OSA's Digital Library

Optical Materials Express

Optical Materials Express

  • Editor: David J. Hagan
  • Vol. 2, Iss. 6 — Jun. 1, 2012
  • pp: 771–781

Padé approximant spectral fit for FDTD simulation of graphene in the near infrared

Adam Mock  »View Author Affiliations


Optical Materials Express, Vol. 2, Issue 6, pp. 771-781 (2012)
http://dx.doi.org/10.1364/OME.2.000771


View Full Text Article

Enhanced HTML    Acrobat PDF (1533 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

A parameterization of the dispersive conductivity of highly-doped graphene has been developed and is presented for use in finite-difference time-domain simulation of near infrared graphene-based photonic and plasmonic devices. The parameterization is based on fitting a Padé approximant to the conductivity arising from interband electronic transitions. The resulting parameterization provides an accurate spectral representation of the conductivity in the wavelength range 1.3 – 2.3μm which is important for near infrared graphene plasmonics. Finite-difference time-domain simulations of straight graphene plasmonic waveguides of infinite and finite width are presented.

© 2012 OSA

OCIS Codes
(000.4430) General : Numerical approximation and analysis
(230.7370) Optical devices : Waveguides
(240.6680) Optics at surfaces : Surface plasmons
(240.6690) Optics at surfaces : Surface waves
(160.4236) Materials : Nanomaterials
(350.4238) Other areas of optics : Nanophotonics and photonic crystals

ToC Category:
IR Materials

History
Original Manuscript: March 15, 2012
Revised Manuscript: April 23, 2012
Manuscript Accepted: April 26, 2012
Published: May 7, 2012

Virtual Issues
Nanocarbon for Photonics and Optoelectronics (2012) Optical Materials Express

Citation
Adam Mock, "Padé approximant spectral fit for FDTD simulation of graphene in the near infrared," Opt. Mater. Express 2, 771-781 (2012)
http://www.opticsinfobase.org/ome/abstract.cfm?URI=ome-2-6-771


