Abstract

We report on the possibility of adopting active gain materials (specifically, made of fluorescent dyes) to mitigate the losses in a 3D periodic array of dielectric-core metallic-shell nanospheres. We find the modes with complex wavenumber in the structure, and describe the composite material in terms of homogenized effective permittivity, comparing results from modal analysis and Maxwell Garnett theory. We then design two metamaterials in which the epsilon-near-zero frequency region overlaps with the emission band of the adopted gain media, and we show that metamaterials with effective parameters with low losses are feasible, thanks to the gain materials. Even though fluorescent dyes embedded in the nanoshells’ dielectric cores are employed in this study, the formulation provided is general, and could account for the usage of other active materials, such as semiconductors and quantum dots.

© 2011 Optical Society of America

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    [CrossRef]
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2011 (6)

G. Strangi, A. De Luca, S. Ravaine, M. Ferrie, and R. Bartolino, “Gain induced optical transparency in metamaterials,” Appl. Phys. Lett. 98(25), 251912 (2011).
[CrossRef]

A. De Luca, M. P. Grzelczak, I. Pastoriza-Santos, L. M. Liz-Marzán, M. La Deda, M. Striccoli, and G. Strangi, “Dispersed and encapsulated gain medium in plasmonic nanoparticles: a multipronged approach to mitigate optical losses,” ACS Nano 5(7), 5823–5829 (2011).
[CrossRef] [PubMed]

A. D. Boardman, V. V. Grimalsky, Y. S. Kivshar, S. V. Koshevaya, M. Lapine, N. M. Litchinitser, V. N. Malnev, M. Noginov, Y. G. Rapoport, and V. M. Shalaev, “Active and tunable metamaterials,” Laser Photon. Rev. 5(2), 287–307 (2011).
[CrossRef]

S. Campione, S. Steshenko, and F. Capolino, “Description and characterization of the complex modes in a linear chain of gold metal nanospheres,” Proc. SPIE 7946, 79461V (2011).
[CrossRef]

A. L. Fructos, S. Campione, F. Capolino, and F. Mesa, “Characterization of complex plasmonic modes in two-dimensional periodic arrays of metal nanospheres,” J. Opt. Soc. Am. B 28(6), 1446–1458 (2011).
[CrossRef]

A. Fang, Z. Huang, T. Koschny, and C. M. Soukoulis, “Overcoming the losses of a split ring resonator array with gain,” Opt. Express 19(13), 12688–12699 (2011).
[CrossRef] [PubMed]

2010 (5)

S. Wuestner, A. Pusch, K. L. Tsakmakidis, J. M. Hamm, and O. Hess, “Overcoming losses with gain in a negative refractive index metamaterial,” Phys. Rev. Lett. 105(12), 127401 (2010).
[CrossRef] [PubMed]

S. Campione, A. Vallecchi, and F. Capolino, “Closed form formulas and tunability of resonances in pairs of gold-dielectric nanoshells,” Proc. SPIE 7757, 775738 (2010).
[CrossRef]

M. C. Gather, K. Meerholz, N. Danz, and K. Leosson, “Net optical gain in a plasmonic waveguide embedded in a fluorescent polymer,” Nat. Photonics 4(7), 457–461 (2010).
[CrossRef]

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]

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]

2009 (3)

R. Bardhan, N. K. Grady, J. R. Cole, A. Joshi, and N. J. Halas, “Fluorescence enhancement by Au nanostructures: nanoshells and nanorods,” ACS Nano 3(3), 744–752 (2009).
[CrossRef] [PubMed]

A. Fang, T. Koschny, M. Wegener, and C. M. Soukoulis, “Self-consistent calculation of metamaterials with gain,” Phys. Rev. B 79(24), 241104 (2009).
[CrossRef]

Y. Sivan, S. 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]

2008 (3)

J. A. Gordon and R. W. Ziolkowski, “CNP optical metamaterials,” Opt. Express 16(9), 6692–6716 (2008).
[CrossRef] [PubMed]

