Abstract

We realize all-optical sensitive phase shifting based on nonlinear out-of-plane coupling to a slab waveguide through Fano resonance of a slab 1-D photonic crystal (PhC). We use a graphene layer as the nonlinear material and change its refractive index by the input light intensity through Kerr nonlinear effect to obtain a shift in the Fano resonance frequency. The Fano resonance and self-focusing effect lead to light-intensity enhancement on the graphene in the PhC, reinforcing the nonlinear effect of refractive index in the graphene. Through finite-difference time-domain simulation, we demonstrate that the phase changing sensitivity obtained can be 4 orders higher than that by a single graphene under the same input light intensity. Moreover the threshold pump intensity for all-optical sensitive phase shifting in the coupled light to the waveguide is as low as ~4 MW per square centimeter. The results are applicable in micro optical integrated circuits for phase shifters, phase modulators, power limiters, and phase logic elements for optical computation, digital phase shift keying in communication systems, and non-contact sensitive signal detectors.

© 2014 Optical Society of America

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  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]
  2. S. J. Koester and M. Li, “Waveguide-coupled graphene optoelectronics,” IEEE J. Sel. Top. Quantum Electron. 20(1), 6000211 (2014).
    [CrossRef]
  3. A. Majumdar, J. Kim, J. Vuckovic, and F. Wang, “Electrical control of silicon photonic crystal cavity by graphene,” Nano Lett. 13(2), 515–518 (2013).
    [CrossRef] [PubMed]
  4. J. T. Kim, J. Kim, H. Choi, C. G. Choi, and S. Y. Choi, “Graphene-based photonic devices for soft hybrid optoelectronic systems,” Nanotechnology 23(34), 344005 (2012).
    [CrossRef] [PubMed]
  5. S. J. Koester and M. Li, “High-speed waveguide-coupled graphene-on-graphene optical modulators,” Appl. Phys. Lett. 100(17), 171107 (2012).
    [CrossRef]
  6. Q. Bao, H. Zhang, B. Wang, Z. Ni, C. Haley, Y. X. Lim, Y. Wang, D. Y. Tang, and K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics 5, 411–415 (2011).
  7. K. F. Maka, L. Jub, F. Wangb, and T. F. Heinza, “Optical spectroscopy of graphene: From the far infrared to the ultraviolet,” Solid State Commun. 152(15), 1341–1349 (2012).
    [CrossRef]
  8. F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics 4(9), 611–622 (2010).
    [CrossRef]
  9. A. R. Wright, X. G. Xu, J. C. Cao, and C. Zhang, “Strong nonlinear optical response of graphene in the terahertz regime,” Appl. Phys. Lett. 95(7), 072101 (2009).
    [CrossRef]
  10. Z. Zheng, C. Zhao, S. Lu, Y. Chen, Y. Li, H. Zhang, and S. Wen, “Microwave and optical saturable absorption in graphene,” Opt. Express 20(21), 23201–23214 (2012).
    [CrossRef] [PubMed]
  11. L. Zhibo, Z. X. Liang, Y. X. Qing, C. Y. Sheng, and T. J. Guo, “Nonlinear optical properties of graphene-based materials,” Chin. Sci. Bull. 57(23), 2971–2982 (2012).
    [CrossRef]
  12. G. Q. Xie, J. Ma, P. Lv, W. L. Gao, P. Yuan, L. J. Qian, H. H. Yu, H. J. Zhang, J. Y. Wang, and D. Y. Tang, “Graphene saturable absorber for Q-switching and mode locking at 2 μm wavelength,” Opt. Mater. Express 2(6), 878–883 (2012).
    [CrossRef]
  13. H. Zhang, S. Virally, Q. Bao, L. K. Ping, S. Massar, N. Godbout, and P. Kockaert, “Z-scan measurement of the nonlinear refractive index of graphene,” Opt. Lett. 37(11), 1856–1858 (2012).
    [CrossRef] [PubMed]
  14. S. Fan and J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65(23), 235112 (2002).
    [CrossRef]
  15. S. I. Inoue and Y. Aoyagi, “Design and Fabrication of Two-Dimensional Photonic Crystals with Predetermined Nonlinear Optical Properties,” Phys. Rev. Lett. 94(10), 103904 (2005).
    [CrossRef] [PubMed]
  16. A. D. Bristow, D. O. Kundys, A. Z. García-Déniz, J.-P. R. Wells, A. M. Fox, M. S. Skolnick, D. M. Whittaker, A. Tahraoui, T. F. Krauss, and J. S. Roberts, “Enhanced all-optical tuning of leaky eigenmodes in photonic crystal waveguides,” Opt. Lett. 31(15), 2284–2286 (2006).
    [CrossRef] [PubMed]
  17. A. D. Bristow, D. O. Kundys, A. Z. García-Déniz, J. P. R. Wells, A. M. Fox, M. S. Skolnick, D. M. Whittaker, A. Tahraoui, T. F. Krauss, and J. S. Roberts, “Ultrafast nonlinear tuning of the reflection properties of AlGaAs photonic crystal waveguides by two-photon absorption,” J. Appl. Phys. 96(9), 4729–4734 (2004).
    [CrossRef]
  18. D. Nau, R. P. Bertram, K. Buse, T. Zentgraf, J. Kuhl, S. G. Tikhodeev, N. A. Gippius, and H. Giessen, “Optical switching in metallic photonic crystal slabs with photo addressable polymers,” Appl. Phys. B 85, 543–547 (2006).
  19. M. Mecklenburg, J. Woo, and B. C. Regan, “Tree-level electron-photon interactions in graphene,” Phys. Rev. B 81, 245401 (2010).
  20. L. A. Falkovsky, “Optical properties of graphene,” J. Phys. Conf. Ser. 129, 012004 (2008).
    [CrossRef]
  21. M. A. K. Othman, C. Guclu, and F. Capolino, “Graphene–dielectric composite metamaterials: evolution from elliptic to hyperbolic wavevector dispersion and the transverse epsilon-near-zero condition,” Journal of Nanophotonics 7(1), 073089 (2013).
    [CrossRef]

