.

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]

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, 64–67 (2011).
[Crossref]

Webster, M.

B. Milivojevic, C. Raabe, A. Shastri, M. Webster, P. Metz, S. Sunder, B. Chattin, S. Wiese, B. Dama, and K. Shastri, “112 Gb/s DP-QPSK transmission over 2427  km SSMF using small size silicon photonics IQ modulator and low power CMOS driver,” in Optical Fiber Conference (Optical Society of America, 2013), paper OTh1D.1.

Wiese, S.

B. Milivojevic, C. Raabe, A. Shastri, M. Webster, P. Metz, S. Sunder, B. Chattin, S. Wiese, B. Dama, and K. Shastri, “112 Gb/s DP-QPSK transmission over 2427  km SSMF using small size silicon photonics IQ modulator and low power CMOS driver,” in Optical Fiber Conference (Optical Society of America, 2013), paper OTh1D.1.

Willner, A. E.

Xiao, X.

Xu, C.

Xu, H.

Xu, Y.

Yang, J.

Yang, J.-Y.

Yang, L.

Yariv, A.

A. Yariv, “Critical coupling and its control in optical waveguide–ring resonator systems,” IEEE Photon. Technol. Lett. 14, 483–485 (2002).
[Crossref]

Yin, X.

M. Liu, X. Yin, and X. Zhang, “Double-layer graphene optical modulator,” Nano Lett. 12, 1482–1485 (2012).
[Crossref]

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]

Yu, H.

Yu, J.

Yu, Y.

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, 64–67 (2011).
[Crossref]

Zhang, B.

Zhang, L.

Zhang, X.

M. Liu, X. Yin, and X. Zhang, “Double-layer graphene optical modulator,” Nano Lett. 12, 1482–1485 (2012).
[Crossref]

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]

IEEE Photon. Technol. Lett. (1)

A. Yariv, “Critical coupling and its control in optical waveguide–ring resonator systems,” IEEE Photon. Technol. Lett. 14, 483–485 (2002).
[Crossref]

J. Appl. Phys. (1)

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

J. Phys.: Conf. Ser. (1)

L. A. Falkovski, “Optical properties of graphene,” J. Phys.: Conf. Ser. 129, 012004 (2008).
[Crossref]

Nano Lett. (1)

M. Liu, X. Yin, and X. Zhang, “Double-layer graphene optical modulator,” Nano Lett. 12, 1482–1485 (2012).
[Crossref]

Nat. Mater. (1)

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

Nat. Photonics (2)

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

G. T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photonics 4, 518–526 (2010).
[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, 64–67 (2011).
[Crossref]

Opt. Express (4)

Opt. Lett. (1)

Phys. Rev. B (2)

L. A. Falkovsky and S. S. Pershoguba, “Optical far-infrared properties of a graphene monolayer and multilayer,” Phys. Rev. B 76, 153410 (2007).
[Crossref]

T. Stauber, N. M. R. Peres, and A. K. Geim, “Optical conductivity of graphene in the visible region of the spectrum,” Phys. Rev. B 78, 085432 (2008).
[Crossref]

Other (3)

G. T. Reed, Silicon Photonics (Wiley, 2008).

H. Kogelnik, “Theory of dielectric waveguide,” in Integrated Optics, T. Tamir, ed. (Springer-Verlag, 1985), Chap. 2.

B. Milivojevic, C. Raabe, A. Shastri, M. Webster, P. Metz, S. Sunder, B. Chattin, S. Wiese, B. Dama, and K. Shastri, “112 Gb/s DP-QPSK transmission over 2427  km SSMF using small size silicon photonics IQ modulator and low power CMOS driver,” in Optical Fiber Conference (Optical Society of America, 2013), paper OTh1D.1.

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Figures (6)

Fig. 1.
Fig. 1. Upper panel: real part of the graphene conductivity for ω=0.8eV (corresponding to a free-space wavelength equal to 1550 nm) versus the applied chemical potential μC. Inset: same quantity on a broader range of applied chemical potentials. Lower panel: relative dielectric constant of graphene versus the applied chemical potential.
Fig. 2.
Fig. 2. Schematic diagram (not to scale) of a waveguide comprising two graphene layers (red lines) biased so as to obtain electrochemical doping inside the waveguide core. The blue region is alumina.
Fig. 3.
Fig. 3. Upper panel: variation of the phase constant versus the chemical potential. Zero is arbitrarily chosen in correspondence to the phase displacement experienced by the wave when μC=0.50eV. Lower panel: attenuation across a 1 cm long straight waveguide versus the applied chemical potential. Note the log scale in the vertical axis. Computations have been made for λ=1550nm.
Fig. 4.
Fig. 4. Upper panel: schematic diagram of the ring configuration phase modulator. Lower panel: fields in the ring structure, with definition of the straight waveguide and ring single-pass transmission, t and α, respectively. The cross section of the waveguide in the ring is the same as in Fig. 2.
Fig. 5.
Fig. 5. Upper panel: overall bus-to-bus transmission for coupler transmission t=0.9 and ring transmission α=0.99 (dashed line) or α=0.999 (solid line). The abscissa is the round-trip phase shift φ. Lower panel: overall bus-to-bus phase shift. Dashed and solid lines still refer to α=0.99 and α=0.999 and coincide.
Fig. 6.
Fig. 6. Upper panel: phase displacement ψ versus frequency for chemical potential |μC|=0.56eV (filled diamonds), |μC|=0.58eV (filled squares), |μC|=0.60eV (filled circles), |μC|=0.62eV (empty diamonds), |μC|=0.64eV (empty squares), and |μC|=0.66eV (empty circles). Lower panel: insertion loss versus the applied chemical potential.

Equations (18)

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

σRσ02(tanhω+2μC4kBT+tanhω2μC4kBT),
σIσ0[4|μc|πω12πlog(ω+|2μC|)2(ω2|μC|)2+(2T)2],
σ0=e246.0853×105Siemens,
ϵr=1+σIωϵ0,
ns=2π2vF20+ϵ[fd(ϵ)fd(ϵ+2μC)]dϵμC2π2vF2,
V=dϵ0ϵOxide|e|π2vF2μC2+2|μC|.
Δneff=Δϵr2neff(hH).
Q=nS|e|SμC2|e|Sπ2vF2,
E=ΔQ24C.
Q0.59.96×1012Coulomb,
Q0.61.43×1011Coulomb,
E=Q0.62Q0.524C7pJ.
b1a1=tαeiφ1αteiφ.
T=|b1a1|2=(α|t|)2(1α|t|)2,
ψ=phase(b1a1)=arctan(α(1t2)sinφt(1+α2)α(1+t2)cosφ).
Q0.603.18×1012Coulomb,
Q0.623.40×1012Coulomb,
E=Q0.622Q0.6024C0.4pJ

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