Abstract

We solve the equations governing light propagation in a negative-index material with embedded nonlinearly saturable gain material using a frequency-domain model. We show that available gain materials can lead to complete loss compensation only if they are located in the regions where the field enhancement is maximal. We study the increased enhancement of the fields in the gain composite as well as in the metal inclusions and show analytically that the effective gain is determined by the average near-field enhancement.

© 2009 OSA

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2009 (7)

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460(7259), 1110–1112 (2009).
[CrossRef] [PubMed]

N. M. Litchinitser and V. M. Shalaev, “Metamaterials: Loss as a route to transparency,” Nat. Photonics 3(2), 75 (2009).
[CrossRef]

N. Liu, L. Langguth, T. Weiss, J. Kästel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit,” Nat. Mater. 8(9), 758–762 (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]

Z. Liu, M. D. Thoreson, A. V. Kildishev, and V. M. Shalaev, “Translation of nanoantenna hot spots by a metal-dielectric composite superlens,” Appl. Phys. Lett. 95(3), 033114 (2009).
[CrossRef]

E. Plum, V. A. Fedotov, P. Kuo, D. P. Tsai, and N. I. Zheludev, “Towards the lasing spaser: controlling metamaterial optical response with semiconductor quantum dots,” Opt. Express 17(10), 8548–8551 (2009).
[CrossRef] [PubMed]

M. T. Hill, M. Marell, E. S. P. Leong, B. Smalbrugge, Y. Zhu, M. Sun, P. J. van Veldhoven, E. J. Geluk, F. Karouta, Y. S. Oei, R. Nötzel, C. Z. Ning, and M. K. Smit, “Lasing in metal-insulator-metal sub-wavelength plasmonic waveguides,” Opt. Express 17(13), 11107–11112 (2009).
[CrossRef] [PubMed]

2008 (14)

P. Kinsler and M. W. McCall, “Causality-based criteria for a negative refractive index must be used with care,” Phys. Rev. Lett. 101(16), 167401 (2008).
[CrossRef] [PubMed]

G. Zhu, M. Mayy, M. Bahoura, B. A. Ritzo, H. V. Gavrilenko, V. I. Gavrilenko, and M. A. Noginov, “Elongation of surface plasmon polariton propagation length without gain,” Opt. Express 16(20), 15576–15583 (2008).
[CrossRef] [PubMed]

M. Wegener, J. L. García-Pomar, C. M. Soukoulis, N. Meinzer, M. Ruther, and S. Linden, “Toy model for plasmonic metamaterial resonances coupled to two-level system gain,” Opt. Express 16(24), 19785–19798 (2008).
[CrossRef] [PubMed]

K. R. Catchpole and A. Polman, “Plasmonic solar cells,” Opt. Express 16(26), 21793–21800 (2008).
[CrossRef] [PubMed]

N. I. Zheludev, S. L. Prosvirnin, N. Papasimakis, and V. A. Fedotov, “Lasing-spaser,” Nat. Photonics 2(6), 351–354 (2008).
[CrossRef]

J. B. Pendry, “Time reversal and negative refraction,” Science 322(5898), 71–73 (2008).
[CrossRef] [PubMed]

M. A. Noginov, G. Zhu, M. Mayy, B. A. Ritzo, N. Noginova, and V. A. Podolskiy, “Stimulated emission of surface plasmon polaritons,” Phys. Rev. Lett. 101(22), 226806 (2008).
[CrossRef] [PubMed]

I. De Leon and P. Berini, “Theory of surface plasmon-polariton amplification in planar structures incorporating dipolar gain media,” Phys. Rev. B 78(16), 161401 (2008).
[CrossRef]

M. Ambati, S. H. Nam, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Observation of stimulated emission of surface plasmon polaritons,” Nano Lett. 8(11), 3998–4001 (2008).
[CrossRef] [PubMed]

M. Ambati, D. A. Genov, R. F. Oulton, and X. Zhang, ““Active Plasmonics: Surface Plasmon Interaction with optical emitters,” IEEE J. Sel. Top. Quantum Electron. 14(6), 1395–1403 (2008).
[CrossRef]

S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101(4), 047401 (2008).
[CrossRef] [PubMed]

