Abstract

Spaser is an acronym for surface plasmon amplification by stimulated emission of radiation. A spaser is effectively a nanoscale laser with subwavelength dimensions and a low-Q plasmonic resonator, which sustains its oscillations using stimulated emission of surface plasmons. The concept of stimulated emission to sustain plasmonic oscillations in a resonator was first described by David Bergman and Mark Stockman in 2003. Using a unified notation, we provide an up-to-date literature review of the major developments and latest advances in spaser theory and carry out a systematic exposition of some of the key results useful to understand the operation of spasers. Our presentation covers both semiclassical and quantum-mechanical formulations of spaser models as well as various designs and technologies demonstrated/suggested to illustrate key aspects of this technology. Even though many advances have already been made in spaser technology, there are many hurdles that need to be overcome to bring this technology up to the level of modern laser technology. We take especially great care to highlight the main challenges facing various spaser designs and the limitations of widely used methods and materials. This review is written for both specialists in the field and a general engineering–physics–chemistry readership.

© 2017 Optical Society of America

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  266. W. Zhu, L.-M. Si, and M. Premaratne, “Light focusing using epsilon-near-zero metamaterials,” AIP Adv. 3, 112124 (2013).
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  267. M. Kang, H.-X. Cui, T.-F. Li, J. Chen, W. Zhu, and M. Premaratne, “Unidirectional phase singularity in ultrathin metamaterials at exceptional points,” Phys. Rev. A 89, 065801 (2014).
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2016 (12)

W. Xiong, D. Sikdar, L. Yap, P. Guo, M. Premaratne, X. Li, and W. Cheng, “Matryoshka-caged gold nanorods: synthesis, plasmonic properties, and catalytic activity,” Nano Res. 9, 415–423 (2016).
[Crossref]

N.-H. Kaneko, S. Nakamura, and Y. Okazaki, “A review of the quantum current standard,” Meas. Sci. Technol. 27, 032001 (2016).
[Crossref]

C. Kumarasinghe, M. Premaratne, S. Gunapala, and G. Agrawal, “Design of all-optical, hot-electron current-direction-switching device based on geometrical asymmetry,” Sci. Rep. 6, 21470 (2016).
[Crossref]

C. Kumarasinghe, M. Premaratne, S. Gunapala, and G. Agrawal, “Theoretical analysis of hot electron injection from metallic nanotubes into a semiconductor interface,” Phys. Chem. Chem. Phys. 18, 18227–18236 (2016).
[Crossref]

C. Jayasekara, M. Premaratne, S. D. Gunapala, and M. I. Stockman, “MoS2 spaser,” J. Appl. Phys. 119, 133101 (2016).
[Crossref]

B. Dastmalchi, P. Tassin, T. Koschny, and C. M. Soukoulis, “A new perspective on plasmonics: confinement and propagation length of surface plasmons for different materials and geometries,” Adv. Opt. Mater. 4, 177–184 (2016).
[Crossref]

M. Gegg and M. Richter, “Efficient and exact numerical approach for many multi-level systems in open system CQED,” New J. Phys. 18, 043037 (2016).
[Crossref]

N. Arnold, C. Hrelescu, and T. A. Klar, “Minimal spaser threshold within electrodynamic framework: shape, size and modes,” Ann. Phys. 528, 295–306 (2016).
[Crossref]

Y. Zhang, K. Mølmer, and V. May, “Theoretical study of plasmonic lasing in junctions with many molecules,” Phys. Rev. B 94, 045412 (2016).
[Crossref]

V. N. Pustovit, A. M. Urbas, A. V. Chipouline, and T. V. Shahbazyan, “Coulomb and quenching effects in small nanoparticle-based spasers,” Phys. Rev. B 93, 165432 (2016).
[Crossref]

D. Weeraddana, M. Premaratne, and D. Andrews, “Quantum electrodynamics of resonance energy transfer in nanowire systems,” Phys. Rev. B 93, 075151 (2016).
[Crossref]

D. Weeraddana, M. Premaratne, S. D. Gunapala, and D. L. Andrews, “Quantum electrodynamical theory of high-efficiency excitation energy transfer in laser-driven nanostructure systems,” Phys. Rev. B 94, 085133 (2016).
[Crossref]

2015 (23)

D. Weeraddana, M. Premaratne, and D. Andrews, “Direct and third-body mediated resonance energy transfer in dimensionally constrained nanostructures,” Phys. Rev. B 92, 035128 (2015).
[Crossref]

X.-Y. Deng, X.-H. Deng, F.-H. Su, N.-H. Liu, and J.-T. Liu, “Broadband ultra-high transmission of terahertz radiation through monolayer MoS2,” J. Appl. Phys. 118, 224304 (2015).
[Crossref]

V. Pustovit, F. Capolino, and A. Aradian, “Cooperative plasmon-mediated effects and loss compensation by gain dyes near a metal nanoparticle,” J. Opt. Soc. Am. B 32, 188–193 (2015).
[Crossref]

N. Arnold, K. Piglmayer, A. V. Kildishev, and T. A. Klar, “Spasers with retardation and gain saturation: electrodynamic description of fields and optical cross-sections,” Opt. Mater. Express 5, 2546–2577 (2015).
[Crossref]

Y. Tao, Z. Guo, Y. Sun, F. Shen, X. Mao, W. Wang, Y. Li, Y. Liu, X. Wang, and S. Qu, “Sliver spherical nanoshells coated gain-assisted ellipsoidal silica core for low-threshold surface plasmon amplification,” Opt. Commun. 355, 580–585 (2015).
[Crossref]

C. Jayasekara, M. Premaratne, M. I. Stockman, and S. D. Gunapala, “Multimode analysis of highly tunable, quantum cascade powered, circular graphene spaser,” J. Appl. Phys. 118, 173101 (2015).
[Crossref]

M. Richter, M. Gegg, T. S. Theuerholz, and A. Knorr, “Numerically exact solution of the many emitter-cavity laser problem: application to the fully quantized spaser emission,” Phys. Rev. B 91, 035306 (2015).
[Crossref]

J. Waxenegger, A. Trügler, and U. Hohenester, “Plasmonics simulations with the {MNPBEM} toolbox: consideration of substrates and layer structures,” Comput. Phys. Commun. 193, 138–150 (2015).
[Crossref]

C. M. Krauter, S. Bernadotte, C. R. Jacob, M. Pernpointner, and A. Dreuw, “Identification of plasmons in molecules with scaled ab initio approaches,” J. Phys. Chem. C 119, 24564–24573 (2015).
[Crossref]

J. Ma, Z. Wang, and L.-W. Wang, “Interplay between plasmon and single-particle excitations in a metal nanocluster,” Nat. Commun. 6, 10107 (2015).
[Crossref]

U. Hohenester, “Quantum corrected model for plasmonic nanoparticles: a boundary element method implementation,” Phys. Rev. B 91, 205436 (2015).
[Crossref]

F. Xiao, W. Zhu, W. Shang, T. Mei, M. Premaratne, and J. Zhao, “Electrical control of second harmonic generation in a graphene-based plasmonic Fano structure,” Opt. Express 23, 3236–3244 (2015).
[Crossref]

C. Kumarasinghe, M. Premaratne, Q. Bao, and G. Agrawal, “Theoretical analysis of hot electron dynamics in nanorods,” Sci. Rep. 5, 12140 (2015).
[Crossref]

J. B. Khurgin, “How to deal with the loss in plasmonics and metamaterials,” Nat. Nano 10, 2–6 (2015).
[Crossref]

J. B. Khurgin, “Ultimate limit of field confinement by surface plasmon polaritons,” Faraday Discuss. 178, 109–122 (2015).
[Crossref]

W. Xiong, D. Sikdar, L. Yap, M. Premaratne, X. Li, and W. Cheng, “Multilayered core-satellite nanoassemblies with fine-tunable broadband plasmon resonances,” Nanoscale 7, 3445–3452 (2015).
[Crossref]

C. P. Byers, H. Zhang, D. F. Swearer, M. Yorulmaz, B. S. Hoener, D. Huang, A. Hoggard, W.-S. Chang, P. Mulvaney, E. Ringe, N. J. Halas, P. Nordlander, S. Link, and C. F. Landes, “From tunable core-shell nanoparticles to plasmonic drawbridges: active control of nanoparticle optical properties,” Sci. Adv. 1, e1500988 (2015).
[Crossref]

P. Törmä and W. L. Barnes, “Strong coupling between surface plasmon polaritons and emitters: a review,” Rep. Prog. Phys. 78, 013901 (2015).
[Crossref]

A. G. M. da Silva, T. S. Rodrigues, J. Wang, L. K. Yamada, T. V. Alves, F. R. Ornellas, R. A. Ando, and P. H. C. Camargo, “The fault in their shapes: investigating the surface-plasmon-resonance-mediated catalytic activities of silver quasi-spheres, cubes, triangular prisms, and wires,” Langmuir 31, 10272–10278 (2015).
[Crossref]

T. Attanayake, M. Premaratne, and G. Agrawal, “Characterizing the optical response of symmetric hemispherical nano-dimers,” Plasmonics 10, 1453–1466 (2015).
[Crossref]

W. Zhu, D. Sikdar, F. Xiao, M. Kang, and M. Premaratne, “Gold nanoparticles with gain-assisted coating for ultra-sensitive biomedical sensing,” Plasmonics 10, 881–886 (2015).
[Crossref]

D. Sikdar, W. Cheng, and M. Premaratne, “Optically resonant magneto-electric cubic nanoantennas for ultra-directional light scattering,” J. Appl. Phys. 117, 083101 (2015).
[Crossref]

T. Wijesinghe, M. Premaratne, and G. Agrawal, “Low-loss dielectric-loaded graphene surface plasmon polariton waveguide based biochemical sensor,” J. Appl. Phys. 117, 213105 (2015).
[Crossref]

2014 (20)

N. Das, F. F. Masouleh, and H. R. Mashayekhi, “Light absorption and reflection in nanostructured GaAs metal-semiconductor-metal photodetectors,” IEEE Trans. Nanotechnol. 13, 982–989 (2014).
[Crossref]

Z. Kang, H. Lu, J. Chen, K. Chen, F. Xu, and H.-P. Ho, “Plasmonic graded nano-disks as nano-optical conveyor belt,” Opt. Express 22, 19567–19572 (2014).
[Crossref]

D. Sikdar, I. Rukhlenko, W. Cheng, and M. Premaratne, “Tunable broadband optical responses of substrate-supported metal/dielectric/metal nanospheres,” Plasmonics 9, 659–672 (2014).
[Crossref]

C. Kumarasinghe, M. Premaratne, and G. Agrawal, “Dielectric function of spherical dome shells with quantum size effects,” Opt. Express 22, 11966–11984 (2014).
[Crossref]

K. Si, D. Sikdar, Y. Chen, F. Eftekhari, Z. Xu, Y. Tang, W. Xiong, P. Guo, S. Zhang, Y. Lu, Q. Bao, W. Zhu, M. Premaratne, and W. Cheng, “Giant plasmene nanosheets, nanoribbons, and origami,” ACS Nano 8, 11086–11093 (2014).
[Crossref]

J. B. Khurgin and G. Sun, “Comparative analysis of spasers, vertical-cavity surface-emitting lasers and surface-plasmon-emitting diodes,” Nat. Photonics 8, 468–473 (2014).
[Crossref]

L. Fricke, M. Wulf, B. Kaestner, F. Hohls, P. Mirovsky, B. Mackrodt, R. Dolata, T. Weimann, K. Pierz, U. Siegner, and H. W. Schumacher, “Self-referenced single-electron quantized current source,” Phys. Rev. Lett. 112, 226803 (2014).
[Crossref]

T. Wijesinghe, M. Premaratne, and G. Agrawal, “Electrically pumped hybrid plasmonic waveguide,” Opt. Express 22, 2681–2694 (2014).
[Crossref]

W. Zhu, I. Rukhlenko, and M. Premaratne, “Response to ‘Comment on graphene metamaterial for optical reflection modulation’ [Appl. Phys. Lett. 104, 256101 (2014)],” Appl. Phys. Lett. 104, 256102 (2014).
[Crossref]

W. Zhu, F. Xiao, M. Kang, D. Sikdar, and M. Premaratne, “Tunable terahertz left-handed metamaterial based on multi-layer graphene-dielectric composite,” Appl. Phys. Lett. 104, 051902 (2014).
[Crossref]

C. Rupasinghe, I. D. Rukhlenko, and M. Premaratne, “Spaser made of graphene and carbon nanotubes,” ACS Nano 8, 2431–2438 (2014).
[Crossref]

V. Apalkov and M. I. Stockman, “Proposed graphene nanospaser,” Light: Sci. Appl. 3, e191 (2014).
[Crossref]

F. J. G. de Abajo, “Graphene plasmonics: challenges and opportunities,” ACS Photon. 1, 135–152 (2014).
[Crossref]

V. Klimov, G.-Y. Guo, and M. Pikhota, “Plasmon resonances in metal nanoparticles with sharp edges and vertices: a material independent approach,” J. Phys. Chem. C 118, 13052–13058 (2014).
[Crossref]

E. Townsend and G. W. Bryant, “Which resonances in small metallic nanoparticles are plasmonic?” J. Opt. 16, 114022 (2014).
[Crossref]

M. Reddy, R. Vijaya, I. Rukhlenko, and M. Premaratne, “Low-threshold lasing in photonic-crystal heterostructures,” Opt. Express 22, 6229–6238 (2014).
[Crossref]

W. Zhu, M. Premaratne, S. Gunapala, G. Agrawal, and M. Stockman, “Quasi-static analysis of controllable optical cross-sections of a layered nanoparticle with a sandwiched gain layer,” J. Opt. 16, 075003 (2014).
[Crossref]

K. G. Stamplecoskie, M. Grenier, and J. C. Scaiano, “Self-assembled dipole nanolasers,” J. Am. Chem. Soc. 136, 2956–2959 (2014).
[Crossref]

V. M. Parfenyev and S. S. Vergeles, “Quantum theory of a spaser-based nanolaser,” Opt. Express 22, 13671–13679 (2014).
[Crossref]

M. Kang, H.-X. Cui, T.-F. Li, J. Chen, W. Zhu, and M. Premaratne, “Unidirectional phase singularity in ultrathin metamaterials at exceptional points,” Phys. Rev. A 89, 065801 (2014).
[Crossref]

2013 (24)

Y.-W. Huang, W. T. Chen, P. C. Wu, V. A. Fedotov, N. I. Zheludev, and D. P. Tsai, “Toroidal lasing spaser,” Sci. Rep. 3, 1237 (2013).
[Crossref]

W. Zhu, L.-M. Si, and M. Premaratne, “Light focusing using epsilon-near-zero metamaterials,” AIP Adv. 3, 112124 (2013).
[Crossref]

D. G. Baranov, A. P. Vinogradov, A. A. Lisyansky, Y. M. Strelniker, and D. J. Bergman, “Magneto-optical spaser,” Opt. Lett. 38, 2002–2004 (2013).
[Crossref]

O. L. Berman, R. Y. Kezerashvili, and Y. E. Lozovik, “Graphene nanoribbon based spaser,” Phys. Rev. B 88, 235424 (2013).
[Crossref]

C. Rupasinghe, I. D. Rukhlenko, and M. Premaratne, “Design optimization of spasers considering the degeneracy of excited plasmon modes,” Opt. Express 21, 15335–15349 (2013).
[Crossref]

D. Li and M. I. Stockman, “Electric spaser in the extreme quantum limit,” Phys. Rev. Lett. 110, 106803 (2013).
[Crossref]

M. Reddy, S. Kedia, R. Vijaya, A. Ray, S. Sinha, I. Rukhlenko, and M. Premaratne, “Analysis of lasing in dye-doped photonic crystals,” IEEE Photon. J. 5, 4700409 (2013).
[Crossref]

M. Reddy, R. Vijaya, I. Rukhlenko, and M. Premaratne, “Low-threshold lasing in active opal photonic crystals,” Opt. Lett. 38, 1046–1048 (2013).
[Crossref]

X. Meng, A. V. Kildishev, K. Fujita, K. Tanaka, and V. M. Shalaev, “Wavelength-tunable spasing in the visible,” Nano Lett. 13, 4106–4112 (2013).
[Crossref]

D. G. Baranov, E. Andrianov, A. P. Vinogradov, and A. A. Lisyansky, “Exactly solvable toy model for surface plasmon amplification by stimulated emission of radiation,” Opt. Express 21, 10779–10791 (2013).
[Crossref]

P. Ding, J. He, J. Wang, C. Fan, G. Cai, and E. Liang, “Low-threshold surface plasmon amplification from a gain-assisted core-shell nanoparticle with broken symmetry,” J. Opt. 15, 105001 (2013).
[Crossref]

S. Malola, L. Lehtovaara, J. Enkovaara, and H. Häkkinen, “Birth of the localized surface plasmon resonance in monolayer-protected gold nanoclusters,” ACS Nano 7, 10263–10270 (2013).
[Crossref]

K. E. Dorfman, P. K. Jha, D. V. Voronine, P. Genevet, F. Capasso, and M. O. Scully, “Quantum-coherence-enhanced surface plasmon amplification by stimulated emission of radiation,” Phys. Rev. Lett. 111, 043601 (2013).
[Crossref]

M. Jablan, M. Soljaćić, and H. Buljan, “Plasmons in graphene: fundamental properties and potential applications,” Proc. IEEE 101, 1689–1704 (2013).
[Crossref]

E. B. Guidez and C. M. Aikens, “Origin and TDDFT benchmarking of the plasmon resonance in acenes,” J. Phys. Chem. C 117, 21466–21475 (2013).
[Crossref]

S. Bernadotte, F. Evers, and C. R. Jacob, “Plasmons in molecules,” J. Phys. Chem. C 117, 1863–1878 (2013).
[Crossref]

W. Zhu, I. Rukhlenko, and M. Premaratne, “Graphene metamaterial for optical reflection modulation,” Appl. Phys. Lett. 102, 241914 (2013).
[Crossref]

W. Zhu, I. Rukhlenko, L.-M. Si, and M. Premaratne, “Graphene-enabled tunability of optical fishnet metamaterial,” Appl. Phys. Lett. 102, 121911 (2013).
[Crossref]

W. Zhu, I. Rukhlenko, and M. Premaratne, “Application of zero-index metamaterials for surface plasmon guiding,” Appl. Phys. Lett. 102, 011910 (2013).
[Crossref]

T. Wijesinghe and M. Premaratne, “Surface plasmon polaritons propagation through a Schottky junction: influence of the inversion layer,” IEEE Photon. J. 5, 4800216 (2013).
[Crossref]

D. Sikdar, I. Rukhlenko, W. Cheng, and M. Premaratne, “Unveiling ultrasharp scattering-switching signatures of layered gold-dielectric-gold nanospheres,” J. Opt. Soc. Am. B 30, 2066–2074 (2013).
[Crossref]

D. Sikdar, I. Rukhlenko, W. Cheng, and M. Premaratne, “Optimized gold nanoshell ensembles for biomedical applications,” Nanoscale Res. Lett. 8, 142 (2013).
[Crossref]

W. Xiong, D. Sikdar, M. Walsh, K. Si, Y. Tang, Y. Chen, R. Mazid, M. Weyland, I. Rukhlenko, J. Etheridge, M. Premaratne, X. Li, and W. Cheng, “Single-crystal caged gold nanorods with tunable broadband plasmon resonances,” Chem. Commun. 49, 9630–9632 (2013).
[Crossref]

D. Handapangoda, I. Rukhlenko, and M. Premaratne, “Analytical study of optimal design and gain parameters of double-slot plasmonic waveguides,” J. Opt. 15, 035006 (2013).
[Crossref]

2012 (23)

D. Handapangoda, I. Rukhlenko, and M. Premaratne, “Optimizing the design of planar heterostructures for plasmonic waveguiding,” J. Opt. Soc. Am. B 29, 553–558 (2012).
[Crossref]

K. Leosson, “Optical amplification of surface plasmon polaritons: review,” J. Nanophoton. 6, 061801 (2012).
[Crossref]

T. Wijesinghe and M. Premaratne, “Dispersion relation for surface plasmon polaritons on a Schottky junction,” Opt. Express 20, 7151–7164 (2012).
[Crossref]

W. Zhu, I. Rukhlenko, and M. Premaratne, “Light amplification in zero-index metamaterial with gain inserts,” Appl. Phys. Lett. 101, 031907 (2012).
[Crossref]

I. Rukhlenko, M. Premaratne, and G. Agrawal, “Plasmonic modes of metamaterial-based slot waveguides,” Adv. OptoElectron. 2012, 907183 (2012).
[Crossref]

P. Das, T. K. Chini, and J. Pond, “Probing higher order surface plasmon modes on individual truncated tetrahedral gold nanoparticle using cathodoluminescence imaging and spectroscopy combined with FDTD simulations,” J. Phys. Chem. C 116, 15610–15619 (2012).
[Crossref]

S. J. Barrow, X. Wei, J. S. Baldauf, A. M. Funston, and P. Mulvaney, “The surface plasmon modes of self-assembled gold nanocrystals,” Nat. Commun. 3, 1275 (2012).
[Crossref]

O. A. Yeshchenko, I. M. Dmitruk, A. A. Alexeenko, A. V. Kotko, J. Verdal, and A. O. Pinchuk, “Size and temperature effects on the surface plasmon resonance in silver nanoparticles,” Plasmonics 7, 685–694 (2012).
[Crossref]

W. Zhu, I. Rukhlenko, and M. Premaratne, “Maneuvering propagation of surface plasmon polaritons using complementary medium inserts,” IEEE Photon. J. 4, 741–747 (2012).
[Crossref]

W. Zhu, I. Rukhlenko, and M. Premaratne, “Linear transformation optics for plasmonics,” J. Opt. Soc. Am. B 29, 2659–2664 (2012).
[Crossref]

W. Zhu, I. Rukhlenko, and M. Premaratne, “Manipulating energy flow in variable-gap plasmonic waveguides,” Opt. Lett. 37, 5151–5153 (2012).
[Crossref]

D. Y. Fedyanin, A. V. Krasavin, A. V. Arsenin, and A. V. Zayats, “Surface plasmon polariton amplification upon electrical injection in highly integrated plasmonic circuits,” Nano Lett. 12, 2459–2463 (2012).
[Crossref]

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

J. A. Scholl, A. L. Koh, and J. A. Dionne, “Quantum plasmon resonances of individual metallic nanoparticles,” Nature 483, 421–427 (2012).
[Crossref]

U. Hohenester and A. Trügler, “MNPBEM—A Matlab toolbox for the simulation of plasmonic nanoparticles,” Comput. Phys. Commun. 183, 370–381 (2012).
[Crossref]

R. Esteban, A. G. Borisov, P. Nordlander, and J. Aizpurua, “Bridging quantum and classical plasmonics with a quantum-corrected model,” Nat. Commun. 3, 825 (2012).
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M. C. Gather, “A rocky road to plasmonic lasers,” Nat. Photonics 6, 708 (2012).
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M. Khajavikhan, A. Simic, M. Katz, J. H. Lee, B. Slutsky, A. Mizrahi, V. Lomakin, and Y. Fainman, “Thresholdless nanoscale coaxial lasers,” Nature 482, 204–207 (2012).
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J. Y. Suh, C. H. Kim, W. Zhou, M. D. Huntington, D. T. Co, M. R. Wasielewski, and T. W. Odom, “Plasmonic bowtie nanolaser arrays,” Nano Lett. 12, 5769–5774 (2012).
[Crossref]

I. E. Protsenko, “Theory of the dipole nanolaser,” Phys. Usp. 55, 1040–1046 (2012).
[Crossref]

J. B. Khurgin and G. Sun, “Injection pumped single mode surface plasmon generators: threshold, linewidth, and coherence,” Opt. Express 20, 15309–15325 (2012).
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I. Udagedara, I. Rukhlenko, and M. Premaratne, “Complex-ω approach versus complex-k approach in description of gain-assisted surface plasmon-polariton propagation along linear chains of metallic nanospheres,” Phys. Rev. B 83, 115451 (2011).
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2010 (15)

A. Pannipitiya, I. Rukhlenko, M. Premaratne, H. Hattori, and G. Agrawal, “Improved transmission model for metal-dielectric-metal plasmonic waveguides with stub structure,” Opt. Express 18, 6191–6204 (2010).
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I. De Leon and P. Berini, “Amplification of long-range surface plasmons by a dipolar gain medium,” Nat. Photonics 4, 382–387 (2010).
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K. C. Vernon, A. M. Funston, C. Novo, D. E. Gómez, P. Mulvaney, and T. J. Davis, “Influence of particle-substrate interaction on localized plasmon resonances,” Nano Lett. 10, 2080–2086 (2010).
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2009 (13)

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P. Das, T. K. Chini, and J. Pond, “Probing higher order surface plasmon modes on individual truncated tetrahedral gold nanoparticle using cathodoluminescence imaging and spectroscopy combined with FDTD simulations,” J. Phys. Chem. C 116, 15610–15619 (2012).
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D. F. Zaretsky, P. A. Korneev, S. V. Popruzhenko, and W. Becker, “Landau damping in thin films irradiated by a strong laser field,” J. Phys. B 37, 4817–4830 (2004).
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C. J. Powell and J. B. Swan, “Origin of the characteristic electron energy losses in aluminum,” Phys. Rev. 115, 869–875 (1959).
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Premaratne, M.

D. Weeraddana, M. Premaratne, S. D. Gunapala, and D. L. Andrews, “Quantum electrodynamical theory of high-efficiency excitation energy transfer in laser-driven nanostructure systems,” Phys. Rev. B 94, 085133 (2016).
[Crossref]

C. Kumarasinghe, M. Premaratne, S. Gunapala, and G. Agrawal, “Design of all-optical, hot-electron current-direction-switching device based on geometrical asymmetry,” Sci. Rep. 6, 21470 (2016).
[Crossref]

C. Jayasekara, M. Premaratne, S. D. Gunapala, and M. I. Stockman, “MoS2 spaser,” J. Appl. Phys. 119, 133101 (2016).
[Crossref]

W. Xiong, D. Sikdar, L. Yap, P. Guo, M. Premaratne, X. Li, and W. Cheng, “Matryoshka-caged gold nanorods: synthesis, plasmonic properties, and catalytic activity,” Nano Res. 9, 415–423 (2016).
[Crossref]

C. Kumarasinghe, M. Premaratne, S. Gunapala, and G. Agrawal, “Theoretical analysis of hot electron injection from metallic nanotubes into a semiconductor interface,” Phys. Chem. Chem. Phys. 18, 18227–18236 (2016).
[Crossref]

D. Weeraddana, M. Premaratne, and D. Andrews, “Quantum electrodynamics of resonance energy transfer in nanowire systems,” Phys. Rev. B 93, 075151 (2016).
[Crossref]

F. Xiao, W. Zhu, W. Shang, T. Mei, M. Premaratne, and J. Zhao, “Electrical control of second harmonic generation in a graphene-based plasmonic Fano structure,” Opt. Express 23, 3236–3244 (2015).
[Crossref]

