Abstract

The efficient amplification and lasing of electromagnetic radiation at terahertz (THz) frequencies is a non-trivial task achieved mainly by quantum cascade laser configurations with limited tunability and narrowband functionality. There is a strong need for compact and efficient THz electromagnetic sources with a reconfigurable operation in a broad frequency range. Photoexcited graphene can act as the gain medium to produce coherent radiation at low THz frequencies, but its response is very weak due to its ultrathin thickness. In this work, we demonstrate an alternative design to achieve efficient tunable and compact THz amplifiers and lasers with broadband operation based on active THz hyperbolic metamaterials (HMM) designed by multiple stacked photoexcited graphene layers separated by thin dielectric sheets. The hyperbolic THz response of the proposed ultrathin active HMM is analytically and numerically studied and characterized. When the graphene-based HMM structure is periodically patterned, a broadband slow-wave propagation regime is identified, thanks to the hyperbolic dispersion. In this scenario, reconfigurable amplification of THz waves in a broad frequency range is obtained, which can be made tunable by varying the quasi-Fermi level of graphene. We demonstrate that the THz response of the presented tunable THz amplifiers or lasers is controlled by the incident optical pumping (photodoping) and the loaded dielectric materials in the HMM waveguide array, an interesting property that can have great potential for THz amplification, emission, and sensing applications.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2018 (2)

T. Low, P.-Y. Chen, and D. N. Basov, “Superluminal plasmons with resonant gain in population inverted bilayer graphene,” Phys. Rev. B 98(4), 041403 (2018).
[Crossref]

G. Alymov, V. Vyurkov, V. Ryzhii, A. Satou, and D. Svintsov, “Auger recombination in Dirac materials: A tangle of many-body effects,” Phys. Rev. B 97(20), 205411 (2018).
[Crossref]

2017 (3)

P.-Y. Chen, C. Argyropoulos, M. Farhat, and J. S. Gomez-Diaz, “Flatland plasmonics and nanophotonics based on graphene and beyond,” Nanophotonics 6(6), 1239–1262 (2017).
[Crossref]

B. Jin, T. Guo, and C. Argyropoulos, “Enhanced third harmonic generation with graphene metasurfaces,” J. Opt. 19(9), 094005 (2017).
[Crossref]

T. Gric and O. Hess, “Tunable surface waves at the interface separating different graphene-dielectric composite hyperbolic metamaterials,” Opt. Express 25(10), 11466–11476 (2017).
[Crossref] [PubMed]

2016 (8)

T. Li and J. B. Khurgin, “Hyperbolic metamaterials: beyond the effective medium theory,” Optica 3(12), 1388 (2016).
[Crossref]

T. Guo and C. Argyropoulos, “Broadband polarizers based on graphene metasurfaces,” Opt. Lett. 41(23), 5592–5595 (2016).
[Crossref] [PubMed]

J. M. Hamm, A. F. Page, J. Bravo-Abad, F. J. Garcia-Vidal, and O. Hess, “Nonequilibrium plasmon emission drives ultrafast carrier relaxation dynamics in photoexcited graphene,” Phys. Rev. B 93(4), 041408 (2016).
[Crossref]

P.-Y. Y. Chen and J. Jung, “PT Symmetry and Singularity-Enhanced Sensing Based on Photoexcited Graphene Metasurfaces,” Phys. Rev. Appl. 5(6), 064018 (2016).
[Crossref]

E. Malic, T. Winzer, F. Wendler, and A. Knorr, “Review on carrier multiplication in graphene,” Phys. Status Solidi 253(12), 2303–2310 (2016).
[Crossref]

Y.-C. Chang, C.-H. Liu, C.-H. Liu, S. Zhang, S. R. Marder, E. E. Narimanov, Z. Zhong, and T. B. Norris, “Realization of mid-infrared graphene hyperbolic metamaterials,” Nat. Commun. 7(1), 10568 (2016).
[Crossref] [PubMed]

M. Sakhdari, M. Hajizadegan, M. Farhat, and P.-Y. Chen, “Efficient, broadband and wide-angle hot-electron transduction using metal-semiconductor hyperbolic metamaterials,” Nano Energy 26, 371–381 (2016).
[Crossref]

P.-Y. Chen, M. Hajizadegan, M. Sakhdari, and A. Alù, “Giant Photoresponsivity of Midinfrared Hyperbolic Metamaterials in the Photon-Assisted-Tunneling Regime,” Phys. Rev. Appl. 5(4), 041001 (2016).
[Crossref]

2015 (4)

2014 (4)

P. Weis, J. L. Garcia-Pomar, and M. Rahm, “Towards loss compensated and lasing terahertz metamaterials based on optically pumped graphene,” Opt. Express 22(7), 8473–8489 (2014).
[Crossref] [PubMed]

D. Svintsov, V. Ryzhii, A. Satou, T. Otsuji, and V. Vyurkov, “Carrier-carrier scattering and negative dynamic conductivity in pumped graphene,” Opt. Express 22(17), 19873–19886 (2014).
[Crossref] [PubMed]

J. Zhou, A. F. Kaplan, L. Chen, and L. J. Guo, “Experiment and Theory of the Broadband Absorption by a Tapered Hyperbolic Metamaterial Array,” ACS Photonics 1(7), 618–624 (2014).
[Crossref]

D. Lu, J. J. Kan, E. E. Fullerton, and Z. Liu, “Enhancing spontaneous emission rates of molecules using nanopatterned multilayer hyperbolic metamaterials,” Nat. Nanotechnol. 9(1), 48–53 (2014).
[Crossref] [PubMed]

2013 (11)

A. Poddubny, I. Iorsh, P. Belov, and Y. Kivshar, “Hyperbolic metamaterials,” Nat. Photonics 7(12), 948–957 (2013).
[Crossref]

K. V. Sreekanth, A. De Luca, and G. Strangi, “Negative refraction in graphene-based hyperbolic metamaterials,” Appl. Phys. Lett. 103(2), 023107 (2013).
[Crossref]

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 Condens. Matter Mater. Phys. 87(7), 075416 (2013).
[Crossref]

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]

P.-Y. Chen, J. Soric, Y. R. Padooru, H. M. Bernety, A. B. Yakovlev, and A. Alù, “Nanostructured graphene metasurface for tunable terahertz cloaking,” New J. Phys. 15(12), 123029 (2013).
[Crossref]

P.-Y. Chen and A. Alu, “Terahertz Metamaterial Devices Based on Graphene Nanostructures,” IEEE Trans. Terahertz Sci. Technol. 3(6), 748–756 (2013).
[Crossref]

I. Gierz, J. C. Petersen, M. Mitrano, C. Cacho, I. C. E. Turcu, E. Springate, A. Stöhr, A. Köhler, U. Starke, and A. Cavalleri, “Snapshots of non-equilibrium Dirac carrier distributions in graphene,” Nat. Mater. 12(12), 1119–1124 (2013).
[Crossref] [PubMed]

T. Watanabe, T. Fukushima, Y. Yabe, S. A. Boubanga Tombet, A. Satou, A. A. Dubinov, V. Y. Aleshkin, V. Mitin, V. Ryzhii, and T. Otsuji, “The gain enhancement effect of surface plasmon polaritons on terahertz stimulated emission in optically pumped monolayer graphene,” New J. Phys. 15(7), 075003 (2013).
[Crossref]

T. Otsuji, T. Watanabe, S. A. Boubanga Tombet, A. Satou, W. M. Knap, V. V. Popov, M. Ryzhii, and V. Ryzhii, “Emission and Detection of Terahertz Radiation Using Two-Dimensional Electrons in III–V Semiconductors and Graphene,” IEEE Trans. Terahertz Sci. Technol. 3(1), 63–71 (2013).
[Crossref]

M. A. K. 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]

C. Argyropoulos, N. M. Estakhri, F. Monticone, and A. Alù, “Negative refraction, gain and nonlinear effects in hyperbolic metamaterials,” Opt. Express 21(12), 15037–15047 (2013).
[Crossref] [PubMed]

2012 (7)

O. Kidwai, S. V. Zhukovsky, and J. E. Sipe, “Effective-medium approach to planar multilayer hyperbolic metamaterials: Strengths and limitations,” Phys. Rev. A 85(5), 053842 (2012).
[Crossref]

A. Fallahi and J. Perruisseau-Carrier, “Design of tunable biperiodic graphene metasurfaces,” Phys. Rev. B Condens. Matter Mater. Phys. 86(19), 195408 (2012).
[Crossref]

V. V. Popov, O. V. Polischuk, A. R. Davoyan, V. Ryzhii, T. Otsuji, and M. S. Shur, “Plasmonic terahertz lasing in an array of graphene nanocavities,” Phys. Rev. B Condens. Matter Mater. Phys. 86(19), 195437 (2012).
[Crossref]

