Полуклассическая теория спазера на основе графена
Abstract
In the present paper graphene nanoflake generator (spaser) is considered. Consistent derivation of main equations for the description of graphene spaser dynamics with the account of the material dispersion is provided. Single-mode equations and rate equations are derived. Explicit expressions for the parameters in the equations are obtained. Numerical values of these parameters, which describe graphene spaser dynamics, are given.
- plasmonic generator
- graphene spaser
- graphene plasmonics
- Maxwell-Bloch equations
Аннотация (на русском)
Полуклассическая теория спазера на основе графена
В данной работе рассмотрен поверхностный плазмон-поляритонный лазер (спазер), который генерирует поверхностные плазмоны в графеновой чешуйке. Произведен пересмотр основных лазерных уравнений для описания спазера с учетом дисперсии материальных параметров. Выполнен последовательный вывод уравнений динамики спазера, начиная с уравнений Максвелла-Блоха. Получены уравнения динамики спазера в одномодовом приближении и скоростные уравнения. Найдены выражения для параметров уравнений через физические параметры системы. Приведены характерные численные значения параметров скоростных уравнений, описывающих динамику спазера на основе графена.
For citation
Nechepurenko I.A., Dorofeenko A.V., Lozovik I.E. Полуклассическая теория спазера на основе графена // Journal of Radio Electronics. – 2015. – No. 12.
References
- S. A. Maier. Plasmonics: Fundamentals and Applications. New York: Springer Science + Business Media, 2007.
- G. Shvets, I. Tsukerman. Plasmonics and Plasmonic Metamaterials: Analysis and Applications. Singapore: World Scientific, 2012.
- S. Enoch, N. Bonod. Plasmonics: From Basics to Advanced Topics. Berlin: Springer Series in Optical Sciences, 2012.
- S. Zouhdi, A. H. Sihvola, A. P. Vinogradov. Metamaterials and Plasmonics: Fundamentals, Modelling, Applications. New York: Springer Science + Business Media B.V., 2009.
- S. I. Bozhevolnyi. Plasmonic nanoguides and circuits. Singapore: Pan Stanford Publishing Pte Ltd, 2009.
- V. M. Shalaev, S. Kawata. Nanophotonics with Surface Plasmons Amsterdam: Elsevier B.V., 2007.
- A. V. Zayats, S. Maier. Active Plasmonics and Tuneable Plasmonic Metamaterials. Hoboken: John Wiley and Sons, 2013.
- A. K. Sarychev, V. M. Shalaev. Electrodynamics of Metamaterials. Singapore: World Scientific Publishing Co. Pte. Ltd., 2007.
- P. R. West, S. Ishii, G. V. Naik, N. K. Emani, V. M. Shalaev, A. Boltasseva. Searching for better plasmonic materials // Laser & Photonics Reviews. 2010. V. 4. N 6. P. 795-808.
- Y. E. Lozovik, A. V. Klyuchnik. The dielectric function and collective oscillations inhomogeneous systems // Dielectric Susceptibility / Keldysh L. V. и др. North Holland: Amsterdam, 1987. C. 299.
- P. N. Melentiev, A. E. Afanasiev, A. A. Kuzin, A. S. Baturin, V. I. Balykin. Giant optical nonlinearity of a single plasmonic nanostructure // Optics express. 2013. V. 21. N 12. P. 13896-13905.
- P. Melentiev, T. Konstantinova, A. Afanasiev, A. Kuzin, A. Baturin, A. Tausenev, A. Konyaschenko, V. Balykin. Single nano-hole as a new effective nonlinear element for third-harmonic generation // Laser Physics Letters. 2013. V. 10. N 7. P. 075901.
- W. L. Barnes, A. Dereux, T. W. Ebbesen. Surface plasmon subwavelength optics // Nature. 2003. V. 424. N 6950. P. 824-830.
- I. P. Radko, A. B. Evlyukhin, A. Boltasseva, S. I. Bozhevolnyi. Refracting surface plasmon polaritons with nanoparticle arrays // Opt. Express. 2008. V. 16. - N 6. P. 3924-3930.
