Theory of optical second-harmonic generation from a sphere of centrosymmetric material: Small-particle limit

Journal of the Optical Society of America B: Optical Physics

Volumn 21, Issue 7, 2004, Pages 1328-1347

  Dadap, Jerry I ^a   Shan, Jie ^b   Heinz, Tony E ^a  

^a Department of Physics Columbia University ^*  (United States)

^b CASE WESTERN RESERVE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL GEOMETRY; LIGHT EMISSION; LIGHT POLARIZATION; LIGHT SCATTERING; MATHEMATICAL MODELS; NATURAL FREQUENCIES; NONLINEAR OPTICS; OPTICAL MATERIALS; RAYLEIGH SCATTERING;

CENTROSYMMETRIC MATERIAL; LINEAR OPTICAL RESPONSE; SECOND HARMONIC FREQUENCY; SECOND HARMONIC RADIATION;

SECOND HARMONIC GENERATION;

EID: 9644275981     PISSN: 07403224     EISSN: None     Source Type: Journal    
DOI: 10.1364/JOSAB.21.001328     Document Type: Review

References (113)

1. G. Mie, "Beiträge zur Optik trüber Medien, speziell kolloidaler Metallüngen," Ann. Phys. (Leipzig) 25, 377-445 (1908).
2. P. Debye, "Der Lichtdruck auf Kugeln von beliebigem Material," Ann. Phys. (Leipzig) 30, 57-136 (1909).
3. M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969).
4. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).
5. H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).
6. N. Bloembergen and P. S. Pershan, "Light waves at the boundary of nonlinear media," Phys. Rev. 128, 606-622 (1962).
7. C. Flytzanis, F. Hache, M. C. Klein, D. Ricard, and P. Roussignol, "Nonlinear optics in composite materials," Preg. Opt. 29, 321-411 (1991).
8. U. Kreibig, in Handbook of Optical Properties, R. E. Hummel and P. Wißmann, eds. (CRC, Boca Raton, Fla., 1997), Vol. II, p. 145 and references therein.
9. U. Kreibig and M. Vollmer, Optical Properties of Metal Clusters (Springer-Verlag, Berlin 1995).
10. R. F. Haglund, Jr., in Handbook of Optical Properties, R. E. Hummel and P. Wißmann, eds. (CRC, Boca Raton, Fla., 1997), Vol. II, p. 191 and references therein.
11. J. L. Cheung, J. M. Hartings, and R. K. Chang, in Handbook of Optical Properties, R. E. Hummel and P. Wißmann, eds. (CRC, Boca Raton, Fla., 1997), Vol. II, p. 233, and references therein.
12. S. V. Gaponenko, Optical Properties of Semiconductor Nanocrystals (Cambridge University Press, New York, 1998).
13. J. W. Strutt (Lord Rayleigh), "On the light from the sky, its polarization and colour," Philos. Mag. 41, 107-120, 274279 (1871).
14. J. F. McGilp, "Optical characterization of semiconductor surfaces and interfaces," Prog. Surf. Sci. 49, 1-106 (1995).
15. K. B. Eisenthal. "Liquid interfaces probed by second-harmonic and sum-frequency spectroscopy," Chem. Rev. 1343-1360 (1996).
16. Y. R. Shen, "Wave mixing spectroscopy for surface studies," Solid State Commun. 102, 221-229 (1997).
17. T. F. Heinz, "Second-order nonlinear optical effects at surfaces and interfaces," in Nonlinear Surface Electromagnetic Phenomena, H. Ponath and G. Stegeman, eds. (Elsevier, Amsterdam, 1991) pp. 353-416.
18. J. I. Dadap and T. F. Heinz, "Nonlinear optical spectroscopy of surfaces and interfaces," in Encyclopedia of Chemical Physics and Physical Chemistry, J. H. Moore and N. D. Spencer, eds. (Institute of Physics, Bristol, 2001), pp. 1089-1125.