K. Tanabe, “Field enhancement around metal nanoparticles and nanoshells: a systematic investigation,” J. Phys. Chem. C 112(40), 15721–15728 (2008).
[CrossRef]

M. I. Stockman, “Spasers explained,” Nat. Photonics 2(6), 327–329 (2008).
[CrossRef]

2007 (2)

A. K. Sarychev and G. Tartakovsky, “Magnetic plasmonic metamaterials in actively pumped host medium and plasmonic nanolaser,” Phys. Rev. B 75(8), 085436 (2007).
[CrossRef]

M. A. Noginov, G. Zhu, M. Bahoura, J. Adegoke, C. Small, B. A. Ritzo, V. P. Drachev, and V. M. Shalaev, “The effect of gain and absorption on surface plasmons in metal nanoparticles,” Appl. Phys. B 86(3), 455–460 (2007).
[CrossRef]

2006 (3)

J. Zhang, I. Gryczynski, Z. Gryczynski, and J. R. Lakowicz, “Dye-labeled silver nanoshell-bright particle,” J. Phys. Chem. B 110(18), 8986–8991 (2006).
[CrossRef] [PubMed]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006).
[CrossRef] [PubMed]

A. Alù, A. Salandrino, and N. Engheta, “Negative effective permeability and left-handed materials at optical frequencies,” Opt. Express 14(4), 1557–1567 (2006).
[CrossRef] [PubMed]

2005 (1)

M. A. R. C. Alencar, G. S. Maciel, C. B. de Araújo, R. Bertholdo, Y. Messaddeq, and S. J. L. Ribeiro, “Laserlike emission from silica inverse opals infiltrated with Rhodamine 6G,” J. Non-Cryst. Solids 351(21-23), 1846–1849 (2005).
[CrossRef]

2004 (3)

S.-H. Chang and A. Taflove, “Finite-difference time-domain model of lasing action in a four-level two-electron atomic system,” Opt. Express 12(16), 3827–3833 (2004).
[CrossRef] [PubMed]

N. K. Grady, N. J. Halas, and P. Nordlander, “Influence of dielectric function properties on the optical response of plasmon resonant metallic nanoparticles,” Chem. Phys. Lett. 399(1-3), 167–171 (2004).
[CrossRef]

N. M. Lawandy, “Localized surface plasmon singularities in amplifying media,” Appl. Phys. Lett. 85(21), 5040–5042 (2004).
[CrossRef]

2003 (2)

S. Anantha Ramakrishna and J. Pendry, “Removal of absorption and increase in resolution in a near-field lens via optical gain,” Phys. Rev. B 67(20), 201101 (2003).
[CrossRef]

D. J. Bergman and M. I. Stockman, “Surface plasmon amplification by stimulated emission of radiation: quantum generation of coherent surface plasmons in nanosystems,” Phys. Rev. Lett. 90(2), 027402 (2003).
[CrossRef] [PubMed]

2002 (1)

D. Magde, R. Wong, and P. G. Seybold, “Fluorescence quantum yields and their relation to lifetimes of rhodamine 6G and fluorescein in nine solvents: improved absolute standards for quantum yields,” Photochem. Photobiol. 75(4), 327–334 (2002).
[CrossRef] [PubMed]

2000 (2)

I. El-Kady, M. M. Sigalas, R. Biswas, K. M. Ho, and C. M. Soukoulis, “Metallic photonic crystals at optical wavelengths,” Phys. Rev. B 62(23), 15299–15302 (2000).
[CrossRef]

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
[CrossRef] [PubMed]

1999 (1)

D. Magde, G. E. Rojas, and P. G. Seybold, “Solvent dependence of the fluorescence lifetimes of xanthene dyes,” Photochem. Photobiol. 70(5), 737–744 (1999).
[CrossRef]

1998 (1)

