Abstract

We study the propagation characteristics of surface Plasmon polaritons (SPPs) on a patterned graphene sheet incorporating a subwavelength ribbon resonator and a Kerr nonlinear bounding medium (substrate or top cladding) which provides tunable bandpass filtering in the THz regime. We study theoretically and via modeling the tunability of maxima in the transmission spectrum, corresponding to the resonant frequencies of the ribbon resonator, by tuning the graphene Fermi level (via an applied gate voltage) and by altering the intensity of the incident THz wave. We determine the intensity-dependent increase in the refractive index of a Kerr nonlinear medium bounding graphene, via self-phase modulation and via the more efficient process of cross-phase modulation, revealing a noticeable red-shift in the resonant frequencies of the ribbon resonator. These concepts lead to ultrafast switching of SPP transmission through the ribbon (from a high to a low state). Using Kerr nonlinear media to bound graphene increases the tunability of graphene-based devices, enabling nonlinear plasmonic and ultrafast processing in the THz regime.

© 2016 Optical Society of America

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2015 (3)

2014 (11)

N. M. R. Peres, Y. V. Bludov, J. E. Santos, A. P. Jauho, and M. I. Vasilevskiy, “Optical bistability of graphene in the terahertz range,” Phys. Rev. B 90(12), 125425 (2014).
[Crossref]

G. Rosolen and B. Maes, “Graphene ribbons for tunable coupling with plasmonic subwavelength cavities,” J. Opt. Soc. Am. B 31(5), 1096–1102 (2014).
[Crossref]

H. Nasari and M. S. Abrishamian, “All-optical tunable notch filter by use of Kerr nonlinearity in the graphene microribbon array,” J. Opt. Soc. Am. B 31(7), 1691–1697 (2014).
[Crossref]

Y. V. Bludov, D. A. Smirnova, Y. S. Kivshar, N. M. R. Peres, and M. I. Vasilevskiy, “Nonlinear TE polarized surface polaritons on graphene,” Phys. Rev. B 89(3), 035406 (2014).
[Crossref]

H. J. Li, L. L. Wang, J. Q. Liu, Z. R. Huang, B. Sun, and X. Zhai, “Investigation of the graphene based planar plasmonic filters,” J. Appl. Phys. 103, 211104 (2014).

H. Nasari and M. S. Abrishamian, “Electrically tunable graded index planar lens based on graphene,” J. Appl. Phys. 116(8), 083106 (2014).
[Crossref]

H. Nasari and M. S. Abrishamian, “Magnetically tunable focusing in a graded index planar lens based on graphene,” J. Opt. 16(10), 105502 (2014).
[Crossref]

B. G. Ghamsari, A. Olivieri, F. Variola, and P. Berini, “Enhanced Raman scattering in graphene by plasmonic resonant Stokes emission,” Nanophotonics 3(6), 363–371 (2014).
[Crossref]

I. Khromova, A. Andryieuski, and A. Lavrinenko, “Ultrasensitive terahertz/infrared waveguide modulators based on multilayer graphene metamaterials,” Laser Photonics Rev. 8(6), 916–923 (2014).
[Crossref]

Y. Nikitin, T. Low, and L. Martin-Moreno, “Anomalous reflection phase of graphene plasmons and its influence on resonators,” Phys. Rev. B 90(4), 041407 (2014).
[Crossref]

H. Hajian, A. Soltani-Vala, M. Kalafi, and P. T. Leung, “Surface Plasmons of a graphene parallel plate waveguide bounded by Kerr-type nonlinear media,” J. Appl. Phys. 115(8), 083104 (2014).
[Crossref]

2013 (5)

Y. V. Bludov, A. Ferreira, N. M. R. Peres, and M. I. Vasilevskiy, “A primer on surface plasmon-polaritons in graphene,” Int. J. Mod. Phys. B 27(10), 1341001 (2013).
[Crossref]

X. Cai and J. Wei, “Optical nonlinearity characteristics of crystalline InSb semiconductor thin films,” J. Phys. D Appl. Phys. 46(43), 435101 (2013).
[Crossref]

A. Andryieuski and A. V. Lavrinenko, “Graphene metamaterials based tunable terahertz absorber: effective surface conductivity approach,” Opt. Express 21(7), 9144–9155 (2013).
[Crossref] [PubMed]

J. S. Gómez-Díaz, M. Esquius-Morote, and J. Perruisseau-Carrier, “Plane wave excitation-detection of non-resonant plasmons along finite-width graphene strips,” Opt. Express 21(21), 24856–24872 (2013).
[Crossref] [PubMed]

A. Smirnova, A. V. Gorbach, I. V. Iorsh, I. V. Shadrivov, and Y. S. Kivshar, “Nonlinear switching with a graphene coupler,” Phys. Rev. B 88(4), 045443 (2013).
[Crossref]

2012 (11)

L. Wang, W. Cai, X. Zhang, and J. Xu, “Surface Plasmons at the interface between graphene and Kerr-type nonlinear media,” Opt. Lett. 37(13), 2730–2732 (2012).
[Crossref] [PubMed]

C. Rizza, A. Ciattoni, E. Spinozzi, and L. Columbo, “Terahertz active spatial filtering through optically tunable hyperbolic metamaterials,” Opt. Lett. 37(16), 3345–3347 (2012).
[Crossref] [PubMed]

