OSA's Digital Library

Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 22 — Nov. 4, 2013
  • pp: 27460–27480

Plasmonic enhancement of the third order nonlinear optical phenomena: Figures of merit

Jacob B. Khurgin and Greg Sun  »View Author Affiliations

Optics Express, Vol. 21, Issue 22, pp. 27460-27480 (2013)

View Full Text Article

Enhanced HTML    Acrobat PDF (1926 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Recent years have seen increased interest in the plasmonic enhancement of nonlinear optical effects, yet there remains an uncertainty as to the limits of this enhancement. We present a simple and physically transparent theory for the plasmonic enhancement of third order nonlinear optical processes and show that while a huge enhancement of the effective nonlinear index can be attained, the most relevant figure of merit, the phase shift per one absorption length, remains very low. This suggests that while nonlinear plasmonic materials are not suitable for applications requiring high efficiency, for example in all-optical switching and wavelength conversion, they can be very useful for applications where overall high efficiency is not critical, such as in sensing.

© 2013 Optical Society of America

OCIS Codes
(190.4390) Nonlinear optics : Nonlinear optics, integrated optics
(190.4223) Nonlinear optics : Nonlinear wave mixing
(250.5403) Optoelectronics : Plasmonics

ToC Category:

Original Manuscript: August 15, 2013
Revised Manuscript: October 16, 2013
Manuscript Accepted: October 16, 2013
Published: November 4, 2013

Virtual Issues
Surface Plasmon Photonics (2013) Optics Express

Jacob B. Khurgin and Greg Sun, "Plasmonic enhancement of the third order nonlinear optical phenomena: Figures of merit," Opt. Express 21, 27460-27480 (2013)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. T. H. Maiman, “Stimulated Optical Radiation in Ruby,” Nature187(4736), 493–494 (1960). [CrossRef]
  2. P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, “Generation of optical harmonics,” Phys. Rev. Lett.7(4), 118–119 (1961). [CrossRef]
  3. P. D. Maker, R. W. Terhune, M. Nisenoff, and C. M. Savage, “Effects of dispersion and focusing on the production of optical harmonics,” Phys. Rev. Lett.8(1), 21–22 (1962). [CrossRef]
  4. J. A. Giordmaine, “Mixing of light beams in crystals,” Phys. Rev. Lett.8(1), 19–20 (1962). [CrossRef]
  5. J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev.127(6), 1918–1939 (1962). [CrossRef]
  6. N. Bloembergen and P. S. Pershan, “Light waves at the boundary of nonlinear media,” Phys. Rev.128(2), 606–622 (1962). [CrossRef]
  7. N. Bloembergen and Y. R. Shen, “Quantum-theoretical comparison of nonlinear susceptibilities in parametric media, lasers, and Raman Lasers,” Phys. Rev.133(1A), A37–A49 (1964). [CrossRef]
  8. Y. R. Shen, Principles of Nonlinear Optics (Wiley, 1984).
  9. R. W. Boyd, Nonlinear Optics (Academic Press, 1992).
  10. L. B. Fu, M. Rochette, V. G. Ta’eed, D. J. Moss, and B. J. Eggleton, “Investigation of self-phase modulation based optical regeneration in single mode As2Se3 chalcogenide glass fiber,” Opt. Express13(19), 7637–7644 (2005). [CrossRef] [PubMed]
  11. S. X. Qian, J. B. Snow, H. M. Tzeng, and R. K. Chang, “Lasing droplets: Highlighting the liquid-air interface by laser emission,” Science231(4737), 486–488 (1986). [CrossRef] [PubMed]
  12. H. B. Lin and A. J. Campillo, “CW nonlinear optics in droplet microcavities diplaying enhanced gain,” Phys. Rev. Lett.73(18), 2440–2443 (1994). [CrossRef] [PubMed]
  13. J. E. Heebner and R. W. Boyd, “Enhanced all-optical switching by use of a nonlinear fiber ring resonator,” Opt. Lett.24(12), 847–849 (1999). [CrossRef] [PubMed]
  14. V. Berger, “Nonlinear photonic crystals,” Phys. Rev. Lett.81(19), 4136–4139 (1998). [CrossRef]
  15. M. Bajcsy, S. Hofferberth, V. Balic, T. Peyronel, M. Hafezi, A. S. Zibrov, V. Vuletic, and M. D. Lukin, “Efficient all-optical switching using slow light within a hollow fiber,” Phys. Rev. Lett.102(20), 203902 (2009). [CrossRef] [PubMed]
  16. C. Monat, M. de Sterke, and B. J. Eggleton, “Slow light enhanced nonlinear optics in periodic structures,” J. Opt.12(10), 104003 (2010). [CrossRef]
  17. J. B. Khurgin, “Optical buffers based on slow light in electromagnetically induced transparent media and coupled resonator structures: Comparative analysis,” J. Opt. Soc. Am. B22(5), 1062–1074 (2005). [CrossRef]
  18. R. W. Hellwarth, “Control of fluorescent pulsations,” in Advances in Quantum Electronics, R. Singer, ed. (Columbia University, 1961), p. 334.
  19. L. Hargrove, R. L. Fork, and R. L. Pollack, “Locking of HeNe laser modes induced by synchronous intracavity modulation,” Appl. Phys. Lett.5(1), 4–5 (1964). [CrossRef]
  20. A. J. DeMaria, D. A. Stetson, and H. Heyma, “Mode locking of a Nd3+‐doped glass laser,” Appl. Phys. Lett.8(1), 22–24 (1966). [CrossRef]
  21. M. I. Stockman, “Nanoplasmonics: past, present, and glimpse into future,” Opt. Express19(22), 22029–22106 (2011). [CrossRef] [PubMed]
  22. S. Kühn, U. Håkanson, L. Rogobete, and V. Sandoghdar, “Enhancement of single-molecule fluorescence using a gold nanoparticle as an optical nanoantenna,” Phys. Rev. Lett.97(1), 017402 (2006). [CrossRef] [PubMed]
  23. P. Bharadwaj and L. Novotny, “Spectral dependence of single molecule fluorescence enhancement,” Opt. Express15(21), 14266–14274 (2007). [CrossRef] [PubMed]