2014 (1)

S. J. Koester and M. Li, “Waveguide-coupled graphene optoelectronics,” IEEE J. Sel. Top. Quantum Electron. 20(1), 6000211 (2014).
[CrossRef]

2013 (2)

A. Majumdar, J. Kim, J. Vuckovic, and F. Wang, “Electrical control of silicon photonic crystal cavity by graphene,” Nano Lett. 13(2), 515–518 (2013).
[CrossRef] [PubMed]

M. A. K. Othman, C. Guclu, and F. Capolino, “Graphene–dielectric composite metamaterials: evolution from elliptic to hyperbolic wavevector dispersion and the transverse epsilon-near-zero condition,” Journal of Nanophotonics 7(1), 073089 (2013).
[CrossRef]

2012 (7)

J. T. Kim, J. Kim, H. Choi, C. G. Choi, and S. Y. Choi, “Graphene-based photonic devices for soft hybrid optoelectronic systems,” Nanotechnology 23(34), 344005 (2012).
[CrossRef] [PubMed]

S. J. Koester and M. Li, “High-speed waveguide-coupled graphene-on-graphene optical modulators,” Appl. Phys. Lett. 100(17), 171107 (2012).
[CrossRef]

Z. Zheng, C. Zhao, S. Lu, Y. Chen, Y. Li, H. Zhang, and S. Wen, “Microwave and optical saturable absorption in graphene,” Opt. Express 20(21), 23201–23214 (2012).
[CrossRef] [PubMed]

L. Zhibo, Z. X. Liang, Y. X. Qing, C. Y. Sheng, and T. J. Guo, “Nonlinear optical properties of graphene-based materials,” Chin. Sci. Bull. 57(23), 2971–2982 (2012).
[CrossRef]

G. Q. Xie, J. Ma, P. Lv, W. L. Gao, P. Yuan, L. J. Qian, H. H. Yu, H. J. Zhang, J. Y. Wang, and D. Y. Tang, “Graphene saturable absorber for Q-switching and mode locking at 2 μm wavelength,” Opt. Mater. Express 2(6), 878–883 (2012).
[CrossRef]

H. Zhang, S. Virally, Q. Bao, L. K. Ping, S. Massar, N. Godbout, and P. Kockaert, “Z-scan measurement of the nonlinear refractive index of graphene,” Opt. Lett. 37(11), 1856–1858 (2012).
[CrossRef] [PubMed]

K. F. Maka, L. Jub, F. Wangb, and T. F. Heinza, “Optical spectroscopy of graphene: From the far infrared to the ultraviolet,” Solid State Commun. 152(15), 1341–1349 (2012).
[CrossRef]

2011 (2)

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. Haley, Y. X. Lim, Y. Wang, D. Y. Tang, and K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics 5, 411–415 (2011).

2010 (2)

F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics 4(9), 611–622 (2010).
[CrossRef]

M. Mecklenburg, J. Woo, and B. C. Regan, “Tree-level electron-photon interactions in graphene,” Phys. Rev. B 81, 245401 (2010).

2009 (1)

A. R. Wright, X. G. Xu, J. C. Cao, and C. Zhang, “Strong nonlinear optical response of graphene in the terahertz regime,” Appl. Phys. Lett. 95(7), 072101 (2009).
[CrossRef]

2008 (1)

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

2006 (2)

A. D. Bristow, D. O. Kundys, A. Z. García-Déniz, J.-P. R. Wells, A. M. Fox, M. S. Skolnick, D. M. Whittaker, A. Tahraoui, T. F. Krauss, and J. S. Roberts, “Enhanced all-optical tuning of leaky eigenmodes in photonic crystal waveguides,” Opt. Lett. 31(15), 2284–2286 (2006).
[CrossRef] [PubMed]

D. Nau, R. P. Bertram, K. Buse, T. Zentgraf, J. Kuhl, S. G. Tikhodeev, N. A. Gippius, and H. Giessen, “Optical switching in metallic photonic crystal slabs with photo addressable polymers,” Appl. Phys. B 85, 543–547 (2006).

2005 (1)

S. I. Inoue and Y. Aoyagi, “Design and Fabrication of Two-Dimensional Photonic Crystals with Predetermined Nonlinear Optical Properties,” Phys. Rev. Lett. 94(10), 103904 (2005).
[CrossRef] [PubMed]

2004 (1)

A. D. Bristow, D. O. Kundys, A. Z. García-Déniz, J. P. R. Wells, A. M. Fox, M. S. Skolnick, D. M. Whittaker, A. Tahraoui, T. F. Krauss, and J. S. Roberts, “Ultrafast nonlinear tuning of the reflection properties of AlGaAs photonic crystal waveguides by two-photon absorption,” J. Appl. Phys. 96(9), 4729–4734 (2004).
[CrossRef]

2002 (1)

S. Fan and J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65(23), 235112 (2002).
[CrossRef]

Aoyagi, Y.

S. I. Inoue and Y. Aoyagi, “Design and Fabrication of Two-Dimensional Photonic Crystals with Predetermined Nonlinear Optical Properties,” Phys. Rev. Lett. 94(10), 103904 (2005).
[CrossRef] [PubMed]

Bao, Q.

H. Zhang, S. Virally, Q. Bao, L. K. Ping, S. Massar, N. Godbout, and P. Kockaert, “Z-scan measurement of the nonlinear refractive index of graphene,” Opt. Lett. 37(11), 1856–1858 (2012).
[CrossRef] [PubMed]

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

Bertram, R. P.

D. Nau, R. P. Bertram, K. Buse, T. Zentgraf, J. Kuhl, S. G. Tikhodeev, N. A. Gippius, and H. Giessen, “Optical switching in metallic photonic crystal slabs with photo addressable polymers,” Appl. Phys. B 85, 543–547 (2006).

Bonaccorso, F.

F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics 4(9), 611–622 (2010).
[CrossRef]

Bristow, A. D.

A. D. Bristow, D. O. Kundys, A. Z. García-Déniz, J.-P. R. Wells, A. M. Fox, M. S. Skolnick, D. M. Whittaker, A. Tahraoui, T. F. Krauss, and J. S. Roberts, “Enhanced all-optical tuning of leaky eigenmodes in photonic crystal waveguides,” Opt. Lett. 31(15), 2284–2286 (2006).
[CrossRef] [PubMed]

A. D. Bristow, D. O. Kundys, A. Z. García-Déniz, J. P. R. Wells, A. M. Fox, M. S. Skolnick, D. M. Whittaker, A. Tahraoui, T. F. Krauss, and J. S. Roberts, “Ultrafast nonlinear tuning of the reflection properties of AlGaAs photonic crystal waveguides by two-photon absorption,” J. Appl. Phys. 96(9), 4729–4734 (2004).
[CrossRef]

Buse, K.

D. Nau, R. P. Bertram, K. Buse, T. Zentgraf, J. Kuhl, S. G. Tikhodeev, N. A. Gippius, and H. Giessen, “Optical switching in metallic photonic crystal slabs with photo addressable polymers,” Appl. Phys. B 85, 543–547 (2006).

Cao, J. C.

A. R. Wright, X. G. Xu, J. C. Cao, and C. Zhang, “Strong nonlinear optical response of graphene in the terahertz regime,” Appl. Phys. Lett. 95(7), 072101 (2009).
[CrossRef]

Capolino, F.

M. A. K. Othman, C. Guclu, and F. Capolino, “Graphene–dielectric composite metamaterials: evolution from elliptic to hyperbolic wavevector dispersion and the transverse epsilon-near-zero condition,” Journal of Nanophotonics 7(1), 073089 (2013).
[CrossRef]

Chen, Y.

Choi, C. G.

J. T. Kim, J. Kim, H. Choi, C. G. Choi, and S. Y. Choi, “Graphene-based photonic devices for soft hybrid optoelectronic systems,” Nanotechnology 23(34), 344005 (2012).
[CrossRef] [PubMed]

Choi, H.

J. T. Kim, J. Kim, H. Choi, C. G. Choi, and S. Y. Choi, “Graphene-based photonic devices for soft hybrid optoelectronic systems,” Nanotechnology 23(34), 344005 (2012).
[CrossRef] [PubMed]

Choi, S. Y.

J. T. Kim, J. Kim, H. Choi, C. G. Choi, and S. Y. Choi, “Graphene-based photonic devices for soft hybrid optoelectronic systems,” Nanotechnology 23(34), 344005 (2012).
[CrossRef] [PubMed]

Falkovsky, L. A.

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

Fan, S.

S. Fan and J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65(23), 235112 (2002).
[CrossRef]

Ferrari, A. C.

F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics 4(9), 611–622 (2010).
[CrossRef]

Fox, A. M.

A. D. Bristow, D. O. Kundys, A. Z. García-Déniz, J.-P. R. Wells, A. M. Fox, M. S. Skolnick, D. M. Whittaker, A. Tahraoui, T. F. Krauss, and J. S. Roberts, “Enhanced all-optical tuning of leaky eigenmodes in photonic crystal waveguides,” Opt. Lett. 31(15), 2284–2286 (2006).
[CrossRef] [PubMed]

A. D. Bristow, D. O. Kundys, A. Z. García-Déniz, J. P. R. Wells, A. M. Fox, M. S. Skolnick, D. M. Whittaker, A. Tahraoui, T. F. Krauss, and J. S. Roberts, “Ultrafast nonlinear tuning of the reflection properties of AlGaAs photonic crystal waveguides by two-photon absorption,” J. Appl. Phys. 96(9), 4729–4734 (2004).
[CrossRef]

Gao, W. L.

García-Déniz, A. Z.

A. D. Bristow, D. O. Kundys, A. Z. García-Déniz, J.-P. R. Wells, A. M. Fox, M. S. Skolnick, D. M. Whittaker, A. Tahraoui, T. F. Krauss, and J. S. Roberts, “Enhanced all-optical tuning of leaky eigenmodes in photonic crystal waveguides,” Opt. Lett. 31(15), 2284–2286 (2006).
[CrossRef] [PubMed]

A. D. Bristow, D. O. Kundys, A. Z. García-Déniz, J. P. R. Wells, A. M. Fox, M. S. Skolnick, D. M. Whittaker, A. Tahraoui, T. F. Krauss, and J. S. Roberts, “Ultrafast nonlinear tuning of the reflection properties of AlGaAs photonic crystal waveguides by two-photon absorption,” J. Appl. Phys. 96(9), 4729–4734 (2004).
[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(7349), 64–67 (2011).
[CrossRef] [PubMed]

Giessen, H.

D. Nau, R. P. Bertram, K. Buse, T. Zentgraf, J. Kuhl, S. G. Tikhodeev, N. A. Gippius, and H. Giessen, “Optical switching in metallic photonic crystal slabs with photo addressable polymers,” Appl. Phys. B 85, 543–547 (2006).

Gippius, N. A.

D. Nau, R. P. Bertram, K. Buse, T. Zentgraf, J. Kuhl, S. G. Tikhodeev, N. A. Gippius, and H. Giessen, “Optical switching in metallic photonic crystal slabs with photo addressable polymers,” Appl. Phys. B 85, 543–547 (2006).

Godbout, N.

Guclu, C.

M. A. K. Othman, C. Guclu, and F. Capolino, “Graphene–dielectric composite metamaterials: evolution from elliptic to hyperbolic wavevector dispersion and the transverse epsilon-near-zero condition,” Journal of Nanophotonics 7(1), 073089 (2013).
[CrossRef]

Guo, T. J.

L. Zhibo, Z. X. Liang, Y. X. Qing, C. Y. Sheng, and T. J. Guo, “Nonlinear optical properties of graphene-based materials,” Chin. Sci. Bull. 57(23), 2971–2982 (2012).
[CrossRef]

Haley, C.

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

Hasan, T.

F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics 4(9), 611–622 (2010).
[CrossRef]

Heinza, T. F.

K. F. Maka, L. Jub, F. Wangb, and T. F. Heinza, “Optical spectroscopy of graphene: From the far infrared to the ultraviolet,” Solid State Commun. 152(15), 1341–1349 (2012).
[CrossRef]

Inoue, S. I.

S. I. Inoue and Y. Aoyagi, “Design and Fabrication of Two-Dimensional Photonic Crystals with Predetermined Nonlinear Optical Properties,” Phys. Rev. Lett. 94(10), 103904 (2005).
[CrossRef] [PubMed]

Joannopoulos, J. D.

S. Fan and J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65(23), 235112 (2002).
[CrossRef]

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(7349), 64–67 (2011).
[CrossRef] [PubMed]

Jub, L.

K. F. Maka, L. Jub, F. Wangb, and T. F. Heinza, “Optical spectroscopy of graphene: From the far infrared to the ultraviolet,” Solid State Commun. 152(15), 1341–1349 (2012).
[CrossRef]

Kim, J.

A. Majumdar, J. Kim, J. Vuckovic, and F. Wang, “Electrical control of silicon photonic crystal cavity by graphene,” Nano Lett. 13(2), 515–518 (2013).
[CrossRef] [PubMed]

J. T. Kim, J. Kim, H. Choi, C. G. Choi, and S. Y. Choi, “Graphene-based photonic devices for soft hybrid optoelectronic systems,” Nanotechnology 23(34), 344005 (2012).
[CrossRef] [PubMed]

Kim, J. T.

J. T. Kim, J. Kim, H. Choi, C. G. Choi, and S. Y. Choi, “Graphene-based photonic devices for soft hybrid optoelectronic systems,” Nanotechnology 23(34), 344005 (2012).
[CrossRef] [PubMed]

Kockaert, P.

Koester, S. J.

S. J. Koester and M. Li, “Waveguide-coupled graphene optoelectronics,” IEEE J. Sel. Top. Quantum Electron. 20(1), 6000211 (2014).
[CrossRef]

S. J. Koester and M. Li, “High-speed waveguide-coupled graphene-on-graphene optical modulators,” Appl. Phys. Lett. 100(17), 171107 (2012).
[CrossRef]

Krauss, T. F.

A. D. Bristow, D. O. Kundys, A. Z. García-Déniz, J.-P. R. Wells, A. M. Fox, M. S. Skolnick, D. M. Whittaker, A. Tahraoui, T. F. Krauss, and J. S. Roberts, “Enhanced all-optical tuning of leaky eigenmodes in photonic crystal waveguides,” Opt. Lett. 31(15), 2284–2286 (2006).
[CrossRef] [PubMed]

A. D. Bristow, D. O. Kundys, A. Z. García-Déniz, J. P. R. Wells, A. M. Fox, M. S. Skolnick, D. M. Whittaker, A. Tahraoui, T. F. Krauss, and J. S. Roberts, “Ultrafast nonlinear tuning of the reflection properties of AlGaAs photonic crystal waveguides by two-photon absorption,” J. Appl. Phys. 96(9), 4729–4734 (2004).
[CrossRef]

Kuhl, J.

D. Nau, R. P. Bertram, K. Buse, T. Zentgraf, J. Kuhl, S. G. Tikhodeev, N. A. Gippius, and H. Giessen, “Optical switching in metallic photonic crystal slabs with photo addressable polymers,” Appl. Phys. B 85, 543–547 (2006).

Kundys, D. O.

A. D. Bristow, D. O. Kundys, A. Z. García-Déniz, J.-P. R. Wells, A. M. Fox, M. S. Skolnick, D. M. Whittaker, A. Tahraoui, T. F. Krauss, and J. S. Roberts, “Enhanced all-optical tuning of leaky eigenmodes in photonic crystal waveguides,” Opt. Lett. 31(15), 2284–2286 (2006).
[CrossRef] [PubMed]

A. D. Bristow, D. O. Kundys, A. Z. García-Déniz, J. P. R. Wells, A. M. Fox, M. S. Skolnick, D. M. Whittaker, A. Tahraoui, T. F. Krauss, and J. S. Roberts, “Ultrafast nonlinear tuning of the reflection properties of AlGaAs photonic crystal waveguides by two-photon absorption,” J. Appl. Phys. 96(9), 4729–4734 (2004).
[CrossRef]

Li, M.

S. J. Koester and M. Li, “Waveguide-coupled graphene optoelectronics,” IEEE J. Sel. Top. Quantum Electron. 20(1), 6000211 (2014).
[CrossRef]

S. J. Koester and M. Li, “High-speed waveguide-coupled graphene-on-graphene optical modulators,” Appl. Phys. Lett. 100(17), 171107 (2012).
[CrossRef]

Li, Y.

Liang, Z. X.

L. Zhibo, Z. X. Liang, Y. X. Qing, C. Y. Sheng, and T. J. Guo, “Nonlinear optical properties of graphene-based materials,” Chin. Sci. Bull. 57(23), 2971–2982 (2012).
[CrossRef]

Lim, Y. X.

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

Liu, M.

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]

Loh, K. P.

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

Lu, S.

Lv, P.

Ma, J.

Majumdar, A.

A. Majumdar, J. Kim, J. Vuckovic, and F. Wang, “Electrical control of silicon photonic crystal cavity by graphene,” Nano Lett. 13(2), 515–518 (2013).
[CrossRef] [PubMed]

Maka, K. F.

K. F. Maka, L. Jub, F. Wangb, and T. F. Heinza, “Optical spectroscopy of graphene: From the far infrared to the ultraviolet,” Solid State Commun. 152(15), 1341–1349 (2012).
[CrossRef]

Massar, S.

Mecklenburg, M.

M. Mecklenburg, J. Woo, and B. C. Regan, “Tree-level electron-photon interactions in graphene,” Phys. Rev. B 81, 245401 (2010).

Nau, D.

D. Nau, R. P. Bertram, K. Buse, T. Zentgraf, J. Kuhl, S. G. Tikhodeev, N. A. Gippius, and H. Giessen, “Optical switching in metallic photonic crystal slabs with photo addressable polymers,” Appl. Phys. B 85, 543–547 (2006).

Ni, Z.