A. N. Grigorenko, M. Polini, and K. S. Novoselov, “Graphene Plasmonics,” Nat. Photonics 6(11), 749–758 (2012).
[Crossref]

Q. Bao and K. P. Loh, “Graphene photonics, plasmonics, and broadband optoelectronic devices,” ACS Nano 6(5), 3677–3694 (2012).
[Crossref] [PubMed]

J. S. G. Diaz and J. P. Carrier, “Propagation of hybrid transverse magnetic–transverse electric plasmons on magnetically biased graphene sheet,” J. Appl. Phys. 112(12), 124906 (2012).
[Crossref]

G. D. Bouzianas, N. V. Kantartzis, C. S. Antonopoulos, and T. D. Tsiboukis, “Optimal modeling of infinite graphene sheets via a class of generalized FDTD schemes,” IEEE Trans. Magn. 48(2), 379–382 (2012).
[Crossref]

Y. V. Bludov, M. I. Vasilevskiy, and N. M. R. Peres, “Tunable graphene based polarizer,” J. Appl. Phys. 112(8), 084320 (2012).
[Crossref]

S. H. Lee, M. Choi, T. T. Kim, S. Lee, M. Liu, X. Yin, H. K. Choi, S. S. Lee, C. G. Choi, S. Y. Choi, X. Zhang, and B. Min, “Switching terahertz waves with gate-controlled active graphene metamaterials,” Nat. Mater. 11(11), 936–941 (2012).
[Crossref] [PubMed]

P. Liu, W. Cai, L. Wang, X. Zhang, and J. Xu, “Tunable terahertz optical antennas based on graphene ring structures,” Appl. Phys. Lett. 100(15), 153111 (2012).
[Crossref]

M. Kauranen and A. V. Zayats, “Nonlinear Plasmonics,” Nat. Photonics 6(11), 737–748 (2012).
[Crossref]

P. Weis, J. L. Garcia-Pomar, M. Höh, B. Reinhard, A. Brodyanski, and M. Rahm, “Spectrally wide-band terahertz wave modulator based on optically tuned graphene,” ACS Nano 6(10), 9118–9124 (2012).
[Crossref] [PubMed]

2011 (6)

S. G. Rodrigo, S. C. Palacios, F. J. Garcia-Vidal, and L. Martin-Moreno, “Metallic slit array filled with third order nonlinear media: Optical Kerr effect and Third Harmonic generation,” Phys. Rev. B 83(23), 235425 (2011).
[Crossref]

F. H. L. Koppens, D. E. Chang, and F. J. García de Abajo, “Graphene Plasmonics: A platform for strong light-matter interactions,” Nano Lett. 11(8), 3370–3377 (2011).
[Crossref] [PubMed]

A. Vakil and N. Engheta, “Transformation optics using graphene,” Science 332(6035), 1291–1294 (2011).
[Crossref] [PubMed]

M. Currie, J. D. Caldwell, F. J. Bezares, J. Robinson, T. Anderson, H. Chun, and M. Tadjer, “Quantifying pulsed laser induced damage to graphene,” Appl. Phys. Lett. 99(21), 211909 (2011).
[Crossref]

A. Roberts, D. Cormode, C. Reynolds, T. N. Illige, B. J. Leroy, and A. Sandhu, “Response of graphene to femtosecond high intensity laser irradiation,” Appl. Phys. Lett. 99(5), 051912 (2011).
[Crossref]

H. Hirori, A. Doi, F. Blanchard, and K. Tanaka, “Single-cycle terahertz pulses with amplitude exceeding 1MV/cm generated by optical rectification in LiNbO3,” Appl. Phys. Lett. 98(9), 091106 (2011).
[Crossref]

2010 (5)

M. Beck, H. Schäfer, G. Klatt, J. Demsar, S. Winnerl, M. Helm, and T. Dekorsy, “Impulsive terahertz radiation with high electric fields from an amplifier-driven large-area photoconductive antenna,” Opt. Express 18(9), 9251–9257 (2010).
[Crossref] [PubMed]

M. Pu, N. Yao, C. Hu, X. Xin, Z. Zhao, C. Wang, and X. Luo, “Directional coupler and nonlinear Mach-Zehnder interferometer based on metal-insulator-metal plasmonic waveguide,” Opt. Express 18(20), 21030–21037 (2010).
[Crossref] [PubMed]

P. West, S. Ishii, G. Naik, N. Emani, V. Shalaev, and A. Boltasseva, “Searching for better plasmonic materials,” Laser Photonics Rev. 4(6), 795–808 (2010).
[Crossref]

T. Vasko and I. V. Zozoulenko, “Conductivity of a graphene strip: width and gate voltage dependencies,” Appl. Phys. Lett. 97(9), 092115 (2010).
[Crossref]

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

2009 (4)

K. S. Kim, Y. Zhao, H. Jang, S. Y. Lee, J. M. Kim, K. S. Kim, J. H. Ahn, P. Kim, J. Y. Choi, and B. H. Hong, “Large-scale pattern growth of graphene films for stretchable transparent electrodes,” Nature 457(7230), 706–710 (2009).
[Crossref] [PubMed]