- Y. Gong, J. VuCkovic. Design of plasmon cavities for solid-state cavity quantum electrodynamics applications // Applied Physics Letters. 2007. V. 90. N 3. P. 033113-3.
- A. Archambault, T. V. Teperik, F. Marquier, J. J. Greffet. Surface plasmon Fourier optics // Physical Review B. 2009. V. 79. N 19. P. 195414.
- L. Feng, K. A. Tetz, B. Slutsky, V. Lomakin, Y. Fainman. Fourier plasmonics: Diffractive focusing of in-plane surface plasmon polariton waves // Applied Physics Letters. 2007. V. 91. N 8. P. 081101-3.
- R. Zia, M. L. Brongersma. Surface plasmon polariton analogue to Young's double-slit experiment // Nat Nano. 2007. V. 2. N 7. P. 426-429.
- I. Pockrand, J. D. Swalen, J. G. Gordon Ii, M. R. Philpott. Surface plasmon spectroscopy of organic monolayer assemblies // Surface Science. 1978. V. 74. N 1. P. 237-244.
- V. M. Agranovich, D. L. Mills. Surface Polaritons - Electromagnetic Waves at Surfaces and Interfaces. Amsterdam: North-Holland Publ. Co., 1982.
- P. Mulvaney. Surface Plasmon Spectroscopy of Nanosized Metal Particles // Langmuir. 1996. V. 12. N 3. P. 788-800.
- T. Eberlein, U. Bangert, R. R. Nair, R. Jones, M. Gass, A. L. Bleloch, K. S. Novoselov, A. Geim, P. R. Briddon. Plasmon spectroscopy of free-standing graphene films // Physical Review B. 2008. V. 77. N 23. P. 233406.
- R. Tanaka, R. Gomi, K. Funasaka, D. Asakawa, H. Nakanishi, H. Moriwaki. Development of a novel evaluation method for air particles using surface plasmon resonance spectroscopy analysis // Analyst. 2013. V. 138. N 18.- P. 5437-5443.
- D. L. Jeanmaire, R. P. Van Duyne. Surface raman spectroelectrochemistry: Part I. Heterocyclic, aromatic, and aliphatic amines adsorbed on the anodized silver electrode // Journal of Electroanalytical Chemistry and Interfacial Electrochemistry. 1977. V. 84. N 1. P. 1-20.
- A. Otto. Raman spectra of (CN)- adsorbed at a silver surface // Surface Science. 1978. V. 75. N 2. P. L392-L396.
- G. L. Eesley. Relationship between surface-plasmon radiation and enhanced adsorbate Raman scattering // Physical Review B. 1981. V. 24. N 10. P. 5477-5484.
- J. C. Tsang, J. R. Kirtley, J. A. Bradley. Surface-Enhanced Raman Spectroscopy and Surface Plasmons // Physical Review Letters. 1979. V. 43. N 11. P. 772-775.
- C. Fang, D. Brodoceanu, T. Kraus, N. H. Voelcker. Templated silver nanocube arrays for single-molecule SERS detection // RSC Advances. 2013. V. 3. N 13. P. 4288-4293.
- P. Hawrylak, J. J. Quinn. Amplification of bulk and surface plasmons in semiconductor superlattices // Applied Physics Letters. 1986. V. 49. N 5. P. 280-282.
- K. Kempa, P. Bakshi, J. Cen. Plasmon Amplification In Semiconductor Superlattices //1988.10.1117/12.947392. P. 62-67.
- S. A. Maier. Gain-assisted propagation of electromagnetic energy in subwavelength surface plasmon polariton gap waveguides // Optics Communications. 2006. V. 258. N 2. P. 295-299.
- C. Sirtori, C. Gmachl, F. Capasso, J. Faist, D. L. Sivco, A. L. Hutchinson, A. Y. Cho. Long-wavelength (λ ≈ 8-11.5 µm) semiconductor lasers with waveguides based on surface plasmons // Optics Letters. 1998. V. 23. N 17. P. 1366-1368.