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

H. N. S. Krishnamoorthy, Z. Jacob, E. Narimanov, I. Kretzschmar, and V. M. Menon, “Topological transitions in metamaterials,” Science 336(6078), 205–209 (2012).
[Crossref] [PubMed]

C. Guclu, S. Campione, and F. Capolino, “Hyperbolic metamaterial as super absorber for scattered fields generated at its surface,” Phys. Rev. B Condens. Matter Mater. Phys. 86(20), 205130 (2012).
[Crossref]

Y. Guo, W. Newman, C. L. Cortes, and Z. Jacob, “Applications of Hyperbolic Metamaterial Substrates,” Adv. Optoelectron. 2012(1), 1–9 (2012).
[Crossref]

2011 (5)

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
[Crossref] [PubMed]

V. Ryzhii, M. Ryzhii, V. Mitin, and T. Otsuji, “Toward the creation of terahertz graphene injection laser,” J. Appl. Phys. 110(9), 094503 (2011).
[Crossref]

B. Zhang and T. Cui, “An ultrasensitive and low-cost graphene sensor based on layer-by-layer nano self-assembly,” Appl. Phys. Lett. 98(7), 073116 (2011).
[Crossref]

H. Jiang, “Chemical Preparation of Graphene-Based Nanomaterials and Their Applications in Chemical and Biological Sensors,” Small 7(17), 2413–2427 (2011).
[Crossref] [PubMed]

O. Kidwai, S. V. Zhukovsky, and J. E. Sipe, “Dipole radiation near hyperbolic metamaterials: applicability of effective-medium approximation,” Opt. Lett. 36(13), 2530–2532 (2011).
[Crossref] [PubMed]

2010 (2)

2009 (3)

K. T. Delaney, P. Rinke, and C. G. Van de Walle, “Auger recombination rates in nitrides from first principles,” Appl. Phys. Lett. 94(19), 191109 (2009).
[Crossref]

Y. Zhang, T.-T. Tang, C. Girit, Z. Hao, M. C. Martin, A. Zettl, M. F. Crommie, Y. R. Shen, and F. Wang, “Direct observation of a widely tunable bandgap in bilayer graphene,” Nature 459(7248), 820–823 (2009).
[Crossref] [PubMed]

A. V. Kabashin, P. Evans, S. Pastkovsky, W. Hendren, G. A. Wurtz, R. Atkinson, R. Pollard, V. A. Podolskiy, and A. V. Zayats, “Plasmonic nanorod metamaterials for biosensing,” Nat. Mater. 8(11), 867–871 (2009).
[Crossref] [PubMed]

2008 (1)

D. M. Basko, “Theory of resonant multiphonon Raman scattering in graphene,” Phys. Rev. B Condens. Matter Mater. Phys. 78(12), 125418 (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]

V. Ryzhii, M. Ryzhii, and T. Otsuji, “Negative dynamic conductivity of graphene with optical pumping,” J. Appl. Phys. 101(8), 083114 (2007).
[Crossref]

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, “Negative refraction in semiconductor metamaterials,” Nat. Mater. 6(12), 946–950 (2007).
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V. V. Popov, O. V. Polischuk, A. R. Davoyan, V. Ryzhii, T. Otsuji, and M. S. Shur, “Plasmonic terahertz lasing in an array of graphene nanocavities,” Phys. Rev. B Condens. Matter Mater. Phys. 86(19), 195437 (2012).
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Shadrivov, I. V.

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Stone, A. D.

Y. D. Chong, L. Ge, H. Cao, and A. D. Stone, “Coherent Perfect Absorbers: Time-Reversed Lasers,” Phys. Rev. Lett. 105(5), 053901 (2010).
[Crossref] [PubMed]

Strangi, G.

K. V. Sreekanth, A. De Luca, and G. Strangi, “Negative refraction in graphene-based hyperbolic metamaterials,” Appl. Phys. Lett. 103(2), 023107 (2013).
[Crossref]

Svintsov, D.

G. Alymov, V. Vyurkov, V. Ryzhii, A. Satou, and D. Svintsov, “Auger recombination in Dirac materials: A tangle of many-body effects,” Phys. Rev. B 97(20), 205411 (2018).
[Crossref]

D. Svintsov, V. Ryzhii, A. Satou, T. Otsuji, and V. Vyurkov, “Carrier-carrier scattering and negative dynamic conductivity in pumped graphene,” Opt. Express 22(17), 19873–19886 (2014).
[Crossref] [PubMed]

Tang, T.-T.

