We describe theoretically a new long-wave infrared optical modulator based on the characteristics of TM surface plasmons in graphene. Calculations made using a finite-τ random-phase approximation model, of relevant surface plasmon propagation parameters, are presented. We show that the plasmon losses vary as a function of carrier density; for large carrier densities, the interband absorption of the plasmon energy is blocked due to filling of the conduction band states, and for small carrier densities, the plasmon energy is absorbed by interband optical transitions. The carrier density versus plasmon loss curve exhibits a kink at the boundary between these two qualitatively dissimilar absorption mechanisms, corresponding to the intersection between the plasmon dispersion curve and the onset threshold for the interband absorption. The modulator device can be switched between high and low transmission states by varying the carrier density with an applied gate bias voltage. The device is limited in optical frequency to plasmons with photon energies less than the optical phonon energy (200 meV in graphene). An example modulator design for light with vacuum wavelength ${\lambda }_0=10\mu \text{m}$ is presented. This modulator exhibits a contrast ratio in the transmitted optical power between ON and OFF states of $\sim 62\text{\hspace{0.17em} dB}$ . A simple circuit model indicates that the switching speed of the modulator should be limited by the carrier relaxation time $\left(1.35\times {10}^{-13}\text{\hspace{0.17em} s}\right)$ .

© 2010 Optical Society of America

1. J. M. Pitarke, V. M. Silkin, E. V. Chulkov, and P. M. Echenique, “Theory of surface plasmons and surface-plasmon polaritons,” Rep. Prog. Phys. 70, 1-87 (2007). [CrossRef]
2. A. H. C. Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81, 109-162 (2009). [CrossRef]
3. M. Jablan, H. Buljan, and M. Soljacic, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B 80, 024535 (2009). [CrossRef]
4. 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 (2009). [CrossRef]
5. 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]
6. F. Rana, “Graphene terahertz plasmon oscillators,” IEEE Trans. Nanotechnol. 7, 91-99 (2008). [CrossRef]
7. E. H. Hwang and S. Das Sarma, “Dielectric function, screening, and plasmons in two-dimensional graphene,” Phys. Rev. B 75, 205418 (2007). [CrossRef]
8. N. D. Mermin, “Lindhard dielectric function in the relaxation-time approximation,” Phys. Rev. B 1, 2362-2363 (1970). [CrossRef]
9. 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] [PubMed]
10. 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] [PubMed]
11. 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, 3077-3083 (2009). [CrossRef]
12. H. Zhang, D. Y. Tang, L. M. Zhao, Q. L. Bao, and K. P. Loh, “Large energy mode locking of an erbium-doped fiber laser with atomic layer graphene,” Opt. Express 17, 17630-17635 (2009). [CrossRef] [PubMed]

Adv. Funct. Mater.

• 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, 3077-3083 (2009). [CrossRef]

IEEE Trans. Nanotechnol.

• F. Rana, “Graphene terahertz plasmon oscillators,” IEEE Trans. Nanotechnol. 7, 91-99 (2008). [CrossRef]

J. Appl. Phys.

• 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]

Nano Lett.

• 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] [PubMed]

Opt. Express

• H. Zhang, D. Y. Tang, L. M. Zhao, Q. L. Bao, and K. P. Loh, “Large energy mode locking of an erbium-doped fiber laser with atomic layer graphene,” Opt. Express 17, 17630-17635 (2009). [CrossRef] [PubMed]

Phys. Rev. B

• E. H. Hwang and S. Das Sarma, “Dielectric function, screening, and plasmons in two-dimensional graphene,” Phys. Rev. B 75, 205418 (2007). [CrossRef]
• N. D. Mermin, “Lindhard dielectric function in the relaxation-time approximation,” Phys. Rev. B 1, 2362-2363 (1970). [CrossRef]
• M. Jablan, H. Buljan, and M. Soljacic, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B 80, 024535 (2009). [CrossRef]

Rep. Prog. Phys.

• J. M. Pitarke, V. M. Silkin, E. V. Chulkov, and P. M. Echenique, “Theory of surface plasmons and surface-plasmon polaritons,” Rep. Prog. Phys. 70, 1-87 (2007). [CrossRef]

Rev. Mod. Phys.

• A. H. C. Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81, 109-162 (2009). [CrossRef]

Science

• 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 (2009). [CrossRef]
• 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] [PubMed]

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