M. Jablan, H. Buljan, and M. Soljacic, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B 80(24), 245435 (2009).
[Crossref]

J. H. Huang, R. Chang, P. T. Leung, and D. P. Tsai, “Nonlinear dispersion relation for surface plasmons at a metal-Kerr medium interface,” Opt. Commun. 282(7), 1412–1415 (2009).
[Crossref]

B. Krauss, T. Lohmann, D. H. Chae, M. Haluska, K. V. Klitzing, and J. H. Smet, “Laser–induced disassembly of a graphene single crystal in a nano-crystalline network,” Phys. Rev. B 79(16), 165428 (2009).
[Crossref]

2008 (4)

P. N. Incze, Z. Osvath, K. Kamaras, and L. P. Biro, “Anomalies in thickness measurement of graphene and few layer graphite crystals by tapping mode atomic microscopy,” Carbon 46(11), 1435–1442 (2008).
[Crossref]

G. W. Hanson, “Dyadic Green’s function for an anisotropic non-local model of biased graphene,” IEEE Trans. Antenn. Propag. 56(3), 747–757 (2008).
[Crossref]

T. H. Isaac, W. L. Barnes, and E. Hendry, “Determining the terahertz optical properties of subwavelength films using semiconductor surface plasmons,” Appl. Phys. Lett. 93(24), 241115 (2008).
[Crossref]

V. Dubikovskiy, D. J. Hagan, and E. W. Van Stryland, “Large nonlinear refraction in InSb at 10and the effect of Auger recombination,” J. Opt. Soc. Am. B 25(2), 223–235 (2008).
[Crossref]

2007 (1)

A. J. Gallant, M. A. Kaliteevski, D. Wood, M. C. Petty, R. A. Abram, S. Brand, G. P. Swift, D. A. Zeze, and J. M. Chamberlain, “Passband filters for terahertz radiation based on dual metallic photonic structures,” Appl. Phys. Lett. 91(16), 161115 (2007).
[Crossref]

2005 (1)

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438(7065), 197–200 (2005).
[Crossref] [PubMed]

2004 (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,” Science 306(5696), 666–669 (2004).
[Crossref] [PubMed]

2003 (1)

1995 (1)

1993 (1)

1987 (1)

1978 (1)

D. A. B. Miller and M. H. Mozolowski, “Non-linear optical effects in InSb with a cw CO laser,” Opt. Lett. 27, 133 (1978).

Abram, R. A.

A. J. Gallant, M. A. Kaliteevski, D. Wood, M. C. Petty, R. A. Abram, S. Brand, G. P. Swift, D. A. Zeze, and J. M. Chamberlain, “Passband filters for terahertz radiation based on dual metallic photonic structures,” Appl. Phys. Lett. 91(16), 161115 (2007).
[Crossref]

Abrishamian, M. S.

H. Nasari and M. S. Abrishamian, “Nonlinear manipulation of surface Plasmon polaritons in graphene based Bragg reflector,” J. Lightwave Technol. 33(19), 4071–4078 (2015).
[Crossref]

H. Nasari and M. S. Abrishamian, “All-optical tunable notch filter by use of Kerr nonlinearity in the graphene microribbon array,” J. Opt. Soc. Am. B 31(7), 1691–1697 (2014).
[Crossref]

H. Nasari and M. S. Abrishamian, “Magnetically tunable focusing in a graded index planar lens based on graphene,” J. Opt. 16(10), 105502 (2014).
[Crossref]

H. Nasari and M. S. Abrishamian, “Electrically tunable graded index planar lens based on graphene,” J. Appl. Phys. 116(8), 083106 (2014).
[Crossref]

Ahn, J. H.

K. S. Kim, Y. Zhao, H. Jang, S. Y. Lee, J. M. Kim, K. S. Kim, J. H. Ahn, P. Kim, J. Y. Choi, and B. H. Hong, “Large-scale pattern growth of graphene films for stretchable transparent electrodes,” Nature 457(7230), 706–710 (2009).
[Crossref] [PubMed]

Anderson, T.

M. Currie, J. D. Caldwell, F. J. Bezares, J. Robinson, T. Anderson, H. Chun, and M. Tadjer, “Quantifying pulsed laser induced damage to graphene,” Appl. Phys. Lett. 99(21), 211909 (2011).
[Crossref]

Andryieuski, A.

I. Khromova, A. Andryieuski, and A. Lavrinenko, “Ultrasensitive terahertz/infrared waveguide modulators based on multilayer graphene metamaterials,” Laser Photonics Rev. 8(6), 916–923 (2014).
[Crossref]

A. Andryieuski and A. V. Lavrinenko, “Graphene metamaterials based tunable terahertz absorber: effective surface conductivity approach,” Opt. Express 21(7), 9144–9155 (2013).
[Crossref] [PubMed]

Antonopoulos, C. S.

G. D. Bouzianas, N. V. Kantartzis, C. S. Antonopoulos, and T. D. Tsiboukis, “Optimal modeling of infinite graphene sheets via a class of generalized FDTD schemes,” IEEE Trans. Magn. 48(2), 379–382 (2012).
[Crossref]

Bao, Q.

Q. Bao and K. P. Loh, “Graphene photonics, plasmonics, and broadband optoelectronic devices,” ACS Nano 6(5), 3677–3694 (2012).
[Crossref] [PubMed]

Barnes, W. L.