Y. Zhang, T.-T. Tang, C. Girit, Z. Hao, M. C. Martin, A. Zettl, M. F. Crommie, Y. R. Shen, and F. Wang, “Direct observation of a widely tunable bandgap in bilayer graphene,” Nature 459(7248), 820–823 (2009).
[Crossref] [PubMed]

Tonouchi, M.

M. Tonouchi, “Cutting-edge terahertz technology,” Nat. Photonics 1(2), 97–105 (2007).
[Crossref]

Turcu, I. C.

I. Gierz, M. Mitrano, J. C. Petersen, C. Cacho, I. C. Turcu, E. Springate, A. Stöhr, A. Köhler, U. Starke, and A. Cavalleri, “Population inversion in monolayer and bilayer graphene,” J. Phys. Condens. Matter 27(16), 164204 (2015).
[Crossref] [PubMed]

Turcu, I. C. E.

I. Gierz, J. C. Petersen, M. Mitrano, C. Cacho, I. C. E. Turcu, E. Springate, A. Stöhr, A. Köhler, U. Starke, and A. Cavalleri, “Snapshots of non-equilibrium Dirac carrier distributions in graphene,” Nat. Mater. 12(12), 1119–1124 (2013).
[Crossref] [PubMed]

Van de Walle, C. G.

K. T. Delaney, P. Rinke, and C. G. Van de Walle, “Auger recombination rates in nitrides from first principles,” Appl. Phys. Lett. 94(19), 191109 (2009).
[Crossref]

Varlamov, A. A.

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

Vitiello, M. S.

Vyurkov, V.

G. Alymov, V. Vyurkov, V. Ryzhii, A. Satou, and D. Svintsov, “Auger recombination in Dirac materials: A tangle of many-body effects,” Phys. Rev. B 97(20), 205411 (2018).
[Crossref]

D. Svintsov, V. Ryzhii, A. Satou, T. Otsuji, and V. Vyurkov, “Carrier-carrier scattering and negative dynamic conductivity in pumped graphene,” Opt. Express 22(17), 19873–19886 (2014).
[Crossref] [PubMed]

Wang, F.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
[Crossref] [PubMed]

Y. Zhang, T.-T. Tang, C. Girit, Z. Hao, M. C. Martin, A. Zettl, M. F. Crommie, Y. R. Shen, and F. Wang, “Direct observation of a widely tunable bandgap in bilayer graphene,” Nature 459(7248), 820–823 (2009).
[Crossref] [PubMed]

Wasserman, D.

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, “Negative refraction in semiconductor metamaterials,” Nat. Mater. 6(12), 946–950 (2007).
[Crossref] [PubMed]

Watanabe, T.

T. Watanabe, T. Fukushima, Y. Yabe, S. A. Boubanga Tombet, A. Satou, A. A. Dubinov, V. Y. Aleshkin, V. Mitin, V. Ryzhii, and T. Otsuji, “The gain enhancement effect of surface plasmon polaritons on terahertz stimulated emission in optically pumped monolayer graphene,” New J. Phys. 15(7), 075003 (2013).
[Crossref]

T. Otsuji, T. Watanabe, S. A. Boubanga Tombet, A. Satou, W. M. Knap, V. V. Popov, M. Ryzhii, and V. Ryzhii, “Emission and Detection of Terahertz Radiation Using Two-Dimensional Electrons in III–V Semiconductors and Graphene,” IEEE Trans. Terahertz Sci. Technol. 3(1), 63–71 (2013).
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Weis, P.

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E. Malic, T. Winzer, F. Wendler, and A. Knorr, “Review on carrier multiplication in graphene,” Phys. Status Solidi 253(12), 2303–2310 (2016).
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Williams, B.

Winzer, T.

E. Malic, T. Winzer, F. Wendler, and A. Knorr, “Review on carrier multiplication in graphene,” Phys. Status Solidi 253(12), 2303–2310 (2016).
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A. V. Kabashin, P. Evans, S. Pastkovsky, W. Hendren, G. A. Wurtz, R. Atkinson, R. Pollard, V. A. Podolskiy, and A. V. Zayats, “Plasmonic nanorod metamaterials for biosensing,” Nat. Mater. 8(11), 867–871 (2009).
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Yabe, Y.

T. Watanabe, T. Fukushima, Y. Yabe, S. A. Boubanga Tombet, A. Satou, A. A. Dubinov, V. Y. Aleshkin, V. Mitin, V. Ryzhii, and T. Otsuji, “The gain enhancement effect of surface plasmon polaritons on terahertz stimulated emission in optically pumped monolayer graphene,” New J. Phys. 15(7), 075003 (2013).
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Yakovlev, A. B.

P.-Y. Chen, J. Soric, Y. R. Padooru, H. M. Bernety, A. B. Yakovlev, and A. Alù, “Nanostructured graphene metasurface for tunable terahertz cloaking,” New J. Phys. 15(12), 123029 (2013).
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Zayats, A. V.

A. V. Kabashin, P. Evans, S. Pastkovsky, W. Hendren, G. A. Wurtz, R. Atkinson, R. Pollard, V. A. Podolskiy, and A. V. Zayats, “Plasmonic nanorod metamaterials for biosensing,” Nat. Mater. 8(11), 867–871 (2009).
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Zettl, A.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
[Crossref] [PubMed]

Y. Zhang, T.-T. Tang, C. Girit, Z. Hao, M. C. Martin, A. Zettl, M. F. Crommie, Y. R. Shen, and F. Wang, “Direct observation of a widely tunable bandgap in bilayer graphene,” Nature 459(7248), 820–823 (2009).
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Zhang, B.

B. Zhang and T. Cui, “An ultrasensitive and low-cost graphene sensor based on layer-by-layer nano self-assembly,” Appl. Phys. Lett. 98(7), 073116 (2011).
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Zhang, S.

Y.-C. Chang, C.-H. Liu, C.-H. Liu, S. Zhang, S. R. Marder, E. E. Narimanov, Z. Zhong, and T. B. Norris, “Realization of mid-infrared graphene hyperbolic metamaterials,” Nat. Commun. 7(1), 10568 (2016).
[Crossref] [PubMed]

Zhang, Y.

Y. Zhang, T.-T. Tang, C. Girit, Z. Hao, M. C. Martin, A. Zettl, M. F. Crommie, Y. R. Shen, and F. Wang, “Direct observation of a widely tunable bandgap in bilayer graphene,” Nature 459(7248), 820–823 (2009).
[Crossref] [PubMed]

Zhong, Z.

Y.-C. Chang, C.-H. Liu, C.-H. Liu, S. Zhang, S. R. Marder, E. E. Narimanov, Z. Zhong, and T. B. Norris, “Realization of mid-infrared graphene hyperbolic metamaterials,” Nat. Commun. 7(1), 10568 (2016).
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Zhou, J.

J. Zhou, A. F. Kaplan, L. Chen, and L. J. Guo, “Experiment and Theory of the Broadband Absorption by a Tapered Hyperbolic Metamaterial Array,” ACS Photonics 1(7), 618–624 (2014).
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Zhu, G.

Zhukovsky, S. V.

O. Kidwai, S. V. Zhukovsky, and J. E. Sipe, “Effective-medium approach to planar multilayer hyperbolic metamaterials: Strengths and limitations,” Phys. Rev. A 85(5), 053842 (2012).
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O. Kidwai, S. V. Zhukovsky, and J. E. Sipe, “Dipole radiation near hyperbolic metamaterials: applicability of effective-medium approximation,” Opt. Lett. 36(13), 2530–2532 (2011).
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ACS Photonics (1)

J. Zhou, A. F. Kaplan, L. Chen, and L. J. Guo, “Experiment and Theory of the Broadband Absorption by a Tapered Hyperbolic Metamaterial Array,” ACS Photonics 1(7), 618–624 (2014).
[Crossref]

Adv. Optoelectron. (1)

Y. Guo, W. Newman, C. L. Cortes, and Z. Jacob, “Applications of Hyperbolic Metamaterial Substrates,” Adv. Optoelectron. 2012(1), 1–9 (2012).
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Appl. Phys. Lett. (3)

K. V. Sreekanth, A. De Luca, and G. Strangi, “Negative refraction in graphene-based hyperbolic metamaterials,” Appl. Phys. Lett. 103(2), 023107 (2013).
[Crossref]

K. T. Delaney, P. Rinke, and C. G. Van de Walle, “Auger recombination rates in nitrides from first principles,” Appl. Phys. Lett. 94(19), 191109 (2009).
[Crossref]