C. Jayasekara, M. Premaratne, M. I. Stockman, and S. D. Gunapala, “Multimode analysis of highly tunable, quantum cascade powered, circular graphene spaser,” J. Appl. Phys. 118, 173101 (2015).
[Crossref]

T. Attanayake, M. Premaratne, and G. Agrawal, “Characterizing the optical response of symmetric hemispherical nano-dimers,” Plasmonics 10, 1453–1466 (2015).
[Crossref]

W. Zhu, D. Sikdar, F. Xiao, M. Kang, and M. Premaratne, “Gold nanoparticles with gain-assisted coating for ultra-sensitive biomedical sensing,” Plasmonics 10, 881–886 (2015).
[Crossref]

W. Xiong, D. Sikdar, L. Yap, M. Premaratne, X. Li, and W. Cheng, “Multilayered core-satellite nanoassemblies with fine-tunable broadband plasmon resonances,” Nanoscale 7, 3445–3452 (2015).
[Crossref]

T. Wijesinghe, M. Premaratne, and G. Agrawal, “Low-loss dielectric-loaded graphene surface plasmon polariton waveguide based biochemical sensor,” J. Appl. Phys. 117, 213105 (2015).
[Crossref]

D. Weeraddana, M. Premaratne, and D. Andrews, “Direct and third-body mediated resonance energy transfer in dimensionally constrained nanostructures,” Phys. Rev. B 92, 035128 (2015).
[Crossref]

C. Kumarasinghe, M. Premaratne, Q. Bao, and G. Agrawal, “Theoretical analysis of hot electron dynamics in nanorods,” Sci. Rep. 5, 12140 (2015).
[Crossref]

D. Sikdar, W. Cheng, and M. Premaratne, “Optically resonant magneto-electric cubic nanoantennas for ultra-directional light scattering,” J. Appl. Phys. 117, 083101 (2015).
[Crossref]

W. Zhu, F. Xiao, M. Kang, D. Sikdar, and M. Premaratne, “Tunable terahertz left-handed metamaterial based on multi-layer graphene-dielectric composite,” Appl. Phys. Lett. 104, 051902 (2014).
[Crossref]

W. Zhu, I. Rukhlenko, and M. Premaratne, “Response to ‘Comment on graphene metamaterial for optical reflection modulation’ [Appl. Phys. Lett. 104, 256101 (2014)],” Appl. Phys. Lett. 104, 256102 (2014).
[Crossref]

T. Wijesinghe, M. Premaratne, and G. Agrawal, “Electrically pumped hybrid plasmonic waveguide,” Opt. Express 22, 2681–2694 (2014).
[Crossref]

M. Kang, H.-X. Cui, T.-F. Li, J. Chen, W. Zhu, and M. Premaratne, “Unidirectional phase singularity in ultrathin metamaterials at exceptional points,” Phys. Rev. A 89, 065801 (2014).
[Crossref]

C. Rupasinghe, I. D. Rukhlenko, and M. Premaratne, “Spaser made of graphene and carbon nanotubes,” ACS Nano 8, 2431–2438 (2014).
[Crossref]

C. Kumarasinghe, M. Premaratne, and G. Agrawal, “Dielectric function of spherical dome shells with quantum size effects,” Opt. Express 22, 11966–11984 (2014).
[Crossref]

W. Zhu, M. Premaratne, S. Gunapala, G. Agrawal, and M. Stockman, “Quasi-static analysis of controllable optical cross-sections of a layered nanoparticle with a sandwiched gain layer,” J. Opt. 16, 075003 (2014).
[Crossref]

M. Reddy, R. Vijaya, I. Rukhlenko, and M. Premaratne, “Low-threshold lasing in photonic-crystal heterostructures,” Opt. Express 22, 6229–6238 (2014).
[Crossref]

D. Sikdar, I. Rukhlenko, W. Cheng, and M. Premaratne, “Tunable broadband optical responses of substrate-supported metal/dielectric/metal nanospheres,” Plasmonics 9, 659–672 (2014).
[Crossref]

K. Si, D. Sikdar, Y. Chen, F. Eftekhari, Z. Xu, Y. Tang, W. Xiong, P. Guo, S. Zhang, Y. Lu, Q. Bao, W. Zhu, M. Premaratne, and W. Cheng, “Giant plasmene nanosheets, nanoribbons, and origami,” ACS Nano 8, 11086–11093 (2014).
[Crossref]

D. Sikdar, I. Rukhlenko, W. Cheng, and M. Premaratne, “Unveiling ultrasharp scattering-switching signatures of layered gold-dielectric-gold nanospheres,” J. Opt. Soc. Am. B 30, 2066–2074 (2013).
[Crossref]

W. Zhu, I. Rukhlenko, and M. Premaratne, “Graphene metamaterial for optical reflection modulation,” Appl. Phys. Lett. 102, 241914 (2013).
[Crossref]

C. Rupasinghe, I. D. Rukhlenko, and M. Premaratne, “Design optimization of spasers considering the degeneracy of excited plasmon modes,” Opt. Express 21, 15335–15349 (2013).
[Crossref]

D. Sikdar, I. Rukhlenko, W. Cheng, and M. Premaratne, “Optimized gold nanoshell ensembles for biomedical applications,” Nanoscale Res. Lett. 8, 142 (2013).
[Crossref]

M. Reddy, S. Kedia, R. Vijaya, A. Ray, S. Sinha, I. Rukhlenko, and M. Premaratne, “Analysis of lasing in dye-doped photonic crystals,” IEEE Photon. J. 5, 4700409 (2013).
[Crossref]

W. Zhu, I. Rukhlenko, L.-M. Si, and M. Premaratne, “Graphene-enabled tunability of optical fishnet metamaterial,” Appl. Phys. Lett. 102, 121911 (2013).
[Crossref]

D. Handapangoda, I. Rukhlenko, and M. Premaratne, “Analytical study of optimal design and gain parameters of double-slot plasmonic waveguides,” J. Opt. 15, 035006 (2013).
[Crossref]

W. Zhu, L.-M. Si, and M. Premaratne, “Light focusing using epsilon-near-zero metamaterials,” AIP Adv. 3, 112124 (2013).
[Crossref]

W. Zhu, I. Rukhlenko, and M. Premaratne, “Application of zero-index metamaterials for surface plasmon guiding,” Appl. Phys. Lett. 102, 011910 (2013).
[Crossref]

W. Xiong, D. Sikdar, M. Walsh, K. Si, Y. Tang, Y. Chen, R. Mazid, M. Weyland, I. Rukhlenko, J. Etheridge, M. Premaratne, X. Li, and W. Cheng, “Single-crystal caged gold nanorods with tunable broadband plasmon resonances,” Chem. Commun. 49, 9630–9632 (2013).
[Crossref]