T. H. Isaac, W. L. Barnes, and E. Hendry, “Determining the terahertz optical properties of subwavelength films using semiconductor surface plasmons,” Appl. Phys. Lett. 93(24), 241115 (2008).
[Crossref]

Beck, M.

Berini, P.

A. C. Lesina, A. Vaccari, P. Berini, and L. Ramunno, “On the convergence and accuracy of the FDTD method for nanoplasmonics,” Opt. Express 23(8), 10481–10497 (2015).
[Crossref] [PubMed]

B. G. Ghamsari, A. Olivieri, F. Variola, and P. Berini, “Frequency Pulling and Lineshape Broadening in Graphene Raman Spectra by Resonant Stokes Surface Plasmon Polaritons,” Phys. Rev. 91(20), 201408 (2015).
[Crossref]

B. G. Ghamsari, A. Olivieri, F. Variola, and P. Berini, “Enhanced Raman scattering in graphene by plasmonic resonant Stokes emission,” Nanophotonics 3(6), 363–371 (2014).
[Crossref]

Bezares, F. J.

M. Currie, J. D. Caldwell, F. J. Bezares, J. Robinson, T. Anderson, H. Chun, and M. Tadjer, “Quantifying pulsed laser induced damage to graphene,” Appl. Phys. Lett. 99(21), 211909 (2011).
[Crossref]

Biro, L. P.

P. N. Incze, Z. Osvath, K. Kamaras, and L. P. Biro, “Anomalies in thickness measurement of graphene and few layer graphite crystals by tapping mode atomic microscopy,” Carbon 46(11), 1435–1442 (2008).
[Crossref]

Blanchard, F.

H. Hirori, A. Doi, F. Blanchard, and K. Tanaka, “Single-cycle terahertz pulses with amplitude exceeding 1MV/cm generated by optical rectification in LiNbO3,” Appl. Phys. Lett. 98(9), 091106 (2011).
[Crossref]

Bludov, Y. V.

N. M. R. Peres, Y. V. Bludov, J. E. Santos, A. P. Jauho, and M. I. Vasilevskiy, “Optical bistability of graphene in the terahertz range,” Phys. Rev. B 90(12), 125425 (2014).
[Crossref]

Y. V. Bludov, D. A. Smirnova, Y. S. Kivshar, N. M. R. Peres, and M. I. Vasilevskiy, “Nonlinear TE polarized surface polaritons on graphene,” Phys. Rev. B 89(3), 035406 (2014).
[Crossref]

Y. V. Bludov, A. Ferreira, N. M. R. Peres, and M. I. Vasilevskiy, “A primer on surface plasmon-polaritons in graphene,” Int. J. Mod. Phys. B 27(10), 1341001 (2013).
[Crossref]

Y. V. Bludov, M. I. Vasilevskiy, and N. M. R. Peres, “Tunable graphene based polarizer,” J. Appl. Phys. 112(8), 084320 (2012).
[Crossref]

Boardman, A. D.

Boltasseva, A.

P. West, S. Ishii, G. Naik, N. Emani, V. Shalaev, and A. Boltasseva, “Searching for better plasmonic materials,” Laser Photonics Rev. 4(6), 795–808 (2010).
[Crossref]

Bonaccorso, F.

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

Bouzianas, G. D.

G. D. Bouzianas, N. V. Kantartzis, C. S. Antonopoulos, and T. D. Tsiboukis, “Optimal modeling of infinite graphene sheets via a class of generalized FDTD schemes,” IEEE Trans. Magn. 48(2), 379–382 (2012).
[Crossref]

Brand, S.

A. J. Gallant, M. A. Kaliteevski, D. Wood, M. C. Petty, R. A. Abram, S. Brand, G. P. Swift, D. A. Zeze, and J. M. Chamberlain, “Passband filters for terahertz radiation based on dual metallic photonic structures,” Appl. Phys. Lett. 91(16), 161115 (2007).
[Crossref]

Brodyanski, A.

P. Weis, J. L. Garcia-Pomar, M. Höh, B. Reinhard, A. Brodyanski, and M. Rahm, “Spectrally wide-band terahertz wave modulator based on optically tuned graphene,” ACS Nano 6(10), 9118–9124 (2012).
[Crossref] [PubMed]

Buljan, H.

M. Jablan, H. Buljan, and M. Soljacic, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B 80(24), 245435 (2009).
[Crossref]

Cai, W.

P. Liu, W. Cai, L. Wang, X. Zhang, and J. Xu, “Tunable terahertz optical antennas based on graphene ring structures,” Appl. Phys. Lett. 100(15), 153111 (2012).
[Crossref]

L. Wang, W. Cai, X. Zhang, and J. Xu, “Surface Plasmons at the interface between graphene and Kerr-type nonlinear media,” Opt. Lett. 37(13), 2730–2732 (2012).
[Crossref] [PubMed]

Cai, X.

X. Cai and J. Wei, “Optical nonlinearity characteristics of crystalline InSb semiconductor thin films,” J. Phys. D Appl. Phys. 46(43), 435101 (2013).
[Crossref]

Caldwell, J. D.