B. Zhang and T. Cui, “An ultrasensitive and low-cost graphene sensor based on layer-by-layer nano self-assembly,” Appl. Phys. Lett. 98(7), 073116 (2011).
[Crossref]

Eur. Phys. J. B (1)

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

IEEE Trans. Terahertz Sci. Technol. (2)

T. Otsuji, T. Watanabe, S. A. Boubanga Tombet, A. Satou, W. M. Knap, V. V. Popov, M. Ryzhii, and V. Ryzhii, “Emission and Detection of Terahertz Radiation Using Two-Dimensional Electrons in III–V Semiconductors and Graphene,” IEEE Trans. Terahertz Sci. Technol. 3(1), 63–71 (2013).
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P.-Y. Chen and A. Alu, “Terahertz Metamaterial Devices Based on Graphene Nanostructures,” IEEE Trans. Terahertz Sci. Technol. 3(6), 748–756 (2013).
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V. Ryzhii, M. Ryzhii, and T. Otsuji, “Negative dynamic conductivity of graphene with optical pumping,” J. Appl. Phys. 101(8), 083114 (2007).
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V. Ryzhii, M. Ryzhii, V. Mitin, and T. Otsuji, “Toward the creation of terahertz graphene injection laser,” J. Appl. Phys. 110(9), 094503 (2011).
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J. Nanophotonics (1)

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).
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J. Opt. (1)

B. Jin, T. Guo, and C. Argyropoulos, “Enhanced third harmonic generation with graphene metasurfaces,” J. Opt. 19(9), 094005 (2017).
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J. Phys. Condens. Matter (1)

I. Gierz, M. Mitrano, J. C. Petersen, C. Cacho, I. C. Turcu, E. Springate, A. Stöhr, A. Köhler, U. Starke, and A. Cavalleri, “Population inversion in monolayer and bilayer graphene,” J. Phys. Condens. Matter 27(16), 164204 (2015).
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Nano Energy (1)

M. Sakhdari, M. Hajizadegan, M. Farhat, and P.-Y. Chen, “Efficient, broadband and wide-angle hot-electron transduction using metal-semiconductor hyperbolic metamaterials,” Nano Energy 26, 371–381 (2016).
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Nanophotonics (1)

P.-Y. Chen, C. Argyropoulos, M. Farhat, and J. S. Gomez-Diaz, “Flatland plasmonics and nanophotonics based on graphene and beyond,” Nanophotonics 6(6), 1239–1262 (2017).
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Nat. Commun. (1)

Y.-C. Chang, C.-H. Liu, C.-H. Liu, S. Zhang, S. R. Marder, E. E. Narimanov, Z. Zhong, and T. B. Norris, “Realization of mid-infrared graphene hyperbolic metamaterials,” Nat. Commun. 7(1), 10568 (2016).
[Crossref] [PubMed]

Nat. Mater. (4)

A. V. Kabashin, P. Evans, S. Pastkovsky, W. Hendren, G. A. Wurtz, R. Atkinson, R. Pollard, V. A. Podolskiy, and A. V. Zayats, “Plasmonic nanorod metamaterials for biosensing,” Nat. Mater. 8(11), 867–871 (2009).
[Crossref] [PubMed]

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, “Negative refraction in semiconductor metamaterials,” Nat. Mater. 6(12), 946–950 (2007).
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A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6(3), 183–191 (2007).
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I. Gierz, J. C. Petersen, M. Mitrano, C. Cacho, I. C. E. Turcu, E. Springate, A. Stöhr, A. Köhler, U. Starke, and A. Cavalleri, “Snapshots of non-equilibrium Dirac carrier distributions in graphene,” Nat. Mater. 12(12), 1119–1124 (2013).
[Crossref] [PubMed]

Nat. Nanotechnol. (2)

D. Lu, J. J. Kan, E. E. Fullerton, and Z. Liu, “Enhancing spontaneous emission rates of molecules using nanopatterned multilayer hyperbolic metamaterials,” Nat. Nanotechnol. 9(1), 48–53 (2014).
[Crossref] [PubMed]

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
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Nat. Photonics (3)

A. N. Grigorenko, M. Polini, and K. S. Novoselov, “Graphene plasmonics,” Nat. Photonics 6(11), 749–758 (2012).
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A. Poddubny, I. Iorsh, P. Belov, and Y. Kivshar, “Hyperbolic metamaterials,” Nat. Photonics 7(12), 948–957 (2013).
[Crossref]

M. Tonouchi, “Cutting-edge terahertz technology,” Nat. Photonics 1(2), 97–105 (2007).
[Crossref]

Nature (1)

