Spaser Based on Graphene Tube

Document Type : Article

Authors

Department of Electrical Engineering, Sharif University of Technology, Azadi Avenue, Tehran, Iran

Abstract

In this paper, we propose a structure for graphene spaser and develop an electrostatic model for quantizing plasmonic modes. Using this model, one can analyze any spaser consisting of graphene in the electrostatic regime. The proposed structure is investigated analytically and the spasing condition is derived. We show that spasing can occur in some frequencies where the Quality factor of plasmonic modes is higher than some special minimum value. Finally, an algorithmic design procedure is proposed, by which one can design the structure for a given frequency. As an example, a spaser with plasmon energy of 0.1 eV is designed.

Keywords

Main Subjects


References
1. Bergman, D.J. and Stockman, M.I. Surface plasmon
ampli cation by stimulated emission of radiation:
quantum generation of coherent surface plasmons
in nanosystems", Physical Review Letters, 90(2), p.
027402 (2003).
2. Noginov, M., Zhu, G., Belgrave, A., Bakker, R.,
Shalaev, V., Narimanov, E., Stout, S., Herz, E.,
Suteewong, T., and Wiesner, U. Demonstration of a
spaser-based nanolaser", Nature, 460(7259), pp. 1110{
1112 (2009).
3. Stockman, M.I. The spaser as a nanoscale quantum
generator and ultrafast ampli er", Journal of Optics,
12(2), p. 024004 (2010).
4. Zhong, X.L. and Li, Z.Y. All-analytical semiclassical
theory of spaser performance in a plasmonic nanocavity",
Physical Review B, 88(8), p. 085101 (2013).
5. Dorfman, K.E., Jha, P.K., Voronine, D.V., Genevet,
P., Capasso, F., and Scully, M.O. Quantumcoherence-
enhanced surface plasmon ampli cation by
stimulated emission of radiation", Physical Review
Letters, 111(4), p. 043601 (2013).
6. Apalkov, V. and Stockman, M.I. Proposed graphene
nanospaser", Light: Science & Applications, 3(7), p.
e191 (2014).
7. Andrianov, E., Pukhov, A., Dorofeenko, A., Vinogradov,
A., and Lisyansky, A. Forced synchronization
of spaser by an external optical wave", Optics Express,
19(25), pp. 24849{24857 (2011).
8. Khurgin, J.B. and Sun, G. Injection pumped single
mode surface plasmon generators: threshold,
linewidth, and coherence", Optics Express, 20(14), pp.
15309{15325 (2012).
9. Li, D. and Stockman, M.I. Electric spaser in the
extreme quantum limit", Physical Review Letters,
110(10), p. 106803 (2013).
10. Parfenyev, V.M. and Vergeles, S.S. Quantum theory
of a spaser-based nanolaser", Optics Express, 22(11),
pp. 13671{13679 (2014).
11. Rupasinghe, C., Rukhlenko, I.D., and Premaratne, M.
Spaser made of graphene and carbon nanotubes",
ACS Nano, 8(3), pp. 2431{2438 (2014).
12. Jayasekara, C., Premaratne, M., Stockman, M.I., and
Gunapala, S.D. Multimode analysis of highly tunable,
quantum cascade powered, circular graphene spaser",
Journal of Applied Physics, 118(17), p. 173101 (2015).
13. Totero Gongora, J.S., Miroshnichenko, A.E., Kivshar,
Y.S., and Fratalocchi, A. Energy equipartition and
unidirectional emission in a spaser nanolaser", Laser
& Photonics Reviews, 10(3), pp. 432{440 (2016).
14. Richter, M., Gegg, M., Theuerholz, T.S., and Knorr,