M. Currie, J. D. Caldwell, F. J. Bezares, J. Robinson, T. Anderson, H. Chun, and M. Tadjer, “Quantifying pulsed laser induced damage to graphene,” Appl. Phys. Lett. 99(21), 211909 (2011).
[Crossref]

Carrier, J. P.

J. S. G. Diaz and J. P. Carrier, “Propagation of hybrid transverse magnetic–transverse electric plasmons on magnetically biased graphene sheet,” J. Appl. Phys. 112(12), 124906 (2012).
[Crossref]

Chae, D. H.

B. Krauss, T. Lohmann, D. H. Chae, M. Haluska, K. V. Klitzing, and J. H. Smet, “Laser–induced disassembly of a graphene single crystal in a nano-crystalline network,” Phys. Rev. B 79(16), 165428 (2009).
[Crossref]

Chamberlain, J. M.

A. J. Gallant, M. A. Kaliteevski, D. Wood, M. C. Petty, R. A. Abram, S. Brand, G. P. Swift, D. A. Zeze, and J. M. Chamberlain, “Passband filters for terahertz radiation based on dual metallic photonic structures,” Appl. Phys. Lett. 91(16), 161115 (2007).
[Crossref]

Chang, D. E.

F. H. L. Koppens, D. E. Chang, and F. J. García de Abajo, “Graphene Plasmonics: A platform for strong light-matter interactions,” Nano Lett. 11(8), 3370–3377 (2011).
[Crossref] [PubMed]

Chang, R.

J. H. Huang, R. Chang, P. T. Leung, and D. P. Tsai, “Nonlinear dispersion relation for surface plasmons at a metal-Kerr medium interface,” Opt. Commun. 282(7), 1412–1415 (2009).
[Crossref]

Chen, Q.

Choi, C. G.

S. H. Lee, M. Choi, T. T. Kim, S. Lee, M. Liu, X. Yin, H. K. Choi, S. S. Lee, C. G. Choi, S. Y. Choi, X. Zhang, and B. Min, “Switching terahertz waves with gate-controlled active graphene metamaterials,” Nat. Mater. 11(11), 936–941 (2012).
[Crossref] [PubMed]

Choi, H. K.

S. H. Lee, M. Choi, T. T. Kim, S. Lee, M. Liu, X. Yin, H. K. Choi, S. S. Lee, C. G. Choi, S. Y. Choi, X. Zhang, and B. Min, “Switching terahertz waves with gate-controlled active graphene metamaterials,” Nat. Mater. 11(11), 936–941 (2012).
[Crossref] [PubMed]

Choi, J. Y.

K. S. Kim, Y. Zhao, H. Jang, S. Y. Lee, J. M. Kim, K. S. Kim, J. H. Ahn, P. Kim, J. Y. Choi, and B. H. Hong, “Large-scale pattern growth of graphene films for stretchable transparent electrodes,” Nature 457(7230), 706–710 (2009).
[Crossref] [PubMed]

Choi, M.

S. H. Lee, M. Choi, T. T. Kim, S. Lee, M. Liu, X. Yin, H. K. Choi, S. S. Lee, C. G. Choi, S. Y. Choi, X. Zhang, and B. Min, “Switching terahertz waves with gate-controlled active graphene metamaterials,” Nat. Mater. 11(11), 936–941 (2012).
[Crossref] [PubMed]

Choi, S. Y.

S. H. Lee, M. Choi, T. T. Kim, S. Lee, M. Liu, X. Yin, H. K. Choi, S. S. Lee, C. G. Choi, S. Y. Choi, X. Zhang, and B. Min, “Switching terahertz waves with gate-controlled active graphene metamaterials,” Nat. Mater. 11(11), 936–941 (2012).
[Crossref] [PubMed]

Chun, H.

M. Currie, J. D. Caldwell, F. J. Bezares, J. Robinson, T. Anderson, H. Chun, and M. Tadjer, “Quantifying pulsed laser induced damage to graphene,” Appl. Phys. Lett. 99(21), 211909 (2011).
[Crossref]

Ciattoni, A.

Columbo, L.

Cormode, D.

A. Roberts, D. Cormode, C. Reynolds, T. N. Illige, B. J. Leroy, and A. Sandhu, “Response of graphene to femtosecond high intensity laser irradiation,” Appl. Phys. Lett. 99(5), 051912 (2011).
[Crossref]

Currie, M.

M. Currie, J. D. Caldwell, F. J. Bezares, J. Robinson, T. Anderson, H. Chun, and M. Tadjer, “Quantifying pulsed laser induced damage to graphene,” Appl. Phys. Lett. 99(21), 211909 (2011).
[Crossref]

Dekorsy, T.

Demsar, J.

Diaz, J. S. G.

J. S. G. Diaz and J. P. Carrier, “Propagation of hybrid transverse magnetic–transverse electric plasmons on magnetically biased graphene sheet,” J. Appl. Phys. 112(12), 124906 (2012).
[Crossref]

Doi, A.

H. Hirori, A. Doi, F. Blanchard, and K. Tanaka, “Single-cycle terahertz pulses with amplitude exceeding 1MV/cm generated by optical rectification in LiNbO3,” Appl. Phys. Lett. 98(9), 091106 (2011).
[Crossref]

Dubikovskiy, V.

Dubonos, S. V.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438(7065), 197–200 (2005).
[Crossref] [PubMed]

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(5696), 666–669 (2004).
[Crossref] [PubMed]

Emani, N.

P. West, S. Ishii, G. Naik, N. Emani, V. Shalaev, and A. Boltasseva, “Searching for better plasmonic materials,” Laser Photonics Rev. 4(6), 795–808 (2010).
[Crossref]

Engheta, N.

A. Vakil and N. Engheta, “Transformation optics using graphene,” Science 332(6035), 1291–1294 (2011).
[Crossref] [PubMed]

Esquius-Morote, M.

Fan, S.

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]

Ferreira, A.

Y. V. Bludov, A. Ferreira, N. M. R. Peres, and M. I. Vasilevskiy, “A primer on surface plasmon-polaritons in graphene,” Int. J. Mod. Phys. B 27(10), 1341001 (2013).
[Crossref]

Firsov, A. A.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438(7065), 197–200 (2005).
[Crossref] [PubMed]

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(5696), 666–669 (2004).
[Crossref] [PubMed]

Gallant, A. J.

A. J. Gallant, M. A. Kaliteevski, D. Wood, M. C. Petty, R. A. Abram, S. Brand, G. P. Swift, D. A. Zeze, and J. M. Chamberlain, “Passband filters for terahertz radiation based on dual metallic photonic structures,” Appl. Phys. Lett. 91(16), 161115 (2007).
[Crossref]

García de Abajo, F. J.

F. H. L. Koppens, D. E. Chang, and F. J. García de Abajo, “Graphene Plasmonics: A platform for strong light-matter interactions,” Nano Lett. 11(8), 3370–3377 (2011).
[Crossref] [PubMed]

Garcia-Pomar, J. L.

P. Weis, J. L. Garcia-Pomar, M. Höh, B. Reinhard, A. Brodyanski, and M. Rahm, “Spectrally wide-band terahertz wave modulator based on optically tuned graphene,” ACS Nano 6(10), 9118–9124 (2012).
[Crossref] [PubMed]

Garcia-Vidal, F. J.

S. G. Rodrigo, S. C. Palacios, F. J. Garcia-Vidal, and L. Martin-Moreno, “Metallic slit array filled with third order nonlinear media: Optical Kerr effect and Third Harmonic generation,” Phys. Rev. B 83(23), 235425 (2011).
[Crossref]

Geim, A. K.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438(7065), 197–200 (2005).
[Crossref] [PubMed]

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(5696), 666–669 (2004).
[Crossref] [PubMed]

Ghamsari, B. G.

B. G. Ghamsari, A. Olivieri, F. Variola, and P. Berini, “Frequency Pulling and Lineshape Broadening in Graphene Raman Spectra by Resonant Stokes Surface Plasmon Polaritons,” Phys. Rev. 91(20), 201408 (2015).
[Crossref]

B. G. Ghamsari, A. Olivieri, F. Variola, and P. Berini, “Enhanced Raman scattering in graphene by plasmonic resonant Stokes emission,” Nanophotonics 3(6), 363–371 (2014).
[Crossref]

Gómez-Díaz, J. S.

Gorbach, A. V.

A. Smirnova, A. V. Gorbach, I. V. Iorsh, I. V. Shadrivov, and Y. S. Kivshar, “Nonlinear switching with a graphene coupler,” Phys. Rev. B 88(4), 045443 (2013).
[Crossref]

Grigorenko, A. N.

A. N. Grigorenko, M. Polini, and K. S. Novoselov, “Graphene Plasmonics,” Nat. Photonics 6(11), 749–758 (2012).
[Crossref]

Grigorieva, I. V.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438(7065), 197–200 (2005).
[Crossref] [PubMed]

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(5696), 666–669 (2004).
[Crossref] [PubMed]

Hagan, D. J.

Hajian, H.

H. Hajian, A. Soltani-Vala, M. Kalafi, and P. T. Leung, “Surface Plasmons of a graphene parallel plate waveguide bounded by Kerr-type nonlinear media,” J. Appl. Phys. 115(8), 083104 (2014).
[Crossref]

Haluska, M.

B. Krauss, T. Lohmann, D. H. Chae, M. Haluska, K. V. Klitzing, and J. H. Smet, “Laser–induced disassembly of a graphene single crystal in a nano-crystalline network,” Phys. Rev. B 79(16), 165428 (2009).
[Crossref]

Hanson, G. W.

G. W. Hanson, “Dyadic Green’s function for an anisotropic non-local model of biased graphene,” IEEE Trans. Antenn. Propag. 56(3), 747–757 (2008).
[Crossref]

Hasan, T.

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

Heckenberg, N. R.

Helm, M.

Hendry, E.

T. H. Isaac, W. L. Barnes, and E. Hendry, “Determining the terahertz optical properties of subwavelength films using semiconductor surface plasmons,” Appl. Phys. Lett. 93(24), 241115 (2008).
[Crossref]

Hirori, H.

H. Hirori, A. Doi, F. Blanchard, and K. Tanaka, “Single-cycle terahertz pulses with amplitude exceeding 1MV/cm generated by optical rectification in LiNbO3,” Appl. Phys. Lett. 98(9), 091106 (2011).
[Crossref]

Höh, M.