Y. Zhang, T.-T. Tang, C. Girit, Z. Hao, M. C. Martin, A. Zettl, M. F. Crommie, Y. R. Shen, and F. Wang, “Direct observation of a widely tunable bandgap in bilayer graphene,” Nature 459(7248), 820–823 (2009).
[Crossref] [PubMed]

New J. Phys. (2)

P.-Y. Chen, J. Soric, Y. R. Padooru, H. M. Bernety, A. B. Yakovlev, and A. Alù, “Nanostructured graphene metasurface for tunable terahertz cloaking,” New J. Phys. 15(12), 123029 (2013).
[Crossref]

T. Watanabe, T. Fukushima, Y. Yabe, S. A. Boubanga Tombet, A. Satou, A. A. Dubinov, V. Y. Aleshkin, V. Mitin, V. Ryzhii, and T. Otsuji, “The gain enhancement effect of surface plasmon polaritons on terahertz stimulated emission in optically pumped monolayer graphene,” New J. Phys. 15(7), 075003 (2013).
[Crossref]

Opt. Express (7)

Opt. Lett. (3)

Opt. Mater. Express (1)

Optica (1)

Phys. Rev. A (1)

O. Kidwai, S. V. Zhukovsky, and J. E. Sipe, “Effective-medium approach to planar multilayer hyperbolic metamaterials: Strengths and limitations,” Phys. Rev. A 85(5), 053842 (2012).
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Phys. Rev. Appl. (2)

P.-Y. Chen, M. Hajizadegan, M. Sakhdari, and A. Alù, “Giant Photoresponsivity of Midinfrared Hyperbolic Metamaterials in the Photon-Assisted-Tunneling Regime,” Phys. Rev. Appl. 5(4), 041001 (2016).
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P.-Y. Y. Chen and J. Jung, “PT Symmetry and Singularity-Enhanced Sensing Based on Photoexcited Graphene Metasurfaces,” Phys. Rev. Appl. 5(6), 064018 (2016).
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Phys. Rev. B (3)

J. M. Hamm, A. F. Page, J. Bravo-Abad, F. J. Garcia-Vidal, and O. Hess, “Nonequilibrium plasmon emission drives ultrafast carrier relaxation dynamics in photoexcited graphene,” Phys. Rev. B 93(4), 041408 (2016).
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T. Low, P.-Y. Chen, and D. N. Basov, “Superluminal plasmons with resonant gain in population inverted bilayer graphene,” Phys. Rev. B 98(4), 041403 (2018).
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G. Alymov, V. Vyurkov, V. Ryzhii, A. Satou, and D. Svintsov, “Auger recombination in Dirac materials: A tangle of many-body effects,” Phys. Rev. B 97(20), 205411 (2018).
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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 Condens. Matter Mater. Phys. 87(7), 075416 (2013).
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V. V. Popov, O. V. Polischuk, A. R. Davoyan, V. Ryzhii, T. Otsuji, and M. S. Shur, “Plasmonic terahertz lasing in an array of graphene nanocavities,” Phys. Rev. B Condens. Matter Mater. Phys. 86(19), 195437 (2012).
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C. Guclu, S. Campione, and F. Capolino, “Hyperbolic metamaterial as super absorber for scattered fields generated at its surface,” Phys. Rev. B Condens. Matter Mater. Phys. 86(20), 205130 (2012).
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Phys. Rev. Lett. (1)

Y. D. Chong, L. Ge, H. Cao, and A. D. Stone, “Coherent Perfect Absorbers: Time-Reversed Lasers,” Phys. Rev. Lett. 105(5), 053901 (2010).
[Crossref] [PubMed]

Phys. Status Solidi (1)

E. Malic, T. Winzer, F. Wendler, and A. Knorr, “Review on carrier multiplication in graphene,” Phys. Status Solidi 253(12), 2303–2310 (2016).
[Crossref]

Science (1)

H. N. S. Krishnamoorthy, Z. Jacob, E. Narimanov, I. Kretzschmar, and V. M. Menon, “Topological transitions in metamaterials,” Science 336(6078), 205–209 (2012).
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H. Jiang, “Chemical Preparation of Graphene-Based Nanomaterials and Their Applications in Chemical and Biological Sensors,” Small 7(17), 2413–2427 (2011).
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Figures (8)