A. S. Nagra and R. A. York, “FDTD analysis of wave propagation in nonlinear absorbing and gain media,” IEEE Trans. Antenn. Propag. 46(3), 334–340 (1998).
[CrossRef]

1991 (1)

K. E. Peiponen and E. M. Vartiainen, “Kramers-Kronig relations in optical data inversion,” Phys. Rev. B Condens. Matter 44(15), 8301–8303 (1991).
[CrossRef] [PubMed]

1988 (2)

P. Sperber, W. Spangler, B. Meier, and A. Penzkofer, “Experimental and theoretical investigation of tunable picosecond pulse generation in longitudinally pumped dye-laser generators and amplifiers,” Opt. Quantum Electron. 20(5), 395–431 (1988).
[CrossRef]

K. Ohta and H. Ishida, “Comparison among several numerical integration methods for Kramers-Kronig transformation,” Appl. Spectrosc. 42(6), 952–957 (1988).
[CrossRef]

1984 (1)

G. Grönninger and A. Penzkofer, “Determination of energy and duration of picosecond light pulses by bleaching of dyes,” Opt. Quantum Electron. 16(3), 225–233 (1984).
[CrossRef]

1983 (1)

1979 (1)

D. Faubert, S. L. Chin, M. Cormier, and M. Boloten, “Numerical analysis of short laser pulse superposition in a fluorescent dye medium,” Can. J. Phys. 57(2), 160–167 (1979).
[CrossRef]

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.

M. A. Noginov, G. Zhu, M. Bahoura, J. Adegoke, C. Small, B. A. Ritzo, V. P. Drachev, and V. M. Shalaev, “The effect of gain and absorption on surface plasmons in metal nanoparticles,” Appl. Phys. B 86(3), 455–460 (2007).
[CrossRef]

Alencar, M. A. R. C.

M. A. R. C. Alencar, G. S. Maciel, C. B. de Araújo, R. Bertholdo, Y. Messaddeq, and S. J. L. Ribeiro, “Laserlike emission from silica inverse opals infiltrated with Rhodamine 6G,” J. Non-Cryst. Solids 351(21-23), 1846–1849 (2005).
[CrossRef]

Alù, A.

Anantha Ramakrishna, S.

S. Anantha Ramakrishna and J. Pendry, “Removal of absorption and increase in resolution in a near-field lens via optical gain,” Phys. Rev. B 67(20), 201101 (2003).
[CrossRef]

Bahoura, M.

M. A. Noginov, G. Zhu, M. Bahoura, J. Adegoke, C. Small, B. A. Ritzo, V. P. Drachev, and V. M. Shalaev, “The effect of gain and absorption on surface plasmons in metal nanoparticles,” Appl. Phys. B 86(3), 455–460 (2007).
[CrossRef]

Bardhan, R.

R. Bardhan, N. K. Grady, J. R. Cole, A. Joshi, and N. J. Halas, “Fluorescence enhancement by Au nanostructures: nanoshells and nanorods,” ACS Nano 3(3), 744–752 (2009).
[CrossRef] [PubMed]

Bartolino, R.

G. Strangi, A. De Luca, S. Ravaine, M. Ferrie, and R. Bartolino, “Gain induced optical transparency in metamaterials,” Appl. Phys. Lett. 98(25), 251912 (2011).
[CrossRef]

Bergman, D. J.

D. J. Bergman and M. I. Stockman, “Surface plasmon amplification by stimulated emission of radiation: quantum generation of coherent surface plasmons in nanosystems,” Phys. Rev. Lett. 90(2), 027402 (2003).
[CrossRef] [PubMed]

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]

Bertholdo, R.

M. A. R. C. Alencar, G. S. Maciel, C. B. de Araújo, R. Bertholdo, Y. Messaddeq, and S. J. L. Ribeiro, “Laserlike emission from silica inverse opals infiltrated with Rhodamine 6G,” J. Non-Cryst. Solids 351(21-23), 1846–1849 (2005).
[CrossRef]

Biswas, R.