P. Weis, J. L. Garcia-Pomar, M. Höh, B. Reinhard, A. Brodyanski, and M. Rahm, “Spectrally wide-band terahertz wave modulator based on optically tuned graphene,” ACS Nano 6(10), 9118–9124 (2012).
[Crossref] [PubMed]

Hong, B. H.

K. S. Kim, Y. Zhao, H. Jang, S. Y. Lee, J. M. Kim, K. S. Kim, J. H. Ahn, P. Kim, J. Y. Choi, and B. H. Hong, “Large-scale pattern growth of graphene films for stretchable transparent electrodes,” Nature 457(7230), 706–710 (2009).
[Crossref] [PubMed]

Hu, C.

Huang, J. H.

J. H. Huang, R. Chang, P. T. Leung, and D. P. Tsai, “Nonlinear dispersion relation for surface plasmons at a metal-Kerr medium interface,” Opt. Commun. 282(7), 1412–1415 (2009).
[Crossref]

Huang, Z. R.

H. J. Li, L. L. Wang, J. Q. Liu, Z. R. Huang, B. Sun, and X. Zhai, “Investigation of the graphene based planar plasmonic filters,” J. Appl. Phys. 103, 211104 (2014).

Illige, T. N.

A. Roberts, D. Cormode, C. Reynolds, T. N. Illige, B. J. Leroy, and A. Sandhu, “Response of graphene to femtosecond high intensity laser irradiation,” Appl. Phys. Lett. 99(5), 051912 (2011).
[Crossref]

Incze, P. N.

P. N. Incze, Z. Osvath, K. Kamaras, and L. P. Biro, “Anomalies in thickness measurement of graphene and few layer graphite crystals by tapping mode atomic microscopy,” Carbon 46(11), 1435–1442 (2008).
[Crossref]

Iorsh, I. V.

A. Smirnova, A. V. Gorbach, I. V. Iorsh, I. V. Shadrivov, and Y. S. Kivshar, “Nonlinear switching with a graphene coupler,” Phys. Rev. B 88(4), 045443 (2013).
[Crossref]

Isaac, T. H.

T. H. Isaac, W. L. Barnes, and E. Hendry, “Determining the terahertz optical properties of subwavelength films using semiconductor surface plasmons,” Appl. Phys. Lett. 93(24), 241115 (2008).
[Crossref]

Ishii, S.

P. West, S. Ishii, G. Naik, N. Emani, V. Shalaev, and A. Boltasseva, “Searching for better plasmonic materials,” Laser Photonics Rev. 4(6), 795–808 (2010).
[Crossref]

Jablan, M.

M. Jablan, H. Buljan, and M. Soljacic, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B 80(24), 245435 (2009).
[Crossref]

Jang, H.

K. S. Kim, Y. Zhao, H. Jang, S. Y. Lee, J. M. Kim, K. S. Kim, J. H. Ahn, P. Kim, J. Y. Choi, and B. H. Hong, “Large-scale pattern growth of graphene films for stretchable transparent electrodes,” Nature 457(7230), 706–710 (2009).
[Crossref] [PubMed]

Jauho, A. P.

N. M. R. Peres, Y. V. Bludov, J. E. Santos, A. P. Jauho, and M. I. Vasilevskiy, “Optical bistability of graphene in the terahertz range,” Phys. Rev. B 90(12), 125425 (2014).
[Crossref]

Jiang, D.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438(7065), 197–200 (2005).
[Crossref] [PubMed]

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(5696), 666–669 (2004).
[Crossref] [PubMed]

Joannopoulos, J. D.

Kalafi, M.

H. Hajian, A. Soltani-Vala, M. Kalafi, and P. T. Leung, “Surface Plasmons of a graphene parallel plate waveguide bounded by Kerr-type nonlinear media,” J. Appl. Phys. 115(8), 083104 (2014).
[Crossref]

Kaliteevski, M. A.

A. J. Gallant, M. A. Kaliteevski, D. Wood, M. C. Petty, R. A. Abram, S. Brand, G. P. Swift, D. A. Zeze, and J. M. Chamberlain, “Passband filters for terahertz radiation based on dual metallic photonic structures,” Appl. Phys. Lett. 91(16), 161115 (2007).
[Crossref]

Kamaras, K.

P. N. Incze, Z. Osvath, K. Kamaras, and L. P. Biro, “Anomalies in thickness measurement of graphene and few layer graphite crystals by tapping mode atomic microscopy,” Carbon 46(11), 1435–1442 (2008).
[Crossref]

Kantartzis, N. V.

G. D. Bouzianas, N. V. Kantartzis, C. S. Antonopoulos, and T. D. Tsiboukis, “Optimal modeling of infinite graphene sheets via a class of generalized FDTD schemes,” IEEE Trans. Magn. 48(2), 379–382 (2012).
[Crossref]

Katsnelson, M. I.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438(7065), 197–200 (2005).
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Figures (14)

Fig. 1
Fig. 1

(a) Schematic representation and (b) side view of the structure of interest.

Fig. 2
Fig. 2

FDTD-calculated transmittance and reflectance of SPPs propagating along the structure of Fig. 1 with L = 1100 nm, μc = 0.1 eV and d = 200 nm.

