OSA's Digital Library

Journal of the Optical Society of America B

Journal of the Optical Society of America B

| OPTICAL PHYSICS

  • Editor: Henry van Driel
  • Vol. 29, Iss. 7 — Jul. 1, 2012
  • pp: 1799–1809

Purcell factor for a cylindrical nanocavity: ab initio analytical approach

Vladimir Bordo  »View Author Affiliations


JOSA B, Vol. 29, Issue 7, pp. 1799-1809 (2012)
http://dx.doi.org/10.1364/JOSAB.29.001799


View Full Text Article

Enhanced HTML    Acrobat PDF (468 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

The rigorous analytical approach for the calculation of the spontaneous decay rate for a quantum emitter located in a cylindrical cavity of arbitrary diameter and length is developed. The approach is based on the dyadic Green’s function of the Helmholtz equation, which is obtained by introducing the fictitious surface current sheets at both ends of the nanocavity. The cases when an emitter is located on the cavity axis and when the cavity length exceeds essentially its diameter are considered in further detail. The general theory is illustrated by the calculations for the system, which models a quantum dot embedded in a GaAs nanowire.

© 2012 Optical Society of America

OCIS Codes
(020.3690) Atomic and molecular physics : Line shapes and shifts
(020.5580) Atomic and molecular physics : Quantum electrodynamics
(270.5580) Quantum optics : Quantum electrodynamics

ToC Category:
Quantum Optics

History
Original Manuscript: March 29, 2012
Manuscript Accepted: May 9, 2012
Published: June 27, 2012

Citation
Vladimir Bordo, "Purcell factor for a cylindrical nanocavity: ab initio analytical approach," J. Opt. Soc. Am. B 29, 1799-1809 (2012)
http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-29-7-1799


