Abstract

We have studied the dispersion relations of multilayers of silver and a dye-doped dielectric using four methods: standard effective-medium theory (EMT), nonlocal-effect-corrected EMT, nonlinear equations based on the eigenmode method, and a spatial harmonic analysis method. We compare the validity of these methods and show that metallic losses can be greatly compensated by saturated gain. Two realizable applications are also proposed. Loss-compensated metal-dielectric multilayers that have hyperbolic dispersion relationships are beneficial for numerous applications such as subwavelength imaging and quantum optics.

© 2011 OSA

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2011 (1)

C. Rizza, A. Ciattoni, and E. Palange, “Two-peaked and flat-top perfect bright solitons in nonlinear metamaterials with epsilon near zero,” Phys. Rev. A 83(5), 053805 (2011).
[CrossRef]

2010 (10)

V. C. Nguyen, L. Chen, and K. Halterman, “Total transmission and total reflection by zero index metamaterials with defects,” Phys. Rev. Lett. 105(23), 233908 (2010).
[CrossRef] [PubMed]

W. Chen, M. D. Thoreson, S. Ishii, A. V. Kildishev, and V. M. Shalaev, “Ultra-thin ultra-smooth and low-loss silver films on a germanium wetting layer,” Opt. Express 18(5), 5124–5134 (2010).
[CrossRef] [PubMed]

A. Ciattoni, C. Rizza, and E. Palange, “Transmissivity directional hysteresis of a nonlinear metamaterial slab with very small linear permittivity,” Opt. Lett. 35(13), 2130–2132 (2010).
[CrossRef] [PubMed]

M. P. H. Andresen, A. V. Skaldebo, 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(8), 1610–1616 (2010).
[CrossRef]

Z. Liu, K.-P. Chen, X. Ni, V. P. Drachev, V. M. Shalaev, and A. V. Kildishev, “Experimental verification of two-dimensional spatial harmonic analysis at oblique light incidence,” J. Opt. Soc. Am. B 27(12), 2465–2470 (2010).
[CrossRef]

Z. Liu, K. P. Chen, X. Ni, V. P. Drachev, V. M. Shalaev, and A. V. Kildishev, “Experimental verification of two-dimensional spatial harmonic analysis at oblique light incidence,” J. Opt. Soc. Am. B 27(12), 2465–2470 (2010).
[CrossRef]

Z. Jacob, J. Y. Kim, G. V. Naik, A. Boltasseva, E. Narimanov, and V. M. Shalaev, “Engineering photonic density of states using metamaterials,” Appl. Phys. B-Lasers Opt. 1, 264 (2010).

S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H. K. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature 466(7307), 735–738 (2010).
[CrossRef] [PubMed]

I. De Leon and P. Berini, “Amplification of long-range surface plasmons by a dipolar gain medium,” Nat. Photonics 4(6), 382–387 (2010).
[CrossRef]

X. Ni, Z. Liu, A. Boltasseva, and A. V. Kildishev, “The validation of the parallel three-dimensional solver for analysis of optical plasmonic bi-periodic multilayer nanostructures,” Appl. Phys. A-Mater. 100, 365–374 (2010).

2009 (5)

2008 (2)

2007 (6)

A. V. Kildishev and U. K. Chettiar, “Cascading optical negative index metamaterials,” Appl. Comput. Electrom. 22, 172 (2007).

J. Elser, V. A. Podolskiy, I. Salakhutdinov, and I. Avrutsky, “Nonlocal effects in effective-medium response of nanolayered metamaterials,” Appl. Phys. Lett. 90(19), 191109 (2007).
[CrossRef]

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315(5819), 1686 (2007).
[CrossRef] [PubMed]

I. I. Smolyaninov, Y. J. Hung, and C. C. Davis, “Magnifying superlens in the visible frequency range,” Science 315(5819), 1699–1701 (2007).
[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).
[CrossRef] [PubMed]

A. Alù, M. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: Tailoring the radiation phase pattern,” Phys. Rev. B 75(15), 155410 (2007).
[CrossRef]

2006 (7)

2005 (1)

J. Seidel, S. Grafström, and L. Eng, “Stimulated emission of surface plasmons at the interface between a silver film and an optically pumped dye solution,” Phys. Rev. Lett. 94(17), 177401 (2005).
[CrossRef] [PubMed]

1972 (1)

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[CrossRef]

Adegoke, J.

Alekseyev, L.

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]

Alekseyev, L. V.

Alù, A.

A. Alù, M. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: Tailoring the radiation phase pattern,” Phys. Rev. B 75(15), 155410 (2007).
[CrossRef]

Andresen, M. P. H.

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(19), 191109 (2007).
[CrossRef]

Bahoura, M.

Berini, P.

I. De Leon and P. Berini, “Amplification of long-range surface plasmons by a dipolar gain medium,” Nat. Photonics 4(6), 382–387 (2010).
[CrossRef]

Blaikie, R. J.

Bloemer, M. J.

Boltasseva, A.

X. Ni, Z. Liu, A. Boltasseva, and A. V. Kildishev, “The validation of the parallel three-dimensional solver for analysis of optical plasmonic bi-periodic multilayer nanostructures,” Appl. Phys. A-Mater. 100, 365–374 (2010).

Z. Jacob, J. Y. Kim, G. V. Naik, A. Boltasseva, E. Narimanov, and V. M. Shalaev, “Engineering photonic density of states using metamaterials,” Appl. Phys. B-Lasers Opt. 1, 264 (2010).

P. West, S. Ishii, G. Naik, N. Emani, V. M. Shalaev, and A. Boltasseva, “Searching for better plasmonic materials,” Laser Photon. Rev. 4, 765–808 (2009).

Chen, K. P.

Chen, K.-P.

Chen, L.

V. C. Nguyen, L. Chen, and K. Halterman, “Total transmission and total reflection by zero index metamaterials with defects,” Phys. Rev. Lett. 105(23), 233908 (2010).
[CrossRef] [PubMed]

Chen, W.

Chettiar, U. K.

S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H. K. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature 466(7307), 735–738 (2010).
[CrossRef] [PubMed]

Y. Sivan, S. M. Xiao, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Frequency-domain simulations of a negative-index material with embedded gain,” Opt. Express 17(26), 24060–24074 (2009).
[CrossRef] [PubMed]

A. V. Kildishev and U. K. Chettiar, “Cascading optical negative index metamaterials,” Appl. Comput. Electrom. 22, 172 (2007).

Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[CrossRef]

Ciattoni, A.

C. Rizza, A. Ciattoni, and E. Palange, “Two-peaked and flat-top perfect bright solitons in nonlinear metamaterials with epsilon near zero,” Phys. Rev. A 83(5), 053805 (2011).
[CrossRef]

A. Ciattoni, C. Rizza, and E. Palange, “Transmissivity directional hysteresis of a nonlinear metamaterial slab with very small linear permittivity,” Opt. Lett. 35(13), 2130–2132 (2010).
[CrossRef] [PubMed]

D’Aguanno, G.

Davis, C. C.

I. I. Smolyaninov, Y. J. Hung, and C. C. Davis, “Magnifying superlens in the visible frequency range,” Science 315(5819), 1699–1701 (2007).
[CrossRef] [PubMed]

de Ceglia, D.

De Leon, I.

I. De Leon and P. Berini, “Amplification of long-range surface plasmons by a dipolar gain medium,” Nat. Photonics 4(6), 382–387 (2010).
[CrossRef]

Drachev, V. P.

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(19), 191109 (2007).
[CrossRef]

R. Wangberg, J. Elser, E. E. Narimanov, and V. A. Podolskiy, “Nonmagnetic nanocomposites for optical and infrared negative-refractive-index media,” J. Opt. Soc. Am. B 23(3), 498–505 (2006).
[CrossRef]

Emani, N.

P. West, S. Ishii, G. Naik, N. Emani, V. M. Shalaev, and A. Boltasseva, “Searching for better plasmonic materials,” Laser Photon. Rev. 4, 765–808 (2009).

Eng, L.

J. Seidel, S. Grafström, and L. Eng, “Stimulated emission of surface plasmons at the interface between a silver film and an optically pumped dye solution,” Phys. Rev. Lett. 94(17), 177401 (2005).
[CrossRef] [PubMed]

Engheta, N.

A. Alù, M. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: Tailoring the radiation phase pattern,” Phys. Rev. B 75(15), 155410 (2007).
[CrossRef]

A. Salandrino and N. Engheta, “Far-field subdiffraction optical microscopy using metamaterial crystals: Theory and simulations,” Phys. Rev. B 74(7), 075103 (2006).
[CrossRef]

M. Silveirinha and N. Engheta, “Tunneling of electromagnetic energy through subwavelength channels and bends using epsilon-near-zero materials,” Phys. Rev. Lett. 97(15), 157403 (2006).
[CrossRef] [PubMed]

Enoch, S.

J. Zhang, H. Jiang, B. Gralak, S. Enoch, G. Tayeb, and M. Lequime, “Compensation of loss to approach-1 effective index by gain in metal-dielectric stacks,” Eur. Phys. J. Appl. Phys. 46(3), 32603 (2009).
[CrossRef]

Feng, S. M.

S. M. Feng and K. Halterman, “Parametrically shielding electromagnetic fields by nonlinear metamaterials,” Phys. Rev. Lett. 100(6), 063901 (2008).
[CrossRef] [PubMed]

Franz, K. J.

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]

Gmachl, C.

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]

Grafström, S.

J. Seidel, S. Grafström, and L. Eng, “Stimulated emission of surface plasmons at the interface between a silver film and an optically pumped dye solution,” Phys. Rev. Lett. 94(17), 177401 (2005).
[CrossRef] [PubMed]

Gralak, B.

J. Zhang, H. Jiang, B. Gralak, S. Enoch, G. Tayeb, and M. Lequime, “Compensation of loss to approach-1 effective index by gain in metal-dielectric stacks,” Eur. Phys. J. Appl. Phys. 46(3), 32603 (2009).
[CrossRef]

Haakestad, M. W.

Halterman, K.

V. C. Nguyen, L. Chen, and K. Halterman, “Total transmission and total reflection by zero index metamaterials with defects,” Phys. Rev. Lett. 105(23), 233908 (2010).
[CrossRef] [PubMed]

S. M. Feng and K. Halterman, “Parametrically shielding electromagnetic fields by nonlinear metamaterials,” Phys. Rev. Lett. 100(6), 063901 (2008).
[CrossRef] [PubMed]

Hoffman, A. J.

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]

Howard, S. S.

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]

Hung, Y. J.

I. I. Smolyaninov, Y. J. Hung, and C. C. Davis, “Magnifying superlens in the visible frequency range,” Science 315(5819), 1699–1701 (2007).
[CrossRef] [PubMed]

Ishii, S.

W. Chen, M. D. Thoreson, S. Ishii, A. V. Kildishev, and V. M. Shalaev, “Ultra-thin ultra-smooth and low-loss silver films on a germanium wetting layer,” Opt. Express 18(5), 5124–5134 (2010).
[CrossRef] [PubMed]

P. West, S. Ishii, G. Naik, N. Emani, V. M. Shalaev, and A. Boltasseva, “Searching for better plasmonic materials,” Laser Photon. Rev. 4, 765–808 (2009).

Jacob, Z.

Z. Jacob, J. Y. Kim, G. V. Naik, A. Boltasseva, E. Narimanov, and V. M. Shalaev, “Engineering photonic density of states using metamaterials,” Appl. Phys. B-Lasers Opt. 1, 264 (2010).

Z. Jacob, L. V. Alekseyev, and E. Narimanov, “Optical Hyperlens: Far-field imaging beyond the diffraction limit,” Opt. Express 14(18), 8247–8256 (2006).
[CrossRef] [PubMed]

Jiang, H.

J. Zhang, H. Jiang, B. Gralak, S. Enoch, G. Tayeb, and M. Lequime, “Compensation of loss to approach-1 effective index by gain in metal-dielectric stacks,” Eur. Phys. J. Appl. Phys. 46(3), 32603 (2009).
[CrossRef]

Johnson, P. B.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[CrossRef]

Kildishev, A. V.

Z. Liu, K.-P. Chen, X. Ni, V. P. Drachev, V. M. Shalaev, and A. V. Kildishev, “Experimental verification of two-dimensional spatial harmonic analysis at oblique light incidence,” J. Opt. Soc. Am. B 27(12), 2465–2470 (2010).
[CrossRef]

S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H. K. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature 466(7307), 735–738 (2010).
[CrossRef] [PubMed]

X. Ni, Z. Liu, A. Boltasseva, and A. V. Kildishev, “The validation of the parallel three-dimensional solver for analysis of optical plasmonic bi-periodic multilayer nanostructures,” Appl. Phys. A-Mater. 100, 365–374 (2010).

W. Chen, M. D. Thoreson, S. Ishii, A. V. Kildishev, and V. M. Shalaev, “Ultra-thin ultra-smooth and low-loss silver films on a germanium wetting layer,” Opt. Express 18(5), 5124–5134 (2010).
[CrossRef] [PubMed]

Z. Liu, K. P. Chen, X. Ni, V. P. Drachev, V. M. Shalaev, and A. V. Kildishev, “Experimental verification of two-dimensional spatial harmonic analysis at oblique light incidence,” J. Opt. Soc. Am. B 27(12), 2465–2470 (2010).
[CrossRef]

Y. Sivan, S. M. Xiao, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Frequency-domain simulations of a negative-index material with embedded gain,” Opt. Express 17(26), 24060–24074 (2009).
[CrossRef] [PubMed]

A. V. Kildishev and U. K. Chettiar, “Cascading optical negative index metamaterials,” Appl. Comput. Electrom. 22, 172 (2007).

Kim, J. Y.

Z. Jacob, J. Y. Kim, G. V. Naik, A. Boltasseva, E. Narimanov, and V. M. Shalaev, “Engineering photonic density of states using metamaterials,” Appl. Phys. B-Lasers Opt. 1, 264 (2010).

Krogstad, H. E.

Lee, H.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315(5819), 1686 (2007).
[CrossRef] [PubMed]

Lequime, M.

J. Zhang, H. Jiang, B. Gralak, S. Enoch, G. Tayeb, and M. Lequime, “Compensation of loss to approach-1 effective index by gain in metal-dielectric stacks,” Eur. Phys. J. Appl. Phys. 46(3), 32603 (2009).
[CrossRef]

Liu, Z.

Z. Liu, K.-P. Chen, X. Ni, V. P. Drachev, V. M. Shalaev, and A. V. Kildishev, “Experimental verification of two-dimensional spatial harmonic analysis at oblique light incidence,” J. Opt. Soc. Am. B 27(12), 2465–2470 (2010).
[CrossRef]

X. Ni, Z. Liu, A. Boltasseva, and A. V. Kildishev, “The validation of the parallel three-dimensional solver for analysis of optical plasmonic bi-periodic multilayer nanostructures,” Appl. Phys. A-Mater. 100, 365–374 (2010).

Z. Liu, K. P. Chen, X. Ni, V. P. Drachev, V. M. Shalaev, and A. V. Kildishev, “Experimental verification of two-dimensional spatial harmonic analysis at oblique light incidence,” J. Opt. Soc. Am. B 27(12), 2465–2470 (2010).
[CrossRef]

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315(5819), 1686 (2007).
[CrossRef] [PubMed]

Mattiucci, N.

Melville, D. O. S.

Naik, G.

P. West, S. Ishii, G. Naik, N. Emani, V. M. Shalaev, and A. Boltasseva, “Searching for better plasmonic materials,” Laser Photon. Rev. 4, 765–808 (2009).

Naik, G. V.

Z. Jacob, J. Y. Kim, G. V. Naik, A. Boltasseva, E. Narimanov, and V. M. Shalaev, “Engineering photonic density of states using metamaterials,” Appl. Phys. B-Lasers Opt. 1, 264 (2010).

Narimanov, E.

Z. Jacob, J. Y. Kim, G. V. Naik, A. Boltasseva, E. Narimanov, and V. M. Shalaev, “Engineering photonic density of states using metamaterials,” Appl. Phys. B-Lasers Opt. 1, 264 (2010).

Z. Jacob, L. V. Alekseyev, and E. Narimanov, “Optical Hyperlens: Far-field imaging beyond the diffraction limit,” Opt. Express 14(18), 8247–8256 (2006).
[CrossRef] [PubMed]

Narimanov, E. E.

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]

R. Wangberg, J. Elser, E. E. Narimanov, and V. A. Podolskiy, “Nonmagnetic nanocomposites for optical and infrared negative-refractive-index media,” J. Opt. Soc. Am. B 23(3), 498–505 (2006).
[CrossRef]

Nguyen, V. C.

V. C. Nguyen, L. Chen, and K. Halterman, “Total transmission and total reflection by zero index metamaterials with defects,” Phys. Rev. Lett. 105(23), 233908 (2010).
[CrossRef] [PubMed]

Ni, X.

Z. Liu, K. P. Chen, X. Ni, V. P. Drachev, V. M. Shalaev, and A. V. Kildishev, “Experimental verification of two-dimensional spatial harmonic analysis at oblique light incidence,” J. Opt. Soc. Am. B 27(12), 2465–2470 (2010).
[CrossRef]

X. Ni, Z. Liu, A. Boltasseva, and A. V. Kildishev, “The validation of the parallel three-dimensional solver for analysis of optical plasmonic bi-periodic multilayer nanostructures,” Appl. Phys. A-Mater. 100, 365–374 (2010).

S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H. K. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature 466(7307), 735–738 (2010).
[CrossRef] [PubMed]

Z. Liu, K.-P. Chen, X. Ni, V. P. Drachev, V. M. Shalaev, and A. V. Kildishev, “Experimental verification of two-dimensional spatial harmonic analysis at oblique light incidence,” J. Opt. Soc. Am. B 27(12), 2465–2470 (2010).
[CrossRef]

Noginov, M. A.

Palange, E.

C. Rizza, A. Ciattoni, and E. Palange, “Two-peaked and flat-top perfect bright solitons in nonlinear metamaterials with epsilon near zero,” Phys. Rev. A 83(5), 053805 (2011).
[CrossRef]

A. Ciattoni, C. Rizza, and E. Palange, “Transmissivity directional hysteresis of a nonlinear metamaterial slab with very small linear permittivity,” Opt. Lett. 35(13), 2130–2132 (2010).
[CrossRef] [PubMed]

Pendry, J. B.

B. Wood, J. B. Pendry, and D. P. Tsai, “Directed subwavelength imaging using a layered metal-dielectric system,” Phys. Rev. B 74(11), 115116 (2006).
[CrossRef]

Podolskiy, V. A.

S. Thongrattanasiri and V. A. Podolskiy, “Hypergratings: nanophotonics in planar anisotropic metamaterials,” Opt. Lett. 34(7), 890–892 (2009).
[CrossRef] [PubMed]

J. Elser, V. A. Podolskiy, I. Salakhutdinov, and I. Avrutsky, “Nonlocal effects in effective-medium response of nanolayered metamaterials,” Appl. Phys. Lett. 90(19), 191109 (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).
[CrossRef] [PubMed]

R. Wangberg, J. Elser, E. E. Narimanov, and V. A. Podolskiy, “Nonmagnetic nanocomposites for optical and infrared negative-refractive-index media,” J. Opt. Soc. Am. B 23(3), 498–505 (2006).
[CrossRef]

Ritzo, B. A.

Rizza, C.

C. Rizza, A. Ciattoni, and E. Palange, “Two-peaked and flat-top perfect bright solitons in nonlinear metamaterials with epsilon near zero,” Phys. Rev. A 83(5), 053805 (2011).
[CrossRef]

A. Ciattoni, C. Rizza, and E. Palange, “Transmissivity directional hysteresis of a nonlinear metamaterial slab with very small linear permittivity,” Opt. Lett. 35(13), 2130–2132 (2010).
[CrossRef] [PubMed]

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(19), 191109 (2007).
[CrossRef]

Salandrino, A.

A. Alù, M. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: Tailoring the radiation phase pattern,” Phys. Rev. B 75(15), 155410 (2007).
[CrossRef]

A. Salandrino and N. Engheta, “Far-field subdiffraction optical microscopy using metamaterial crystals: Theory and simulations,” Phys. Rev. B 74(7), 075103 (2006).
[CrossRef]

Scalora, M.

Seidel, J.

J. Seidel, S. Grafström, and L. Eng, “Stimulated emission of surface plasmons at the interface between a silver film and an optically pumped dye solution,” Phys. Rev. Lett. 94(17), 177401 (2005).
[CrossRef] [PubMed]

Shalaev, V. M.

S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H. K. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature 466(7307), 735–738 (2010).
[CrossRef] [PubMed]

Z. Jacob, J. Y. Kim, G. V. Naik, A. Boltasseva, E. Narimanov, and V. M. Shalaev, “Engineering photonic density of states using metamaterials,” Appl. Phys. B-Lasers Opt. 1, 264 (2010).

Z. Liu, K.-P. Chen, X. Ni, V. P. Drachev, V. M. Shalaev, and A. V. Kildishev, “Experimental verification of two-dimensional spatial harmonic analysis at oblique light incidence,” J. Opt. Soc. Am. B 27(12), 2465–2470 (2010).
[CrossRef]

W. Chen, M. D. Thoreson, S. Ishii, A. V. Kildishev, and V. M. Shalaev, “Ultra-thin ultra-smooth and low-loss silver films on a germanium wetting layer,” Opt. Express 18(5), 5124–5134 (2010).
[CrossRef] [PubMed]

Z. Liu, K. P. Chen, X. Ni, V. P. Drachev, V. M. Shalaev, and A. V. Kildishev, “Experimental verification of two-dimensional spatial harmonic analysis at oblique light incidence,” J. Opt. Soc. Am. B 27(12), 2465–2470 (2010).
[CrossRef]

Y. Sivan, S. M. Xiao, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Frequency-domain simulations of a negative-index material with embedded gain,” Opt. Express 17(26), 24060–24074 (2009).
[CrossRef] [PubMed]

P. West, S. Ishii, G. Naik, N. Emani, V. M. Shalaev, and A. Boltasseva, “Searching for better plasmonic materials,” Laser Photon. Rev. 4, 765–808 (2009).

M. A. Noginov, G. Zhu, M. Bahoura, J. Adegoke, C. E. Small, B. A. Ritzo, V. P. Drachev, and V. M. Shalaev, “Enhancement of surface plasmons in an Ag aggregate by optical gain in a dielectric medium,” Opt. Lett. 31(20), 3022–3024 (2006).
[CrossRef] [PubMed]

Sibilia, C.

Silveirinha, M.

A. Alù, M. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: Tailoring the radiation phase pattern,” Phys. Rev. B 75(15), 155410 (2007).
[CrossRef]

M. Silveirinha and N. Engheta, “Tunneling of electromagnetic energy through subwavelength channels and bends using epsilon-near-zero materials,” Phys. Rev. Lett. 97(15), 157403 (2006).
[CrossRef] [PubMed]

Sivan, Y.

Sivco, D. L.

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]

Skaar, J.

Skaldebo, A. V.

Small, C. E.

Smolyaninov, I. I.

I. I. Smolyaninov, Y. J. Hung, and C. C. Davis, “Magnifying superlens in the visible frequency range,” Science 315(5819), 1699–1701 (2007).
[CrossRef] [PubMed]

Sun, C.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315(5819), 1686 (2007).
[CrossRef] [PubMed]

Tayeb, G.

J. Zhang, H. Jiang, B. Gralak, S. Enoch, G. Tayeb, and M. Lequime, “Compensation of loss to approach-1 effective index by gain in metal-dielectric stacks,” Eur. Phys. J. Appl. Phys. 46(3), 32603 (2009).
[CrossRef]

Thongrattanasiri, S.

Thoreson, M. D.

Tsai, D. P.

B. Wood, J. B. Pendry, and D. P. Tsai, “Directed subwavelength imaging using a layered metal-dielectric system,” Phys. Rev. B 74(11), 115116 (2006).
[CrossRef]

Wangberg, R.

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]

West, P.

P. West, S. Ishii, G. Naik, N. Emani, V. M. Shalaev, and A. Boltasseva, “Searching for better plasmonic materials,” Laser Photon. Rev. 4, 765–808 (2009).

Wood, B.

B. Wood, J. B. Pendry, and D. P. Tsai, “Directed subwavelength imaging using a layered metal-dielectric system,” Phys. Rev. B 74(11), 115116 (2006).
[CrossRef]

Xiao, S.

S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H. K. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature 466(7307), 735–738 (2010).
[CrossRef] [PubMed]

Xiao, S. M.

Xiong, Y.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315(5819), 1686 (2007).
[CrossRef] [PubMed]

Yuan, H. K.

S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H. K. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature 466(7307), 735–738 (2010).
[CrossRef] [PubMed]

Zhang, J.

J. Zhang, H. Jiang, B. Gralak, S. Enoch, G. Tayeb, and M. Lequime, “Compensation of loss to approach-1 effective index by gain in metal-dielectric stacks,” Eur. Phys. J. Appl. Phys. 46(3), 32603 (2009).
[CrossRef]

Zhang, X.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315(5819), 1686 (2007).
[CrossRef] [PubMed]

Zhu, G.

Appl. Comput. Electrom. (1)

A. V. Kildishev and U. K. Chettiar, “Cascading optical negative index metamaterials,” Appl. Comput. Electrom. 22, 172 (2007).

Appl. Phys. A-Mater. (1)

X. Ni, Z. Liu, A. Boltasseva, and A. V. Kildishev, “The validation of the parallel three-dimensional solver for analysis of optical plasmonic bi-periodic multilayer nanostructures,” Appl. Phys. A-Mater. 100, 365–374 (2010).

Appl. Phys. B-Lasers Opt. (1)

Z. Jacob, J. Y. Kim, G. V. Naik, A. Boltasseva, E. Narimanov, and V. M. Shalaev, “Engineering photonic density of states using metamaterials,” Appl. Phys. B-Lasers Opt. 1, 264 (2010).

Appl. Phys. Lett. (1)

J. Elser, V. A. Podolskiy, I. Salakhutdinov, and I. Avrutsky, “Nonlocal effects in effective-medium response of nanolayered metamaterials,” Appl. Phys. Lett. 90(19), 191109 (2007).
[CrossRef]

Eur. Phys. J. Appl. Phys. (1)

J. Zhang, H. Jiang, B. Gralak, S. Enoch, G. Tayeb, and M. Lequime, “Compensation of loss to approach-1 effective index by gain in metal-dielectric stacks,” Eur. Phys. J. Appl. Phys. 46(3), 32603 (2009).
[CrossRef]

J. Opt. Soc. Am. B (5)

Laser Photon. Rev. (1)

P. West, S. Ishii, G. Naik, N. Emani, V. M. Shalaev, and A. Boltasseva, “Searching for better plasmonic materials,” Laser Photon. Rev. 4, 765–808 (2009).

Nat. Mater. (1)

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]

Nat. Photonics (1)

I. De Leon and P. Berini, “Amplification of long-range surface plasmons by a dipolar gain medium,” Nat. Photonics 4(6), 382–387 (2010).
[CrossRef]

Nature (1)

S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H. K. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature 466(7307), 735–738 (2010).
[CrossRef] [PubMed]

Opt. Express (5)

Opt. Lett. (3)

Phys. Rev. A (1)

C. Rizza, A. Ciattoni, and E. Palange, “Two-peaked and flat-top perfect bright solitons in nonlinear metamaterials with epsilon near zero,” Phys. Rev. A 83(5), 053805 (2011).
[CrossRef]

Phys. Rev. B (4)

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[CrossRef]

B. Wood, J. B. Pendry, and D. P. Tsai, “Directed subwavelength imaging using a layered metal-dielectric system,” Phys. Rev. B 74(11), 115116 (2006).
[CrossRef]

A. Alù, M. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: Tailoring the radiation phase pattern,” Phys. Rev. B 75(15), 155410 (2007).
[CrossRef]

A. Salandrino and N. Engheta, “Far-field subdiffraction optical microscopy using metamaterial crystals: Theory and simulations,” Phys. Rev. B 74(7), 075103 (2006).
[CrossRef]

Phys. Rev. Lett. (4)

M. Silveirinha and N. Engheta, “Tunneling of electromagnetic energy through subwavelength channels and bends using epsilon-near-zero materials,” Phys. Rev. Lett. 97(15), 157403 (2006).
[CrossRef] [PubMed]

J. Seidel, S. Grafström, and L. Eng, “Stimulated emission of surface plasmons at the interface between a silver film and an optically pumped dye solution,” Phys. Rev. Lett. 94(17), 177401 (2005).
[CrossRef] [PubMed]

V. C. Nguyen, L. Chen, and K. Halterman, “Total transmission and total reflection by zero index metamaterials with defects,” Phys. Rev. Lett. 105(23), 233908 (2010).
[CrossRef] [PubMed]

S. M. Feng and K. Halterman, “Parametrically shielding electromagnetic fields by nonlinear metamaterials,” Phys. Rev. Lett. 100(6), 063901 (2008).
[CrossRef] [PubMed]

Science (2)

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315(5819), 1686 (2007).
[CrossRef] [PubMed]

I. I. Smolyaninov, Y. J. Hung, and C. C. Davis, “Magnifying superlens in the visible frequency range,” Science 315(5819), 1699–1701 (2007).
[CrossRef] [PubMed]

Other (7)

E. Narimanov, M. A. Noginov, H. Li, and Y. Barnakov, “Darker than black: Radiation-absorbing metamaterial,” in Quantum Electronics and Laser Science Conference, (Optical Society of America, 2010).

Z. Jacob, I. Smolyaninov, and E. Narimanov, “Single photon gun: Radiative decay engineering with metamaterials,” in CLEO/QELS, (Optical Society of America, 2009).

T. Tumkur, G. Zhu, P. Black, Y. A. Barnakov, C. E. Bonner, and M. A. Noginov, “Control of spontaneous emission with functionalized multilayered hyperbolic metamaterials,” in SPIE, (San Diego, California, USA, 2011), p. 809300.

P. Yeh, Optical Waves in Layered Media (Wiley-Interscience, 2005).

X. Ni, Z. Liu, and A. V. Kildishev, “PhotonicsDB: Optical constants,” (2008). doi:10254/nanohub-r3692.10.

P. Yeh, Optical Waves in Layered Media (John Wiley & Sons, Inc., Hoboken, NJ, 1988).

X. Ni, Z. Liu, F. Gu, M. G. Pacheco, J. Borneman, and A. V. Kildishev, “PhotonicsSHA-2D: Modeling of single-period multilayer optical gratings and metamaterials,” (2011). doi:10254/nanohub-r6977.12.

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Figures (10)

Fig. 1
Fig. 1

Geometry of a metal-dielectric multilayer composite. The permittivities of the metal and dielectric layers are denoted respectively as ε1 and ε2, and the thicknesses are δ1 and δ2. All the layers are parallel to the x-z plane.

Fig. 2
Fig. 2

Extracted imaginary part of the dielectric function of dye-doped epoxy. Note that the real part of the dielectric function (not shown) is dominated by the permittivity of the epoxy, which is about 2.72.

Fig. 3
Fig. 3

Wavelength dependence of the effective anisotropic permittivity for the silver-gain HMM at normal incidence (θ = 0) calculated from EMT1 (dashed-dotted line), EMT2 (dashed line), NLE (solid line), and SHA (dotted line). Top left panel: the real part of the effective permittivity. Top right: the imaginary part of effective permittivity. Bottom panels: relative errors in percent with respect to the SHA results. Note that the results from NLE and SHA are coincident, and their curves are overlapping. The real part of permittivity in the y direction from EMT2 is overlaps with the NLE and SHA curves (therefore it is obscured by the NLE and SHA curves and is not seen in the figure), and the rest of the EMT2 curve partially overlaps with the NLE and SHA curves.