N. Papasimakis, V. A. Fedotov, N. I. Zheludev, and S. L. Prosvirnin, “Metamaterial analog of electromagnetically induced transparency,” Phys. Rev. Lett. 101(25), 253903 (2008).
[CrossRef] [PubMed]

U. K. Chettiar, S. Xiao, A. V. Kildishev, W. Cai, H.-K. Yuan, V. P. Drachev, and V. M. Shalaev, “Optical Metamagnetism and Negative-Index Metamaterials,” MRS Bull. 33, 921 (2008).
[CrossRef]

N. M. Litchinitser, I. R. Gabitov, A. I. Maimistov, and V. M. Shalaev, “Negative refractive index metamaterials in optics,” Progress in Optics 51, 1–67 (2008).
[CrossRef]

2007 (7)

V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics 1(1), 41 (2007).
[CrossRef]

C. M. Soukoulis, S. Linden, and M. Wegener, “Physics. Negative refractive index at optical wavelengths,” Science 315(5808), 47–49 (2007).
[CrossRef] [PubMed]

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

J. A. Gordon and R. W. Ziolkowski, “The design and simulated performance of a coated nano-particle laser,” Opt. Express 15(5), 2622–2653 (2007).
[CrossRef] [PubMed]

W. Cai, U. K. Chettiar, H.-K. Yuan, V. C. de Silva, A. V. Kildishev, V. P. Drachev, and V. M. Shalaev, “Metamagnetics with rainbow colors,” Opt. Express 15(6), 3333 (2007).
[CrossRef] [PubMed]

S. V. Zhukovsky and D. N. Chigrin, “Numerical modeling of lasing in microstructures,” Phys. Status Solidi, B Basic Res. 244(10), 3515–3527 (2007).
[CrossRef]

2006 (9)

T. A. Klar, A. V. Kildishev, V. P. Drachev, and V. M. Shalaev, “Negative-index materials: going optical,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1106–1115 (2006).
[CrossRef]

A. K. Popov and V. M. Shalaev, “Compensating losses in negative-index metamaterials by optical parametric amplification,” Opt. Lett. 31(14), 2169–2171 (2006).
[CrossRef] [PubMed]

U. K. Chettiar, A. V. Kildishev, T. A. Klar, and V. M. Shalaev, “Negative index metamaterial combining magnetic resonators with metal films,” Opt. Express 14(17), 7872–7877 (2006).
[CrossRef] [PubMed]

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

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]

S. A. Maier, “Gain-assisted propagation of electromagnetic energy in subwavelength surface plasmon polariton gap waveguides,” Opt. Commun. 258(2), 295–299 (2006).
[CrossRef]

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

U. Leonhardt, “Optical conformal mapping,” Science 312(5781), 1777–1780 (2006).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[CrossRef] [PubMed]

2005 (2)

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. M. Shalaev, W. Cai, U. K. Chettiar, H. K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, “Negative index of refraction in optical metamaterials,” Opt. Lett. 30(24), 3356–3358 (2005).
[CrossRef] [PubMed]

2004 (3)

M. P. Nezhad, K. Tetz, and Y. Fainman, “Gain assisted propagation of surface plasmon polaritons on planar metallic waveguides,” Opt. Express 12(17), 4072–4079 (2004).
[CrossRef] [PubMed]

I. Avrutsky, “Surface plasmons at nanoscale relief gratings between a metal and a dielectric medium with optical gain,” Phys. Rev. B 70(15), 155416 (2004).
[CrossRef]

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

2003 (3)

S. A. Ramakrishna and J. B. 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]

T. Koschny, P. Markoš, D. R. Smith, and C. M. Soukoulis, “Resonant and antiresonant frequency dependence of the effective parameters of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 68(6), 065602 (2003).
[CrossRef] [PubMed]

2002 (1)

D. R. Smith, S. Schultz, P. Markoš, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65(19), 195104 (2002).
[CrossRef]

2001 (1)

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001).
[CrossRef] [PubMed]

2000 (4)

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

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84(18), 4184–4187 (2000).
[CrossRef] [PubMed]

V. I. Klimov, A. A. Mikhailovsky, S. Xu, A. Malko, J. A. Hollingsworth, C. A. Leatherdale, H.-J. Eisler, and M. G. Bawendi, “Optical gain and stimulated emission in nanocrystal quantum dots,” Science 290(5490), 314–317 (2000).
[CrossRef] [PubMed]

A. K. Sarychev, R. C. McPhedran, and V. M. Shalaev, “Electrodynamics of metal-dielectric composites and electromagnetic crystals,” Phys. Rev. B 62(12), 8531–8539 (2000).
[CrossRef]

1999 (1)

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magentism from conductors and enhanced nonlinear phenomena,” IEEE Microw. Theory Tech. 47(11), 2075–2084 (1999).
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1998 (1)

W. L. Barnes, “Fluorescence near interfaces: the role of photonic mode density,” J. Mod. Opt. 45, 661 (1998).
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1997 (1)

F. Hide, B. J. Schwartz, M. A. Dias-Garcia, and A. J. Heeger, “Conjugated polymers as solid-state laser materials,” Synth. Met. 91(1-3), 35–40 (1997).
[CrossRef]

1989 (1)

A. N. Sudarkin and P. A. Demkovich, “Excitation of Excitation of surface electromagnetic waves on the boundary of a metal with an amplifying medium,” Sov. Phys. Tech. Phys. 34, 764 (1989).

1984 (1)

G. W. Ford and W. H. Weber, “Electromagnetic interactions of molecules with metal surfaces,” Phys. Rep. 113(4), 195–287 (1984).
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1975 (1)

C. V. Shank, “Physics of dye lasers,” Rev. Mod. Phys. 47(3), 649–657 (1975).
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Alekseyev, L. V.

A. J. Hoffman, L. V. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, “Negative refraction in semiconductor metamaterials,” Nat. Mater. 6(12), 946–950 (2007).
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Z. Jacob, L. V. Alekseyev, and E. E. Narimanov, “Optical Hyperlens: Far-field imaging beyond the diffraction limit,” Opt. Express 14(18), 8247–8256 (2006).
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M. Ambati, D. A. Genov, R. F. Oulton, and X. Zhang, ““Active Plasmonics: Surface Plasmon Interaction with optical emitters,” IEEE J. Sel. Top. Quantum Electron. 14(6), 1395–1403 (2008).
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M. Ambati, S. H. Nam, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Observation of stimulated emission of surface plasmon polaritons,” Nano Lett. 8(11), 3998–4001 (2008).
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Bakker, R.

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460(7259), 1110–1112 (2009).
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W. L. Barnes, “Fluorescence near interfaces: the role of photonic mode density,” J. Mod. Opt. 45, 661 (1998).
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M. Ambati, S. H. Nam, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Observation of stimulated emission of surface plasmon polaritons,” Nano Lett. 8(11), 3998–4001 (2008).
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V. I. Klimov, A. A. Mikhailovsky, S. Xu, A. Malko, J. A. Hollingsworth, C. A. Leatherdale, H.-J. Eisler, and M. G. Bawendi, “Optical gain and stimulated emission in nanocrystal quantum dots,” Science 290(5490), 314–317 (2000).
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M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460(7259), 1110–1112 (2009).
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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).
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I. De Leon and P. Berini, “Theory of surface plasmon-polariton amplification in planar structures incorporating dipolar gain media,” Phys. Rev. B 78(16), 161401 (2008).
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I. De Leon and P. Berini, “Modeling surface plasmon-polariton gain in planar metallic structures,” Opt. Express (to appear).
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S. V. Zhukovsky and D. N. Chigrin, “Numerical modeling of lasing in microstructures,” Phys. Status Solidi, B Basic Res. 244(10), 3515–3527 (2007).
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I. De Leon and P. Berini, “Theory of surface plasmon-polariton amplification in planar structures incorporating dipolar gain media,” Phys. Rev. B 78(16), 161401 (2008).
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I. De Leon and P. Berini, “Modeling surface plasmon-polariton gain in planar metallic structures,” Opt. Express (to appear).
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de Silva, V. C.

Demkovich, P. A.

A. N. Sudarkin and P. A. Demkovich, “Excitation of Excitation of surface electromagnetic waves on the boundary of a metal with an amplifying medium,” Sov. Phys. Tech. Phys. 34, 764 (1989).

Dias-Garcia, M. A.

F. Hide, B. J. Schwartz, M. A. Dias-Garcia, and A. J. Heeger, “Conjugated polymers as solid-state laser materials,” Synth. Met. 91(1-3), 35–40 (1997).
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U. K. Chettiar, S. Xiao, A. V. Kildishev, W. Cai, H.-K. Yuan, V. P. Drachev, and V. M. Shalaev, “Optical Metamagnetism and Negative-Index Metamaterials,” MRS Bull. 33, 921 (2008).
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W. Cai, U. K. Chettiar, H.-K. Yuan, V. C. de Silva, A. V. Kildishev, V. P. Drachev, and V. M. Shalaev, “Metamagnetics with rainbow colors,” Opt. Express 15(6), 3333 (2007).
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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).
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T. A. Klar, A. V. Kildishev, V. P. Drachev, and V. M. Shalaev, “Negative-index materials: going optical,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1106–1115 (2006).
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V. M. Shalaev, W. Cai, U. K. Chettiar, H. K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, “Negative index of refraction in optical metamaterials,” Opt. Lett. 30(24), 3356–3358 (2005).
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S. Xiao, U. K. Chettiar, A. V. Kildishev, V. P. Drachev, and V. M. Shalaev, “Yellow-light negative-index metamaterials,” Opt. Lett. (accepted).
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V. I. Klimov, A. A. Mikhailovsky, S. Xu, A. Malko, J. A. Hollingsworth, C. A. Leatherdale, H.-J. Eisler, and M. G. Bawendi, “Optical gain and stimulated emission in nanocrystal quantum dots,” Science 290(5490), 314–317 (2000).
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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).
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A. Salandrino and N. Engheta, “Subdiffraction optical microscopy using metamaterial crystals: Theory and simulations,” Phys. Rev. B 74(7), 075103 (2006).
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Fang, A.

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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E. Plum, V. A. Fedotov, P. Kuo, D. P. Tsai, and N. I. Zheludev, “Towards the lasing spaser: controlling metamaterial optical response with semiconductor quantum dots,” Opt. Express 17(10), 8548–8551 (2009).
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N. Liu, L. Langguth, T. Weiss, J. Kästel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit,” Nat. Mater. 8(9), 758–762 (2009).
[CrossRef] [PubMed]

Ford, G. W.

G. W. Ford and W. H. Weber, “Electromagnetic interactions of molecules with metal surfaces,” Phys. Rep. 113(4), 195–287 (1984).
[CrossRef]

Franz, K. J.

A. J. Hoffman, L. V. 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]

Gabitov, I. R.

N. M. Litchinitser, I. R. Gabitov, A. I. Maimistov, and V. M. Shalaev, “Negative refractive index metamaterials in optics,” Progress in Optics 51, 1–67 (2008).
[CrossRef]

García-Pomar, J. L.

Gavrilenko, H. V.

Gavrilenko, V. I.

Geluk, E. J.

Genov, D. A.

M. Ambati, S. H. Nam, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Observation of stimulated emission of surface plasmon polaritons,” Nano Lett. 8(11), 3998–4001 (2008).
[CrossRef] [PubMed]

S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101(4), 047401 (2008).
[CrossRef] [PubMed]

M. Ambati, D. A. Genov, R. F. Oulton, and X. Zhang, ““Active Plasmonics: Surface Plasmon Interaction with optical emitters,” IEEE J. Sel. Top. Quantum Electron. 14(6), 1395–1403 (2008).
[CrossRef]

Giessen, H.

N. Liu, L. Langguth, T. Weiss, J. Kästel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit,” Nat. Mater. 8(9), 758–762 (2009).
[CrossRef] [PubMed]

Gmachl, C.

A. J. Hoffman, L. V. 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]

Gordon, J. A.

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]

Heeger, A. J.

F. Hide, B. J. Schwartz, M. A. Dias-Garcia, and A. J. Heeger, “Conjugated polymers as solid-state laser materials,” Synth. Met. 91(1-3), 35–40 (1997).
[CrossRef]

Herz, E.

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460(7259), 1110–1112 (2009).
[CrossRef] [PubMed]

Hide, F.

F. Hide, B. J. Schwartz, M. A. Dias-Garcia, and A. J. Heeger, “Conjugated polymers as solid-state laser materials,” Synth. Met. 91(1-3), 35–40 (1997).
[CrossRef]

Hill, M. T.

Hoffman, A. J.

A. J. Hoffman, L. V. 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]

Holden, A. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magentism from conductors and enhanced nonlinear phenomena,” IEEE Microw. Theory Tech. 47(11), 2075–2084 (1999).
[CrossRef]

Hollingsworth, J. A.

V. I. Klimov, A. A. Mikhailovsky, S. Xu, A. Malko, J. A. Hollingsworth, C. A. Leatherdale, H.-J. Eisler, and M. G. Bawendi, “Optical gain and stimulated emission in nanocrystal quantum dots,” Science 290(5490), 314–317 (2000).
[CrossRef] [PubMed]

Howard, S. S.

A. J. Hoffman, L. V. 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]

Jacob, Z.

Karouta, F.

Kästel, J.

N. Liu, L. Langguth, T. Weiss, J. Kästel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit,” Nat. Mater. 8(9), 758–762 (2009).
[CrossRef] [PubMed]

Kildishev, A. V.

Z. Liu, M. D. Thoreson, A. V. Kildishev, and V. M. Shalaev, “Translation of nanoantenna hot spots by a metal-dielectric composite superlens,” Appl. Phys. Lett. 95(3), 033114 (2009).
[CrossRef]

U. K. Chettiar, S. Xiao, A. V. Kildishev, W. Cai, H.-K. Yuan, V. P. Drachev, and V. M. Shalaev, “Optical Metamagnetism and Negative-Index Metamaterials,” MRS Bull. 33, 921 (2008).
[CrossRef]

W. Cai, U. K. Chettiar, H.-K. Yuan, V. C. de Silva, A. V. Kildishev, V. P. Drachev, and V. M. Shalaev, “Metamagnetics with rainbow colors,” Opt. Express 15(6), 3333 (2007).
[CrossRef] [PubMed]

U. K. Chettiar, A. V. Kildishev, T. A. Klar, and V. M. Shalaev, “Negative index metamaterial combining magnetic resonators with metal films,” Opt. Express 14(17), 7872–7877 (2006).
[CrossRef] [PubMed]

T. A. Klar, A. V. Kildishev, V. P. Drachev, and V. M. Shalaev, “Negative-index materials: going optical,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1106–1115 (2006).
[CrossRef]

V. M. Shalaev, W. Cai, U. K. Chettiar, H. K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, “Negative index of refraction in optical metamaterials,” Opt. Lett. 30(24), 3356–3358 (2005).
[CrossRef] [PubMed]

S. Xiao, U. K. Chettiar, A. V. Kildishev, V. P. Drachev, and V. M. Shalaev, “Yellow-light negative-index metamaterials,” Opt. Lett. (accepted).
[PubMed]

Kinsler, P.

P. Kinsler and M. W. McCall, “Causality-based criteria for a negative refractive index must be used with care,” Phys. Rev. Lett. 101(16), 167401 (2008).
[CrossRef] [PubMed]

Klar, T. A.

T. A. Klar, A. V. Kildishev, V. P. Drachev, and V. M. Shalaev, “Negative-index materials: going optical,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1106–1115 (2006).
[CrossRef]

U. K. Chettiar, A. V. Kildishev, T. A. Klar, and V. M. Shalaev, “Negative index metamaterial combining magnetic resonators with metal films,” Opt. Express 14(17), 7872–7877 (2006).
[CrossRef] [PubMed]

Klimov, V. I.

V. I. Klimov, A. A. Mikhailovsky, S. Xu, A. Malko, J. A. Hollingsworth, C. A. Leatherdale, H.-J. Eisler, and M. G. Bawendi, “Optical gain and stimulated emission in nanocrystal quantum dots,” Science 290(5490), 314–317 (2000).
[CrossRef] [PubMed]

Koschny, T.

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]

T. Koschny, P. Markoš, D. R. Smith, and C. M. Soukoulis, “Resonant and antiresonant frequency dependence of the effective parameters of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 68(6), 065602 (2003).
[CrossRef] [PubMed]

Kuo, P.

Langguth, L.

N. Liu, L. Langguth, T. Weiss, J. Kästel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit,” Nat. Mater. 8(9), 758–762 (2009).
[CrossRef] [PubMed]

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

Leatherdale, C. A.

V. I. Klimov, A. A. Mikhailovsky, S. Xu, A. Malko, J. A. Hollingsworth, C. A. Leatherdale, H.-J. Eisler, and M. G. Bawendi, “Optical gain and stimulated emission in nanocrystal quantum dots,” Science 290(5490), 314–317 (2000).
[CrossRef] [PubMed]

Leong, E. S. P.

Leonhardt, U.

U. Leonhardt, “Optical conformal mapping,” Science 312(5781), 1777–1780 (2006).
[CrossRef] [PubMed]

Linden, S.

Litchinitser, N. M.

N. M. Litchinitser and V. M. Shalaev, “Metamaterials: Loss as a route to transparency,” Nat. Photonics 3(2), 75 (2009).
[CrossRef]

N. M. Litchinitser, I. R. Gabitov, A. I. Maimistov, and V. M. Shalaev, “Negative refractive index metamaterials in optics,” Progress in Optics 51, 1–67 (2008).
[CrossRef]

Liu, M.

S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101(4), 047401 (2008).
[CrossRef] [PubMed]

Liu, N.

N. Liu, L. Langguth, T. Weiss, J. Kästel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit,” Nat. Mater. 8(9), 758–762 (2009).
[CrossRef] [PubMed]

Liu, Z.

Z. Liu, M. D. Thoreson, A. V. Kildishev, and V. M. Shalaev, “Translation of nanoantenna hot spots by a metal-dielectric composite superlens,” Appl. Phys. Lett. 95(3), 033114 (2009).
[CrossRef]

Maier, S. A.

S. A. Maier, “Gain-assisted propagation of electromagnetic energy in subwavelength surface plasmon polariton gap waveguides,” Opt. Commun. 258(2), 295–299 (2006).
[CrossRef]

Maimistov, A. I.

N. M. Litchinitser, I. R. Gabitov, A. I. Maimistov, and V. M. Shalaev, “Negative refractive index metamaterials in optics,” Progress in Optics 51, 1–67 (2008).
[CrossRef]

Malko, A.

V. I. Klimov, A. A. Mikhailovsky, S. Xu, A. Malko, J. A. Hollingsworth, C. A. Leatherdale, H.-J. Eisler, and M. G. Bawendi, “Optical gain and stimulated emission in nanocrystal quantum dots,” Science 290(5490), 314–317 (2000).
[CrossRef] [PubMed]

Marell, M.

Markoš, P.

T. Koschny, P. Markoš, D. R. Smith, and C. M. Soukoulis, “Resonant and antiresonant frequency dependence of the effective parameters of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 68(6), 065602 (2003).
[CrossRef] [PubMed]

D. R. Smith, S. Schultz, P. Markoš, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65(19), 195104 (2002).
[CrossRef]

Mayy, M.

M. A. Noginov, G. Zhu, M. Mayy, B. A. Ritzo, N. Noginova, and V. A. Podolskiy, “Stimulated emission of surface plasmon polaritons,” Phys. Rev. Lett. 101(22), 226806 (2008).
[CrossRef] [PubMed]

G. Zhu, M. Mayy, M. Bahoura, B. A. Ritzo, H. V. Gavrilenko, V. I. Gavrilenko, and M. A. Noginov, “Elongation of surface plasmon polariton propagation length without gain,” Opt. Express 16(20), 15576–15583 (2008).
[CrossRef] [PubMed]

McCall, M. W.

P. Kinsler and M. W. McCall, “Causality-based criteria for a negative refractive index must be used with care,” Phys. Rev. Lett. 101(16), 167401 (2008).
[CrossRef] [PubMed]

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A. K. Sarychev, R. C. McPhedran, and V. M. Shalaev, “Electrodynamics of metal-dielectric composites and electromagnetic crystals,” Phys. Rev. B 62(12), 8531–8539 (2000).
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Meinzer, N.

Mikhailovsky, A. A.

V. I. Klimov, A. A. Mikhailovsky, S. Xu, A. Malko, J. A. Hollingsworth, C. A. Leatherdale, H.-J. Eisler, and M. G. Bawendi, “Optical gain and stimulated emission in nanocrystal quantum dots,” Science 290(5490), 314–317 (2000).
[CrossRef] [PubMed]

Nam, S. H.

M. Ambati, S. H. Nam, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Observation of stimulated emission of surface plasmon polaritons,” Nano Lett. 8(11), 3998–4001 (2008).
[CrossRef] [PubMed]

Narimanov, E. E.

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460(7259), 1110–1112 (2009).
[CrossRef] [PubMed]

A. J. Hoffman, L. V. 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]

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

Nemat-Nasser, S. C.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84(18), 4184–4187 (2000).
[CrossRef] [PubMed]

Nezhad, M. P.

Ning, C. Z.

Noginov, M. A.

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460(7259), 1110–1112 (2009).
[CrossRef] [PubMed]

G. Zhu, M. Mayy, M. Bahoura, B. A. Ritzo, H. V. Gavrilenko, V. I. Gavrilenko, and M. A. Noginov, “Elongation of surface plasmon polariton propagation length without gain,” Opt. Express 16(20), 15576–15583 (2008).
[CrossRef] [PubMed]

M. A. Noginov, G. Zhu, M. Mayy, B. A. Ritzo, N. Noginova, and V. A. Podolskiy, “Stimulated emission of surface plasmon polaritons,” Phys. Rev. Lett. 101(22), 226806 (2008).
[CrossRef] [PubMed]

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]

Noginova, N.

M. A. Noginov, G. Zhu, M. Mayy, B. A. Ritzo, N. Noginova, and V. A. Podolskiy, “Stimulated emission of surface plasmon polaritons,” Phys. Rev. Lett. 101(22), 226806 (2008).
[CrossRef] [PubMed]

Nötzel, R.

Oei, Y. S.

Oulton, R. F.

M. Ambati, D. A. Genov, R. F. Oulton, and X. Zhang, ““Active Plasmonics: Surface Plasmon Interaction with optical emitters,” IEEE J. Sel. Top. Quantum Electron. 14(6), 1395–1403 (2008).
[CrossRef]

Padilla, W. J.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84(18), 4184–4187 (2000).
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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).
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S. Xiao, U. K. Chettiar, A. V. Kildishev, V. P. Drachev, and V. M. Shalaev, “Yellow-light negative-index metamaterials,” Opt. Lett. (accepted).
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M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460(7259), 1110–1112 (2009).
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IEEE J. Sel. Top. Quantum Electron. (2)

M. Ambati, D. A. Genov, R. F. Oulton, and X. Zhang, ““Active Plasmonics: Surface Plasmon Interaction with optical emitters,” IEEE J. Sel. Top. Quantum Electron. 14(6), 1395–1403 (2008).
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IEEE Microw. Theory Tech. (1)

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Nano Lett. (1)

M. Ambati, S. H. Nam, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Observation of stimulated emission of surface plasmon polaritons,” Nano Lett. 8(11), 3998–4001 (2008).
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Nat. Mater. (2)

N. Liu, L. Langguth, T. Weiss, J. Kästel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit,” Nat. Mater. 8(9), 758–762 (2009).
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Nat. Photonics (3)

V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics 1(1), 41 (2007).
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N. M. Litchinitser and V. M. Shalaev, “Metamaterials: Loss as a route to transparency,” Nat. Photonics 3(2), 75 (2009).
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Nature (1)

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460(7259), 1110–1112 (2009).
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Opt. Commun. (1)

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Opt. Express (11)

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M. P. Nezhad, K. Tetz, and Y. Fainman, “Gain assisted propagation of surface plasmon polaritons on planar metallic waveguides,” Opt. Express 12(17), 4072–4079 (2004).
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U. K. Chettiar, A. V. Kildishev, T. A. Klar, and V. M. Shalaev, “Negative index metamaterial combining magnetic resonators with metal films,” Opt. Express 14(17), 7872–7877 (2006).
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Z. Jacob, L. V. Alekseyev, and E. E. Narimanov, “Optical Hyperlens: Far-field imaging beyond the diffraction limit,” Opt. Express 14(18), 8247–8256 (2006).
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The field distributions for samples 1 and 2 are similar for the pump wavelength and the chosen level of pumping because for that high pump-field, nearly all the electrons have left the lower (absorbing) level, so that the gain-composite is close to being transparent at all wavelengths.

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Figures (7)

Fig. 1
Fig. 1

(Color online) (a) Schematic of stimulated emission from a pumped, broadened two-level system. (b) Same as (a) for a four-level system. (c) Schematic illustration of a quarter unit cell of the fishnet structure studied in simulations. Silver components are shown in blue, spacer layer in light-blue and the gain-composite in red. In some simulations below (sample 3), the gain is also included in the spacer.