  24. M. Moskovits, L. Tay, J. Yang, and T. Haslett, “SERS and the single molecule,” Top. Appl. Phys.82, 215–227 (2002). [CrossRef]
  25. K. Kneipp, Y. Wang, H. Kneipp, L. T. Perelman, I. Itzkan, R. R. Dasari, and M. S. Feld, “Single molecule detection using surface-enhanced Raman scattering (SERS),” Phys. Rev. Lett.78(9), 1667–1670 (1997). [CrossRef]
  26. S. Nie and S. R. Emory, “Probing single molecules and single nanoparticles by surface-enhanced Raman scattering,” Science275(5303), 1102–1106 (1997). [CrossRef] [PubMed]
  27. G. Sun, J. B. Khurgin, and R. A. Soref, “Practical enhancement of photoluminescence by metal nanoparticles,” Appl. Phys. Lett.94(10), 101103 (2009). [CrossRef]
  28. G. Sun, J. B. Khurgin, and A. Bratkovsky, “Coupled-mode theory of field enhancement in complex metal nanostructures,” Phys. Rev. B84(4), 045415 (2011). [CrossRef]
  29. G. Sun and J. B. Khurgin, “Theory of optical emission enhancement by coupled metal nanoparticles: An analytical approach,” Appl. Phys. Lett.98(11), 113116 (2011). [CrossRef]
  30. J. B. Khurgin and G. Sun, “Scaling of losses with size and wavelength in nanoplasmonics and metamaterials,” Appl. Phys. Lett.99(21), 211106 (2011). [CrossRef]
  31. J. B. Khurgin and G. Sun, “Practicality of compensating the loss in the plasmonic waveguides using semiconductor gain medium,” Appl. Phys. Lett.100(1), 011105 (2012). [CrossRef]
  32. J. B. Khurgin, G. Sun, and R. A. Soref, “Electroluminescence efficiency enhancement using metal nanoparticles,” Appl. Phys. Lett.93(2), 021120 (2008). [CrossRef]
  33. J. B. Khurgin, G. Sun, and R. A. Soref, “Practical limits of absorption enhancement near metal nanoparticles,” Appl. Phys. Lett.94(7), 071103 (2009). [CrossRef]
  34. G. Sun and J. B. Khurgin, “Origin of giant difference between fluorescence, resonance and non-resonance Raman scattering enhancement by surface plasmons,” Phys. Rev. A85(6), 063410 (2012). [CrossRef]
  35. K. Okamoto, I. Niki, A. Scherer, Y. Narukawa, T. Mukai, and Y. Kawakami, “Surface plasmon enhanced spontaneous emission rate of InGaN/GaN quantum wells probed by time-resolved photoluminescence spectroscopy,” Appl. Phys. Lett.87(7), 071102 (2005). [CrossRef]
  36. S. Pillai, K. R. Catchpole, T. Trupke, and M. A. Green, “Surface plasmon enhanced silicon solar cells,” J. Appl. Phys.101(9), 093105 (2007). [CrossRef]
  37. S. C. Lee, S. Krishna, and S. R. J. Brueck, “Quantum dot infrared photodetector enhanced by surface plasma wave excitation,” Opt. Express17(25), 23160–23168 (2009). [CrossRef] [PubMed]
  38. M. B. Dühring, N. Asger Mortensen, and O. Sigmund, “Plasmonic versus dielectric enhancement in thin-film solar cells,” Appl. Phys. Lett.100(21), 211914 (2012). [CrossRef]
  39. M. Fleischmann, P. J. Hendra, and A. J. McQuillan, “Raman spectra of pyridine adsorbed at a silver electrode,” Chem. Phys. Lett.26(2), 163–166 (1974). [CrossRef]
  40. D. A. Weitz, S. Garoff, J. I. Gersten, and A. Nitzan, “The enhancement of Raman scattering, resonance Raman scattering, and fluorescence from molecules adsorbed on a rough silver surface,” J. Chem. Phys.78(9), 5324 (1983). [CrossRef]
  41. M. Moskovits, “Surface-enhanced spectroscopy,” Rev. Mod. Phys.57(3), 783–826 (1985). [CrossRef]
  42. S. I. Anisimov, B. L. Kapeliovich, and T. L. Perelman, “Electron emission from metal surfaces exposed to ultrashort laser pulses,” Sov. Phys. JETP39, 375–377 (1974).
  43. C. K. Chen, A. R. B. de Castro, and Y. R. Shen, “Surface-enhanced second-harmonic generation,” Phys. Rev. Lett.46(2), 145–148 (1981). [CrossRef]
  44. A. Wokaun, J. G. Bergman, J. P. Heritage, A. M. Glass, P. F. Liao, and D. H. Olson, “Surface second-harmonic generation from metal island films and microlithographic structures,” Phys. Rev. B24(2), 849–856 (1981). [CrossRef]
  45. M. Kauranen and A. V. Zayats, “Nonlinear plasmonics,” Nat. Photonics6(11), 737–748 (2012). [CrossRef]
  46. M. A. Vincenti, D. de Ceglia, V. Roppo, and M. Scalora, “Harmonic generation in metallic, GaAs-filled nanocavities in the enhanced transmission regime at visible and UV wavelengths,” Opt. Express19(3), 2064–2078 (2011). [CrossRef] [PubMed]
  47. A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, “Nano-optics of surface plasmon polaritons,” Phys. Rep.408(3-4), 131–314 (2005). [CrossRef]
  48. B. Sharma, R. R. Frontiera, A. Henry, E. Ringe, and R. P. van Duyne, “SERS: Materials, applications, and the future,” Mater. Today15(1-2), 16–25 (2012). [CrossRef]
  49. I. I. Smolyaninov, A. V. Zayats, and C. C. Davis, “Near-field second harmonic generation from a rough metal surface,” Phys. Rev. B56(15), 9290–9293 (1997). [CrossRef]
  50. S. I. Bozhevolnyi, J. Beermann, and V. Coello, “Direct observation of localized second-harmonic enhancement in random metal nanostructures,” Phys. Rev. Lett.90(19), 197403 (2003). [CrossRef] [PubMed]
  51. C. Anceau, S. Brasselet, J. Zyss, and P. Gadenne, “Local second-harmonic generation enhancement on gold nanostructures probed by two-photon microscopy,” Opt. Lett.28(9), 713–715 (2003). [CrossRef] [PubMed]
  52. J. L. Coutaz, M. Nevière, E. Pic, and R. Reinisch, “Experimental study of surface-enhanced second-harmonic generation on silver gratings,” Phys. Rev. B Condens. Matter32(4), 2227–2232 (1985). [CrossRef] [PubMed]
  53. S. Linden, F. B. P. Niesler, J. Förstner, Y. Grynko, T. Meier, and M. Wegener, “Collective effects in second-harmonic generation from split-ring-resonator arrays,” Phys. Rev. Lett.109(1), 015502 (2012). [CrossRef] [PubMed]
  54. M. W. Klein, C. Enkrich, M. Wegener, and S. Linden, “Second-harmonic generation from magnetic metamaterials,” Science313(5786), 502–504 (2006). [CrossRef] [PubMed]
  55. N. Feth, S. Linden, M. W. Klein, M. Decker, F. B. P. Niesler, Y. Zeng, W. Hoyer, J. Liu, S. W. Koch, J. V. Moloney, and M. Wegener, “Second-harmonic generation from complementary split-ring resonators,” Opt. Lett.33(17), 1975–1977 (2008). [CrossRef] [PubMed]
  56. M. D. McMahon, R. Lopez, R. F. Haglund, E. A. Ray, and P. H. Bunton, “Second-harmonic generation from arrays of symmetric gold nanoparticles,” Phys. Rev. B73(4), 041401 (2006). [CrossRef]
  57. T. Xu, X. Jiao, G. P. Zhang, and S. Blair, “Second-harmonic emission from sub-wavelength apertures: effects of aperture symmetry and lattice arrangement,” Opt. Express15(21), 13894–13906 (2007). [CrossRef] [PubMed]
  58. A. Lesuffleur, L. K. S. Kumar, and R. Gordon, “Enhanced second harmonic generation from nanoscale double-hole arrays in a gold film,” Appl. Phys. Lett.88(26), 261104 (2006). [CrossRef]
  59. J. Homola, “Surface plasmon resonance sensors for detection of chemical and biological species,” Chem. Rev.108(2), 462–493 (2008). [CrossRef] [PubMed]
  60. S. Link and M. A. El-Sayed, “Spectral properties and relaxation dynamics of surface plasmon electronic oscillations in gold and silver nanodots and nanorods,” J. Phys. Chem.103(40), 8410–8426 (1999). [CrossRef]
  61. H. Baida, D. Mongin, D. Christofilos, G. Bachelier, A. Crut, P. Maioli, N. Del Fatti, and F. Vallée, “Ultrafast nonlinear optical response of a single gold nanorod near its surface plasmon resonance,” Phys. Rev. Lett.107(5), 057402 (2011). [CrossRef] [PubMed]
  62. M. Abb, P. Albella, J. Aizpurua, and O. L. Muskens, “All-optical control of a single plasmonic nanoantenna-ITO hybrid,” Nano Lett.11(6), 2457–2463 (2011). [CrossRef] [PubMed]
  63. I. I. Smolyaninov, A. V. Zayats, A. Gungor, and C. C. Davis, “Single-photon tunneling via localized surface plasmons,” Phys. Rev. Lett.88(18), 187402 (2002). [CrossRef] [PubMed]
  64. A. V. Krasavin and N. I. Zheludev, “Active plasmonics: controlling signals in Au/ Ga waveguide using nanoscale structural transformations,” Appl. Phys. Lett.84(8), 1416–1418 (2004). [CrossRef]