19. H. Wang, E. C. Y. Yan, E. Borguet, and K. B. Eisenthal, "Second harmonic generation from the surface of centrosymmetric particles in bulk solution," Chem. Phys. Lett. 259, 15-20 (1996).
20. J. M. Hartings, A. Poon, X. Pu, R. K. Chang, and T. M. Leslie, " Second harmonic generation and fluorescence images from surfactants on hanging droplets," Chem. Phys. Lett. 281, 389-393 (1997).
21. A. Srivastava and K. B. Eisenthal, "Kinetics of molecular transport across a liposome bilayer," Chem. Phys. Lett. 292, 345-351 (1998).
22. H. Wang, E. C. Y. Yan, Y. Liu, and K. B. Eisenthal, "Energetics and population of molecules at microscopic liquid and solid surfaces," J. Phys. Chem. B 102, 4446-4450 (1998).
23. N. Yang, W. E. Angerer, and A. G. Yodh, "Angle-resolved second-harmonic light scattering from colloidal particles," Phys. Rev. Lett. 87, 103902 (2001).
24. J. I. Dadap, J. Shan, K. B. Eisenthal, and T. F. Heinz, "Second-harmonic Rayleigh scattering from a sphere of centrosymmetric material," Phys. Rev. Lett. 83, 40454048 (1999).
25. A. V. Baranov, Ya. S. Bebovich, and V. I. Petrov, "Study of surface-enhanced Raman-scattering initiated by adsorption of molecules on colloidal-silver microparticles," Opt. Spectrosc. 58, 353-356 (1985) [Opt. Spectrosk. 58, 578582 (1985)].
26. C. K. Johnson and S. A. Soper, "Nonlinear surfaceenhanced spectroscopy of silver colloids and pyridine: hyper-Raman and second-harmonic scattering," J. Phys. Chem. 93, 7281-7285 (1989).
27. P. Galletto, P. F. Brevet, H. H. Girault. R. Antoine, and M. Broyer, "Enhancement of the second harmonic response by adsorbates on gold colloids: the effect of aggregation," J. Phys. Chem. B 103, 8706-8710 (1999).
28. Y. Fang, "Optical absorption of nanoscale colloidal silver: Aggregate band and adsorbate-silver surface band," J. Chem. Phys. 108, 4315-4318 (1998).
29. H. F. Wang, T. Troxler, A. G. Yeh, and H. L. Dai, "In situ, nonlinear optical probe of surfactant adsorption on the surface of microparticles in colloids," Langmuir 16, 24752481 (2000).
30. E. C. Y. Yan, Y. Liu, and K. B. Eisenthal, "In situ studies of molecular transfer between microparticles by second-harmonic generation," J. Phys. Chem. B 105, 8531-8537 (2001).
31. E. C. Y. Yan and K. B. Eisenthal, "Effect of cholesterol on molecular transport of organic cations across liposome bilayers probed by second harmonic generation," Biophys. J. 79, 898-903 (2000).
32. X.-M. Shang, Y. Liu, E. C. Y. Yan, and K. B. Eisenthal, "Effects of counterions on molecular transport across liposome bilayer. probed by second harmonic generation," J. Phys. Chem. B 105, 12816-12822 (2001).
33. E. C. Y. Yan, Y. Liu, and K. B. Eisenthal, "New method for determination of surface potential of microscopic particles by second harmonic generation." J. Phys. Chem. B 102, 6331-6336 (1998).
34. Y. Liu, E. C. Y. Yan, X.-L. Zhae, and K. B. Eisenthal, "Surface potential of charged tiposomes determined by second harmonic generation," Langmuir 17, 2063-2066 (2001).
35. 2 particles in aqueous suspension by second-harmonic generation," J. Phys. Chem. B 103, 2480-2486 (1999).
36. F. W. Vance, B. I. Lemon, and J. T. Hupp, "Enormous hyper-Rayleigh scattering from nanocrystalline gold particle suspensions," J. Phys. Chem. B 102, 10091-10093 (1998).
37. R. C. Johnson, J. T. Li, J. T. Hupp, and G. C. Schatz, " Hyper-Rayleigh scattering studies of silver, copper, and platinum nanoparticle suspensions," Chem. Phys. Lett. 356, 534-540 (2002).
38. P. Galletto, P. F. Brevet, H. H. Girault, R. Antoine, and M. Broyer, "Size dependence of the surface plasmon enhanced second harmonic response of gold colloids: towards a new calibration method," Chem. Commun. 581-582 (1999).
39. B. S. Santos, G. A. L. Pereira, D. V. Petrov, C. de Mello Donegá, "First hyperpolarizability of CdS nanoparticles studied by hyper-Rayleigh scattering," Opt. Commun. 178, 187-192 (2000).
40. 1-xS nanocrystals," J. Phys. Chem. B 106, 5325-5334 (2002).
41. M. Jacobsohn and U. Banin, "Size dependence of second harmonic generation in CdSe nanocrystal quantum dots." J. Phys. Chem. B 104 1-5 (2000).
42. M. J. Ellen, T. Mokari, and U. Banin, "Surface exchange effect on hyper Rayleigh scattering in CdSe nanocrystals," J. Phys. Chem. B 105, 12726-12731 (2001).
43. C. Landes, M. Braun, and M. A. El-Sayed, "The effect of surface adsorption on the hyper-Rayleigh scattering of large and small CdSe nanoparticles," Chem. Phys. Lett. 363, 465-470 (2002).
44. 2," Spectrochim. Acta, Part A 58, 3149-3157 (2002).
45. Y. Zhang, M. Ma, X. Wang, D. Fu, N. Gu, J. Liu, Z. Lu, Y. Ma, L. Xu, and K. Chen, "First-order hyperpolarizability of ZnS nanocrystal quantum dots studied by hyper-Rayleigh scattering," J. Phys. Chem. Solids 63 2115-2118 (2002).
46. Y. Zhang, M Ma, X. Wang, D. G. Fu, H. Q. Zhang, N. Gu, J. Z. Liu, Z. H. Lu, L. Xu, and K. J. Chen, "Second-order optical nonlinearity of surface-capped CdS nanoparticles and effect of surface modification," J. Phys. Chem. Solids 64, 927-931 (2003).
47. E. C. Hao, G. C. Schatz, R. C. Johnson, and J. T. Hupp, " Hyper-Rayleigh scattering from silver nanoparticles," J. Chem. Phys. 117, 5963-5966 (2002).
48. S. Roke, W. G. Roeterdink, J. E. G. J. Wijnhoven, A. V. Petukhov, A. W. Kleyn, and M. Bonn, "Vibrational sum frequency scattering from a submicron suspension," Phys. Rev. Lett. 91, 258302 (2003).
49. J. Nappa, G. Revillod, J.-P. Abid, I. Russier-Antoine. C. Jonin, E. Benichou. H. H. Girault, and P. F. Brevet, "HyperRayleigh scattering of gold nanorods and their relationship with linear assemblies of gold nanospheres," Faraday Discuss. 125, 145-156 (2004).
50. O. A. Aktsipetrov. P. V. Elyutin, A. A. Nikulin, and E. A. Ostrovskaya, "Size effects in optical second-harmonic generation by metallic nanocrystals and semiconductor quantum dots: the role of quantum chaotic dynamics," Phys. Rev. B 51. 17591-17599 (1995).
51. O. A. Aktsipetrov, P. V. Elyutin, A. A. Fedyanin, A. A. Nikulin, and A. N. Rubtsov, "Second-harmonic generation in metal and semiconductor low-dimensional structures," Surf. Sci. 325, 343-355 (1995).
52. T. Kuroda, S. Matsushita, F. Minami, K. Inoue, A. V. Baranov, "Observation of homogeneous broadening in semiconductor nanocrystals by resonant second-harmonic scattering spectroscopy," Phys. Rev. B 55 R16041-R16044 (1997).
53. R. Antoine, M. Pellarin, B. Palapant, M. Broyer, B. Prével, P. Galletto, P. F. Brevet, and H. H. Girault, "Surface plasmon enhanced second harmonic response from gold clusters embedded in an alumina matrix," J. Appl. Phys. 84, 4532-4536 (1998).
54. A. Brysch, G. Bour, R. Neuendorf, and U. Kreibig, "Nonlinear optical spectroscopy of embedded semiconductor clusters," Appl. Phys. B 68 447-451 (1999).
55. M. L. Sandrock, C. D. Pibel, F. M. Geiger, and C. A. Foss, Jr., "Synthesis and second-harmonic generation studies of noncentrosymmetric gold nanostructures," J. Phys. Chem. B 103, 2668-2673 (1999).
56. 2," Appl. Phys. Lett. 78, 766-768 (2001).
57. 2 films," Appl. Phys. Lett. 81, 3034-3036 (2002).
58. A. M. Malvezzi, M. Allione, M. Patrini, A. Stella, P. Cheyssac, and R. Kofman. "Melting-induced enhancement of the second-harmonic generation from metal nanoparticles," Phys. Rev. Lett. 89. 087401 (2002).
59. N. Thantu, R. S. Schley, and B. S. Justus, "Tunable room temperature second harmonic generation in glasses doped with CuCl nanocrystalline quantum dots," Opt. Commun. 220, 203-210 (2003).
60. A. Podlipensky, J. Lange, G. Seifert, H. Graener, and I. Cravetchi, "Second-harmonic generation from ellipsoidal silver nanoparticles embedded in silica glass," Opt. Lett. 28, 716-718 (2003).
61. R. Bavli, D. Yogev, S. Efrima, and G. Berkovic, "Second harmonic-generation studies of silver metal liquid-like films," J. Phys. Chem. 95, 7422-7426 (1991).
62. T. Götz. M. Buck, C. Dressier, F. Eisert, and F. Träger, " Optical second-harmonic generation by supported metalclusters size and shape effects," Appl. Phys. A 60, 607612 (1995).
63. C. P. Collier, R. J. Saykaly, J. J. Shiang, S. E. Heinrichs, and J. R. Heath, "Reversible tuning of silver quantum dot monolayers through the metal-insulator transition," Science 277, 1978-1981 (1997).
64. T. Muller, P. H. Vaccaro, F. Balzer, and H.-G. Rubahn, "Size dependent optical second harmonic generation from surface bound Na clusters: comparison between experiment and theory," Opt. Commun. 135, 103-108 (1997).
65. J.-H. Klein-Wiele, R Simon, and H.-G. Rubahn, "Size-dependent plasmon lifetimes and electron-phonon coupling time constants for surface bound Na clusters," Phys. Rev. Lett. 80, 45-48 (1998 ).
66. M. Simon, F. Träger, A. Assion, B. Lang, S. Voll, and G. Gerber, "Femtosecond time-resolved second-harmonic generation at the surface of alkali metal clusters," Chem. Phys. Lett. 296, 579-584 (1998).
67. B. Lamprecht, A. Leitner, F. R. Aussenegg, "SHG studies of plasmon dephasing in nanoparticles," Appl. Phys. B 68, 419-423 (1999 ).
68. S. Baldelli, A. S. Eppler, E. Anderson, Y. R. Shen, and G. A. Somorjai, "Surface enhanced sum frequency generation of carbon monoxide adsorbed on platinum nanoparticle arrays," J. Chem. Phys. 113, 5432-5438 (2000).
69. T. V. Murzina, A. A. Nikulin, O. A. Aktsipetrov. J. W. Ostrander, A. A. Mamedov, N. A. Kotov, M. A. C. Devillers, and J. Roark, "Nonlinear magneto-optical Kerr effect in hyper-Rayleigh scattering from layer-by-layer assembled films of yttrium iron garnet nanoparticles," Appl. Phys. Lett. 79, 1309-1311 (2001).
70. O. A. Aktsipetrov. "Nonlinear magneto-optics in magnetic nanoparticles," Colloids Surf., A 202, 165-173 (2002).
71. R. Srinivasan. Y. Tian, and I. I. Suni, "Surface plasmon effects on surface second harmonic generation during Au nanoparticle deposition onto H-Si(111)," Surf. Sci. 490, 308-314 (2001).
72. N. Yang, W. E. Angerer, and A. G. Yodh, "Second-harmonic microscopy of single micrometer-size particles on a substrate," Phys. Rev. A 64 045801 (2001).
73. H. Unterhalt, G. Rupprechter, and H.-J. Freund, "Vibrational sum frequency spectroscopy on Pd(111) and supported Pd nanoparticles: CO adsorption from ultrahigh vacuum to atmospheric pressure," J. Phys. Chem. B 106, 356-367 (2002).
74. G. Ma and H. C. Allen, "Diffuse reflection broad bandwidth sum frequency generation from particle surfaces," J. Am. Chem. Soc. 124 9374-9375 (2002).
75. H. Tuovinen. M. Kauranen, K. Jefimovs, P. Vahimaa, T. Vallius, J. Turunen, N. V. Tkachenko, and H. Lemmetyinen, "Linear and second-order nonlinear optical properties of arrays of noncentrosymmetric gold nanoparticles," J. Nonlinear Opt. Phys. Mater. 11, 421-432 (2002).
76. T. S. Koffas, J. Kim, C. C. Lawrence, and G. A. Somorjai, " Detection of immobilized protein on latex microspheres by IR-visible sum frequency generation and scanning force microscopy," Langmuir 19, 3563-3566 (2003).
77. J. Martorell, R. Vilaseca. and R. Corbalán, "Second harmonic generation in a photonic crystal," Appl. Phys. Lett. 70, 702-704 (1997).
78. J. Martorell, R. Vilaseca, and R. Corbalán, "Scattering of second-harmonic light from small spherical particles ordered in a crystalline lattice," Phys. Rev. A 55, 4520-4525 (1997).
79. 3 particle using Nd-YAG laser," Electron. Lett. 28. 286-287 (1992).
80. V. Boutou, C. Favre, and J.-P. Wolf, "Femtosecond-laser induced SHG and SFG from charged water microdroplets," in Conference on Lasers and Electro-Optics, Vol. 88 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2003), paper CMAA4.
81. P. J. Campagnola, M.-D. Wei, A. Lewis, and L. M. Loew, " High-resolution nonlinear optical imaging of live cells by second harmonic generation," Biophys. J. 77, 3341-3349 (1999).
82. P. J. Campagnola, A. C. Millard, M. Terasaki, P. E. Hoppe, C. J. Malone. and W. A. Mohler, "Three-dimensional high-resolution second-harmonic generation imaging of endogeneous structural proteins in biological tissues," Biophys. J. 81, 493-508 (2002).
83. L. Moreaux, O. Sandre, S. Charpak, M. Blanchard-Desce, and J. Mertz, "Coherent scattering in multi-harmonic light microscopy," Biophys. J. 80, 1568-1574 (2001).
84. W. R. Zipfel, R. M. Williams, R. Christie. A. Y. Nikitin, B. T. Hyman, and W. W. Webb, "Live tissue intrinsic emission microscopy using multiphoton-excited native fluorescence and second harmonic generation," Proc. Natl. Acad. Sci. U.S.A. 100, 7075-7080 (2003).
85. E. C. Y. Yan and K. B. Eisenthal, "Rotational dynamics of anisotropic microscopic particles studied by second harmonic generation," J. Phys. Chem. B 104, 6686-6689 (2000).
86. G. S. Agarwal and S. S. Jha, "Theory of second harmonic-generation at a metal-surface with surface-plasmon excitation," Solid State Commun. 41, 499-501 (1982).
87. N. Bloembergen, R. K. Chang, S. S. Jha, and C. H. Lee, "Optical second-harmonic generation in reflection from media with inversion symmetry," Phys. Rev. 174, 813-822 (1968).
88. X. M. Hua and J. I. Gersten, "Theory of second-harmonic generation by small metal spheres," Phys. Rev. B 33, 3756-3764 (1986).
89. T. P. Shen and D. Rogovin, "Coherent frequency mixing in microparticle composites," Phys. Rev. A 42, 4255-4268 (1990).
90. K. Y. Lo and J. T. Lue, "Quantum-size effect on optical second-harmonic generation in small metallic particles," Phys. Rev. B 51, 2467-2472 (1995).
91. A. Guerrero and B. S. Mendoza, "Model for great enhancement of second-harmonic generation in quantum dots," J. Opt. Soc. Am. B 12 559-569 (1995).
92. V. L. Brudny, B. S. Mendoza, and W L. Mochán, " Second-harmonic generation from spherical particles," Phys. Rev. B 62, 11152-11162 (2000).
93. W. L. Mochán, J. A. Maytorena, B. S. Mendoza, and V. L. Brudny, "Second harmonic generation in arrays of spherical particles," Phys. Rev. B 68, 085318 (2003).
94. V. L. Brudny, W. L. Mochán, J. A. Maytorena, and B. S. Mendoza, "Second harmonic generation from a collection of nanoparticles," Phys. Status Solidi B 240, 518-526 (2003).
95. E. V. Makeev and S. E. Skipetrov, "Second harmonic generation in suspensions of spherical particles," Opt. Commun. 224, 139-147 (2003).
96. D. Ostling, P. Stampfli, and K. H. Bennemann, "Theory of nonlinear-optical properties of small metallic spheres," Z. Phys. D 28, 169-175 (1993).
97. J. P. Dewitz, W. Hübner, and K. H. Bennemann, "Theory for nonlinear Mie-scattering from spherical metal clusters," Z. Phys. D 37, 75-84 (1996).
98. K. Hayata and M. Koshiba, "Theory of surface-emitting second-harmonic generation from optically trapped microspheres," Phys. Rev. A 46, 6104-6107 (1992).
99. C. K. Chen, T. F. Heinz, D. Ricard, and Y. R. Shen, " Surface-enhanced second-harmonic generation and Raman-scattering," Phys. Rev. B 27 1965-1979 (1983).
100. G. Berkovic and S. Efrima, "Second harmonic-generation from composite films of spheroidal metal particles," Langmuir 9, 355-357 (1993).
101. Y.R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984).
102. see Ref. 17 or P. Guyot-Sionnest and Y. R. Shen, "Bulk contribution in surface second-harmonic generation," Phys. Rev. B 38, 7985-7989 (1988).
103. L. D. Landau, E. M. Lifshitz, and L. P. Pitaevskii, Electrodynamics of Continuous Media, 2nd ed. (Pergamon, New York, 1984), pp. 268-269.
104. J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, New York, 1975).
105. C. T Tai. "Equivalent layers of surface-charge, current sheet, and polarization in the eigenfunction-expansions of Green's functions in electromagnetic theory," IEEE Trans. Antennas Propag. 29, 733-739 (1981).
106. D. Y. Smith, E. Shiles, and M. Inokuti. in Handbook of Optical Constants of Solids, E. D. Palik, ed. (Academic. Orlando, 1985), p. 369.
107. R. W. Terhune, P. D. Maker, and C. M. Savage, "Measurements of nonlinear light scattering," Phys. Rev. Lett. 14, 681-684 (1965).
108. R. Bersohn, Y. H. Pao, and H. L. Friseh, "Double-quantum light scattering by molecules," J. Chem. Phys. 45, 31843198 (1966).
109. P. D. Maker, "Spectral broadening of elastic secondharmonic light scattering in liquids," Phys. Rev. A 1, 923951 (1970).
110. V. Mizrahi and J. E. Sipe, "Phenomenological treatment of surface second-harmonic generation," J. Opt. Soc. Am. B 5, 660-667 (1988).
111. K. Clays and A. Persoons, "Hyper-Rayleigh scattering in solution," Phys. Rev. Lett. 66, 2980-2983 (1991).
112. E. H. Hill, "The theory of vector spherical harmonics," Am. J. Phys. 22, 211-214 (1954).
113. P. M. Morse and H. Feshbach, Methods of Theoretical Physics, Part II (McGraw-Hill, New York, 1953). pp. 1898-1901.