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

Othman, M. A. K.

M. A. K. Othman, C. Guclu, and F. Capolino, “Graphene–dielectric composite metamaterials: evolution from elliptic to hyperbolic wavevector dispersion and the transverse epsilon-near-zero condition,” Journal of Nanophotonics 7(1), 073089 (2013).
[CrossRef]

Ping, L. K.

Qian, L. J.

Qing, Y. X.

L. Zhibo, Z. X. Liang, Y. X. Qing, C. Y. Sheng, and T. J. Guo, “Nonlinear optical properties of graphene-based materials,” Chin. Sci. Bull. 57(23), 2971–2982 (2012).
[CrossRef]

Regan, B. C.

M. Mecklenburg, J. Woo, and B. C. Regan, “Tree-level electron-photon interactions in graphene,” Phys. Rev. B 81, 245401 (2010).

Roberts, J. S.

A. D. Bristow, D. O. Kundys, A. Z. García-Déniz, J.-P. R. Wells, A. M. Fox, M. S. Skolnick, D. M. Whittaker, A. Tahraoui, T. F. Krauss, and J. S. Roberts, “Enhanced all-optical tuning of leaky eigenmodes in photonic crystal waveguides,” Opt. Lett. 31(15), 2284–2286 (2006).
[CrossRef] [PubMed]

A. D. Bristow, D. O. Kundys, A. Z. García-Déniz, J. P. R. Wells, A. M. Fox, M. S. Skolnick, D. M. Whittaker, A. Tahraoui, T. F. Krauss, and J. S. Roberts, “Ultrafast nonlinear tuning of the reflection properties of AlGaAs photonic crystal waveguides by two-photon absorption,” J. Appl. Phys. 96(9), 4729–4734 (2004).
[CrossRef]

Sheng, C. Y.

L. Zhibo, Z. X. Liang, Y. X. Qing, C. Y. Sheng, and T. J. Guo, “Nonlinear optical properties of graphene-based materials,” Chin. Sci. Bull. 57(23), 2971–2982 (2012).
[CrossRef]

Skolnick, M. S.

A. D. Bristow, D. O. Kundys, A. Z. García-Déniz, J.-P. R. Wells, A. M. Fox, M. S. Skolnick, D. M. Whittaker, A. Tahraoui, T. F. Krauss, and J. S. Roberts, “Enhanced all-optical tuning of leaky eigenmodes in photonic crystal waveguides,” Opt. Lett. 31(15), 2284–2286 (2006).
[CrossRef] [PubMed]

A. D. Bristow, D. O. Kundys, A. Z. García-Déniz, J. P. R. Wells, A. M. Fox, M. S. Skolnick, D. M. Whittaker, A. Tahraoui, T. F. Krauss, and J. S. Roberts, “Ultrafast nonlinear tuning of the reflection properties of AlGaAs photonic crystal waveguides by two-photon absorption,” J. Appl. Phys. 96(9), 4729–4734 (2004).
[CrossRef]

Sun, Z.

F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics 4(9), 611–622 (2010).
[CrossRef]

Tahraoui, A.

A. D. Bristow, D. O. Kundys, A. Z. García-Déniz, J.-P. R. Wells, A. M. Fox, M. S. Skolnick, D. M. Whittaker, A. Tahraoui, T. F. Krauss, and J. S. Roberts, “Enhanced all-optical tuning of leaky eigenmodes in photonic crystal waveguides,” Opt. Lett. 31(15), 2284–2286 (2006).
[CrossRef] [PubMed]

A. D. Bristow, D. O. Kundys, A. Z. García-Déniz, J. P. R. Wells, A. M. Fox, M. S. Skolnick, D. M. Whittaker, A. Tahraoui, T. F. Krauss, and J. S. Roberts, “Ultrafast nonlinear tuning of the reflection properties of AlGaAs photonic crystal waveguides by two-photon absorption,” J. Appl. Phys. 96(9), 4729–4734 (2004).
[CrossRef]

Tang, D. Y.

Tikhodeev, S. G.

D. Nau, R. P. Bertram, K. Buse, T. Zentgraf, J. Kuhl, S. G. Tikhodeev, N. A. Gippius, and H. Giessen, “Optical switching in metallic photonic crystal slabs with photo addressable polymers,” Appl. Phys. B 85, 543–547 (2006).

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(7349), 64–67 (2011).
[CrossRef] [PubMed]

Virally, S.

Vuckovic, J.

A. Majumdar, J. Kim, J. Vuckovic, and F. Wang, “Electrical control of silicon photonic crystal cavity by graphene,” Nano Lett. 13(2), 515–518 (2013).
[CrossRef] [PubMed]

Wang, B.

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

Wang, F.

A. Majumdar, J. Kim, J. Vuckovic, and F. Wang, “Electrical control of silicon photonic crystal cavity by graphene,” Nano Lett. 13(2), 515–518 (2013).
[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]

Wang, J. Y.

Wang, Y.

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

Wangb, F.

K. F. Maka, L. Jub, F. Wangb, and T. F. Heinza, “Optical spectroscopy of graphene: From the far infrared to the ultraviolet,” Solid State Commun. 152(15), 1341–1349 (2012).
[CrossRef]

Wells, J. P. R.

A. D. Bristow, D. O. Kundys, A. Z. García-Déniz, J. P. R. Wells, A. M. Fox, M. S. Skolnick, D. M. Whittaker, A. Tahraoui, T. F. Krauss, and J. S. Roberts, “Ultrafast nonlinear tuning of the reflection properties of AlGaAs photonic crystal waveguides by two-photon absorption,” J. Appl. Phys. 96(9), 4729–4734 (2004).
[CrossRef]

Wells, J.-P. R.

Wen, S.

Whittaker, D. M.

A. D. Bristow, D. O. Kundys, A. Z. García-Déniz, J.-P. R. Wells, A. M. Fox, M. S. Skolnick, D. M. Whittaker, A. Tahraoui, T. F. Krauss, and J. S. Roberts, “Enhanced all-optical tuning of leaky eigenmodes in photonic crystal waveguides,” Opt. Lett. 31(15), 2284–2286 (2006).
[CrossRef] [PubMed]

A. D. Bristow, D. O. Kundys, A. Z. García-Déniz, J. P. R. Wells, A. M. Fox, M. S. Skolnick, D. M. Whittaker, A. Tahraoui, T. F. Krauss, and J. S. Roberts, “Ultrafast nonlinear tuning of the reflection properties of AlGaAs photonic crystal waveguides by two-photon absorption,” J. Appl. Phys. 96(9), 4729–4734 (2004).
[CrossRef]

Woo, J.

M. Mecklenburg, J. Woo, and B. C. Regan, “Tree-level electron-photon interactions in graphene,” Phys. Rev. B 81, 245401 (2010).

Wright, A. R.

A. R. Wright, X. G. Xu, J. C. Cao, and C. Zhang, “Strong nonlinear optical response of graphene in the terahertz regime,” Appl. Phys. Lett. 95(7), 072101 (2009).
[CrossRef]

Xie, G. Q.

Xu, X. G.

A. R. Wright, X. G. Xu, J. C. Cao, and C. Zhang, “Strong nonlinear optical response of graphene in the terahertz regime,” Appl. Phys. Lett. 95(7), 072101 (2009).
[CrossRef]

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]

Yu, H. H.

Yuan, P.

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]

D. Nau, R. P. Bertram, K. Buse, T. Zentgraf, J. Kuhl, S. G. Tikhodeev, N. A. Gippius, and H. Giessen, “Optical switching in metallic photonic crystal slabs with photo addressable polymers,” Appl. Phys. B 85, 543–547 (2006).

Zhang, C.

A. R. Wright, X. G. Xu, J. C. Cao, and C. Zhang, “Strong nonlinear optical response of graphene in the terahertz regime,” Appl. Phys. Lett. 95(7), 072101 (2009).
[CrossRef]

Zhang, H.

Zhang, H. J.

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]

Zhao, C.

Zheng, Z.

Zhibo, L.

L. Zhibo, Z. X. Liang, Y. X. Qing, C. Y. Sheng, and T. J. Guo, “Nonlinear optical properties of graphene-based materials,” Chin. Sci. Bull. 57(23), 2971–2982 (2012).
[CrossRef]

Appl. Phys. B (1)

D. Nau, R. P. Bertram, K. Buse, T. Zentgraf, J. Kuhl, S. G. Tikhodeev, N. A. Gippius, and H. Giessen, “Optical switching in metallic photonic crystal slabs with photo addressable polymers,” Appl. Phys. B 85, 543–547 (2006).

Appl. Phys. Lett. (2)

S. J. Koester and M. Li, “High-speed waveguide-coupled graphene-on-graphene optical modulators,” Appl. Phys. Lett. 100(17), 171107 (2012).
[CrossRef]

A. R. Wright, X. G. Xu, J. C. Cao, and C. Zhang, “Strong nonlinear optical response of graphene in the terahertz regime,” Appl. Phys. Lett. 95(7), 072101 (2009).
[CrossRef]

Chin. Sci. Bull. (1)

L. Zhibo, Z. X. Liang, Y. X. Qing, C. Y. Sheng, and T. J. Guo, “Nonlinear optical properties of graphene-based materials,” Chin. Sci. Bull. 57(23), 2971–2982 (2012).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

S. J. Koester and M. Li, “Waveguide-coupled graphene optoelectronics,” IEEE J. Sel. Top. Quantum Electron. 20(1), 6000211 (2014).
[CrossRef]