- A. Tredicucci, C. Gmachl, F. Capasso, A. L. Hutchinson, D. L. Sivco, A. Y. Cho. Single-mode surface-plasmon laser // Applied Physics Letters. 2000. V. 76. N 16. P. 2164-2166.
- A. Babuty, A. Bousseksou, J. P. Tetienne, I. M. Doyen, C. Sirtori, G. Beaudoin, I. Sagnes, Y. De Wilde, R. Colombelli. Semiconductor Surface Plasmon Sources // Physical Review Letters. 2010. V. 104. N 22. P. 226806.
- R. F. Oulton, V. J. Sorger, T. Zentgraf, R.-M. Ma, C. Gladden, L. Dai, G. Bartal, X. Zhang. Plasmon lasers at deep subwavelength scale // Nature. 2009. V. 461. N 7264. P. 629-632.
- M. A. Noginov, G. Zhu, M. Mayy, B. A. Ritzo, N. Noginova, V. A. Podolskiy. Stimulated Emission of Surface Plasmon Polaritons // Physical Review Letters. 2008. V. 101. N 22. P. 226806.
- A. Lisyansky, I. Nechepurenko, A. Dorofeenko, A. Vinogradov, A. Pukhov. Channel spaser: Coherent excitation of one-dimensional plasmons from quantum dots located along a linear channel // Physical Review B. 2011. V. 84. N 15. P. 153409.
- D. J. Bergman, M. I. Stockman. Surface Plasmon Amplification by Stimulated Emission of Radiation: Quantum Generation of Coherent Surface Plasmons in Nanosystems // Physical Review Letters. 2003. V. 90. N 2. P. 027402.
- I. E. Protsenko, A. V. Uskov, O. A. Zaimidoroga, V. N. Samoilov, E. P. O'Reilly. Dipole nanolaser // Phys. Rev. A. 2005. V. 71. N 6. P. 063812.
- E. S. Andrianov, A. A. Pukhov, A. V. Dorofeenko, A. P. Vinogradov, A. A. Lisyansky. Stationary behavior of a chain of interacting spasers // Phys. Rev. B. 2012. V. 85. N 16. P. 165419.
- E. S. Andrianov, A. A. Pukhov, A. V. Dorofeenko, A. P. Vinogradov, A. A. Lisyansky. Forced synchronization of spaser by an external optical wave // Opt. Express. 2011. V. 19. N 25. P. 24849-24857.
- E. S. Andrianov, A. A. Pukhov, A. V. Dorofeenko, A. P. Vinogradov, A. A. Lisyansky. Dipole Response of Spaser on an External Optical Wave // Optics Letters. 2011. V. 36. N 21. P. 4302-4304.
- А. П. Виноградов, Е. С. Андрианов, А. А. Пухов, А. В. Дорофеенко, А. А. Лисянский. Квантовая плазмоника метаматериалов: перспективы компенсации потерь при помощи спазеров // Успехи физических наук. 2012. Т. 182. № 10. С. 1122-1130.
- M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, U. Wiesner. Demonstration of a spaser-based nanolaser // Nature. 2009. V. 460. N 7259. P. 1110-1112.
- Y.-J. Lu, J. Kim, H.-Y. Chen, C. Wu, N. Dabidian, C. E. Sanders, C.-Y. Wang, M.-Y. Lu, B.-H. Li, X. Qiu, W.-H. Chang, L.-J. Chen, G. Shvets, C.-K. Shih, S. Gwo. Plasmonic Nanolaser Using Epitaxially Grown Silver Film // Science. 2012. V. 337. N 6093. P. 450-453.
- 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, M. K. Smit. Lasing in metal-insulator-metal sub-wavelength plasmonic waveguides // Opt. Express. 2009. V. 17. N 13. P. 11107-11112.
- J. Y. Suh, C. H. Kim, W. Zhou, M. D. Huntington, D. T. Co, M. R. Wasielewski, T. W. Odom. Plasmonic Bowtie Nanolaser Arrays // Nano Letters. 2012. V. 12. N 11. P. 5769-5774.
- F. van Beijnum, P. J. van Veldhoven, E. J. Geluk, M. J. A. de Dood, G. W. 't Hooft, M. P. van Exter. Surface Plasmon Lasing Observed in Metal Hole Arrays // Physical Review Letters. 2013. V. 110. N 20. P. 206802.
- P. Berini, I. De Leon. Surface plasmon-polariton amplifiers and lasers // Nat Photon. 2012. V. 6. N 1. P. 16-24.
- M. S. Tame, K. R. McEnery, S. K. Ozdemir, J. Lee, S. A. Maier, M. S. Kim. Quantum plasmonics // Nat Phys. 2013. V. 9. N 6. P. 329-340.
- Z. Jacob, V. M. Shalaev. Plasmonics Goes Quantum // Science. 2011. V. 334. N 6055. P. 463-464.
- L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen. Graphene plasmonics for tunable terahertz metamaterials // Nature nanotechnology. 2011. V. 6. N 10. P. 630-634.
- F. H. Koppens, D. E. Chang, F. J. Garcia de Abajo. Graphene plasmonics: a platform for strong light-matter interactions // Nano letters. 2011. V. 11. N 8. P. 3370-3377.
- A. Grigorenko, M. Polini, K. Novoselov. Graphene plasmonics // Nature photonics. 2012. V. 6. N 11. P. 749-758.
- F. J. García de Abajo. Graphene plasmonics: challenges and opportunities // ACS Photonics. 2014. V. 1. N 3. P. 135-152.
- T. Low, P. Avouris. Graphene plasmonics for terahertz to mid-infrared applications // ACS Nano. 2014. V. 8. N 2. P. 1086-1101.
- S. A. Maier. Graphene plasmonics: All eyes on flatland // Nature Physics. 2012. V. 8. N 8. P. 581-582.
- K. Novoselov, A. K. Geim, S. Morozov, D. Jiang, M. K. I. Grigorieva, S. Dubonos, A. Firsov. Two-dimensional gas of massless Dirac fermions in graphene // Nature. 2005. V. 438. N 7065. P. 197-200.
- Y. Zhang, Y.-W. Tan, H. L. Stormer, P. Kim. Experimental observation of the quantum Hall effect and Berry's phase in graphene // Nature. 2005. V. 438. N 7065. P. 201-204.
- K. I. Bolotin, K. Sikes, Z. Jiang, M. Klima, G. Fudenberg, J. Hone, P. Kim, H. Stormer. Ultrahigh electron mobility in suspended graphene // Solid State Communications. 2008. V. 146. N 9. P. 351-355.
- A. A. Balandin, S. Ghosh, W. Bao, I. Calizo, D. Teweldebrhan, F. Miao, C. N. Lau. Superior thermal conductivity of single-layer graphene // Nano Letters. 2008. V. 8. N 3. P. 902-907.
- E. Hwang, S. D. Sarma. Dielectric function, screening, and plasmons in two-dimensional graphene // Physical Review B. 2007. V. 75. N 20. P. 205418.
- T. Otsuji, V. Popov, V. Ryzhii. Active graphene plasmonics for terahertz device applications // Journal of Physics D: Applied Physics. 2014. V. 47. N 9. P. 094006.
- O. L. Berman, R. Y. Kezerashvili, Y. E. Lozovik. Graphene nanoribbon based spaser // Physical Review B. 2013. V. 88. N 23. P. 235424.
- C. Rupasinghe, I. D. Rukhlenko, M. Premaratne. Spaser Made of Graphene and Carbon Nanotubes // ACS Nano. 2014. V. 8. N 3. P. 2431-2438.
- V. Apalkov, M. I. Stockman. Proposed graphene nanospaser // Light Sci. Appl. 2014. V. 3. P. e191.
- A. E. Siegman. Lasers. Mill Valley, CA: University Science Books 1986.
- H. Haken. Laser Theory. Berlin: Springer-Verlag, 1984.
- Я. И. Ханин. Основы динамики лазеров. Москва: Наука, 2006.
- Y. E. Lozovik, I. Nechepurenko, A. Dorofeenko, E. Andrianov, A. Pukhov. Highly sensitive spectroscopy based on a surface plasmon polariton quantum generator // Laser Physics Letters. 2014. V. 11. N 12. P. 125701.