Abstract

The tunability of slow light in graphene-based hyperbolic metamaterial waveguide operating in SCLU telecom bands is investigated. For the first time it has been shown that proper design of a GHMM structure forming waveguide layer and the geometry of the waveguide itself allows stopped light to be obtained in an almost freely selected range of wavelengths within SCLU bands. In particular, the possibility of controlling light propagation in GHMM waveguides by external biasing has been presented. The change of external electric field enables the stop light of the selected wavelength as well as the control of a number of modes, which can be stopped, cut off or supported. Proposed GHMM waveguides could offer great opportunities in the field of integrated photonics that are compatible with CMOS technology, especially since such structures can be utilized as photonic memory cells, tunable optical buffers, delays, optical modulators etc.

© 2017 Optical Society of America

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2016 (3)

B. Janaszek, A. Tyszka-Zawadzka, and P. Szczepański, “Tunable graphene-based hyperbolic metamaterial operating in SCLU telecom bands,” Opt. Express 24(21), 24129–24136 (2016).
[Crossref] [PubMed]

S. Xiao, X. Zhu, B.-H. Li, and N. A. Mortensen, “Graphene-plasmon polaritons: From fundamental properties to potential applications,” Front. Phys. 11(2), 117801 (2016).
[Crossref]

H. Xu, L. Wu, X. Dai, Y. Gao, and Y. Xiang, “Tunable infrared plasmonic waveguides using graphene based hyperbolic metamaterials,” Optik-Int. J. Light Electron. Opt. 127(20), 9640–9646 (2016).
[Crossref]

2015 (6)

R. Ning, S. Liu, H. Zhang, B. Bian, and X. Kong, “Tunable absorption in graphene-based hyperbolic metamaterials for mid-infrared range,” Physica B 457, 144–148 (2015).
[Crossref]

B. Zhu, G. Ren, Y. Gao, Y. Yang, B. Wu, Y. Lian, and S. Jian, “Local field enhancement in infrared graphene-dielectric hyperbolic slot waveguides,” IEEE Photonics Technol. Lett. 27(3), 276–279 (2015).
[Crossref]

C. T. Phare, Y. H. D. Lee, J. Cardenas, and M. Lipson, “Graphene electro-optic modulator with 30 GHz bandwidth,” Nat. Photonics 9(8), 511–514 (2015).
[Crossref]

L. Ferrari, C. Wu, D. Lepage, X. Zhang, and Z. Liu, “Hyperbolic metamaterials and their applications,” Prog. Quantum Electron. 40, 1–40 (2015).
[Crossref]

B. Li, Y. He, and S. He, “Investigation of light trapping effect in hyperbolic metamaterial slow-light waveguides,” App. Phys. Exp. 8(8), 082601 (2015).
[Crossref]

A. D. Neira, G. A. Wurtz, and A. V. Zayats, “Superluminal and stopped light due to mode coupling in confined hyperbolic metamaterial waveguides,” Sci. Rep. 5, 17678 (2015).
[Crossref] [PubMed]

2014 (6)

S. Ishii, M. Y. Shalaginov, V. E. Babicheva, A. Boltasseva, and A. V. Kildishev, “Plasmonic waveguides cladded by hyperbolic metamaterials,” Opt. Lett. 39(16), 4663–4666 (2014).
[Crossref] [PubMed]

L. Zhang, Z. Zhang, C. Kang, B. Cheng, L. Chen, X. Yang, J. Wang, W. Li, and B. Wang, “Tunable bulk polaritons of graphene-based hyperbolic metamaterials,” Opt. Express 22(11), 14022–14030 (2014).
[Crossref] [PubMed]

Y. Xiang, J. Guo, X. Dai, S. Wen, and D. Tang, “Engineered surface Bloch waves in graphene-based hyperbolic metamaterials,” Opt. Express 22(3), 3054–3062 (2014).
[Crossref] [PubMed]

R. Ning, S. Liu, H. Zhang, B. Bian, and X. Kong, “A wide-angle broadband absorber in graphene-based hyperbolic metamaterials,” Eur. Phys. J. Appl. Phys. 68(2), 20401 (2014).
[Crossref]

K. L. Tsakmakidis, T. W. Pickering, J. M. Hamm, A. F. Page, and O. Hess, “Completely stopped and dispersionless light in plasmonic waveguides,” Phys. Rev. Lett. 112(16), 167401 (2014).
[Crossref] [PubMed]

W. Li, B. Chen, C. Meng, W. Fang, Y. Xiao, X. Li, Z. Hu, Y. Xu, L. Tong, H. Wang, W. Liu, J. Bao, and Y. R. Shen, “Ultrafast all-optical graphene modulator,” Nano Lett. 14(2), 955–959 (2014).
[Crossref] [PubMed]

2013 (8)

G. V. Naik, V. M. Shalaev, and A. Boltasseva, “Alternative plasmonic materials: beyond gold and silver,” Adv. Mater. 25(24), 3264–3294 (2013).
[Crossref] [PubMed]

V. P. Drachev, V. A. Podolskiy, and A. V. Kildishev, “Hyperbolic metamaterials: new physics behind a classical problem,” Opt. Express 21(12), 15048–15064 (2013).
[Crossref] [PubMed]

I. V. Iorsh, I. S. Mukhin, I. V. Shadrivov, P. A. Belov, and Y. S. Kivshar, “Hyperbolic metamaterials based on multilayer graphene structures,” Phys. Rev. B 87(7), 075416 (2013).
[Crossref]

M. A. Othman, C. Guclu, and F. Capolino, “Graphene-based tunable hyperbolic metamaterials and enhanced near-field absorption,” Opt. Express 21(6), 7614–7632 (2013).
[Crossref] [PubMed]

M. A. K. Othman, C. Guclu, and F. Capolino, “Graphene-dielectric composite metamaterials: evolution from elliptic to hyperbolic wavevector dispersion and the transverse epsilon-near-zero condition,” J. Nanophotonics 7(1), 073089 (2013).
[Crossref]

A. M. DaSilva, Y.-C. Chang, T. Norris, and A. H. MacDonald, “Enhancement of photonic density of states in finite graphene multilayers,” Phys. Rev. B 88(19), 195411 (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]

S. A. Taya and I. M. Qadoura, “Guided modes in slab waveguides with negative index cladding and substrate,” Optik (Stuttg.) 124(13), 1431–1436 (2013).
[Crossref]

2012 (4)

O. Hess, J. B. Pendry, S. A. Maier, R. F. Oulton, J. M. Hamm, and K. L. Tsakmakidis, “Active nanoplasmonic metamaterials,” Nat. Mater. 11(7), 573–584 (2012).
[Crossref] [PubMed]

Y. He, S. He, and X. Yang, “Optical field enhancement in nanoscale slot waveguides of hyperbolic metamaterials,” Opt. Lett. 37(14), 2907–2909 (2012).
[Crossref] [PubMed]

Y. Guo, W. Newman, C. L. Cortes, and Z. Jacob, “Applications of hyperbolic metamaterial substrates,” Adv. Optoelectron. 2012, 452502 (2012).
[Crossref]

R. Mroczyński and R. B. Beck, “Reliability issues of double gate dielectric stacks based on hafnium dioxide (HfO2) layers for non-volatile semiconductor memory (NVSM) applications,” Microelectron. Reliab. 52(1), 107–111 (2012).
[Crossref]

2010 (1)

W. T. Lu, Y. J. Huang, B. D. F. Casse, R. K. Banyal, and S. Sridhar, “Storing light in active optical waveguides with single-negative materials,” Appl. Phys. Lett. 96(21), 211112 (2010).
[Crossref] [PubMed]

2009 (2)

T. Jiang, J. Zhao, and Y. Feng, “Stopping light by an air waveguide with anisotropic metamaterial cladding,” Opt. Express 17(1), 170–177 (2009).
[Crossref] [PubMed]

B. Corcoran, C. Monat, C. Grillet, D. J. Moss, B. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Green light emission in silicon through slow-light enhanced third-harmonic generation in photonic-crystal waveguides,” Nat. Photonics 3(4), 206–210 (2009).
[Crossref]

2008 (2)