A. Numerically exact solution of the many emittercavity
laser problem: Application to the fully quantized
spaser emission", Physical Review B, 91(3), p.
035306 (2015).
15. Meng, X., Liu, J., Kildishev, A.V., and Shalaev, V.M.
Highly directional spaser array for the red wavelength
region", Laser & Photonics Reviews, 8(6), pp. 896{903
(2014).
16. Liu, B., Zhu, W., Gunapala, S.D., Stockman, M.I.,
and Premaratne, M. Open resonator electric spaser",
ACS Nano, 11(12), pp. 12573{12582 (2017).
17. Kumarapperuma, L., Premaratne, M., Jha, P.K.,
Stockman, M.I., and Agrawal, G.P. Complete characterization
of the spasing (ll) curve of a three-level
quantum coherence enhanced spaser for design optimization",
Applied Physics Letters, 112(20), p. 201108
(2018).
18. Veltri, A., Chipouline, A., and Aradian, A. Multipolar,
timedynamical model for the loss compensation
and lasing of a spherical plasmonic nanoparticle spaser
immersed in an active gain medium", Scienti c Reports,
6, p. 33018 (2016).
19. Andrianov, E., Pukhov, A., Dorofeenko, A., Vinogradov,
A., and Lisyansky, A. Spaser operation below
threshold: autonomous vs. driven spasers", Optics
Express, 23(17), pp. 21983{21993 (2015).
20. Ye, Y., Liu, F., Cui, K., Feng, X., Zhang, W., and
Huang, Y. Free electrons excited spaser", Optics
Express, 26(24), pp. 31402{31412 (2018).
21. Shahbazyan, T.V. Mode volume, energy transfer, and
spaser threshold in plasmonic systems with gain", ACS
Photonics, 4(4), pp. 1003{1008 (2017).
22. Passarelli, N., Bustos-Maruun, R.A., and Coronado,
E.A. Spaser and optical ampli cation conditions
in gold-coated active nanoparticles", The Journal
of Physical Chemistry C, 120(43), pp. 24941{24949
(2016).
23. Jayasekara, C., Premaratne, M., Gunapala, S.D., and
Stockman, M.I. Mos2 spaser", Journal of Applied
Physics, 119(13), p. 133101 (2016).
24. Gegg, M., Theuerholz, T.S., Knorr, A., and Richter,
M. Fully quantized spaser physics: towards exact
modeling of mesoscopic CQED systems", In Ultrafast
Phenomena and Nanophotonics XIX, 9361, p.
93610Y. International Society for Optics and Photonics
(2015).
25. Petrosyan, L. and Shahbazyan, T. Spaser quenching
by o resonant plasmon modes", Physical Review B,
96(7), p. 075423 (2017).
3094 S. Behjati Ardakani and R. Faez/Scientia Iranica, Transactions D: Computer Science & ... 27 (2020) 3084{3095
26. Warnakula, T., Stockman, M.I., and Premaratne, M.
Improved scheme for modeling a spaser made of
identical gain elements", JOSA B, 35(6), pp. 1397{
1407 (2018).
27. Zheng, C., Jia, T., Zhao, H., Zhang, S., Feng, D., and
Sun, Z. Low threshold tunable spaser based on multipolar
fano resonances in disk-ring plasmonic nanostructures",
Journal of Physics D: Applied Physics,
49(1), p. 015101 (2015).
28. Wan, M., Gu, P., Liu, W., Chen, Z., and Wang, Z.
Low threshold spaser based on deep-subwavelength
spherical hyperbolic metamaterial cavities", Applied
Physics Letters, 110(3), p. 031103 (2017).
29. Song, P., Wang, J.H., Zhang, M., Yang, F., Lu, H.J.,
Kang, B., Xu, J.J., and Chen, H.Y. Three-level spaser
for next-generation luminescent nanoprobe", Science
Advances, 4(8), p. eaat0292 (2018).
30. Ardakani, S.B. and Faez, R. Doped silicon quantum
dots as sources of coherent surface plasmons",
Journal of Optics, 20(12), p. 125001 (2018). URL
http://stacks.iop.org/2040-8986/20/i=12/a=125001
31. Ardakani, S.B. and Faez, R., A Tunable Spherical
Graphene Spaser, arXiv preprint arXiv:1712.01322
(2017).
32. Novoselov, K.S., Geim, A.K., Morozov, S., Jiang, D.,
Katsnelson, M., Grigorieva, I., Dubonos, S. and Firsov,
A. Two-dimensional gas of massless dirac fermions in
graphene", Nature, 438(7065), pp. 197{200 (2005).
33. Majdi, M. and Fathi, D. Graphene-based nano biosensor:
Sensitivity improvement", Scientia Iranica,
24(6), pp. 3531{3535 (2017).
34. Faramarzi, V., Ahmadi, V., Ghane Golmohamadi, F.,
and Fotouhi, B. A biosensor based on plasmonic wave
excitation with di ractive grating structure", Scientia
Iranica, 24(6), pp. 3441{3447 (2017).
35. Derakhshi, M. and Fathi, D. Terahertz plasmonic
switch based on periodic array of graphene/silicon",
Scientia Iranica, 24(6), pp. 3452{3457 (2017).
36. Jablan, M., Buljan, H., and Soljacic, M. Plasmonics
in graphene at infrared frequencies", Physical Review
B, 80(24), p. 245435 (2009).
37. Chuang, S., Physics of Photonic Devices, Wiley Series
in Pure and Applied Optics, John Wiley & Sons (2009).
URL https://books.google.com/books?id=x5Cd
PDf1kC.
38. Vurgaftman, I., Meyer, J., and Ram-Mohan, L. Band
parameters for iii{v compound semiconductors and
their alloys", Journal of Applied Physics, 89(11), pp.
5815{5875 (2001).
39. Elias, D., Gorbachev, R., Mayorov, A., Morozov, S.,
Zhukov, A., Blake, P., Ponomarenko, L., Grigorieva, I.,
Novoselov, K., Guinea, F., et al. Dirac cones reshaped
by interaction e ects in suspended graphene", Nature
Physics, 7(9), p. 701 (2011).
40. Christensen, T., From Classical to Quantum Plasmonics
in Three and Two Dimensions, Springer (2017).
41. Abramowitz, M. and Stegun, I.A., Handbook of Mathematical
Functions: With Formulas, Graphs, and
Mathematical Tables, 55, Courier Corporation (1964).
42. Longe, P. and Bose, S. Collective excitations in
metallic graphene tubules", Physical Review B, 48(24),
p. 18239 (1993).
43. Arista, N.R. and Fuentes, M.A. Interaction of charged
particles with surface plasmons in cylindrical channels
in solids", Physical Review B, 63(16), p. 165401 (2001).
44. Ashcroft, N. and Mermin, N., Solid State Physics,
HRW International Editions, Holt, Rinehart and Winston
(1976). URL https://books.google.com/books?
id=1C9HAQAAIAAJ.
45. Scully, M. and Zubairy, M., Quantum Optics,
Cambridge University Press (1997). URL
https://books.google.com/books?id=9lkgAwAAQBAJ.
46. Hassani, S., Mathematical Physics: A Modern Introduction
to Its Foundations, Springer International
Publishing (2013), URL https://books.google.
com/books?id=uRa4BAAAQBAJ.
47. Mikhailov, S. and Ziegler, K. New electromagnetic
mode in graphene", Physical Review Letters, 99(1), p.
016803 (2007).
48. Gao, Y., Ren, G., Zhu, B., Liu, H., Lian, Y., and Jian,
S. Analytical model for plasmon modes in graphenecoated
nanowire", Optics Express, 22(20), pp. 24322{
24331 (2014).
49. Jalali-Mola, Z. and Jafari, S. Electromagnetic modes
from stoner enhancement: Graphene as a case study",
Journal of Magnetism and Magnetic Materials, 471,
pp. 220{235 (2019).