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. P. Lodahl, A. F. van Driel, I. S. Nikolaev, A. Irman, K. Overgaard, D. Vanmaekelbergh, and W. L. Vos, “Controlling the dynamics of spontaneous emission from quantum dots by photonic crystals,” Nature 430, 654–657 (2004). [CrossRef]
  2. S. Noda, M. Fujita, and T. Asano, “Spontaneous-emission control by photonic crystals and nanocavities,” Nat. Photon. 1, 449–458 (2007). [CrossRef]
  3. S. Noda, “Seeking the ultimate nanolaser,” Science 314, 260–261 (2006). [CrossRef]
  4. P. J. Pauzauskie and P. Yang, “Nanowire photonics,” Mater. Today 9(10), 36–45 (2006). [CrossRef]
  5. C. Z. Ning, “Semiconductor nanolasers,” Phys. Status Solidi B 247, 774–788 (2010).
  6. D. Vanmaekelbergh and L. K. van Vugt, “ZnO nanowire lasers,” Nanoscale 3, 2783–2800 (2011). [CrossRef]
  7. S. Strauf and F. Jahnke, “Single quantum dot nanolaser,” Laser Photon. Rev. 5, 607–633 (2011).
  8. B. Lounis and M. Oritt, “Single-photon sources,” Rep. Prog. Phys. 68, 1129–1179 (2005). [CrossRef]
  9. J. Claudon, J. Bleuse, N. S. Malik, M. Bazin, P. Jaffrennou, N. Gregersen, C. Sauvan, P. Lalanne, and J.-M. Gérard, “A highly efficient single-photon source based on a quantum dot in a photonic nanowire,” Nat. Photon. 4, 174–177 (2010). [CrossRef]
  10. J. Bleuse, J. Claudon, M. Creasey, N. S. Malik, J.-M. Gérard, I. Maksymov, J.-P. Hugonin, and P. Lalanne, “Inhibition, enhancement, and control of spontaneous emission in photonic nanowires,” Phys. Rev. Lett. 106, 103601 (2011). [CrossRef]
  11. A. Mohan, M. Felici, P. Gallo, B. Dwir, A. Rudra, J. Faist, and E. Kapon, “Polarization-entangled photons produced with high-symmetry site-controlled quantum dots,” Nat. Photon. 4, 302–306 (2010). [CrossRef]
  12. D. Bouwmeester, A. Ekert, and A. Zeilinger, eds., The Physics of Quantum Information (Springer, 2000).
  13. P. R. Berman, ed., Cavity Quantum Electrodynamics(Academic, 1994).
  14. H. Mabuchi and A. C. Doherty, “Cavity quantum electrodynamics: coherence in context,” Science 298, 1372–1377 (2002). [CrossRef]
  15. E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev. 69, 681 (1946).
  16. K. J. Vahala, “Optical microcavities,” Nature 424, 839–846 (2003). [CrossRef]
  17. M. Pelton, C. Santori, J. Vučković, B. Zhang, G. S. Solomon, J. Plant, and Y. Yamamoto, “Efficient source of single photons: a single quantum dot in a micropost microcavity,” Phys. Rev. Lett. 89, 233602 (2002). [CrossRef]
  18. I. Friedler, C. Sauvan, J. P. Hugonin, P. Lalanne, J. Claudon, and J. M. Gérard, “Solid-state single photon sources: the nanowire antenna,” Opt. Express 17, 2095–2110 (2009). [CrossRef]
  19. N. Gregersen, T. R. Nielsen, J. Mørk, J. Claudon, and J.-M. Gérard, “Designs for high-efficiency electrically pumped photonic nanowire single-photon sources,” Opt. Express 18, 21204–21218 (2010). [CrossRef]
  20. S. N. Dorenbos, H. Sasakura, M. P. van Kouwen, N. Akopian, S. Adachi, N. Namekata, M. Jo, J. Motohisa, Y. Kobayashi, K. Tomioka, T. Fukui, S. Inoue, H. Kumano, C. M. Natarajan, R. H. Hadfield, T. Zijlstra, T. M. Klapwijk, V. Zwiller, and I. Suemune, “Position controlled nanowires for infrared single photon emission,” Appl. Phys. Lett. 97, 171106 (2010). [CrossRef]
  21. R. Singh, and G. Bester, “Nanowire quantum dots as an ideal source of entangled photon pairs,” Phys. Rev. Lett. 103, 063601 (2009). [CrossRef]
  22. G. L. Yip, “Launching efficiency of the HE11 surface wave mode on a dielectric rod,” IEEE Trans. Microwave Theory Tech. MTT-18, 1033–1041 (1970).
  23. D. Y. Chu, and S.-T. Ho, “Spontaneous emission from excitons in cylindrical waveguides and the spontaneous-emission factor of microcavity ring lasers,” J. Opt. Soc. Am. B 10, 381–390 (1993). [CrossRef]
  24. H. Nha, and W. Jhe, “Cavity quantum electrodynamics for a cylinder: inside a hollow dielectric and near a solid dielectric cylinder,” Phys. Rev. A 56, 2213–2220 (1997). [CrossRef]
  25. W. Żakowicz, and M. Janowicz, “Spontaneous emission in the presence of a dielectric cylinder,” Phys. Rev. A 62, 013820 (2000). [CrossRef]
  26. V. V. Klimov, M. Ducloy, and V. S. Letokhov, “Spontaneous emission of an atom in the presence of nanobodies,” Quantum Electron. 31, 569–586 (2001). [CrossRef]
  27. T. Søndergaard, and B. Tromborg, “General theory for spontaneous emission in active dielectric microstructures: example of a fiber amplifier,” Phys. Rev. A 64, 033812 (2001). [CrossRef]
  28. V. V. Klimov, and M. Ducloy, “Spontaneous emission rate of an excited atom placed near a nanofiber,” Phys. Rev. A 69, 013812 (2004). [CrossRef]
  29. D. P. Fussell, R. C. McPhedran, and C. Martijn de Sterke, “Decay rate and level shift in a circular dielectric waveguide,” Phys. Rev. A 71, 013815 (2005). [CrossRef]
  30. F. Le Kien, S. Dutta Gupta, V. I. Balykin, and K. Hakuta, “Spontaneous emission of a cesium atom near a nanofiber: efficient coupling of light to guided modes,” Phys. Rev. A 72, 032509 (2005). [CrossRef]
  31. A. V. Maslov, M. I. Bakunov, and C. Z. Ning, “Distribution of optical emission between guided modes and free space in a semiconductor nanowire,” J. Appl. Phys. 99, 024314(2006). [CrossRef]
  32. D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, “Strong coupling of single emitters to surface plasmons,” Phys. Rev. B 76, 035420 (2007). [CrossRef]
  33. G. Y. Chen, Y. N. Chen, and D. S. Chuu, “Spontaneous emission of quantum dot excitons into surface plasmons in a nanowire,” Opt. Lett. 33, 2212–2214 (2008). [CrossRef]
  34. Y. N. Chen, G. Y. Chen, D. S. Chuu, and T. Brandes, “Quantum-dot exciton dynamics with a surface plasmon: band-edge quantum optics,” Phys. Rev. A 79, 033815 (2009). [CrossRef]
  35. I. D. Rukhlenko, D. Handapangoda, M. Premarante, A. V. Fedorov, A. V. Baranov, and C. Jagadish, “Spontaneous emission of guided polaritons by quantum dot coupled to metallic nanowire: beyond the dipole approximation,” Opt. Express 17, 17570–17581 (2009). [CrossRef]
  36. R. Esteban, T. V. Teperik, and J. J. Greffet, “Optical patch antennas for single photon emission using surface plasmon resonances,” Phys. Rev. Lett. 104, 026802 (2010). [CrossRef]
  37. J. Barthes, G. Colas des Francs, A. Bouhelier, J.-C. Weeber, and A. Dereux, “Purcell factor for a point-like dipolar emitter coupled to a two-dimensional waveguide,” Phys. Rev. B 84, 073403 (2011). [CrossRef]
  38. V. G. Bordo, “Reflection and diffraction at the end of a cylindrical dielectric nanowire: exact analytical solution,” Phys. Rev. B 78, 085318 (2008). [CrossRef]
  39. V. G. Bordo, “Erratum: Reflection and diffraction at the end of a cylindrical dielectric nanowire: exact analytical solution,” Phys. Rev. B 79, 039901(E) (2009). [CrossRef]
  40. V. G. Bordo, “Model of Fabry-Pérot-type electromagnetic modes of a cylindrical nanowire,” Phys. Rev. B 81, 035420 (2010). [CrossRef]
  41. V. G. Bordo, “Ab initio analytical model of light transmission through a cylindrical subwavelength hole in an optically thick film,” Phys. Rev. B 84, 075465 (2011). [CrossRef]
  42. C. T. Tai, Dyadic Green Functions in Electromagnetic Theory (IEEE, 1994).
  43. J. E. Sipe, “New Green-function formalism for surface optics,” J. Opt. Soc. Am. B 4, 481–489 (1987). [CrossRef]
  44. F. Wijnands, J. B. Pendry, F. J. Garcia-Vidal, P. M. Bell, P. J. Roberts, and L. Martín Moreno, “Green’s functions for Maxwell’s equations: application to spontaneous emission,” Opt. Quantum Electron. 29, 199–216 (1997). [CrossRef]
  45. J. A. Stratton, Electromagnetic Theory (McGraw-Hill, 1941).
  46. R. E. Collin, Field Theory of Guided Waves (IEEE, 1991).
  47. S. A. Schelkunoff, “On diffraction and radiation of electromagnetic waves,” Phys. Rev. 56, 308–316 (1939). [CrossRef]
  48. J. M. Wylie and J. E. Sipe, “Quantum electrodynamics near an interface,” Phys. Rev. A 30, 1185–1193 (1984). [CrossRef]
  49. A. W. Snyder and J. D. Love, Optical Waveguide Theory(Chapman and Hall, 1983).
  50. We use here the term “evanescent modes” to specify the modes that are evanescent in the radial direction. This definition is distinct from that used in [49].
  51. The quantities γcs/γ0 and FPinf are denoted in [18] as γ and PM, respectively.
  52. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products (Academic, 1994).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited