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Effect of nonlinear cap layer on TM-polarized surface waves in a graphene-based photonic crystal

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Abstract

In this paper, we investigated the effect of nonlinear cap layer and the chemical potential of the graphene on the p-polarized surface waves (SWs) in a one-dimensional graphene-based photonic crystal (GBPC). Three different cases were considered for the dielectric tensor of the nonlinear cap layer: (1) perpendicular uniaxial approximation, (2) parallel uniaxial approximation and (3) generic case. The results of the study indicated that the effect of nonlinear cap layer on TM SWs may be neglected due to the perpendicular approximation. On the other hand, in parallel approximation as well as generic form of dielectric function, the frequency of the TM SWs within the graphene-induced band gap (GIPBG) may be controlled by the nonlinear cap layer and the chemical potential of the graphene. Moreover, according to the results, in the GIPBG of GBPC with self-defocusing cap layer, enhancing chemical potential and optical nonlinearity shift the frequency of the SWs in the same direction. However, with respect to the self-focusing cap layer, enhancing chemical potential and optical nonlinearity shift the frequency of the SWs in the opposite direction. Consequently, by adjusting the chemical potential in the self-defocusing cap layer, the tunability range of the SW frequency may be extended and in the case of self-focusing, optical nonlinear effects may be eliminated.

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References

  • Abramowitz, M., Stegun, A.S.: Handbook of Mathematical Function. Dover, New York (1972)

    MATH  Google Scholar 

  • Berman, O.L., Kezerashvili, R.Y.: Graphene-based one-dimensional photonic crystal. J. Phys. Condens. Matter 24, 015305 (2012)

    Article  ADS  Google Scholar 

  • Berman, O.L., Bayko, V.S., Kezerashvili, R.Y., Kolesnikov, A.A., Lozovik, Y.E.: Graphene-based photonic crystal. Phys. Lett. A 374, 4784-4786 (2010)

    Article  ADS  Google Scholar 

  • Bludov, YuV, Peres, N.M.R., Vasilevskiy, M.I.: Graphene-based polaritonic crystal. Phys. Rev. B 85, 245409 (2012)

    Article  ADS  Google Scholar 

  • Bludov, Y.V., Smirnova, D.A., Kivshar, Y.S., Peres, N.M.R., Vasilevskiy, M.I.: Nonlinear TE-polarized surface polaritons on graphene. Phys. Rev. B 89, 035406 (2014)

    Article  ADS  Google Scholar 

  • Boardman, A.D., Maradudin, A.A., Stegman, G.I., Twardowski, T., Wright, E.M.: Exact theory of nonlinear p-polarized optical waves. Phys. Rev. A 35, 1159–1164 (1987)

    Article  ADS  Google Scholar 

  • Bonaccorso, F., Sun, Z., Hasan, T., Ferrari, A.C.: Graphene photonics and optoelectronics. Nat. Photon. 4, 611–615 (2010)

    Article  ADS  Google Scholar 

  • Depine, R.A.: Graphene Optics: Electromagnetic Solution of Canonical Problems. Morgan & Claypool Publishers, San Rafael (2016)

    Book  Google Scholar 

  • Eyni, Z., Milanchian, K.: Controlling TE surface waves by self-defocusing cap layer in graphene based photonic crystal. J. Nanophoton. 12(3), 036007 (2018)

    Article  ADS  Google Scholar 

  • Eyni, Z., Namdar, A., Roshan Entezar, S., Tajalli, H.: Dispersion properties of nonlinear surface waves in one-dimensional photonic crystals with a nonlinear self-defocusing cap layer of left-handed metamaterial. J. Opt. Soc. Am. B 27, 2116–2121 (2010a)

    Article  ADS  Google Scholar 

  • Eyni, Z., Roshan Entezar, S., Namdar, A., Tajalli, H.: Tamm states of a nonlinear slab sandwiched between a uniform medium and a one-dimensional photonic crystal. PIERL 18, 115–124 (2010b)

