OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 18 — Aug. 27, 2012
  • pp: 20330–20341

Switching energy limits of waveguide-coupled graphene-on-graphene optical modulators

Steven J. Koester, Huan Li, and Mo Li  »View Author Affiliations

Optics Express, Vol. 20, Issue 18, pp. 20330-20341 (2012)

View Full Text Article

Enhanced HTML    Acrobat PDF (891 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



The fundamental switching energy limitations for waveguide coupled graphene-on-graphene optical modulators are described. The minimum energy is calculated under the constraints of fixed insertion loss and extinction ratio. Analytical relations for the switching energy both for realistic structures and in the quantum capacitance limit are derived and compared with numerical simulations. The results show that sub-femtojoule per bit switching energies and peak-to-peak voltages less than 0.1 V are achievable in graphene-on-graphene optical modulators using the constraint of 3 dB extinction ratio and 3 dB insertion loss. The quantum-capacitance limited switching energy for a single TE-mode modulator geometry is found to be < 0.5 fJ/bit at λ = 1.55 μm, and the dependences of the minimum energy on the waveguide geometry, wavelength, and graphene location are investigated. The low switching energy is a result of the very strong optical absorption in graphene, and the extremely-small operating voltages needed as the device approaches the quantum capacitance regime.

© 2012 OSA

OCIS Codes
(250.7360) Optoelectronics : Waveguide modulators
(250.4110) Optoelectronics : Modulators

ToC Category:

Original Manuscript: June 13, 2012
Revised Manuscript: August 11, 2012
Manuscript Accepted: August 11, 2012
Published: August 20, 2012