T. Wijesinghe and M. Premaratne, “Surface plasmon polaritons propagation through a Schottky junction: influence of the inversion layer,” IEEE Photon. J. 5, 4800216 (2013).
[Crossref]

M. Reddy, R. Vijaya, I. Rukhlenko, and M. Premaratne, “Low-threshold lasing in active opal photonic crystals,” Opt. Lett. 38, 1046–1048 (2013).
[Crossref]

W. Zhu, I. Rukhlenko, and M. Premaratne, “Maneuvering propagation of surface plasmon polaritons using complementary medium inserts,” IEEE Photon. J. 4, 741–747 (2012).
[Crossref]

T. Wijesinghe and M. Premaratne, “Dispersion relation for surface plasmon polaritons on a Schottky junction,” Opt. Express 20, 7151–7164 (2012).
[Crossref]

I. Rukhlenko, M. Premaratne, and G. Agrawal, “Plasmonic modes of metamaterial-based slot waveguides,” Adv. OptoElectron. 2012, 907183 (2012).
[Crossref]

W. Zhu, I. Rukhlenko, and M. Premaratne, “Linear transformation optics for plasmonics,” J. Opt. Soc. Am. B 29, 2659–2664 (2012).
[Crossref]

W. Zhu, I. Rukhlenko, and M. Premaratne, “Manipulating energy flow in variable-gap plasmonic waveguides,” Opt. Lett. 37, 5151–5153 (2012).
[Crossref]

W. Zhu, I. Rukhlenko, and M. Premaratne, “Light amplification in zero-index metamaterial with gain inserts,” Appl. Phys. Lett. 101, 031907 (2012).
[Crossref]

D. Handapangoda, I. Rukhlenko, and M. Premaratne, “Optimizing the design of planar heterostructures for plasmonic waveguiding,” J. Opt. Soc. Am. B 29, 553–558 (2012).
[Crossref]

D. Handapangoda, M. Premaratne, I. Rukhlenko, and C. Jagadish, “Optimal design of composite nanowires for extended reach of surface plasmon-polaritons,” Opt. Express 19, 16058–16074 (2011).
[Crossref]

I. Udagedara, I. Rukhlenko, and M. Premaratne, “Complex-ω approach versus complex-k approach in description of gain-assisted surface plasmon-polariton propagation along linear chains of metallic nanospheres,” Phys. Rev. B 83, 115451 (2011).
[Crossref]

I. Rukhlenko, A. Pannipitiya, M. Premaratne, and G. Agrawal, “Exact dispersion relation for nonlinear plasmonic waveguides,” Phys. Rev. B 84, 113409 (2011).
[Crossref]

I. B. Udagedara, I. D. Rukhlenko, and M. Premaratne, “Surface plasmon-polariton propagation in piecewise linear chains of composite nanospheres: the role of optical gain and chain layout,” Opt. Express 19, 19973–19986 (2011).
[Crossref]

I. Rukhlenko, A. Pannipitiya, and M. Premaratne, “Dispersion relation for surface plasmon polaritons in metal/nonlinear-dielectric/metal slot waveguides,” Opt. Lett. 36, 3374–3376 (2011).
[Crossref]

A. Pannipitiya, I. Rukhlenko, and M. Premaratne, “Analytical modeling of resonant cavities for plasmonic-slot-waveguide junctions,” IEEE Photon. J. 3, 220–233 (2011).
[Crossref]

A. Pannipitiya, I. Rukhlenko, M. Premaratne, H. Hattori, and G. Agrawal, “Improved transmission model for metal-dielectric-metal plasmonic waveguides with stub structure,” Opt. Express 18, 6191–6204 (2010).
[Crossref]

V. Amaratunga, M. Premaratne, H. Hattori, H. Tan, and C. Jagadish, “Performance assessment of hybrid surface emitting lasers with lateral one-dimensional photonic-crystal mirrors,” J. Opt. Soc. Am. B 27, 806–817 (2010).
[Crossref]

D. Handapangoda, I. Rukhlenko, M. Premaratne, and C. Jagadish, “Optimization of gain-assisted waveguiding in metal-dielectric nanowires,” Opt. Lett. 35, 4190–4192 (2010).
[Crossref]

I. Udagedara, M. Premaratne, I. Rukhlenko, H. Hattori, and G. Agrawal, “Unified perfectly matched layer for finite-difference time-domain modeling of dispersive optical materials,” Opt. Express 17, 21179–21190 (2009).
[Crossref]

H. T. Hattori, Z. Li, D. Liu, I. Rukhlenko, and M. Premaratne, “Coupling of light from microdisk lasers into plasmonic nano-antennas,” Opt. Express 17, 20878–20884 (2009).
[Crossref]

V. Amaratunga, H. Hattori, M. Premaratne, H. Tan, and C. Jagadish, “Directional optically pumped laterally coupled DFB lasers with circular mirrors,” J. Lightwave Technol. 27, 1425–1433 (2009).
[Crossref]

M. Premaratne, D. Neišić, and G. Agrawal, “Pulse amplification and gain recovery in semiconductor optical amplifiers: a systematic analytical approach,” J. Lightwave Technol. 26, 1653–1660 (2008).
[Crossref]

M. Premaratne and A. Lowery, “Modulation resonance enhancement in SCH quantum-well lasers with an external Bragg reflector,” IEEE J. Quantum Electron. 34, 716–728 (1998).
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[Crossref]

M. Premaratne and G. P. Agrawal, Light Propagation in Gain Media: Optical Amplifiers (Cambridge University, 2011).

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M. Reddy, S. Kedia, R. Vijaya, A. Ray, S. Sinha, I. Rukhlenko, and M. Premaratne, “Analysis of lasing in dye-doped photonic crystals,” IEEE Photon. J. 5, 4700409 (2013).
[Crossref]

Reddy, M.

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A. Boltasseva, V. S. Volkov, R. B. Nielsen, E. Moreno, S. G. Rodrigo, and S. I. Bozhevolnyi, “Triangular metal wedges for subwavelength plasmon-polariton guiding at telecom wavelengths,” Opt. Express 16, 5252–5260 (2008).
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[Crossref]

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D. Sikdar, I. Rukhlenko, W. Cheng, and M. Premaratne, “Tunable broadband optical responses of substrate-supported metal/dielectric/metal nanospheres,” Plasmonics 9, 659–672 (2014).
[Crossref]

M. Reddy, R. Vijaya, I. Rukhlenko, and M. Premaratne, “Low-threshold lasing in photonic-crystal heterostructures,” Opt. Express 22, 6229–6238 (2014).
[Crossref]

W. Zhu, I. Rukhlenko, and M. Premaratne, “Response to ‘Comment on graphene metamaterial for optical reflection modulation’ [Appl. Phys. Lett. 104, 256101 (2014)],” Appl. Phys. Lett. 104, 256102 (2014).
[Crossref]

W. Zhu, I. Rukhlenko, and M. Premaratne, “Application of zero-index metamaterials for surface plasmon guiding,” Appl. Phys. Lett. 102, 011910 (2013).
[Crossref]

D. Handapangoda, I. Rukhlenko, and M. Premaratne, “Analytical study of optimal design and gain parameters of double-slot plasmonic waveguides,” J. Opt. 15, 035006 (2013).
[Crossref]

W. Zhu, I. Rukhlenko, L.-M. Si, and M. Premaratne, “Graphene-enabled tunability of optical fishnet metamaterial,” Appl. Phys. Lett. 102, 121911 (2013).
[Crossref]

M. Reddy, S. Kedia, R. Vijaya, A. Ray, S. Sinha, I. Rukhlenko, and M. Premaratne, “Analysis of lasing in dye-doped photonic crystals,” IEEE Photon. J. 5, 4700409 (2013).
[Crossref]

D. Sikdar, I. Rukhlenko, W. Cheng, and M. Premaratne, “Optimized gold nanoshell ensembles for biomedical applications,” Nanoscale Res. Lett. 8, 142 (2013).
[Crossref]

D. Sikdar, I. Rukhlenko, W. Cheng, and M. Premaratne, “Unveiling ultrasharp scattering-switching signatures of layered gold-dielectric-gold nanospheres,” J. Opt. Soc. Am. B 30, 2066–2074 (2013).
[Crossref]

W. Zhu, I. Rukhlenko, and M. Premaratne, “Graphene metamaterial for optical reflection modulation,” Appl. Phys. Lett. 102, 241914 (2013).
[Crossref]

W. Xiong, D. Sikdar, M. Walsh, K. Si, Y. Tang, Y. Chen, R. Mazid, M. Weyland, I. Rukhlenko, J. Etheridge, M. Premaratne, X. Li, and W. Cheng, “Single-crystal caged gold nanorods with tunable broadband plasmon resonances,” Chem. Commun. 49, 9630–9632 (2013).
[Crossref]

M. Reddy, R. Vijaya, I. Rukhlenko, and M. Premaratne, “Low-threshold lasing in active opal photonic crystals,” Opt. Lett. 38, 1046–1048 (2013).
[Crossref]

W. Zhu, I. Rukhlenko, and M. Premaratne, “Maneuvering propagation of surface plasmon polaritons using complementary medium inserts,” IEEE Photon. J. 4, 741–747 (2012).
[Crossref]

I. Rukhlenko, M. Premaratne, and G. Agrawal, “Plasmonic modes of metamaterial-based slot waveguides,” Adv. OptoElectron. 2012, 907183 (2012).
[Crossref]

W. Zhu, I. Rukhlenko, and M. Premaratne, “Manipulating energy flow in variable-gap plasmonic waveguides,” Opt. Lett. 37, 5151–5153 (2012).
[Crossref]

W. Zhu, I. Rukhlenko, and M. Premaratne, “Linear transformation optics for plasmonics,” J. Opt. Soc. Am. B 29, 2659–2664 (2012).
[Crossref]

W. Zhu, I. Rukhlenko, and M. Premaratne, “Light amplification in zero-index metamaterial with gain inserts,” Appl. Phys. Lett. 101, 031907 (2012).
[Crossref]

D. Handapangoda, I. Rukhlenko, and M. Premaratne, “Optimizing the design of planar heterostructures for plasmonic waveguiding,” J. Opt. Soc. Am. B 29, 553–558 (2012).
[Crossref]

D. Handapangoda, M. Premaratne, I. Rukhlenko, and C. Jagadish, “Optimal design of composite nanowires for extended reach of surface plasmon-polaritons,” Opt. Express 19, 16058–16074 (2011).
[Crossref]

I. Udagedara, I. Rukhlenko, and M. Premaratne, “Complex-ω approach versus complex-k approach in description of gain-assisted surface plasmon-polariton propagation along linear chains of metallic nanospheres,” Phys. Rev. B 83, 115451 (2011).
[Crossref]

I. Rukhlenko, A. Pannipitiya, M. Premaratne, and G. Agrawal, “Exact dispersion relation for nonlinear plasmonic waveguides,” Phys. Rev. B 84, 113409 (2011).
[Crossref]

I. Rukhlenko, A. Pannipitiya, and M. Premaratne, “Dispersion relation for surface plasmon polaritons in metal/nonlinear-dielectric/metal slot waveguides,” Opt. Lett. 36, 3374–3376 (2011).
[Crossref]

A. Pannipitiya, I. Rukhlenko, and M. Premaratne, “Analytical modeling of resonant cavities for plasmonic-slot-waveguide junctions,” IEEE Photon. J. 3, 220–233 (2011).
[Crossref]

A. Pannipitiya, I. Rukhlenko, M. Premaratne, H. Hattori, and G. Agrawal, “Improved transmission model for metal-dielectric-metal plasmonic waveguides with stub structure,” Opt. Express 18, 6191–6204 (2010).
[Crossref]

D. Handapangoda, I. Rukhlenko, M. Premaratne, and C. Jagadish, “Optimization of gain-assisted waveguiding in metal-dielectric nanowires,” Opt. Lett. 35, 4190–4192 (2010).
[Crossref]

I. Udagedara, M. Premaratne, I. Rukhlenko, H. Hattori, and G. Agrawal, “Unified perfectly matched layer for finite-difference time-domain modeling of dispersive optical materials,” Opt. Express 17, 21179–21190 (2009).
[Crossref]

H. T. Hattori, Z. Li, D. Liu, I. Rukhlenko, and M. Premaratne, “Coupling of light from microdisk lasers into plasmonic nano-antennas,” Opt. Express 17, 20878–20884 (2009).
[Crossref]

Rukhlenko, I. D.

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Figures (8)

Figure 1
Figure 1 Historical evidence of use of plasmonic effects: (left) the Lycurgus Cup, thought to have been made in or about the fourth century A.D., exhibits a color-changing property that makes its glass take on different hues, depending on the light source. It appears jade-green when looked at in reflected light. However, when light is shone into the cup, it appears translucent-red from outside. The glass contains gold and silver alloyed nanoparticles. (right) Stained glass window at Lancaster Cathedral showing Edmund and Thomas of Canterbury. Here, trapped gold nanoparticles in the glass were used to generate the ruby-red color, and trapped silver nanoparticles in glass were used to generate the deep yellow color.
Figure 2
Figure 2 Optical spectrum of a single 100 electron Au–jellium sphere (rs=3 a0, R=0.74  nm). The x axis indicates frequency in units of the classical surface plasmon frequency, ωsp. The bulk plasmon frequency, ωp, is also indicated. Reprinted from Townsend and Bryant, J. Opt. 16, 114022 (2014) [191]. © IOP Publishing. Reproduced with permission. All rights reserved.
Figure 3
Figure 3 Metallic nanoshell with a dielectric core. The regions, V1, V2, and V3 represent the core, metallic shell, and free space, respectively. The boundaries of these regions are represented by the surfaces S1 and S2, which are also the inner and outer surfaces of the metal shell, respectively. © 2007 IEEE. Reprinted, with permission, from Mayergoyz and Zhang, IEEE Trans. Magn. 43, 1689–1692 (2007) [195].
Figure 4
Figure 4 Two-level spaser model considered by Stockman [200] where an external pump provides energy to two-level chromophores with rate Γ12g and the excited state loses energy at rate Γ21 to the environment other than the spasing plasmonic mode. We also assume that the non-diagonal components (coherence terms) of the density matrix decay with the rate γph. Ωa(m)p is the single-plasmon Rabi frequency representing the spasing transition in the pth chromophore.
Figure 5
Figure 5 Three-level coherent pumping spaser model considered by Dorfman et al. [203]. The gain medium is made of chromophores having three levels: a ground state |1 and two excited states |2 and |3. An incoherent pumping source provide energy to the chromophore by coupling states |1 and |3. This transition is designated by Γ13g. Transition |2 and |3 is driven by an external coherent source. This transition is designated by Γ23. The state |3 relaxes to the state |2 at a rate Γ32, and the state |2 decays to |1 at the rate Γ21. Also, it is possible for the state |3 to relax to the state |1 at the rate Γ31. Ωpa(m) and Ωpa(s) are the pth chromophore’s single-plasmon Rabi frequencies representing transitions between levels 31 and 32, respectively.
Figure 6
Figure 6 Laser structure developed by Noginov and colleagues that consists of a gold core surrounded by a silica shell in which organic dye molecules are embedded. The molecules provide the laser’s optical gain. The energy (photons) pumped into the system is transferred to the collective motion of the electrons on the gold core’s surface and stimulates the coherent emission and amplification of so-called surface plasmon waves. These waves are ultimately converted into laser light of wavelength 531 nm. Adapted by permission from Macmillan Publishers Ltd.: Garcia-Vidal and Moreno, Nature 461, 604–605 (2009) [246]. Copyright 2009.
Figure 7
Figure 7 Coumarin 6 (C6) dye molecules are self-assembled around an Ag nanoparticle to create a spaser. The inset shows the absorption spectra for C6 and Ag decahedra in solution, and the emission spectrum for C6. It clearly shows the spectral overlap of both dye and Ag particles–plasmon absorption with dye emission, which is a critical requirement for spasing to take place. Reprinted (adapted) with permission from Stamplecoskie et al., J. Am. Chem. Soc. 136, 2956–2959 (2014) [248]. Copyright 2014 American Chemical Society.
Figure 8
Figure 8 Oulton and co-workers’ laser, whose working principle is also based on surface plasmon waves, consists of a CdS nanowire separated from an Ag surface by a 5 nm insulating gap made of MgF2 [232]. It was observed that the spot size was set by this MgF2 layer. The emergent, 489 nm wavelength laser light is emitted from a strongly confined spot within the gap region. Adapted by permission from Macmillan Publishers Ltd.: Garcia-Vidal and Moreno, Nature 461, 604–605 (2009) [246]. Copyright 2009.

Tables (2)

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Table 1. Seven Defining Constants of the SI

Tables Icon

Table 2. D(E)=2VkdnkDk(k)δ(EE(k)) and Ne(0)=0EFD(E)FFD(0,E)dE, where Dk(k)=(1/2π)n and n=1,2,3

Equations (55)

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Ne(T)=0D(E)FFD(T,E)dE.
ϵDrude(ω)=ϵ0ϵ0ωp2ω2+iγ(ω)ω,
γn(ω)=γ(ω)+2g1vFD,
g1=1κ1κ1x3/2(x+κ)1/2dx;κ=ωEF.
δ=c2γ(ω)ωωp2,
ϵ(ω)=ϵb(ω)ϵ0+ϵDrude(ω)=ϵb(ω)ϵ0ωp2ω2+iγ(ω)ω.
ϵLorentz(ω)=ϵb(ω)+ϵ0ωp2ω02ω2iγ(ω)ω.
ϵgraphene(ω)=ϵ0+iσgraphene(ω)ωd,
σgraphene(ω)=e28[tanh(ω+2EF4kBT)+tanh(ω2EF4kBT)]ie28πln[(ω+2EF)2(ω2EF)2+(2kBT)2]+ie2π(EFω+iγ),
σgraphene,Drude(ω)=iσ0ω+iγ,
σgraphene(ω)iσ0ω+iγ+e24(θ(ω2EF)iπln|ω+2EFω2EF|),
Q=ω2(Im(ϵ(ω))2ddωRe(ϵ(ω)).
σgraphene(ω)={(iωϵ1D/k1,)+(iωϵ2D/k2,),if  TM(k1,+k2,)/iωμ0,if  TE.
σgraphene(ω)={2iωϵD/k,if  TM2k/iωμ0,if  TE,
FOMconf=4πcϵDσ0ω,FOMprop=sd.
2ϕ=0if  ϕV1V2V3,
ϕ(Q)=14πϵ0(S1σ1(M)rMQdSM+S2σ2(M)rMQdSM).
ϕ±(Q)n=±σ(Q)2ϵ0+14πϵ0Sσ(M)rMQ·nQrMQ3dSM,
[ϵ1(KS1+2π)ϵ1KS1ϵ0KS2ϵ0(KS22π)][σ1σ2]=ϵ+[(KS12π)KS1KS2(KS2+2π)][σ1σ2],
ϵ(r)=ϵ0[1+(ϵ+ϵ01)η+(r)+(ϵ1ϵ01)η1(r)],
·[ϵ(r)ϕ(r)]=0,
1sη(r)(1ϵ+ϵ0)η+(r)+(1ϵ1ϵ0)η1(r),
ϕ(r)=φ0(r)+1sVddVη(r)G(rr)·ϕ(r)φ0(r)+1sΓ^ϕ(r),
φ|ψ=Vdη(r)φ*·ψdV.
|φ=|φ0+n(r|φnφn|φn)*|φnsn/s1,
Epl(r)=nAn[a^n+a^n]φn(r),
H(p)(m)2L=ωma^ma^m+12ω21(|22||11|).
H(p)(m)ID=Am[a^m+a^m]d^(p)·φm(rp)=(Ωa(m)p|21|+Ωa(m)p*|12|)(a^m+a^m),
U=exp(iH(p)(m)2Lt)=exp(iωmta^ma^m)exp(i2ω21t(|22||11|)).
H^(p)(m)ID=UH(p)(m)IDU=[Ωp(m)pexp(i(ω21+ωm)t)a^m|21|+Ωp(m)pexp(i(ω21ωm)t)|21|a^mΩp(m)p*exp(i(ω21+ωm)t)a^m|12|+Ωp(m)p*exp(i(ω21+ωm)t)a^m|12|].
H(p)(m)2LIDH(p)(m)2L+H(p)(m)ID=ωma^ma^m+12ω21(|22||11|)+[Ωa(m)(p