    Google Scholar 

  • Falkovsky, L., Pershoguba, S.: Optical far-infrared properties of a graphene monolayer and multilayer. Phys. Rev. B 76(15), 153410 (2007)

    Article  ADS  Google Scholar 

  • Farmer, A., Friedli, A.C., Wright, S.M., Robertson, W.M.: Biosensing using surface electromagnetic waves in photonic band gap multilayers. Sens. Actuators B: Chem. 173, 79–84 (2012)

    Article  Google Scholar 

  • Foresi, J., Villeneuve, P.R., Ferrera, J., Thoen, E., Steinmeyer, G., Fan, S., Joannopoulos, J., Kimerling, K., Smith, H.I., Ippen, E.: Photonic-bandgap microcavities in optical waveguides. Nature 390, 143–145 (1997)

    Article  ADS  Google Scholar 

  • Gómez-Díaz, J.S., Perruisseau-Carrier, J.: Graphene-based plasmonic switches at near infrared frequencies. Opt. Express 21, 15490–1554 (2013)

    Article  ADS  Google Scholar 

  • Gong, Q., Hu, X.: Photonic Crystals: Principles and Applications. CRC Press, Boca Raton (2013)

    Google Scholar 

  • Hajian, H., Soltani-Vala, A., Kalafi, M., Leung, P.T.: Surface plasmons of a graphene parallel plate wavegude bounded by Kerr-type nonlinear media. J. Appl. Phys. 115, 083104 (2014)

    Article  ADS  Google Scholar 

  • Hajian, H., Rukhlenko, I.D., Leung, P.T., Caglayan, H., Ozbay, E.: Guided plasmon modes of a graphene-coated Kerr slab. Plasmonics 11, 735–741 (2016)

    Article  Google Scholar 

  • Joannopoulos, J.D., Johnson, S.G., Winn, J.N., Meade, R.D.: Photonic Crystals: Molding the Flow of Light. Princeton University Press, Princeton (2011)

    Book  MATH  Google Scholar 

  • Kaso, A., John, S.: Nonlinear Bloch waves in resonantly doped photonic crystals. Phys. Rev. E 74, 046611 (2006)

    Article  ADS  Google Scholar 

  • Kivshar, Y.S.: Nonlinear Tamm states and surface effects in periodic photonic structures. Laser Phys. Lett. 5, 703–713 (2008)

    Article  ADS  Google Scholar 

  • Li, Y., Qi, L., Yu, J., Chen, Z., Yao, Y., Liu, X.: One-dimensional multiband terahertz graphene photonic crystal filters. Opt. Mater. Express 7(4), 001228–001239 (2017)

    Article  ADS  Google Scholar 

  • Low, T., Avouris, P.: Graphene plasmonics for terahertz to mid-infrared applications. ACS Nano 8(2), 1086–1101 (2014)

    Article  Google Scholar 

  • Madani, A., Roshan Entezar, S.: Optical properties of one-dimensional photonic crystals containing graphene sheets. Physica B 431, 1–5 (2013)

    Article  ADS  Google Scholar 

  • Meade, R.D., Brommer, K.D., Rappe, A.M., Joannopoulos, J.D.: Electromagnetic Bloch waves at the surface of a photonic crystal. Phys. Rev. B. 44, 10961–10964 (1991)

    Article  ADS  Google Scholar 

  • Michelotti, F., Sinibaldi, A., Munzert, P., Danz, N., Descrovi, E.: Probing losses of dielectric multilayers by means of Bloch surface waves. Opt. Lett. 38, 616–618 (2013)

    Article  ADS  Google Scholar 

  • Mingaleev, S., Kivshar, Y.S.: Nonlinear photonic crystals toward all-optical technologies. Opt. Photon. News 13(7), 48–51 (2002)