Steven J. Koester, Huan Li, and Mo Li, "Switching energy limits of waveguide-coupled graphene-on-graphene optical modulators," Opt. Express 20, 20330-20341 (2012)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. F. Xia, T. Mueller, Y. M. Lin, A. Valdes-Garcia, and P. Avouris, “Ultrafast graphene photodetector,” Nat. Nanotechnol.4(12), 839–843 (2009). [CrossRef] [PubMed]
  2. T. Mueller, F. Xia, and P. Avouris, “Graphene photodetectors for high-speed optical communications,” Nat. Photonics4(5), 297–301 (2010). [CrossRef]
  3. M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature474(7349), 64–67 (2011). [CrossRef] [PubMed]
  4. B. Sensale-Rodriguez, R. Yan, M. M. Kelly, T. Fang, K. Tahy, W. S. Hwang, D. Jena, L. Liu, and H. G. Xing, “Broadband graphene terahertz modulators enabled by intraband transitions,” Nat. Commun.3, 780 (2012). [CrossRef] [PubMed]
  5. Q. Bao, H. Zhang, B. Wang, Z. Ni, C. H. Y. X. Lim, Y. Wang, D. Y. Tang, and K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics5(7), 411–415 (2011). [CrossRef]
  6. Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene mode-locked ultrafast laser,” ACS Nano4(2), 803–810 (2010). [CrossRef] [PubMed]
  7. Q. Bao, H. Zhang, Y. Wang, Z. Ni, Y. Yan, Z. X. Shen, K. P. Loh, and D. Y. Tang, “Atomic-layer graphene as a saturable absorber for ultrafast pulsed lasers,” Adv. Funct. Mater.19(19), 3077–3083 (2009). [CrossRef]
  8. X. Li, W. Cai, J. An, S. Kim, J. Nah, D. Yang, R. Piner, A. Velamakanni, I. Jung, E. Tutuc, S. K. Banerjee, L. Colombo, and R. S. Ruoff, “Large-area synthesis of high-quality and uniform graphene films on copper foils,” Science324(5932), 1312–1314 (2009). [CrossRef] [PubMed]
  9. B. Jalali and S. Fathpour, “Silicon photonics,” IEEE J. Lightwave Tech.24(12), 4600–4615 (2006). [CrossRef]
  10. S. J. Koester and M. Li, “High-speed waveguide-coupled graphene-on-graphene optical modulators,” Appl. Phys. Lett.100(17), 171107 (2012). [CrossRef]
  11. M. Liu, X. Yin, and X. Zhang, “Double-layer graphene optical modulator,” Nano Lett.12(3), 1482–1485 (2012). [CrossRef] [PubMed]
  12. D. A. B. Miller, “Energy consumption in optical modulators for interconnects,” Opt. Express20(S2Suppl 2), A293–A308 (2012). [CrossRef] [PubMed]
  13. F. Y. Gardes, D. J. Thomson, N. G. Emerson, and G. T. Reed, “40 Gb/s silicon photonics modulator for TE and TM polarisations,” Opt. Express19(12), 11804–11814 (2011). [CrossRef] [PubMed]
  14. T. Fang, A. Konar, H. Xing, and D. Jena, “Carrier statistics and quantum capacitance of graphene sheets and ribbons,” Appl. Phys. Lett.91(9), 092109 (2007). [CrossRef]
  15. Z. Q. Li, E. A. Henriksen, Z. Jiang, Z. Hao, M. C. Martin, P. Kim, H. L. Stormer, and D. N. Basov, “Dirac charge dynamics in graphene by infrared spectroscopy,” Nat. Phys.4(7), 532–535 (2008). [CrossRef]
  16. J. Horng, C.-F. Chen, B. Geng, C. Girit, Y. Zhang, Z. Hao, H. A. Bechtel, M. Martin, A. Zettl, M. F. Crommie, Y. R. Shen, and F. Wang, “Drude conductivity of Dirac fermions in graphene,” Phys. Rev. B83(16), 165113 (2011). [CrossRef]
  17. G. W. Hanson, “Dyadic Green’s functions and guided surface waves for a surface conductivity model of graphene,” J. Appl. Phys.103(6), 064302 (2008). [CrossRef]
  18. J. D. Joannopoulos, Photonic Crystals: Molding the Flow of Light, 2nd edition (Princeton University Press, 2008).
  19. H. Li, Y. Anugrah, S. J. Koester, and M. Li, “Optical absorption in graphene integrated on silicon waveguides,” arXiv:1205.4050v1, 2012.
  20. M. R. Watts, W. A. Zortman, D. C. Trotter, R. W. Young, and A. L. Lentine, “Vertical junction silicon microdisk modulators and switches,” Opt. Express19(22), 21989–22003 (2011). [CrossRef] [PubMed]
  21. J. Liu, M. Beals, A. Pomerene, S. Bernardis, R. Sun, J. Cheng, L. C. Kimerling, and J. Michel, “Waveguide-integrated, ultralow-energy GeSi electro-absorption modulators,” Nat. Photonics2(7), 433–437 (2008). [CrossRef]
  22. N.-N. Feng, D. Feng, S. Liao, X. Wang, P. Dong, H. Liang, C.-C. Kung, W. Qian, J. Fong, R. Shafiiha, Y. Luo, J. Cunningham, A. V. Krishnamoorthy, and M. Asghari, “30GHz Ge electro-absorption modulator integrated with 3 μm silicon-on-insulator waveguide,” Opt. Express19(8), 7062–7067 (2011). [CrossRef] [PubMed]
  23. R. K. Schaevitz, E. H. Edwards, J. E. Roth, E. T. Fei, Y. Rong, P. Wahl, T. I. Kamins, J. S. Harris, and D. A. B. Miller, “Simple electroabsorption calculator for designing 1310 nm and 1550 nm modulators using germanium quantum wells,” IEEE J. Quantum Electron.48(2), 187–197 (2012). [CrossRef]
  24. S. Ren, Y. Rong, S. A. Claussen, R. K. Schaevitz, T. I. Kamins, J. S. Harris, and D. A. B. Miller, “Ge/SiGe quantum well waveguide modulator monolithically integrated with SOI waveguides,” IEEE Photon. Technol. Lett.24(6), 461–463 (2012). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited