Abstract

We demonstrate numerically that one-dimensional metamaterials with a gain medium can exhibit a near-unity-refractive-index for TE-modes, which resembles the effect of electro-magnetically induced transparency. Our results are further supported by rigorous coupled wave analysis simulations. Additionally, we analyze the behavior of the modal gain and derive an approximate analytical solution of the dispersion equation that is superior to earlier solutions. Finally, a generalization to the case of ultralow refractive index has been considered.

© 2017 Optical Society of America

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References

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  1. M. Fleischhauer, A. Imamoglu, and J.P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005).
    [Crossref]
  2. S. Zhang, D.A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101, 047401 (2008).
    [Crossref] [PubMed]
  3. J. Mørk, P. Lunnemann, W. Xue, Y. Chen, P. Kaer, and T. R. Nielsen, “Slow and fast light in semiconductor waveguides,” Semicond. Sci. Technol. 25, 083002 (2010).
    [Crossref]
  4. Z. Zhu, X. Yang, J. Gu, J. Jiang, W. Yue, Z. Tian, M. Tonouchi, J. Han, and W. Zhang, “Broadband plasmon induced transparency in terahertz metamaterials,” Nanotechnology 24, 214003 (2013).
    [Crossref] [PubMed]
  5. Y. Yang, I.I. Kravchenko, D.P. Briggs, and J. Valentine, “All-dielectric metasurface analogue of electromagnetically induced transparency,” Nature Commun. 5, 5753 (2014).
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  6. S.G. Lee, S.Y. Jung, H.S. Kim, S. Lee, and J.M. Park, “Electromagnetically induced transparency based on guided-mode resonance,” Opt. Lett. 40, 4241–4244 (2015).
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    [Crossref]
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    [Crossref]
  10. G. Strangi, A. De Luca, S. Ravaine, M. Ferrie, and R. Bartolino, “Gain induced optical transparency in metamaterials,” Appl. Phys. Lett. 98, 251912 (2011).
    [Crossref]
  11. C. Du, Q. Jing, and Z. Hu, “Coupler-free transition from light to surface plasmon polariton,” Phys. Rev. A 91, 013817 (2015).
    [Crossref]
  12. Y.F. Huang, S. Chattopadhyay, Y.J. Jen, C.Y. Peng, T.A. Liu, Y.K. Hsu, C.L. Pan, H.C. Lo, C.H. Hsu, Y.H. Chang, C.S. Lee, K.H. Chen, and L.C. Chen, “Improved broadband and quasiomnidirectional anti-reflection properties with biomimetic silicon nanostructures,” Nature Nanotech. 2, 770–774 (2007).
    [Crossref]
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  14. B. Nistad and J. Skaar, “Causality and electromagnetic properties of active media,” Phys. Rev. E 78, 036603 (2007).
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    [Crossref]
  17. A.V. Chebykin, A.A. Orlov, C.R. Simovski, Yu.S. Kivshar, and P.A. Belov, “Nonlocal effective parameters of multilayered metal-dielectric metamaterials,” Phys. Rev. B 86, 115–420 (2012).
    [Crossref]
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    [Crossref]
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    [Crossref]
  22. L.A. Coldrene and S.W. Corzine, Diode Lasers and Photonic Integrated Circuits (Wiley, New York, 1995).
  23. A.A. Krokhin, J. Arriaga, L.N. Gumen, and V.P. Drachev, “High-frequency homogenization for layered hyperbolic metamaterials,” Phys. Rev. B 93, 075418 (2016).
    [Crossref]
  24. J. Elser, V.A. Podolskiy, I. Salakhutdinov, and I. Avrutsky, “Nonlocal effects in effective-medium response of nanolayered metamaterials,” Appl. Phys. Lett. 90, 191109 (2007).
    [Crossref]
  25. R.L. Chern, “Spatial dispersion and nonlocal effective permittivity for periodic layered metamaterials,” Opt. Express 21, 16514–16527 (2013).
    [Crossref] [PubMed]
  26. A.V. Goncharenko, V.U. Nazarov, and K.R. Chen, “Design of metamaterials with predetermined optical properties for broadband applications,” Proc. SPIE 8269, 82690Q (2012).
    [Crossref]

2017 (1)

2016 (4)

X. Chen and W. Fan, “Polarization-intensitive tunable multiple electromagnetically induced transparencies analogue in terahertz graphene metamaterial,” Opt. Mater. Express 6, 2607–2615 (2016).
[Crossref]

Z. Wei, X. Li, N. Zhong, X. Tan, X. Zhang, H. Liu, H. Meng, and R. Liang, “Analogue electromagnetically induced transparency based on low-loss metamaterial and its application in nanosensor and slow-light device,” Plasmonics 12, 641–647 (2016).
[Crossref]

T.G. Mackay and A. Lakhtakia, “On the propagation of Voight waves in energetically active materials,” Eur. J. Phys. 37, 064002 (2016).
[Crossref]

A.A. Krokhin, J. Arriaga, L.N. Gumen, and V.P. Drachev, “High-frequency homogenization for layered hyperbolic metamaterials,” Phys. Rev. B 93, 075418 (2016).
[Crossref]

2015 (4)

2014 (2)

Y. Yang, I.I. Kravchenko, D.P. Briggs, and J. Valentine, “All-dielectric metasurface analogue of electromagnetically induced transparency,” Nature Commun. 5, 5753 (2014).
[Crossref]

A.A. Zyablovsky, A.P. Vinogradov, A.A. Pukhov, A.V. Dorofeenko, and A.A. Lisyansky, “PT-symmetry in optics,” Physics-Uspekhi 57, 1063–1082 (2014).
[Crossref]

2013 (2)

Z. Zhu, X. Yang, J. Gu, J. Jiang, W. Yue, Z. Tian, M. Tonouchi, J. Han, and W. Zhang, “Broadband plasmon induced transparency in terahertz metamaterials,” Nanotechnology 24, 214003 (2013).
[Crossref] [PubMed]

R.L. Chern, “Spatial dispersion and nonlocal effective permittivity for periodic layered metamaterials,” Opt. Express 21, 16514–16527 (2013).
[Crossref] [PubMed]

2012 (2)

A.V. Goncharenko, V.U. Nazarov, and K.R. Chen, “Design of metamaterials with predetermined optical properties for broadband applications,” Proc. SPIE 8269, 82690Q (2012).
[Crossref]

A.V. Chebykin, A.A. Orlov, C.R. Simovski, Yu.S. Kivshar, and P.A. Belov, “Nonlocal effective parameters of multilayered metal-dielectric metamaterials,” Phys. Rev. B 86, 115–420 (2012).
[Crossref]

2011 (1)

G. Strangi, A. De Luca, S. Ravaine, M. Ferrie, and R. Bartolino, “Gain induced optical transparency in metamaterials,” Appl. Phys. Lett. 98, 251912 (2011).
[Crossref]

2010 (2)

J. Mørk, P. Lunnemann, W. Xue, Y. Chen, P. Kaer, and T. R. Nielsen, “Slow and fast light in semiconductor waveguides,” Semicond. Sci. Technol. 25, 083002 (2010).
[Crossref]

M.P.H. Andresen, A.V. Skaldebø, M.W. Haakestad, H.E. Krogstad, and J. Skaar, “Effect of gain saturation in a gain compensated perfect lens,” J. Opt. Soc. Am. B 27, 1610–1616 (2010).
[Crossref]

2008 (1)

S. Zhang, D.A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101, 047401 (2008).
[Crossref] [PubMed]

2007 (3)

J. Elser, V.A. Podolskiy, I. Salakhutdinov, and I. Avrutsky, “Nonlocal effects in effective-medium response of nanolayered metamaterials,” Appl. Phys. Lett. 90, 191109 (2007).
[Crossref]

B. Nistad and J. Skaar, “Causality and electromagnetic properties of active media,” Phys. Rev. E 78, 036603 (2007).
[Crossref]

Y.F. Huang, S. Chattopadhyay, Y.J. Jen, C.Y. Peng, T.A. Liu, Y.K. Hsu, C.L. Pan, H.C. Lo, C.H. Hsu, Y.H. Chang, C.S. Lee, K.H. Chen, and L.C. Chen, “Improved broadband and quasiomnidirectional anti-reflection properties with biomimetic silicon nanostructures,” Nature Nanotech. 2, 770–774 (2007).
[Crossref]

2005 (1)

M. Fleischhauer, A. Imamoglu, and J.P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005).
[Crossref]

2002 (1)

Y.A. Romanov, J.Y. Romanova, L.G. Mourokh, and N.J.M. Horing, “Self-induced and induced transparencies of two-dimensional and three-dimensional superlattices,” Phys. Rev. B 66, 045319 (2002).
[Crossref]

1956 (1)

S.M. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov. Phys. JETP 2, 466–475 (1956).

Andresen, M.P.H.

Arriaga, J.

A.A. Krokhin, J. Arriaga, L.N. Gumen, and V.P. Drachev, “High-frequency homogenization for layered hyperbolic metamaterials,” Phys. Rev. B 93, 075418 (2016).
[Crossref]

Avrutsky, I.

J. Elser, V.A. Podolskiy, I. Salakhutdinov, and I. Avrutsky, “Nonlocal effects in effective-medium response of nanolayered metamaterials,” Appl. Phys. Lett. 90, 191109 (2007).
[Crossref]

Bartolino, R.

G. Strangi, A. De Luca, S. Ravaine, M. Ferrie, and R. Bartolino, “Gain induced optical transparency in metamaterials,” Appl. Phys. Lett. 98, 251912 (2011).
[Crossref]

Belov, P.A.

A.V. Chebykin, A.A. Orlov, C.R. Simovski, Yu.S. Kivshar, and P.A. Belov, “Nonlocal effective parameters of multilayered metal-dielectric metamaterials,” Phys. Rev. B 86, 115–420 (2012).
[Crossref]

Briggs, D.P.

Y. Yang, I.I. Kravchenko, D.P. Briggs, and J. Valentine, “All-dielectric metasurface analogue of electromagnetically induced transparency,” Nature Commun. 5, 5753 (2014).
[Crossref]

Chang, Y.C.

Chang, Y.H.

Y.F. Huang, S. Chattopadhyay, Y.J. Jen, C.Y. Peng, T.A. Liu, Y.K. Hsu, C.L. Pan, H.C. Lo, C.H. Hsu, Y.H. Chang, C.S. Lee, K.H. Chen, and L.C. Chen, “Improved broadband and quasiomnidirectional anti-reflection properties with biomimetic silicon nanostructures,” Nature Nanotech. 2, 770–774 (2007).
[Crossref]

Chattopadhyay, S.

Y.F. Huang, S. Chattopadhyay, Y.J. Jen, C.Y. Peng, T.A. Liu, Y.K. Hsu, C.L. Pan, H.C. Lo, C.H. Hsu, Y.H. Chang, C.S. Lee, K.H. Chen, and L.C. Chen, “Improved broadband and quasiomnidirectional anti-reflection properties with biomimetic silicon nanostructures,” Nature Nanotech. 2, 770–774 (2007).
[Crossref]

Chebykin, A.V.

A.V. Chebykin, A.A. Orlov, C.R. Simovski, Yu.S. Kivshar, and P.A. Belov, “Nonlocal effective parameters of multilayered metal-dielectric metamaterials,” Phys. Rev. B 86, 115–420 (2012).
[Crossref]

Chen, K.H.

Y.F. Huang, S. Chattopadhyay, Y.J. Jen, C.Y. Peng, T.A. Liu, Y.K. Hsu, C.L. Pan, H.C. Lo, C.H. Hsu, Y.H. Chang, C.S. Lee, K.H. Chen, and L.C. Chen, “Improved broadband and quasiomnidirectional anti-reflection properties with biomimetic silicon nanostructures,” Nature Nanotech. 2, 770–774 (2007).
[Crossref]

Chen, K.R.

A.V. Goncharenko, V.U. Nazarov, and K.R. Chen, “Design of metamaterials with predetermined optical properties for broadband applications,” Proc. SPIE 8269, 82690Q (2012).
[Crossref]

Chen, L.C.

Y.F. Huang, S. Chattopadhyay, Y.J. Jen, C.Y. Peng, T.A. Liu, Y.K. Hsu, C.L. Pan, H.C. Lo, C.H. Hsu, Y.H. Chang, C.S. Lee, K.H. Chen, and L.C. Chen, “Improved broadband and quasiomnidirectional anti-reflection properties with biomimetic silicon nanostructures,” Nature Nanotech. 2, 770–774 (2007).
[Crossref]

Chen, X.

Chen, Y.

J. Mørk, P. Lunnemann, W. Xue, Y. Chen, P. Kaer, and T. R. Nielsen, “Slow and fast light in semiconductor waveguides,” Semicond. Sci. Technol. 25, 083002 (2010).
[Crossref]

Chern, R.L.

Coldrene, L.A.

L.A. Coldrene and S.W. Corzine, Diode Lasers and Photonic Integrated Circuits (Wiley, New York, 1995).

Corzine, S.W.

L.A. Coldrene and S.W. Corzine, Diode Lasers and Photonic Integrated Circuits (Wiley, New York, 1995).

De Luca, A.

G. Strangi, A. De Luca, S. Ravaine, M. Ferrie, and R. Bartolino, “Gain induced optical transparency in metamaterials,” Appl. Phys. Lett. 98, 251912 (2011).
[Crossref]

Dorofeenko, A.V.

A.A. Zyablovsky, A.P. Vinogradov, A.A. Pukhov, A.V. Dorofeenko, and A.A. Lisyansky, “PT-symmetry in optics,” Physics-Uspekhi 57, 1063–1082 (2014).
[Crossref]

Drachev, V.P.

A.A. Krokhin, J. Arriaga, L.N. Gumen, and V.P. Drachev, “High-frequency homogenization for layered hyperbolic metamaterials,” Phys. Rev. B 93, 075418 (2016).
[Crossref]

Du, C.

C. Du, Q. Jing, and Z. Hu, “Coupler-free transition from light to surface plasmon polariton,” Phys. Rev. A 91, 013817 (2015).
[Crossref]

Elser, J.

J. Elser, V.A. Podolskiy, I. Salakhutdinov, and I. Avrutsky, “Nonlocal effects in effective-medium response of nanolayered metamaterials,” Appl. Phys. Lett. 90, 191109 (2007).
[Crossref]

Fainman, Y.

Fan, W.

Ferrie, M.

G. Strangi, A. De Luca, S. Ravaine, M. Ferrie, and R. Bartolino, “Gain induced optical transparency in metamaterials,” Appl. Phys. Lett. 98, 251912 (2011).
[Crossref]

Fleischhauer, M.

M. Fleischhauer, A. Imamoglu, and J.P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005).
[Crossref]

Genov, D.A.

S. Zhang, D.A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101, 047401 (2008).
[Crossref] [PubMed]

Goncharenko, A.V.

A.V. Goncharenko, Y.C. Chang, R.J. Knize, and A.O. Pinchuk, “Extraordinary high- and low-momentum lossless plasmonic modes in one-dimensional metamaterials,” Opt. Mater. Express 7, 766–776 (2017).
[Crossref]

A.V. Goncharenko, V.U. Nazarov, and K.R. Chen, “Design of metamaterials with predetermined optical properties for broadband applications,” Proc. SPIE 8269, 82690Q (2012).
[Crossref]

Gu, J.

Z. Zhu, X. Yang, J. Gu, J. Jiang, W. Yue, Z. Tian, M. Tonouchi, J. Han, and W. Zhang, “Broadband plasmon induced transparency in terahertz metamaterials,” Nanotechnology 24, 214003 (2013).
[Crossref] [PubMed]

Gumen, L.N.

A.A. Krokhin, J. Arriaga, L.N. Gumen, and V.P. Drachev, “High-frequency homogenization for layered hyperbolic metamaterials,” Phys. Rev. B 93, 075418 (2016).
[Crossref]

Haakestad, M.W.

Hågenvik, H.O.

H.O. Hågenvik, M.E. Malema, and J. Skaar, “Fourier theory of linear gain media,” Phys. Rev. A 91, 043826 (2015).
[Crossref]

Han, J.

Z. Zhu, X. Yang, J. Gu, J. Jiang, W. Yue, Z. Tian, M. Tonouchi, J. Han, and W. Zhang, “Broadband plasmon induced transparency in terahertz metamaterials,” Nanotechnology 24, 214003 (2013).
[Crossref] [PubMed]

Horing, N.J.M.

Y.A. Romanov, J.Y. Romanova, L.G. Mourokh, and N.J.M. Horing, “Self-induced and induced transparencies of two-dimensional and three-dimensional superlattices,” Phys. Rev. B 66, 045319 (2002).
[Crossref]

Hsu, C.H.

Y.F. Huang, S. Chattopadhyay, Y.J. Jen, C.Y. Peng, T.A. Liu, Y.K. Hsu, C.L. Pan, H.C. Lo, C.H. Hsu, Y.H. Chang, C.S. Lee, K.H. Chen, and L.C. Chen, “Improved broadband and quasiomnidirectional anti-reflection properties with biomimetic silicon nanostructures,” Nature Nanotech. 2, 770–774 (2007).
[Crossref]

Hsu, Y.K.

Y.F. Huang, S. Chattopadhyay, Y.J. Jen, C.Y. Peng, T.A. Liu, Y.K. Hsu, C.L. Pan, H.C. Lo, C.H. Hsu, Y.H. Chang, C.S. Lee, K.H. Chen, and L.C. Chen, “Improved broadband and quasiomnidirectional anti-reflection properties with biomimetic silicon nanostructures,” Nature Nanotech. 2, 770–774 (2007).
[Crossref]

Hu, Z.

C. Du, Q. Jing, and Z. Hu, “Coupler-free transition from light to surface plasmon polariton,” Phys. Rev. A 91, 013817 (2015).
[Crossref]

Huang, Y.F.

Y.F. Huang, S. Chattopadhyay, Y.J. Jen, C.Y. Peng, T.A. Liu, Y.K. Hsu, C.L. Pan, H.C. Lo, C.H. Hsu, Y.H. Chang, C.S. Lee, K.H. Chen, and L.C. Chen, “Improved broadband and quasiomnidirectional anti-reflection properties with biomimetic silicon nanostructures,” Nature Nanotech. 2, 770–774 (2007).
[Crossref]

Imamoglu, A.

M. Fleischhauer, A. Imamoglu, and J.P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005).
[Crossref]

Jen, Y.J.

Y.F. Huang, S. Chattopadhyay, Y.J. Jen, C.Y. Peng, T.A. Liu, Y.K. Hsu, C.L. Pan, H.C. Lo, C.H. Hsu, Y.H. Chang, C.S. Lee, K.H. Chen, and L.C. Chen, “Improved broadband and quasiomnidirectional anti-reflection properties with biomimetic silicon nanostructures,” Nature Nanotech. 2, 770–774 (2007).
[Crossref]

Jiang, J.

Z. Zhu, X. Yang, J. Gu, J. Jiang, W. Yue, Z. Tian, M. Tonouchi, J. Han, and W. Zhang, “Broadband plasmon induced transparency in terahertz metamaterials,” Nanotechnology 24, 214003 (2013).
[Crossref] [PubMed]

Jing, Q.

C. Du, Q. Jing, and Z. Hu, “Coupler-free transition from light to surface plasmon polariton,” Phys. Rev. A 91, 013817 (2015).
[Crossref]

Jung, S.Y.

Kaer, P.

J. Mørk, P. Lunnemann, W. Xue, Y. Chen, P. Kaer, and T. R. Nielsen, “Slow and fast light in semiconductor waveguides,” Semicond. Sci. Technol. 25, 083002 (2010).
[Crossref]

Kante, B.

Kim, H.S.

Kivshar, Yu.S.

A.V. Chebykin, A.A. Orlov, C.R. Simovski, Yu.S. Kivshar, and P.A. Belov, “Nonlocal effective parameters of multilayered metal-dielectric metamaterials,” Phys. Rev. B 86, 115–420 (2012).
[Crossref]

Knize, R.J.

Kravchenko, I.I.

Y. Yang, I.I. Kravchenko, D.P. Briggs, and J. Valentine, “All-dielectric metasurface analogue of electromagnetically induced transparency,” Nature Commun. 5, 5753 (2014).
[Crossref]

Krogstad, H.E.

Krokhin, A.A.

A.A. Krokhin, J. Arriaga, L.N. Gumen, and V.P. Drachev, “High-frequency homogenization for layered hyperbolic metamaterials,” Phys. Rev. B 93, 075418 (2016).
[Crossref]

Lakhtakia, A.

T.G. Mackay and A. Lakhtakia, “On the propagation of Voight waves in energetically active materials,” Eur. J. Phys. 37, 064002 (2016).
[Crossref]

Lee, C.S.

Y.F. Huang, S. Chattopadhyay, Y.J. Jen, C.Y. Peng, T.A. Liu, Y.K. Hsu, C.L. Pan, H.C. Lo, C.H. Hsu, Y.H. Chang, C.S. Lee, K.H. Chen, and L.C. Chen, “Improved broadband and quasiomnidirectional anti-reflection properties with biomimetic silicon nanostructures,” Nature Nanotech. 2, 770–774 (2007).
[Crossref]

Lee, S.

Lee, S.G.

Li, X.

Z. Wei, X. Li, N. Zhong, X. Tan, X. Zhang, H. Liu, H. Meng, and R. Liang, “Analogue electromagnetically induced transparency based on low-loss metamaterial and its application in nanosensor and slow-light device,” Plasmonics 12, 641–647 (2016).
[Crossref]

Liang, R.

Z. Wei, X. Li, N. Zhong, X. Tan, X. Zhang, H. Liu, H. Meng, and R. Liang, “Analogue electromagnetically induced transparency based on low-loss metamaterial and its application in nanosensor and slow-light device,” Plasmonics 12, 641–647 (2016).
[Crossref]

Lisyansky, A.A.

A.A. Zyablovsky, A.P. Vinogradov, A.A. Pukhov, A.V. Dorofeenko, and A.A. Lisyansky, “PT-symmetry in optics,” Physics-Uspekhi 57, 1063–1082 (2014).
[Crossref]

Liu, H.

Z. Wei, X. Li, N. Zhong, X. Tan, X. Zhang, H. Liu, H. Meng, and R. Liang, “Analogue electromagnetically induced transparency based on low-loss metamaterial and its application in nanosensor and slow-light device,” Plasmonics 12, 641–647 (2016).
[Crossref]

Liu, M.

S. Zhang, D.A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101, 047401 (2008).
[Crossref] [PubMed]

Liu, T.A.

Y.F. Huang, S. Chattopadhyay, Y.J. Jen, C.Y. Peng, T.A. Liu, Y.K. Hsu, C.L. Pan, H.C. Lo, C.H. Hsu, Y.H. Chang, C.S. Lee, K.H. Chen, and L.C. Chen, “Improved broadband and quasiomnidirectional anti-reflection properties with biomimetic silicon nanostructures,” Nature Nanotech. 2, 770–774 (2007).
[Crossref]

Lo, H.C.

Y.F. Huang, S. Chattopadhyay, Y.J. Jen, C.Y. Peng, T.A. Liu, Y.K. Hsu, C.L. Pan, H.C. Lo, C.H. Hsu, Y.H. Chang, C.S. Lee, K.H. Chen, and L.C. Chen, “Improved broadband and quasiomnidirectional anti-reflection properties with biomimetic silicon nanostructures,” Nature Nanotech. 2, 770–774 (2007).
[Crossref]

Lunnemann, P.

J. Mørk, P. Lunnemann, W. Xue, Y. Chen, P. Kaer, and T. R. Nielsen, “Slow and fast light in semiconductor waveguides,” Semicond. Sci. Technol. 25, 083002 (2010).
[Crossref]

Mackay, T.G.

T.G. Mackay and A. Lakhtakia, “On the propagation of Voight waves in energetically active materials,” Eur. J. Phys. 37, 064002 (2016).
[Crossref]

Malema, M.E.

H.O. Hågenvik, M.E. Malema, and J. Skaar, “Fourier theory of linear gain media,” Phys. Rev. A 91, 043826 (2015).
[Crossref]

Marangos, J.P.

M. Fleischhauer, A. Imamoglu, and J.P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005).
[Crossref]

Meng, H.

Z. Wei, X. Li, N. Zhong, X. Tan, X. Zhang, H. Liu, H. Meng, and R. Liang, “Analogue electromagnetically induced transparency based on low-loss metamaterial and its application in nanosensor and slow-light device,” Plasmonics 12, 641–647 (2016).
[Crossref]

Mørk, J.

J. Mørk, P. Lunnemann, W. Xue, Y. Chen, P. Kaer, and T. R. Nielsen, “Slow and fast light in semiconductor waveguides,” Semicond. Sci. Technol. 25, 083002 (2010).
[Crossref]

Mourokh, L.G.

Y.A. Romanov, J.Y. Romanova, L.G. Mourokh, and N.J.M. Horing, “Self-induced and induced transparencies of two-dimensional and three-dimensional superlattices,” Phys. Rev. B 66, 045319 (2002).
[Crossref]

Nazarov, V.U.

A.V. Goncharenko, V.U. Nazarov, and K.R. Chen, “Design of metamaterials with predetermined optical properties for broadband applications,” Proc. SPIE 8269, 82690Q (2012).
[Crossref]

Nielsen, T. R.

J. Mørk, P. Lunnemann, W. Xue, Y. Chen, P. Kaer, and T. R. Nielsen, “Slow and fast light in semiconductor waveguides,” Semicond. Sci. Technol. 25, 083002 (2010).
[Crossref]

Nistad, B.

B. Nistad and J. Skaar, “Causality and electromagnetic properties of active media,” Phys. Rev. E 78, 036603 (2007).
[Crossref]

Orlov, A.A.

A.V. Chebykin, A.A. Orlov, C.R. Simovski, Yu.S. Kivshar, and P.A. Belov, “Nonlocal effective parameters of multilayered metal-dielectric metamaterials,” Phys. Rev. B 86, 115–420 (2012).
[Crossref]

Pan, C.L.

Y.F. Huang, S. Chattopadhyay, Y.J. Jen, C.Y. Peng, T.A. Liu, Y.K. Hsu, C.L. Pan, H.C. Lo, C.H. Hsu, Y.H. Chang, C.S. Lee, K.H. Chen, and L.C. Chen, “Improved broadband and quasiomnidirectional anti-reflection properties with biomimetic silicon nanostructures,” Nature Nanotech. 2, 770–774 (2007).
[Crossref]

Park, J.M.

Peng, C.Y.

Y.F. Huang, S. Chattopadhyay, Y.J. Jen, C.Y. Peng, T.A. Liu, Y.K. Hsu, C.L. Pan, H.C. Lo, C.H. Hsu, Y.H. Chang, C.S. Lee, K.H. Chen, and L.C. Chen, “Improved broadband and quasiomnidirectional anti-reflection properties with biomimetic silicon nanostructures,” Nature Nanotech. 2, 770–774 (2007).
[Crossref]

Pinchuk, A.O.

Podolskiy, V.A.

J. Elser, V.A. Podolskiy, I. Salakhutdinov, and I. Avrutsky, “Nonlocal effects in effective-medium response of nanolayered metamaterials,” Appl. Phys. Lett. 90, 191109 (2007).
[Crossref]

Pukhov, A.A.

A.A. Zyablovsky, A.P. Vinogradov, A.A. Pukhov, A.V. Dorofeenko, and A.A. Lisyansky, “PT-symmetry in optics,” Physics-Uspekhi 57, 1063–1082 (2014).
[Crossref]

Ravaine, S.

G. Strangi, A. De Luca, S. Ravaine, M. Ferrie, and R. Bartolino, “Gain induced optical transparency in metamaterials,” Appl. Phys. Lett. 98, 251912 (2011).
[Crossref]

Romanov, Y.A.

Y.A. Romanov, J.Y. Romanova, L.G. Mourokh, and N.J.M. Horing, “Self-induced and induced transparencies of two-dimensional and three-dimensional superlattices,” Phys. Rev. B 66, 045319 (2002).
[Crossref]

Romanova, J.Y.

Y.A. Romanov, J.Y. Romanova, L.G. Mourokh, and N.J.M. Horing, “Self-induced and induced transparencies of two-dimensional and three-dimensional superlattices,” Phys. Rev. B 66, 045319 (2002).
[Crossref]

Rytov, S.M.

S.M. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov. Phys. JETP 2, 466–475 (1956).

Salakhutdinov, I.

J. Elser, V.A. Podolskiy, I. Salakhutdinov, and I. Avrutsky, “Nonlocal effects in effective-medium response of nanolayered metamaterials,” Appl. Phys. Lett. 90, 191109 (2007).
[Crossref]

Shahin, S.

Simovski, C.R.

A.V. Chebykin, A.A. Orlov, C.R. Simovski, Yu.S. Kivshar, and P.A. Belov, “Nonlocal effective parameters of multilayered metal-dielectric metamaterials,” Phys. Rev. B 86, 115–420 (2012).
[Crossref]

Skaar, J.

H.O. Hågenvik, M.E. Malema, and J. Skaar, “Fourier theory of linear gain media,” Phys. Rev. A 91, 043826 (2015).
[Crossref]

M.P.H. Andresen, A.V. Skaldebø, M.W. Haakestad, H.E. Krogstad, and J. Skaar, “Effect of gain saturation in a gain compensated perfect lens,” J. Opt. Soc. Am. B 27, 1610–1616 (2010).
[Crossref]

B. Nistad and J. Skaar, “Causality and electromagnetic properties of active media,” Phys. Rev. E 78, 036603 (2007).
[Crossref]

Skaldebø, A.V.

Smalley, J.S.T.

Strangi, G.

G. Strangi, A. De Luca, S. Ravaine, M. Ferrie, and R. Bartolino, “Gain induced optical transparency in metamaterials,” Appl. Phys. Lett. 98, 251912 (2011).
[Crossref]

Tan, X.

Z. Wei, X. Li, N. Zhong, X. Tan, X. Zhang, H. Liu, H. Meng, and R. Liang, “Analogue electromagnetically induced transparency based on low-loss metamaterial and its application in nanosensor and slow-light device,” Plasmonics 12, 641–647 (2016).
[Crossref]

Tian, Z.

Z. Zhu, X. Yang, J. Gu, J. Jiang, W. Yue, Z. Tian, M. Tonouchi, J. Han, and W. Zhang, “Broadband plasmon induced transparency in terahertz metamaterials,” Nanotechnology 24, 214003 (2013).
[Crossref] [PubMed]

Tonouchi, M.

Z. Zhu, X. Yang, J. Gu, J. Jiang, W. Yue, Z. Tian, M. Tonouchi, J. Han, and W. Zhang, “Broadband plasmon induced transparency in terahertz metamaterials,” Nanotechnology 24, 214003 (2013).
[Crossref] [PubMed]

Valentine, J.

Y. Yang, I.I. Kravchenko, D.P. Briggs, and J. Valentine, “All-dielectric metasurface analogue of electromagnetically induced transparency,” Nature Commun. 5, 5753 (2014).
[Crossref]

Vallini, F.

Vinogradov, A.P.

A.A. Zyablovsky, A.P. Vinogradov, A.A. Pukhov, A.V. Dorofeenko, and A.A. Lisyansky, “PT-symmetry in optics,” Physics-Uspekhi 57, 1063–1082 (2014).
[Crossref]

Wang, Y.

S. Zhang, D.A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101, 047401 (2008).
[Crossref] [PubMed]

Wei, Z.

Z. Wei, X. Li, N. Zhong, X. Tan, X. Zhang, H. Liu, H. Meng, and R. Liang, “Analogue electromagnetically induced transparency based on low-loss metamaterial and its application in nanosensor and slow-light device,” Plasmonics 12, 641–647 (2016).
[Crossref]

Xue, W.

J. Mørk, P. Lunnemann, W. Xue, Y. Chen, P. Kaer, and T. R. Nielsen, “Slow and fast light in semiconductor waveguides,” Semicond. Sci. Technol. 25, 083002 (2010).
[Crossref]

Yang, X.

Z. Zhu, X. Yang, J. Gu, J. Jiang, W. Yue, Z. Tian, M. Tonouchi, J. Han, and W. Zhang, “Broadband plasmon induced transparency in terahertz metamaterials,” Nanotechnology 24, 214003 (2013).
[Crossref] [PubMed]

Yang, Y.

Y. Yang, I.I. Kravchenko, D.P. Briggs, and J. Valentine, “All-dielectric metasurface analogue of electromagnetically induced transparency,” Nature Commun. 5, 5753 (2014).
[Crossref]

Yue, W.

Z. Zhu, X. Yang, J. Gu, J. Jiang, W. Yue, Z. Tian, M. Tonouchi, J. Han, and W. Zhang, “Broadband plasmon induced transparency in terahertz metamaterials,” Nanotechnology 24, 214003 (2013).
[Crossref] [PubMed]

Zhang, S.

S. Zhang, D.A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101, 047401 (2008).
[Crossref] [PubMed]

Zhang, W.

Z. Zhu, X. Yang, J. Gu, J. Jiang, W. Yue, Z. Tian, M. Tonouchi, J. Han, and W. Zhang, “Broadband plasmon induced transparency in terahertz metamaterials,” Nanotechnology 24, 214003 (2013).
[Crossref] [PubMed]

Zhang, X.

Z. Wei, X. Li, N. Zhong, X. Tan, X. Zhang, H. Liu, H. Meng, and R. Liang, “Analogue electromagnetically induced transparency based on low-loss metamaterial and its application in nanosensor and slow-light device,” Plasmonics 12, 641–647 (2016).
[Crossref]

S. Zhang, D.A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101, 047401 (2008).
[Crossref] [PubMed]

Zhong, N.

Z. Wei, X. Li, N. Zhong, X. Tan, X. Zhang, H. Liu, H. Meng, and R. Liang, “Analogue electromagnetically induced transparency based on low-loss metamaterial and its application in nanosensor and slow-light device,” Plasmonics 12, 641–647 (2016).
[Crossref]

Zhu, Z.

Z. Zhu, X. Yang, J. Gu, J. Jiang, W. Yue, Z. Tian, M. Tonouchi, J. Han, and W. Zhang, “Broadband plasmon induced transparency in terahertz metamaterials,” Nanotechnology 24, 214003 (2013).
[Crossref] [PubMed]

Zyablovsky, A.A.

A.A. Zyablovsky, A.P. Vinogradov, A.A. Pukhov, A.V. Dorofeenko, and A.A. Lisyansky, “PT-symmetry in optics,” Physics-Uspekhi 57, 1063–1082 (2014).
[Crossref]

Appl. Phys. Lett. (2)

G. Strangi, A. De Luca, S. Ravaine, M. Ferrie, and R. Bartolino, “Gain induced optical transparency in metamaterials,” Appl. Phys. Lett. 98, 251912 (2011).
[Crossref]

J. Elser, V.A. Podolskiy, I. Salakhutdinov, and I. Avrutsky, “Nonlocal effects in effective-medium response of nanolayered metamaterials,” Appl. Phys. Lett. 90, 191109 (2007).
[Crossref]

Eur. J. Phys. (1)

T.G. Mackay and A. Lakhtakia, “On the propagation of Voight waves in energetically active materials,” Eur. J. Phys. 37, 064002 (2016).
[Crossref]

J. Opt. Soc. Am. B (1)

Nanotechnology (1)

Z. Zhu, X. Yang, J. Gu, J. Jiang, W. Yue, Z. Tian, M. Tonouchi, J. Han, and W. Zhang, “Broadband plasmon induced transparency in terahertz metamaterials,” Nanotechnology 24, 214003 (2013).
[Crossref] [PubMed]

Nature Commun. (1)

Y. Yang, I.I. Kravchenko, D.P. Briggs, and J. Valentine, “All-dielectric metasurface analogue of electromagnetically induced transparency,” Nature Commun. 5, 5753 (2014).
[Crossref]

Nature Nanotech. (1)

Y.F. Huang, S. Chattopadhyay, Y.J. Jen, C.Y. Peng, T.A. Liu, Y.K. Hsu, C.L. Pan, H.C. Lo, C.H. Hsu, Y.H. Chang, C.S. Lee, K.H. Chen, and L.C. Chen, “Improved broadband and quasiomnidirectional anti-reflection properties with biomimetic silicon nanostructures,” Nature Nanotech. 2, 770–774 (2007).
[Crossref]