  65. D. Pacifici, H. J. Lezec, and H. A. Atwater, “All-optical modulation by plasmonic excitation of CdSe quantum dots,” Nat. Photonics1(7), 402–406 (2007). [CrossRef]
  66. A. V. Krasavin, T. P. Vo, W. Dickson, P. M. Bolger, and A. V. Zayats, “All-plasmonic modulation via stimulated emission of copropagating surface plasmon polaritons on a substrate with gain,” Nano Lett.11(6), 2231–2235 (2011). [CrossRef] [PubMed]
  67. K. F. MacDonald, Z. L. Samson, M. I. Stockman, and M. I. Zheludev, “Ultrafast active plasmonics,” Nat. Photonics3(1), 55–58 (2009). [CrossRef]
  68. A. V. Krasavin, S. Randhawa, J.-S. Bouillard, J. Renger, R. Quidant, and A. V. Zayats, “Optically-programmable nonlinear photonic component for dielectric-loaded plasmonic circuitry,” Opt. Express19(25), 25222–25229 (2011). [CrossRef] [PubMed]
  69. E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A Hybridization Model for the Plasmon Response of Complex Nanostructures,” Science302(5644), 419–422 (2003). [CrossRef] [PubMed]
  70. J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1999) p.158.
  71. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B6(12), 4370–4379 (1972). [CrossRef]
  72. H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, “Silver nanowires as surface plasmon resonators,” Phys. Rev. Lett.95(25), 257403 (2005). [CrossRef] [PubMed]
  73. S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.-Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature440(7083), 508–511 (2006). [CrossRef] [PubMed]
  74. H. T. Miyazaki and Y. Kurokawa, “Squeezing visible light waves into a 3-nm-thick and 55-nm-long plasmon cavity,” Phys. Rev. Lett.96(9), 097401 (2006). [CrossRef] [PubMed]
  75. J.-C. Weeber, A. Bouhelier, G. Colas de Francs, L. Markey, and A. Dereux, “Submicrometer in-plane integrated surface plasmon cavities,” Nano Lett.7(5), 1352–1359 (2007). [CrossRef] [PubMed]
  76. E. J. R. Vesseur, R. de Waele, H. J. Lezec, H. A. Atwater, F. J. García de Abajo, and A. Polman, “Surface plasmon polariton modes in a single-crystal Au nanoresonator fabricated using focused-ion-beam milling,” Appl. Phys. Lett.92(8), 083110 (2008). [CrossRef]
  77. S. Wu, X. C. Zhang, and R. L. Fork, “Direct experimental observation of interactive third and fifth order nonlinearities in a time- and space-resolved four-wave mixing experiment,” Appl. Phys. Lett.61(8), 919–921 (1992). [CrossRef]
  78. B. Borchers, C. Brée, S. Birkholz, A. Demircan, and G. Steinmeyer, “Saturation of the all-optical Kerr effect in solids,” Opt. Lett.37(9), 1541–1543 (2012). [CrossRef] [PubMed]
  79. G. Sun and J. B. Khurgin, “Comparative study of field enhancement between isolated and coupled metal nanoparticles: an analytical approach,” Appl. Phys. Lett.97(26), 263110 (2010). [CrossRef]
  80. G. Sun and J. B. Khurgin, “Optimization of the nanolens consisting of coupled metal nanoparticles: an analytical approach,” Appl. Phys. Lett.98(15), 153115 (2011). [CrossRef]
  81. J. B. Khurgin, “Performance of nonlinear photonic crystal devices at high bit rates,” Opt. Lett.30(6), 643–645 (2005). [CrossRef] [PubMed]
  82. J. E. Heebner and R. W. Boyd, “Enhanced all-optical switching by use of a nonlinear fiber ring resonator,” Opt. Lett.24(12), 847–849 (1999). [CrossRef] [PubMed]
  83. G. P. Agrawal, Nonlinear Fiber Optics, 5th ed. (Academic Press, 2012).
  84. F. G. Della Corte, M. Esposito Montefusco, L. Moretti, I. Rendina, and G. Cocorullo, “Temperature dependence analysis of the thermo-optic effect in silicon by single and double oscillator models,” J. Appl. Phys.88(12), 7115–7119 (2000). [CrossRef]
  85. I. Karakurt, C. H. Adams, P. Leiderer, J. Boneberg, and R. F. Haglund., “Nonreciprocal switching of VO2 thin films on microstructured surfaces,” Opt. Lett.35(10), 1506–1508 (2010). [CrossRef] [PubMed]

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