    Article  ADS  Google Scholar 

  • Nair, R.R., Blake, P., Grigorenko, A.N., Novoselov, K.S., Booth, T.J., Stauber, T., Peres, N.M.R., Geim, A.K.: Fine structure constant defines visual transparency of grapheme. Science 320, 1308 (2008)

    Article  ADS  Google Scholar 

  • Namdar, A., Shadrivov, I.V., Kivshar, Y.S.: Excitation of backward Tamm states at an interface between a periodic photonic crystal and a left-handed metamaterial. Phys. Rev. A. 75, 053812 (2007)

    Article  ADS  Google Scholar 

  • Namdar, A., Roshan, E.S., Tajalli, H., Eyni, Z.: Backward nonlinear surface Tamm states in left-handed metamaterials. Opt. Express 16, 10543–10548 (2008)

    Article  ADS  Google Scholar 

  • Novoselov, K.S., Geim, A.K., Morozov, S.V., Jiang, D., Zhang, Y., Dubonos, S.V., Grigorieva, I.V., Firsov, A.A.: Electric field effect in atomically thin carbo filts. Science 306, 666–669 (2004)

    Article  ADS  Google Scholar 

  • Ogawa, S., Imada, M., Yoshimoto, S., Okano, M., Noda, S.: Control of light emission by 3D photonic crystals. Science 305, 227–229 (2004)

    Article  ADS  Google Scholar 

  • Qi, L., Liu, C.: Complex band structures of 1D anisotropic graphene photonic crystal. Photon. Res. 5(6), 543–551 (2017)

    Article  Google Scholar 

  • Rindorf, L., Jensen, J.B., Dufva, M., Pedersen, L.H., Hoiby, P.E., Bang, O.: Photonic crystal fiber long-period gratings for biochemical sensing. Opt. Express 14, 8224–8231 (2006)

    Article  ADS  Google Scholar 

  • Roshan Entezar, S.R., Namdar, A., Eyni, Z., Tajalli, H.: Nonlinear surface waves in one-dimensional photonic crystals containing left-handed metamaterials. Phys. Rev. A. 78, 023816 (2008)

    Article  ADS  Google Scholar 

  • Sinibaldi, A., Rizzo, R., Figliozzi, G., Descrovi, E., Danz, N., Munzert, P., Anopchenko, A., Michelotti, F.: A full ellipsometric approach to optical sensing with Bloch surface waves on photonic crystals. Opt. Express. 21, 23331–23344 (2013)

    Article  ADS  Google Scholar 

  • Soboleva, I.V., Romodina, M., Lyubin, E., Fedyanin, A.: Optical effects induced by Bloch surface waves in one-dimensional photonic crystals. Appl. Sci. 8, 127 (2018)

    Article  Google Scholar 

  • Yablonovitch, E.: Photonic band-gap structures. J. Opt. Soc. Am. B. 10, 283–295 (1993)

    Article  ADS  Google Scholar 

  • Yariv, A., Yeh, P.: Optical Waves in Layered Media. Wiley, New York (1988)

    Google Scholar 

  • Yeh, P., Yariv, A., Cho, A.Y.: Optical surface waves in periodic layered media. Appl. Phys. Lett. 32, 104–105 (1978)

    Article  ADS  Google Scholar 

  • Zhang, Y., Han, S., Zhang, S., Liu, P., Shi, Y.: High-Q and high-sensitivity photonic crystal cavity sensor. IEEE Photon. J. 7, 1–6 (2015)

    Google Scholar 

Download references

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  1. Department of Physics, Payame Noor University, PO Box, 19395-3697, Tehran, Iran

    Zahra Eyni & Karim Milanchian

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  1. Zahra Eyni
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  2. Karim Milanchian
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Correspondence to Zahra Eyni.

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Eyni, Z., Milanchian, K. Effect of nonlinear cap layer on TM-polarized surface waves in a graphene-based photonic crystal. Opt Quant Electron 52, 207 (2020). https://doi.org/10.1007/s11082-020-02301-z

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