Fig. 1
Fig. 1 (a) Schematic of the terahertz gain coherent response by an optically pumped graphene monolayer. (b) Frequency dispersion of the real and imaginary parts of the graphene conductivity with (pumped) and without (passive) optical photoexcitation. Inset: Schematic of the optically pumped graphene process. (c) Computed reflectance and transmittance in dB versus frequency for a graphene monolayer with (pumped) and without (passive) optical photoexcitation under normal incident TM polarized wave excitation.
Fig. 2
Fig. 2 (a) Real and (b) imaginary parts of the effective transverse relative permittivity ε t = ε t j ε t of the pumped and unpumped graphene HMM multilayer structure with a schematic shown in the inset. The graphene layers are seperated by dielectric slabs with equal thicknesses d and permittivities ε d . (c) Computed reflectance and transmittance in dB versus frequency of the HMM based on active (pumped) and passive graphene layers under normal incident TM polarized wave excitation.
Fig. 3
Fig. 3 (a) The proposed patterned HMM structure composed of N = 10 patterned graphene sheets stacked between dielectric layers. P is the period of the device, W is the width of the air slots, and t is the thickness of each dielectric spacer layer. (b) Dispersion diagram of the proposed structure. In this case, the dimension parameters are P = 1.9 µm, W = 0.5 µm, t = 0.1 µm and the quasi-Fermi level of the pumped graphene is 50 meV.
Fig. 4
Fig. 4 (a) Reflectance and (b) transmittance in dB computed as a function of the incident frequency and quasi-Fermi level of the THz slow-wave HMM graphene structure shown in Fig. 3(a) with geometrical parameters P = 1.9 µm, W = 0.5 µm, and t = 0.1 µm.
Fig. 5
Fig. 5 (a) Transmission line model used to analyze the structure shown in Fig. 3(a). The source impedance is Z S = Z 0 , where Z 0 is the free space impedance, Z in is the input impedance, Z 1 is the characteristic impedance of the proposed HMM structure, β is the effective propagation constant, and d 1 is the total thickness of the proposed device. (b) Real and imaginary parts of the input impedance computed by the transmission line model. (c) Computed absolute values of the transfer matrix elements M 11 and M 22 . In all these cases, the quasi-Fermi level is fixed to 27 meV leading to the lasing point shown in Fig. 4.
Fig. 6
Fig. 6 (a) Simulation and analytical results of the computed gain coefficient in dB of the proposed slow-wave graphene HMM structure. (b) The absolute value of the M 22 coefficient as a function of the incident frequency and quasi-Fermi level. In both captions, the dimension parameters are fixed to P = 1.9 µm, W = 0.5 µm, t = 0.1 µm. The quasi-Fermi level of the pumped graphene is fixed to 50 meV in caption (a).
Fig. 7
Fig. 7 Contour plots of the gain in dB scale as a function of the (a) period, (b) air width, and (c) quasi-Fermi level versus the frequency of the incoming THz radiation. The graphene quasi-Fermi level is fixed to 50 meV in captions (a) and (b). The air width is fixed to W = 0.5 µm in caption (a). The period is fixed to P = 2.1 µm in caption (b). The parameters of the slow-wave graphene HMM structure are fixed to P = 1.9 µm, W = 0.5 µm in caption (c).
Fig. 8
Fig. 8 The lasing frequency as a function of the dielectric constant for the proposed active graphene-based HMM structure (a) embedded in different dielectric materials, and (b) covered with a very thin dielectric layer. Insets: The corresponding schematics of the proposed graphene-based HMM sensor.

Equations (5)

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σ=j q 2 π 2 1 ωj τ 1 [ 0 ε( f 1 (ε) ε f 2 (ε) ε )dε ]j q 2 π 2 (ωj τ 1 ) 0 f 2 ( ε ) f 1 (ε) (ωj τ 1 ) 2 4 ε 2 / 2 dε ,
σ= j q 2 k B T π 2 (ωj τ 1 ) ( E F k B T +2ln( e E F / ( k B T) +1)) j q 2 (ωj τ 1 ) π 2 0 f D (ε) f D (ε) (ωj τ 1 ) 2 4 ε 2 / 2 dε ,
tan[k' PW 2 ] ε z k'' k' tanh[k'' W 2 ]=0,
Z in = Z 1 Z 0 +i Z 1 tan(β d 1 ) Z 1 +i Z 0 tan(β d 1 ) ,
R= Z in Z 0 Z in + Z 0 ; T= 2 Z in Z in + Z 0 .