Opt. Express (1)

Opt. Lett. (1)

Opt. Mater. Express (3)

Phys. Rev. A (2)

H.O. Hågenvik, M.E. Malema, and J. Skaar, “Fourier theory of linear gain media,” Phys. Rev. A 91, 043826 (2015).
[Crossref]

C. Du, Q. Jing, and Z. Hu, “Coupler-free transition from light to surface plasmon polariton,” Phys. Rev. A 91, 013817 (2015).
[Crossref]

Phys. Rev. B (3)

Y.A. Romanov, J.Y. Romanova, L.G. Mourokh, and N.J.M. Horing, “Self-induced and induced transparencies of two-dimensional and three-dimensional superlattices,” Phys. Rev. B 66, 045319 (2002).
[Crossref]

A.A. Krokhin, J. Arriaga, L.N. Gumen, and V.P. Drachev, “High-frequency homogenization for layered hyperbolic metamaterials,” Phys. Rev. B 93, 075418 (2016).
[Crossref]

A.V. Chebykin, A.A. Orlov, C.R. Simovski, Yu.S. Kivshar, and P.A. Belov, “Nonlocal effective parameters of multilayered metal-dielectric metamaterials,” Phys. Rev. B 86, 115–420 (2012).
[Crossref]

Phys. Rev. E (1)

B. Nistad and J. Skaar, “Causality and electromagnetic properties of active media,” Phys. Rev. E 78, 036603 (2007).
[Crossref]

Phys. Rev. Lett. (1)

S. Zhang, D.A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101, 047401 (2008).
[Crossref] [PubMed]

Physics-Uspekhi (1)

A.A. Zyablovsky, A.P. Vinogradov, A.A. Pukhov, A.V. Dorofeenko, and A.A. Lisyansky, “PT-symmetry in optics,” Physics-Uspekhi 57, 1063–1082 (2014).
[Crossref]

Plasmonics (1)

Z. Wei, X. Li, N. Zhong, X. Tan, X. Zhang, H. Liu, H. Meng, and R. Liang, “Analogue electromagnetically induced transparency based on low-loss metamaterial and its application in nanosensor and slow-light device,” Plasmonics 12, 641–647 (2016).
[Crossref]

Proc. SPIE (1)

A.V. Goncharenko, V.U. Nazarov, and K.R. Chen, “Design of metamaterials with predetermined optical properties for broadband applications,” Proc. SPIE 8269, 82690Q (2012).
[Crossref]

Rev. Mod. Phys. (1)

M. Fleischhauer, A. Imamoglu, and J.P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005).
[Crossref]

Semicond. Sci. Technol. (1)

J. Mørk, P. Lunnemann, W. Xue, Y. Chen, P. Kaer, and T. R. Nielsen, “Slow and fast light in semiconductor waveguides,” Semicond. Sci. Technol. 25, 083002 (2010).
[Crossref]

Sov. Phys. JETP (1)

S.M. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov. Phys. JETP 2, 466–475 (1956).

Other (1)

L.A. Coldrene and S.W. Corzine, Diode Lasers and Photonic Integrated Circuits (Wiley, New York, 1995).

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Figures (6)

Fig. 1
Fig. 1

Fragment (two unit cells) of the structure under consideration. Here h = ∞ for the infinite superlattice and h < ∞ for the finite one. The dashed curve shows the profile of the electric field distribution.

Fig. 2
Fig. 2

Im2 (blue curves) and f = d2/d (green curves) vs k0d for the symmetric TE mode.

Fig. 3
Fig. 3

Reflectance (R), transmittance (T), and absorbance (A) vs the normalized slab thickness h/λ0 for the symmetric TE mode.

Fig. 4
Fig. 4

The modal gain coefficient for the symmetric TE mode.

Fig. 5
Fig. 5

The discrepancies | − 1| vs k0d, calculated with the use of different approximate solutions of the dispersion equation for the symmetric TE mode.

Fig. 6
Fig. 6

The dependencies of (f) and Im2(f) at 1 = −122.19 + i3.115 and Re2 = 12, for d = 100 nm and d = 200 nm.

Equations (10)

Equations on this page are rendered with MathJax. Learn more.

k 1 tan k 1 d 1 2 + k 2 tan k 2 d 2 2 = 0 ,
( 0 ) = f 1 1 + f 2 2 ,
( 0 ) 1 δ ,
( 0 ) + 1 12 ( k 0 d ) 2 [ ( ( 0 ) ) 2 α ] = ( 0 ) + B 2 ( k 0 d ) 2 ,
( 0 ) + B 2 ( k 0 d ) 2 + B 4 ( k 0 d ) 4 + B 6 ( k 0 d ) 6
c 2 2 + c 1 + c 0 = 0 ,
c 1 2 4 c 0 c 2 c 1 2 c 2 .
Γ i = d i | E | 2 d z d | E | 2 d z ,
E y ( z ) = { γ cos ( α 1 d 1 ) + sin ( α 1 d 1 ) if z d 1 , γ cos ( α 2 d 2 ) + k 1 k 2 sin ( α 2 d 2 ) if z d 2 ,
γ = sin ( α 1 d 1 ) + ( k 1 / k 2 ) sin ( α 2 d 2 ) cos ( α 2 d 2 ) cos ( α 1 d 1 ) .

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