T. F. Krauss, “Why do we need slow light,” Nat. Photonics 2(8), 448–450 (2008).
[Crossref]

R. Mroczyński, N. Kwietniewski, M. Ćwil, P. Hoffmann, R. B. Beck, and A. Jakubowski, “Improvement of electro-physical properties of ultra-thin PECVD silicon oxynitride layers by high-temperature annealing,” Vacuum 82(10), 1013–1019 (2008).
[Crossref]

2007 (5)

L. A. Falkovsky and A. A. Varlamov, “Space-time dispersion of graphene conductivity,” Eur. Phys. J. B 56(4), 281–284 (2007).
[Crossref]

T. Baba and D. Mori, “Slow light engineering in photonic crystals,” J. Phys. D Appl. Phys. 40(9), 2659–2665 (2007).
[Crossref]

T. Krauss, “Slow light in photonic crystal waveguides,” J. Phys. D Appl. Phys. 40(9), 2666–2670 (2007).
[Crossref]

K. L. Tsakmakidis, A. D. Boardman, and O. Hess, “‘Trapped rainbow’ storage of light in metamaterials,” Nature 450(7168), 397–401 (2007).
[Crossref] [PubMed]

M. Sandtke and L. Kuipers, “Slow guided surface plasmons at telecom frequencies,” Nat. Photonics 1(10), 573–576 (2007).
[Crossref]

2006 (2)

K. L. Tsakmakidis, C. Hermann, A. Klaedtke, C. Jamois, and O. Hess, “Surface plasmon polaritons in generalized slab heterostructures with negative permittivity and permeability,” Phys. Rev. B 73(8), 085104 (2006).
[Crossref]

K. L. Tsakmakidis, A. Klaedtke, D. P. Aryal, C. Jamois, and O. Hess, “Sigle mode operation in the slow-light using oscillatory waves in generalized left-handed heterostructures,” Phys. Rev. Lett. 89(20), 201103 (2006).

2005 (4)

G. D’Aguanno, N. Mattiucci, M. Scalora, and M. J. Bloemer, “TE and TM guided modes in an air waveguide with negative-index-material cladding,” Phys. Rev. E 71(4), 046603 (2005).
[Crossref] [PubMed]

A. Karalis, E. Lidorikis, M. Ibanescu, J. D. Joannopoulos, and M. Soljacić, “Surface-plasmon-assisted guiding of broadband slow and subwavelength light in air,” Phys. Rev. Lett. 95(6), 063901 (2005).
[Crossref] [PubMed]

J. T. Mok and B. J. Eggleton, “Photonics: Expect more delays,” Nature 433(7028), 811–812 (2005).
[Crossref] [PubMed]

Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, “Active control of slow light on a chip with photonic crystal waveguides,” Nature 438(7064), 65–69 (2005).
[Crossref] [PubMed]

2003 (2)

M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, “Observation of ultraslow light propagation in a ruby crystal at room temperature,” Phys. Rev. Lett. 90(11), 113903 (2003).
[Crossref] [PubMed]

I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, “Guided modes in negative-refractive-index waveguides,” Phys. Rev. E.  67(5), 057602 (2003).
[Crossref] [PubMed]

2002 (1)

K. Inoue, N. Kawai, Y. Sugimoto, M. Carlsson, N. Ikeda, and K. Asakawa, “Observation of small group velocity in two-dimensional AlGaAs-based photonic crystal slabs,” Phys. Rev. B 65(12), 121308 (2002).
[Crossref]

2001 (2)

C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature 409(6819), 490–493 (2001).
[Crossref] [PubMed]

A. V. Turukhin, V. S. Sudarshanam, M. S. Shahriar, J. A. Musser, B. S. Ham, and P. R. Hemmer, “Observation of ultraslow and stored light pulses in a solid,” Phys. Rev. Lett. 88(2), 023602 (2001).
[Crossref] [PubMed]

1999 (1)

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 Metres per second in an ultracold atomic gas,” Nature 397(6720), 594–598 (1999).
[Crossref]

Al Sayem, A.

A. Al Sayem, A. Shahriar, M. R. C. Mahdy, and M. S. Rahman, “Control of reflection through epsilon near zero graphene based anisotropic metamaterial,” in Proceedings of IEEE Conference on Electrical and Computer Engineering (IEEE, 2014), pp. 812–815.
[Crossref]

A. Al Sayem, M. R. C. Mahdy, D. N. Hasan, and M. A. Matin, “Tunable slow light with graphene based hyperbolic metamaterial,” in Proceedings of IEEE Conference on Electrical and Computer Engineering (IEEE, 2014) pp. 230–233.
[Crossref]

Andryieuski, A.

Aryal, D. P.

K. L. Tsakmakidis, A. Klaedtke, D. P. Aryal, C. Jamois, and O. Hess, “Sigle mode operation in the slow-light using oscillatory waves in generalized left-handed heterostructures,” Phys. Rev. Lett. 89(20), 201103 (2006).

Asakawa, K.

K. Inoue, N. Kawai, Y. Sugimoto, M. Carlsson, N. Ikeda, and K. Asakawa, “Observation of small group velocity in two-dimensional AlGaAs-based photonic crystal slabs,” Phys. Rev. B 65(12), 121308 (2002).
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B. Corcoran, C. Monat, C. Grillet, D. J. Moss, B. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Green light emission in silicon through slow-light enhanced third-harmonic generation in photonic-crystal waveguides,” Nat. Photonics 3(4), 206–210 (2009).
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C. T. Phare, Y. H. D. Lee, J. Cardenas, and M. Lipson, “Graphene electro-optic modulator with 30 GHz bandwidth,” Nat. Photonics 9(8), 511–514 (2015).
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Opt. Express (7)

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S. A. Taya and I. M. Qadoura, “Guided modes in slab waveguides with negative index cladding and substrate,” Optik (Stuttg.) 124(13), 1431–1436 (2013).
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K. L. Tsakmakidis, C. Hermann, A. Klaedtke, C. Jamois, and O. Hess, “Surface plasmon polaritons in generalized slab heterostructures with negative permittivity and permeability,” Phys. Rev. B 73(8), 085104 (2006).
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Figures (7)

Fig. 1
Fig. 1 Scheme of (a) analyzed waveguide and (b) its effective representation.
Fig. 2
Fig. 2 Permittivity tensor components for boundary wavelengths of SCLU bands, λ = 1.46 μm and λ = 1.675 μm, as a function of gate voltage Vg and for different structure parameters (a) td = 8 nm, Ng = 4 and (b) td = 6 nm, Ng = 6.
Fig. 3
Fig. 3 Normalized propagation constant β/k0 of the fundamental mode TM0 as a function of normalized waveguide width W/λ for (a) different numbers of graphene layers Ng, and (b) various values of dielectric layer thickness td. Normalized power flow P as a function of normalized waveguide width W/λ for (c) different numbers of graphene layers Ng, and (d) various values of dielectric layer thickness td.
Fig. 4
Fig. 4 Slow light for GHMM waveguide propagation constant β as a function of waveguide width W for selected wavelengths from SCLU bands and different biasing voltage (a) Vg = 1 V and (b) Vg = 2 V.
Fig. 5
Fig. 5 Normalized propagation constant β/k0 of the fundamental mode TM0 as a function of normalized waveguide width W/λ for various values of gate voltage Vg.
Fig. 6
Fig. 6 Wavelength of stopped light as a function of biasing voltage.
Fig. 7
Fig. 7 Normalized propagation constant β/k0 as a function of normalized waveguide width W/λ for different orders of TM mode and different biasing voltage (a) Vg = 0.62 V, (b) Vg = 0.66 V, (c) Vg = 0.71 V and (d) Vg = 0.8 V.

Equations (7)

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ε=[ ε || 0 0 0 ε || 0 0 0 ε ],
ε || = t g ε g + t d ε d t g + t d , ε = ε g ε d ( t g + t d ) t g ε d + t d ε g ,
ε g =1j σ(ω, μ c ) ω ε o t g ,
σ(ω, μ c )= j4π q 2 k B T h 2 (ωj2τ) [ μ c k B T +2ln( e μ / k B T +1 ) ]+ j4π q 2 ( ωj2τ ) h 2 0 f D (ξ) f D (ξ) ( ωj2τ ) 2 16( πξ h ) dξ,
| μ c |= υ F π| a 0 ( V g V dirac ) | ,
tan( γ f W 2 )= γ 1 γ f ε ε 1       for even modes,
cot( γ f W 2 )= γ 1 γ f ε ε 1       for odd modes,

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