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. 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,” Science306, 666–669 (2004). [CrossRef] [PubMed]
  2. A. K. Geim, “Graphene: status and propects,” Science324, 1530–1534 (2009). [CrossRef] [PubMed]
  3. A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater.6, 183–191 (2007). [CrossRef] [PubMed]
  4. F. Xia, T. Mueller, Y. Lin, A. Valdes-Garcia, and P. Avouris, “Ultrafast graphene photodetector,” Nat. Nanotechnol.4, 839–843 (2009). [CrossRef] [PubMed]
  5. T. Mueller, F. Xia, and P. Avouris, “Graphene photodetectors for high-speed optical communications,” Nat. Photonics4, 297–301 (2010). [CrossRef]
  6. E. D. Fabrizio, A. E. Nikolaenko, and N. I. Zheludev, “Graphene in a photonic metamaterial,” Opt. Express18, 8359–8353 (2010).
  7. D. R. Andersen, “Graphene-based long-wave infrared tm surface plasmon modulator,” J. Opt. Soc. Am. B27, 818–823 (2010). [CrossRef]
  8. G. W. Hanson, “Quasi-transverse electromagnetic modes supported by a graphene parallel-plate waveguide,” J. Appl. Phys.104, 084314 (2008). [CrossRef]
  9. P. Blake, P. D. Brimicombe, R. R. Nair, T. J. Booth, D. Jiang, F. Schedin, L. A. Ponomorenko, S. V. Morozov, H. F. Gleeson, E. W. Hill, A. K. Geim, and K. S. Novoselov, “Graphene-based liquid crystal device,” Nano Lett.8, 1704–1708 (2008). [CrossRef] [PubMed]
  10. 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. Express17, 17630–17635 (2009). [CrossRef] [PubMed]
  11. 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, 803–810 (2010). [CrossRef] [PubMed]
  12. Y.-W. Song, S.-Y. Jang, W.-S. Han, and M.-K. Bae, “Graphene mode-lockers for fiber lasers functioned with evanescent field interaction,” Appl. Phys. Lett.96, 051122 (2010). [CrossRef]
  13. W. D. Tan, C. Y. Su, R. J. Knize, G. Q. Zie, L. J. Li, and D. Y. Tang, “Mode locking of ceramic Nd:yttrium aluminum garnet with graphene as a saturable absorber,” Appl. Phys. Lett.96, 031106 (2010). [CrossRef]
  14. A. Vakil and N. Engheta, “Transformation optics using graphene,” Science332, 1291–1294 (2011). [CrossRef] [PubMed]
  15. K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag.14, 302–307 (1966). [CrossRef]
  16. A. Taflove and S. C. Hagness, Computational Electrodynamics (Artech House, Massachusetts, 2000).
  17. M. Okoniewski, M. Mrozowski, and M. A. Stuchly, “Simple treatment of multi-term dispersion in fdtd,” IEEE Microw. Guid. Wave Lett.7, 121–123 (1997). [CrossRef]
  18. F. Hao and P. Nordlander, “Efficient dielectric function for FDTD simulation of the optical properties of silver and gold nanoparticles,” Chem. Phys. Lett.446, 115–118 (2007). [CrossRef]
  19. A. Vial, A.-S. Grimault, D. Macías, D. Barchiesi, and M. L. de la Chapelle, “Improved analytical fit of gold dispersion: Application to the modeling of extinction spectra with a finite-difference time-domain method,” Phys. Rev. B71, 085416 (2005). [CrossRef]
  20. I. T. Rekanos and T. G. Papadopoulos, “FDTD modeling of wave propagation in Cole–Cole media with multiple relaxation times,” IEEE Antennas Wireless Propag. Lett.9, 67–69 (2010). [CrossRef]
  21. G. A. Baker and P. Graves-Morris, Padé Approximants (Cambridge University Press, New York, 1996). [CrossRef] [PubMed]
  22. S. Dey and R. Mittra, “Efficient computation of resonant frequencies and quality factors of cavities via a combination of the finite-difference time-domain technique and the Padé approximation,” IEEE Microw. Guid. Wave Lett.8, 415–417 (1998). [CrossRef]
  23. A. Mock and J. D. O’Brien, “Direct extraction of large quality factors and resonant frequencies from Padé interpolated resonance spectra,” Opt. Quantum Electron.40, 1187–1192 (2008). [CrossRef]
  24. G. D. Bouzianas, N. V. Kantartzis, C. S. Antonopoulos, and T. D. Tsiboukis, “Optimal modeling of innite graphene sheets via a class of generalized FDTD schemes,” IEEE Trans. Magn.48, 379–382 (2012). [CrossRef]
  25. H. Wang, Y. Wu, B. Lassiter, C. L. Nehl, J. H. Hafner, P. Nordlander, and H. J. Halas, “Symmetry breaking in individual plasmonic nanoparticles,” Proc. Natl. Acad. Sci. USA103, 10856–10860 (2006). [CrossRef] [PubMed]
  26. M. T. Hill, Y.-S. Oei, B. Smalbrugge, Y. Zhu, T. de Vries, P. J. van Veldhoven, F. W. M. van Otten, T. J. Eijkemans, J. P. Turkiewicz, H. de Waardt, E. J. Geluk, S.-H. Kwon, Y.-H. Lee, R. Notzel, and M. K. Smit, “Lasing in metal-coated nanocavities,” Nat. Photonics1, 589–594 (2007). [CrossRef]
  27. I. Ahmed, E. H. Khoo, O. Kurniawan, and E. P. Li, “Modeling and simulation of active plasmonics with the FDTD method by using solid state and Lorentz–Drude dispersive model,” J. Opt. Soc. Am. B28, 352–359 (2011). [CrossRef]
  28. A. Mock, “Modal analysis of nanoplasmonic multilayer spherical resonators,” IEEE Photonics J.3, 765–776 (2011). [CrossRef]
  29. K. Ziegler, “Minimal conductivity of graphene: Nonuniversal values from the kubo formula,” Phys. Rev. B75, 233407 (2007). [CrossRef]
  30. L. A. Falkovsky and S. S. Pershoguba, “Optical far-infrared properties of a graphene monolayer and multilayer,” Phys. Rev. B76, 153410 (2007). [CrossRef]
  31. G. W. Hanson, “Dyadic greens functions and guided surface waves for a surface conductivity model of graphene,” J. Appl. Phys.103, 064302 (2008). [CrossRef]
  32. F. Mak, M. Y. Sfeir, Y. Wu, C. H. Lui, J. A. Misewich, and T. F. Heinz, “Measurement of the optical conductivity of graphene,” Phys. Rev. Lett.101, 196405 (2008). [CrossRef] [PubMed]
  33. 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,” Science320, 1308 (2008). [CrossRef] [PubMed]
  34. J. M. Dawlaty, S. Shivaraman, J. Strait, P. George, M. Chandrashenkar, F. Rana, M. G. Spencer, D. Veksler, and Y. Chen, “Measurement of the optical absorption spectra of epitaxial graphene from terahertz to visible,” Appl. Phys. Lett.93, 131905 (2008). [CrossRef]
  35. M. Jablan, H. Buljan, and M. Soljačić, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B80, 245435 (2009). [CrossRef]
  36. D. K. Cheng, Field and Wave Electromagnetics (Addison Wesley, New York, 1992).
  37. T. Stauber, N. M. Peres, and A. K. Geim, “Optical conductivity of graphene in the visible region of the spectrum,” Phys. Rev. B78, 085432 (2008). [CrossRef]
  38. W. Zhao, P. Tan, J. Zhang, and J. Liu, “Charge transfer and optical phonon mixing in few-layer graphene chemically doped with sulfuric acid,” Phys. Rev. B82, 245423 (2010). [CrossRef]
  39. A. Asi and L. Shafai, “Dispersion analysis of anisotropic inhomogeneous waveguides using compact 2D-FDTD,” Electron. Lett.28, 1451–1452 (1992). [CrossRef]
  40. S. Xiao, R. Vahldieck, and H. Jin, “Full-wave analysis of guided wave structures using a novel 2-D FDTD,” IEEE Microw. Guid. Wave Lett.2, 165–167 (1992). [CrossRef]
  41. S. Xiao and R. Vahldieck, “An efficient 2-D FDTD algorithm using real variables [guided wavestructure analysis],” IEEE Microw. Guid. Wave Lett.3, 127–129 (1993). [CrossRef]
  42. Y. Chen and R. Mittra, “A highly efficient finite-difference time domain algorithm for analyzing axisymmetric waveguides,” Microwave Opt. Technol. Lett.15, 201–203 (1997). [CrossRef]
  43. M. Qiu, “Analysis of guided modes in photonic crystal fibers using the finite-difference time-domain method,” Microwave Opt. Technol. Lett.30, 327–330 (2001). [CrossRef]
  44. A. Mock and J. D. O’Brien, “Dependence of silicon-on-insulator waveguide loss on lower oxide cladding thickness,” in Integrated Photonics and Nanophotonics Research and Applications Topical Meeting (Optical Society of America, Boston, MA, USA, 2008),p. IWG4.
  45. A. Mock and P. Trader, “Photonic crystal fiber analysis using cylindrical FDTD with Bloch boundary conditions,” PIERS Online6, 783–787 (2010). [CrossRef]
  46. W. Kuang, W. J. Kim, A. Mock, and J. D. O’Brien, “Propagation loss of line-defect photonic crystal slab waveguides,” IEEE J. Sel. Top. Quantum Electron.12, 1183–1195 (2006). [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