Fig. 3
Fig. 3

(a) Graphene Fermi level vs. gate voltage for different thicknesses of silicon dioxide. (b) Real part of the effective mode index of propagating SPPs as a function of frequency with the relative permittivity of the surrounding media and Fermi level of graphene as parameters.

Fig. 4
Fig. 4

(a) Spatial distribution of Ez in the x-z plane in the steady-state case for a suspended graphene sheet at the frequency of 5 THz and μc = 0.2 eV. Comparison of λspp extracted from the subcell FDTD results and (14): (b) as a function of the graphene Fermi level at the frequency of 5 THz; and (c) as a function of frequency at μc = 0.1 eV.

Fig. 5
Fig. 5

(a) Tunability of the proposed band-pass filter by altering the graphene Fermi level for the case of L = 1100 nm and d = 200 nm (structure depicted in Fig. 1(a)). (b) Spatial distribution of Ex in the x-z plane in the steady-state case at 4.88 THz for L = 1100 nm and d = 200 nm for two values of graphene Fermi level: μc = 0.1 and 0.16 eV.

Fig. 6
Fig. 6

(a) Frequency and (b) quality factor of the first resonant mode vs graphene Fermi level for the results of Fig. 5.

Fig. 7
Fig. 7

(a) Transmittance of the band-pass filter for μc = 0.15 eV, d = 200 nm and different resonator lengths (structure depicted in Fig. 1(a)). (b) Resonant frequency and (c) quality factor of the first resonant mode vs. resonator length for the results of Part (a).

Fig. 8
Fig. 8

(a)Transmittance of the band-pass filter with μc = 0.1 eV, L = 1100 nm, d = 200 nm and different values of the relative permittivity of the insulating layer below graphene. (b) Resonant frequency and (c) quality factor of the first resonant mode vs. relative permittivity of the insulating layer below graphene in Part (a).

Fig. 9
Fig. 9

(a) Intensity dependence of the guided SPP wavelength along graphene on a Kerr nonlinear substrate. The inset shows a sketch of the structure. (b) Spatial distribution of Ez in the x-z plane in the linear and nonlinear regimes.

Fig. 10
Fig. 10

(a) FDTD-calculated transmittance spectra for different values of incident SPP intensity due to a Kerr nonlinearity in the substrate. (b) Extinction ratio vs. frequency for an intensity of 0.72 MW/cm2. The inset shows a schematic of the structure investigated.

Fig. 11
Fig. 11

(a) FDTD-calculated transmittance spectra for different values of incident SPP intensity due to a Kerr nonlinearity in the top cladding. (b) Extinction ratio vs. frequency for an intensity of 0.95 MW/cm2. The inset shows a schematic of the structure investigated.

Fig. 12
Fig. 12

FDTD-calculated transmittance spectra for different values of pump intensity, in the XPM configuration, due to a Kerr nonlinearity in the substrate, near (a) the first and (b) second resonant modes. The insets show a schematic of the structure investigated. (c) Extinction ratio vs. frequency around the first and second resonant modes for a pump intensity of 96.8 KW/cm2. (d) First and second resonant frequencies vs. pump intensity.

Fig. 13
Fig. 13

FDTD-calculated spatial distribution of Hy in the x-z plane at steady-state for the structure of Fig. 12, near (a) the first and (b) second resonant modes, in the linear and nonlinear regimes, demonstrating switching.

Fig. 14
Fig. 14

FDTD-calculated transmittance spectra for different values of pump intensity, in the XPM configuration, due to a Kerr nonlinearity in the top cladding, near (a) the first and (b) second resonant modes. The insets show a schematic of the structure investigated. (c) Extinction ratio vs. frequency near the first and second resonant modes for a pump intensity of 107.1 KW/cm2. (d) First and second resonant frequencies vs. pump intensity.

Equations (15)

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σ intra ( ω, μ c ,Γ,T )=j e 2 K B T π 2 ( ωj2Γ ) × ( μ c / K B T+2ln( exp( μ c / K T B )+1 ) )
σ inter ( ω, μ c ,Γ,T )=j e 2 4π ln[ 2| μ c |( ωj2Γ ) 2| μ c |+( ωj2Γ ) ].
2Re( β )L+2 φ r =2mπ
χ eff,g ( 1 ) =F/ ( jωZ ω 2 G ) ,
F= e 2 K B T aε Δ 0 ( μ c / K B T+2ln( exp( μ c / K B T )+1 ) ),
G=π 2 ,
Z=2π 2 Γ
D= ε 0 ε E+ P L + P NL D
G 2 P L t 2 +Z P L t =FE( t ),
P NL D ( t )= ε 0 χ eff,D ( 3 ) E 3 ( t )
E n+1 = D n+1 a L P L n b L P L n1 c L E n ε 0 ε + ε 0 χ eff,D ( 3 ) ( E n ) 2
n s = V g ε 0 ε r / eh,
n s = 2 π 2 v F 2 0 ε[ f d ( ε ) f d ( ε+2 μ c ) ] dε
ε r1 β 2 ε r1 k 0 2 + ε r2 β 2 ε r2 k 0 2 = jσ( ω ) ω ε 0
β k 0 jc ε 0 σ [ ε r1 ( ε r1 + ε l 3 ε r1 ε l ) 1/2 + ε r2 ]

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