J. Appl. Phys. (1)

A. D. Bristow, D. O. Kundys, A. Z. García-Déniz, J. P. R. Wells, A. M. Fox, M. S. Skolnick, D. M. Whittaker, A. Tahraoui, T. F. Krauss, and J. S. Roberts, “Ultrafast nonlinear tuning of the reflection properties of AlGaAs photonic crystal waveguides by two-photon absorption,” J. Appl. Phys. 96(9), 4729–4734 (2004).
[CrossRef]

J. Phys. Conf. Ser. (1)

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

Journal of Nanophotonics (1)

M. A. K. Othman, C. Guclu, and F. Capolino, “Graphene–dielectric composite metamaterials: evolution from elliptic to hyperbolic wavevector dispersion and the transverse epsilon-near-zero condition,” Journal of Nanophotonics 7(1), 073089 (2013).
[CrossRef]

Nano Lett. (1)

A. Majumdar, J. Kim, J. Vuckovic, and F. Wang, “Electrical control of silicon photonic crystal cavity by graphene,” Nano Lett. 13(2), 515–518 (2013).
[CrossRef] [PubMed]

Nanotechnology (1)

J. T. Kim, J. Kim, H. Choi, C. G. Choi, and S. Y. Choi, “Graphene-based photonic devices for soft hybrid optoelectronic systems,” Nanotechnology 23(34), 344005 (2012).
[CrossRef] [PubMed]

Nat. Photonics (2)

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

F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics 4(9), 611–622 (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(7349), 64–67 (2011).
[CrossRef] [PubMed]

Opt. Express (1)

Opt. Lett. (2)

Opt. Mater. Express (1)

Phys. Rev. B (2)

S. Fan and J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65(23), 235112 (2002).
[CrossRef]

M. Mecklenburg, J. Woo, and B. C. Regan, “Tree-level electron-photon interactions in graphene,” Phys. Rev. B 81, 245401 (2010).

Phys. Rev. Lett. (1)

S. I. Inoue and Y. Aoyagi, “Design and Fabrication of Two-Dimensional Photonic Crystals with Predetermined Nonlinear Optical Properties,” Phys. Rev. Lett. 94(10), 103904 (2005).
[CrossRef] [PubMed]

Solid State Commun. (1)

K. F. Maka, L. Jub, F. Wangb, and T. F. Heinza, “Optical spectroscopy of graphene: From the far infrared to the ultraviolet,” Solid State Commun. 152(15), 1341–1349 (2012).
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

Structure studied. It consists of a one dimensional PhC slab, which is illuminated vertically, and two dielectric waveguides. The PhC slab has 9 periods of Si and air with a single layer of graphene (Gr) in the middle Si layer. We consider an equivalent composite of Gr and Si with d = 0.02a at y = 0.03a. The horizontal width of the composite layer is the same as that of the silicon layer.

Fig. 2
Fig. 2

The transmission coefficient (upper plot) of power from top to bottom in the PhC without graphene (for vertical incidence of the pump) and the coupling coefficient in one of the waveguide (lower plot) versus normalized frequency (a/λ)

Fig. 3
Fig. 3

The distribution of the square of electric field amplitude inside the PhC for f = a/λ = 0.525.

Fig. 4
Fig. 4

The transmission coefficient (upper plot) of the PhC (for normal incidence) and coupling coefficient in the waveguide (lower plot) for various number of graphene layers (N).

Fig. 5
Fig. 5

The phase change of the light coupled to one of the waveguides versus peak intensity of incident beam (pump) for f = a/λ = 0.522, 0.523 and 0.524.

Fig. 6
Fig. 6

The coupling coefficient (upper plot) and the average coupling intensity Iout (lower plot) versus peak intensity of the incidence beam (pump) for f = a/λ = 0.522, 0.523 and 0.524.

Fig. 7
Fig. 7

Distribution of square of electric field amplitude in the structure for the normalized frequency of 0.522 for pump intensities of 2 MW/cm2 (a), 3 MW/cm2 (b), and 4 MW/cm2 (c).

Fig. 8
Fig. 8

Improved structures that can double the coupling coefficient or power efficiency. A silver or other high reflective metal layer (blue) is set in (a) and an extended region of photonic crystal in the right hand side in (b).

Equations (13)

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

σ(ω) σ 0 2 [ tanh( ω+2 E F 4 K B T )+tanh( ω2 E F 4 K B T ) ],
σ 0 = e 2 4 =6.08× 10 5 Ω,
ε g =1+i σ ω ε 0 d g ,
(σ σ 0 )/ σ 0 <<1.
σ σ 0 .
ε c = ε d +i σ ω ε 0 d = ε d +i σ ω ε 0 d g ρ,
Δ n g = n 2 I / (1+I/ I s ),
Δ ε c =ρΔ ε g ,
Δ ε g =Δ( n g 2 k g 2 ),
Δ ε g >Δ( n g 2 ).
η c1 = P c1 / P in ; η c2 = P c2 / P in ,
η c1 = η c2 = η c .
T= P t / P in ,

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