I. El-Kady, M. M. Sigalas, R. Biswas, K. M. Ho, and C. M. Soukoulis, “Metallic photonic crystals at optical wavelengths,” Phys. Rev. B 62(23), 15299–15302 (2000).
[CrossRef]

Boardman, A. D.

A. D. Boardman, V. V. Grimalsky, Y. S. Kivshar, S. V. Koshevaya, M. Lapine, N. M. Litchinitser, V. N. Malnev, M. Noginov, Y. G. Rapoport, and V. M. Shalaev, “Active and tunable metamaterials,” Laser Photon. Rev. 5(2), 287–307 (2011).
[CrossRef]

Boloten, M.

D. Faubert, S. L. Chin, M. Cormier, and M. Boloten, “Numerical analysis of short laser pulse superposition in a fluorescent dye medium,” Can. J. Phys. 57(2), 160–167 (1979).
[CrossRef]

Campione, S.

S. Campione, S. Steshenko, and F. Capolino, “Description and characterization of the complex modes in a linear chain of gold metal nanospheres,” Proc. SPIE 7946, 79461V (2011).
[CrossRef]

A. L. Fructos, S. Campione, F. Capolino, and F. Mesa, “Characterization of complex plasmonic modes in two-dimensional periodic arrays of metal nanospheres,” J. Opt. Soc. Am. B 28(6), 1446–1458 (2011).
[CrossRef]

S. Campione, A. Vallecchi, and F. Capolino, “Closed form formulas and tunability of resonances in pairs of gold-dielectric nanoshells,” Proc. SPIE 7757, 775738 (2010).
[CrossRef]

Capolino, F.

S. Campione, S. Steshenko, and F. Capolino, “Description and characterization of the complex modes in a linear chain of gold metal nanospheres,” Proc. SPIE 7946, 79461V (2011).
[CrossRef]

A. L. Fructos, S. Campione, F. Capolino, and F. Mesa, “Characterization of complex plasmonic modes in two-dimensional periodic arrays of metal nanospheres,” J. Opt. Soc. Am. B 28(6), 1446–1458 (2011).
[CrossRef]

S. Campione, A. Vallecchi, and F. Capolino, “Closed form formulas and tunability of resonances in pairs of gold-dielectric nanoshells,” Proc. SPIE 7757, 775738 (2010).
[CrossRef]

Chang, S.-H.

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. 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]

Chin, S. L.

D. Faubert, S. L. Chin, M. Cormier, and M. Boloten, “Numerical analysis of short laser pulse superposition in a fluorescent dye medium,” Can. J. Phys. 57(2), 160–167 (1979).
[CrossRef]

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]

Cole, J. R.

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M. C. Gather, K. Meerholz, N. Danz, and K. Leosson, “Net optical gain in a plasmonic waveguide embedded in a fluorescent polymer,” Nat. Photonics 4(7), 457–461 (2010).
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M. A. R. C. Alencar, G. S. Maciel, C. B. de Araújo, R. Bertholdo, Y. Messaddeq, and S. J. L. Ribeiro, “Laserlike emission from silica inverse opals infiltrated with Rhodamine 6G,” J. Non-Cryst. Solids 351(21-23), 1846–1849 (2005).
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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).
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A. Fang, Z. Huang, T. Koschny, and C. M. Soukoulis, “Overcoming the losses of a split ring resonator array with gain,” Opt. Express 19(13), 12688–12699 (2011).
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D. Faubert, S. L. Chin, M. Cormier, and M. Boloten, “Numerical analysis of short laser pulse superposition in a fluorescent dye medium,” Can. J. Phys. 57(2), 160–167 (1979).
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G. Strangi, A. De Luca, S. Ravaine, M. Ferrie, and R. Bartolino, “Gain induced optical transparency in metamaterials,” Appl. Phys. Lett. 98(25), 251912 (2011).
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M. C. Gather, K. Meerholz, N. Danz, and K. Leosson, “Net optical gain in a plasmonic waveguide embedded in a fluorescent polymer,” Nat. Photonics 4(7), 457–461 (2010).
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R. Bardhan, N. K. Grady, J. R. Cole, A. Joshi, and N. J. Halas, “Fluorescence enhancement by Au nanostructures: nanoshells and nanorods,” ACS Nano 3(3), 744–752 (2009).
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R. Bardhan, N. K. Grady, J. R. Cole, A. Joshi, and N. J. Halas, “Fluorescence enhancement by Au nanostructures: nanoshells and nanorods,” ACS Nano 3(3), 744–752 (2009).
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N. K. Grady, N. J. Halas, and P. Nordlander, “Influence of dielectric function properties on the optical response of plasmon resonant metallic nanoparticles,” Chem. Phys. Lett. 399(1-3), 167–171 (2004).
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S. Wuestner, A. Pusch, K. L. Tsakmakidis, J. M. Hamm, and O. Hess, “Overcoming losses with gain in a negative refractive index metamaterial,” Phys. Rev. Lett. 105(12), 127401 (2010).
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S. Wuestner, A. Pusch, K. L. Tsakmakidis, J. M. Hamm, and O. Hess, “Overcoming losses with gain in a negative refractive index metamaterial,” Phys. Rev. Lett. 105(12), 127401 (2010).
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I. El-Kady, M. M. Sigalas, R. Biswas, K. M. Ho, and C. M. Soukoulis, “Metallic photonic crystals at optical wavelengths,” Phys. Rev. B 62(23), 15299–15302 (2000).
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D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006).
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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).
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Y. Sivan, S. 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).
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A. D. Boardman, V. V. Grimalsky, Y. S. Kivshar, S. V. Koshevaya, M. Lapine, N. M. Litchinitser, V. N. Malnev, M. Noginov, Y. G. Rapoport, and V. M. Shalaev, “Active and tunable metamaterials,” Laser Photon. Rev. 5(2), 287–307 (2011).
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A. Fang, Z. Huang, T. Koschny, and C. M. Soukoulis, “Overcoming the losses of a split ring resonator array with gain,” Opt. Express 19(13), 12688–12699 (2011).
[CrossRef] [PubMed]

A. Fang, T. Koschny, M. Wegener, and C. M. Soukoulis, “Self-consistent calculation of metamaterials with gain,” Phys. Rev. B 79(24), 241104 (2009).
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A. D. Boardman, V. V. Grimalsky, Y. S. Kivshar, S. V. Koshevaya, M. Lapine, N. M. Litchinitser, V. N. Malnev, M. Noginov, Y. G. Rapoport, and V. M. Shalaev, “Active and tunable metamaterials,” Laser Photon. Rev. 5(2), 287–307 (2011).
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A. De Luca, M. P. Grzelczak, I. Pastoriza-Santos, L. M. Liz-Marzán, M. La Deda, M. Striccoli, and G. Strangi, “Dispersed and encapsulated gain medium in plasmonic nanoparticles: a multipronged approach to mitigate optical losses,” ACS Nano 5(7), 5823–5829 (2011).
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J. Zhang, I. Gryczynski, Z. Gryczynski, and J. R. Lakowicz, “Dye-labeled silver nanoshell-bright particle,” J. Phys. Chem. B 110(18), 8986–8991 (2006).
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A. D. Boardman, V. V. Grimalsky, Y. S. Kivshar, S. V. Koshevaya, M. Lapine, N. M. Litchinitser, V. N. Malnev, M. Noginov, Y. G. Rapoport, and V. M. Shalaev, “Active and tunable metamaterials,” Laser Photon. Rev. 5(2), 287–307 (2011).
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A. D. Boardman, V. V. Grimalsky, Y. S. Kivshar, S. V. Koshevaya, M. Lapine, N. M. Litchinitser, V. N. Malnev, M. Noginov, Y. G. Rapoport, and V. M. Shalaev, “Active and tunable metamaterials,” Laser Photon. Rev. 5(2), 287–307 (2011).
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A. De Luca, M. P. Grzelczak, I. Pastoriza-Santos, L. M. Liz-Marzán, M. La Deda, M. Striccoli, and G. Strangi, “Dispersed and encapsulated gain medium in plasmonic nanoparticles: a multipronged approach to mitigate optical losses,” ACS Nano 5(7), 5823–5829 (2011).
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A. D. Boardman, V. V. Grimalsky, Y. S. Kivshar, S. V. Koshevaya, M. Lapine, N. M. Litchinitser, V. N. Malnev, M. Noginov, Y. G. Rapoport, and V. M. Shalaev, “Active and tunable metamaterials,” Laser Photon. Rev. 5(2), 287–307 (2011).
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M. C. Gather, K. Meerholz, N. Danz, and K. Leosson, “Net optical gain in a plasmonic waveguide embedded in a fluorescent polymer,” Nat. Photonics 4(7), 457–461 (2010).
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A. D. Boardman, V. V. Grimalsky, Y. S. Kivshar, S. V. Koshevaya, M. Lapine, N. M. Litchinitser, V. N. Malnev, M. Noginov, Y. G. Rapoport, and V. M. Shalaev, “Active and tunable metamaterials,” Laser Photon. Rev. 5(2), 287–307 (2011).
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M. A. Noginov, G. Zhu, M. Bahoura, J. Adegoke, C. Small, B. A. Ritzo, V. P. Drachev, and V. M. Shalaev, “The effect of gain and absorption on surface plasmons in metal nanoparticles,” Appl. Phys. B 86(3), 455–460 (2007).
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N. K. Grady, N. J. Halas, and P. Nordlander, “Influence of dielectric function properties on the optical response of plasmon resonant metallic nanoparticles,” Chem. Phys. Lett. 399(1-3), 167–171 (2004).
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A. De Luca, M. P. Grzelczak, I. Pastoriza-Santos, L. M. Liz-Marzán, M. La Deda, M. Striccoli, and G. Strangi, “Dispersed and encapsulated gain medium in plasmonic nanoparticles: a multipronged approach to mitigate optical losses,” ACS Nano 5(7), 5823–5829 (2011).
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D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006).
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S. Wuestner, A. Pusch, K. L. Tsakmakidis, J. M. Hamm, and O. Hess, “Overcoming losses with gain in a negative refractive index metamaterial,” Phys. Rev. Lett. 105(12), 127401 (2010).
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A. D. Boardman, V. V. Grimalsky, Y. S. Kivshar, S. V. Koshevaya, M. Lapine, N. M. Litchinitser, V. N. Malnev, M. Noginov, Y. G. Rapoport, and V. M. Shalaev, “Active and tunable metamaterials,” Laser Photon. Rev. 5(2), 287–307 (2011).
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G. Strangi, A. De Luca, S. Ravaine, M. Ferrie, and R. Bartolino, “Gain induced optical transparency in metamaterials,” Appl. Phys. Lett. 98(25), 251912 (2011).
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M. A. R. C. Alencar, G. S. Maciel, C. B. de Araújo, R. Bertholdo, Y. Messaddeq, and S. J. L. Ribeiro, “Laserlike emission from silica inverse opals infiltrated with Rhodamine 6G,” J. Non-Cryst. Solids 351(21-23), 1846–1849 (2005).
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M. A. Noginov, G. Zhu, M. Bahoura, J. Adegoke, C. Small, B. A. Ritzo, V. P. Drachev, and V. M. Shalaev, “The effect of gain and absorption on surface plasmons in metal nanoparticles,” Appl. Phys. B 86(3), 455–460 (2007).
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D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006).
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D. Magde, R. Wong, and P. G. Seybold, “Fluorescence quantum yields and their relation to lifetimes of rhodamine 6G and fluorescein in nine solvents: improved absolute standards for quantum yields,” Photochem. Photobiol. 75(4), 327–334 (2002).
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A. D. Boardman, V. V. Grimalsky, Y. S. Kivshar, S. V. Koshevaya, M. Lapine, N. M. Litchinitser, V. N. Malnev, M. Noginov, Y. G. Rapoport, and V. M. Shalaev, “Active and tunable metamaterials,” Laser Photon. Rev. 5(2), 287–307 (2011).
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Y. Sivan, S. 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).
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I. El-Kady, M. M. Sigalas, R. Biswas, K. M. Ho, and C. M. Soukoulis, “Metallic photonic crystals at optical wavelengths,” Phys. Rev. B 62(23), 15299–15302 (2000).
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Small, C.

M. A. Noginov, G. Zhu, M. Bahoura, J. Adegoke, C. Small, B. A. Ritzo, V. P. Drachev, and V. M. Shalaev, “The effect of gain and absorption on surface plasmons in metal nanoparticles,” Appl. Phys. B 86(3), 455–460 (2007).
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D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006).
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A. Fang, Z. Huang, T. Koschny, and C. M. Soukoulis, “Overcoming the losses of a split ring resonator array with gain,” Opt. Express 19(13), 12688–12699 (2011).
[CrossRef] [PubMed]

A. Fang, T. Koschny, M. Wegener, and C. M. Soukoulis, “Self-consistent calculation of metamaterials with gain,” Phys. Rev. B 79(24), 241104 (2009).
[CrossRef]

I. El-Kady, M. M. Sigalas, R. Biswas, K. M. Ho, and C. M. Soukoulis, “Metallic photonic crystals at optical wavelengths,” Phys. Rev. B 62(23), 15299–15302 (2000).
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P. Sperber, W. Spangler, B. Meier, and A. Penzkofer, “Experimental and theoretical investigation of tunable picosecond pulse generation in longitudinally pumped dye-laser generators and amplifiers,” Opt. Quantum Electron. 20(5), 395–431 (1988).
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P. Sperber, W. Spangler, B. Meier, and A. Penzkofer, “Experimental and theoretical investigation of tunable picosecond pulse generation in longitudinally pumped dye-laser generators and amplifiers,” Opt. Quantum Electron. 20(5), 395–431 (1988).
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D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006).
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G. Strangi, A. De Luca, S. Ravaine, M. Ferrie, and R. Bartolino, “Gain induced optical transparency in metamaterials,” Appl. Phys. Lett. 98(25), 251912 (2011).
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A. De Luca, M. P. Grzelczak, I. Pastoriza-Santos, L. M. Liz-Marzán, M. La Deda, M. Striccoli, and G. Strangi, “Dispersed and encapsulated gain medium in plasmonic nanoparticles: a multipronged approach to mitigate optical losses,” ACS Nano 5(7), 5823–5829 (2011).
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Figures (7)

Fig. 1
Fig. 1

3D periodic array of dielectric-core metallic-shell nanospheres embedded in a homogeneous medium with permittivity ε h . The core radius is r1, with permittivity ε1; the shell outer radius is r2, with permittivity ε2; a, b and c are the periodicities along x-, y- and z-direction, respectively. (a) The shell is made of silver. (b) The shell is made of gold.

Fig. 2
Fig. 2

Wavenumber dispersion diagram versus frequency for T-pol for the structure in Fig. 1(a), using the polarizability in Eq. (3). (a) Real part and (b) imaginary part of the wavenumber k z = β z + i α z , for lossy, lossless and loss-compensated cases.

Fig. 3
Fig. 3

(a) Real part and (b) imaginary part of the effective relative permittivity for the structure in Fig. 1(a) computed in three different ways: by Maxwell Garnett, by using the polarizability in (2) (MG – CM); the polarizability in Eq. (3) (MG – Mie); and mode analysis.

Fig. 4
Fig. 4

(a) Real and (b) imaginary parts of the relative effective permittivity for the case in Fig. 3, obtained from mode analysis with polarizability in Eq. (3), in the epsilon-near-zero region around 526 THz.

Fig. 5
Fig. 5

Wavenumber dispersion diagram versus frequency for T-pol for the structure in Fig. 1(b), using the polarizability in Eq. (3). (a) Real part and (b) imaginary part of the wavenumber k z = β z + i α z , for lossy, lossless and loss compensated cases.

Fig. 6
Fig. 6

(a) Real part and (b) imaginary part of the effective relative permittivity for the structure in Fig. 1(b) computed in three different ways: by Maxwell Garnett, by using the polarizability in Eq. (2) (MG – CM); the polarizability in Eq. (3) (MG – Mie); and mode analysis.

Fig. 7
Fig. 7

(a) Real and (b) imaginary parts of the relative effective permittivity for the case in Fig. 5, obtained from mode analysis with polarizability in Eq. (3), in the epsilon-near-zero region around 421 THz.

Equations (14)

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p = α ee E loc ,
α ee 1 = 1 4 π ε h ε 0 r 2 3 ( ε 2 + 2 ε h ) ( ε 1 + 2 ε 2 ) + 2 β ( ε 2 ε h ) ( ε 1 ε 2 ) ( ε 2 ε h ) ( ε 1 + 2 ε 2 ) + β ( 2 ε 2 + ε h ) ( ε 1 ε 2 ) i k 3 6 π ε h ε 0 ,
α ee = 6 π i ε h ε 0 k 3 ψ 1 ( k r 2 ) A m 2 ψ 1 ( k r 2 ) B ξ 1 ( k r 2 ) A m 2 ξ 1 ( k r 2 ) B , A = ψ 1 ( m 2 k r 2 ) C χ 1 ( m 2 k r 2 ) ,
B = ψ 1 ( m 2 k r 2 ) C χ 1 ( m 2 k r 2 ) , C = m 2 ψ 1 ( m 2 k r 1 ) ψ 1 ( m 1 k r 1 ) m 1 ψ 1 ( m 2 k r 1 ) ψ 1 ( m 1 k r 1 ) m 2 χ 1 ( m 2 k r 1 ) ψ 1 ( m 1 k r 1 ) m 1 χ 1 ( m 2 k r 1 ) ψ 1 ( m 1 k r 1 ) ,
ε m = ε ω p 2 ω ( ω + i γ ) ,
A _ ( k B ) p 0 = α ee E inc ( r 0 ) ,    A _ ( k B ) = I _ α ee G _ ( r 0 , r 0 , k B ) ,
ε eff = ε h + ε h N D 1 [ ε 0 ε h α ee 1 + i k 3 6 π ] 1 3 ,       μ eff = 1 + 1 N D 1 [ α mm 1 + i k 3 6 π ] 1 3 ,
n eff = k z k 0 ,
2 t 2 P e ( r , t ) + Δ ω a t P e ( r , t ) + ω a 2 P e ( r , t ) = σ a Δ N ( r , t ) E ( r , t ) ,
P e ( r ) = ε 0 χ e E ( r ) , χ e = 1 ε 0 σ a Δ N ω 2 + i Δ ω a ω ω a 2 .
D ( r ) = ε 0 E ( r ) + P r ( r ) + P e ( r ) = ε 0 ε r E ( r ) + P e ( r ) ,
ε g = ε 0 ε r + σ a Δ N ω 2 + i Δ ω a ω ω a 2
Δ N = ( τ 21 τ 10 ) Γ pump 1 + ( τ 32 + τ 21 + τ 10 ) Γ pump N ¯ 0
ε g = ε 0 ε r + σ a ω 2 + i Δ ω a ω ω a 2 ( τ 21 τ 10 ) Γ pump 1 + ( τ 32 + τ 21 + τ 10 ) Γ pump N ¯ 0

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