Fig. 2
Fig. 2

(Color online) (a) Pump-field normalized by the saturation field | E p u m p / E s a t | and (b) imaginary part of the relative permittivity ε r ' ' in a quarter unit cell for sample C for a cross-section in the middle of the spacer layer. The perforation is outlined by the solid line. (c) The permittivity in a cross-section along the dashed line in (b). The dashed line represents the borderline between absorption and gain ( ε r = 0 ). (d)-(f) Same as (a)-(c), respectively, for a cross-section 15 nm above the upper metal layer. Here, λ p u m p = λ 30 = 718   nm .

Fig. 3
Fig. 3

(Color online) (a) Transmission (black), reflection (magenta) and absorption (green) for a fishnet structure without dye (solid line), with pumped dye molecules in a coating layer (dash-dotted line) and with pumped emitters in coating and spacer layers (dashed line). (b) Reduction in absorption for sample 2 (dash-dotted blue line) and sample 3 (dashed black line).

Fig. 4
Fig. 4

(Color online) Real parts (blue) and imaginary parts (red) of retrieved effective parameters for samples 1 (solid lines) and 3 (dashed lines).

Fig. 5
Fig. 5

(Color online) (a) E-field distribution in a quarter unit cell for sample 3 for a cross-section located in the middle of the spacer layer. (b) Same as (a) for a cross-section 15 nm above the fishnet. Here, λ = 746   nm .

Fig. 6
Fig. 6

(Color online) (a) Average E-field enhancement ρ 2 | E ( x , λ ) | 2 d 3 x / | E i n c | 2 d 3 x for sample 1 (solid blue line) and sample 3 (dashed blue line). Also shown is the maximal enhancement normalized by a factor of 10 (red dash-dotted line). (b) Generated power density in the regions occupied by the gain-composite (dashed, sample 3) compared with the normalized average gain profile ( g n = max λ ( A A g ) ( g / max λ ( g ) ) ) (black solid line). (c) Absorbed power density in the Ag fishnet layers without dye (solid, sample 1) and with dye (dashed, sample 3).

Fig. 7
Fig. 7

(Color online) (a) Same as Fig. 5(a) for a cross-section in the middle of the upper Ag layer for sample A. (b) Same as (a) for sample C. (c) Difference of the field maps of (a) and (b).

Equations (10)

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N 2 = N L a b s ( λ p u m p ) | E ¯ p u m p ( λ p u m p ) | 2 1 + L a b s ( λ p u m p ) | E ¯ p u m p ( λ p u m p ) | 2 + q i L e m ( λ ) | E ¯ ( λ ) | 2 ,
σ a b s ( λ ) = L a b s ( λ ) σ a b s , 0 ,                             L a b s ( λ 30 ) = 1 , σ e m ( λ ) = L e m ( λ ) σ e m , 0 , ​                               L e m ( λ 21 ) = 1 ,
| E s a t | 2 4 h ϵ 0 n λ 30 1 τ σ a b s , 0 ,
α ( λ , λ p u m p ) = σ a b s ( λ ) N 0 ( λ p u m p ) = σ a b s , 0 L 30 ( λ ) N 0 ( λ p u m p ) , g ( λ , λ p u m p ) = σ e m ( λ ) N 2 ( λ p u m p ) = σ e m , 0 L 21 ( λ ) N 2 ( λ p u m p ) ,
α g 2 = ω c n ,                       n = ε r 2 n
ε r ( λ ) = n λ 2 π N 1 + L a b s ( λ p u m p ) | E ¯ p u m p | 2 [ σ a b s , 0 L a b s ( λ ) σ e m , 0 L e m ( λ ) L a b s ( λ p u m p ) | E ¯ p u m p | 2 ] .
Q A g / e m = 1 2 ω ε 0 ε r ( ω , x ) | E ( ω , x ) | 2 d 3 x ,
A s t I A g / e m I i n c = Z 0 ω S ε 0 ε r ( ω , x ) | E ( ω , x ) E i n c | 2 d 3 x ,
n ˙ s t = n h o s t 2 Z 0 σ e m ( ω ) N 2 ( x ) | E ( ω , x ) | 2 d 3 x ω .
A s t n ˙ s t n ˙ i n c = n h o s t σ e m ( ω ) N 2 ( x ) | E ( ω , x ) | 2 d 3 x S | E i n c | 2 = Z 0 ω S ε 0 ε r ( ω , x ) | E ( ω , x ) E i n c | 2 d 3 x ,

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