Fig. 4
Fig. 4

Incidence-angle dependence of the effective anisotropic permittivity for the silver-gain HMM at a wavelength of 720 nm calculated from EMT1 (dashed-dotted line), EMT2 (dashed line), NLE (solid line), and SHA (dotted line). Top left panel: real part of the effective permittivity. Top right: imaginary part of effective permittivity. Bottom panels: relative errors in percent with respect to the SHA results. Note that the results from NLE and SHA are coincident, and their curves are overlapping.

Fig. 5
Fig. 5

Effective anisotropic permittivity for the silver-gain HMM with different metal-layer thicknesses at a wavelength of 720 nm at normal incidence (θ = 0) calculated from EMT1 (dashed-dotted line), EMT2 (dashed line), NLE (solid line), and SHA (dotted line). The volume fraction of the metal layer (δ1/δ) is kept constant at 0.5. Top left panel: real part of the effective permittivity. Top right: imaginary part of effective permittivity. Bottom panels: relative errors in percent with respect to the SHA results. Note that the results from NLE and SHA are coincident, and their curves are overlapping.

Fig. 6
Fig. 6

Effective anisotropic permittivity for the silver-gain HMM with different metal volume fractions at a wavelength of 720 nm at normal incidence (θ = 0) calculated from EMT1 (dashed-dotted line), EMT2 (dashed line), NLE (solid line), and SHA (dotted line). The period (δ) is kept constant at 60 nm. Top left panel: real part of the effective permittivity. Top right: imaginary part of effective permittivity. Bottom panels: relative errors in percent with respect to the SHA results. Note that the results from NLE and SHA are coincident, and their curves are overlapping.

Fig. 7
Fig. 7

Effective anisotropic permittivity calculated from NLE and SHA for a silver-dielectric HMM metamaterial with gain (solid line) and without gain (circles). Left panel: real part of permittivity. Right panel: imaginary part of permittivity.

Fig. 8
Fig. 8

(a) Schematic of the hypergrating structure. (b) Field intensity map plotted in the x-y plane at a wavelength of 716 nm with gain. (c) Field intensity plotted at a distance 345 nm into the HMM slab with gain (solid line) and without gain (dashed line). The dashed line in (b) indicates the position of the cross section of (c).

Fig. 9
Fig. 9

Effective permittivity calculated from NLE and SHA for the silver-dielectric ENZ metamaterial with gain (solid line) and without gain (circles). (a) Real part and (b) imaginary part.

Fig. 10
Fig. 10

(a) Transmittance, reflectance, and absorptance spectra calculated by SHA for a 100-layer silver-gain HMM with a silver-layer thickness of 5 nm and a gain-layer thickness of 45 nm. (b) Electric field and (c) the phase of the electric field plotted along the propagation direction at a wavelength of 729 nm with gain (solid line) and without gain (dashed line).

Equations (11)

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

cosh( g 2 δ 2 )cosh( g 1 δ 1 )+ 1 2 ( g 1 g 2 + g 2 g 1 )sinh( g 2 δ 2 )sinh( g 1 δ 1 )=cosh( αδ+ι2πq )
cosh( g 2 δ 2 )cosh( g 1 δ 1 )+ 1 2 ( g 1 ε 2 g 2 ε 1 + g 2 ε 1 g 1 ε 2 )sinh( g 2 δ 2 )sinh( g 1 δ 1 )=cosh( αδ+ι2πq ),
g 1 = k x,TE 2 ε 1 k 0 2 g 2 = k x,TE 2 ε 2 k 0 2 ,
g 1 = k x,TM 2 ε 1 k 0 2 g 2 = k x,TM 2 ε 2 k 0 2 ,
k x 2 ε y + k y 2 ε x = k 0 2 ,
g 1 2 r 2 + g 2 2 ( 1r ) 2 +r( 1r )( g 1 2 ε 2 ε 1 + g 2 2 ε 1 ε 2 )= k y 2 .
k x 2 [ r ε 1 1 +( 1r ) ε 2 1 ] ε y 1 + k y 2 r ε 1 +( 1r ) ε 2 ε x = k 0 2 .
ε x =r ε 1 +( 1r ) ε 2 ε y 1 =r ε 1 1 +( 1r ) ε 2 1 .
ε 1 = ε x ε y ( ε x ε y )( 4r( 1r ) ε y + ε x ε y ) +2r ε y 2r , ε 2 = ε x + ε y ± ( ε x ε y )( 4r( 1r ) ε y + ε x ε y ) +2r ε y 2( 1r ) .
ε x = ε x ( 1 Δ x ) 1 ε y = ε y ( 1 Δ y ) 1 ,
Δ x = 1 12 δ 2 r 2 ( 1r ) 2 ( ε 1 ε 2 ) 2 / ε x Δ y = Δ x ( ε y 2 ε x 2 ε 1 2 ε 2 2 α 2 ( ε 1 1 + ε 2 1 ) 2 ε y 2 / ε x ).

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