Abstract

The basics of four-wave mixing (FWM) and recent advances in FWM microscopy are reviewed with a particular emphasis on applications in the field of nanomaterials. The vast progress in nanostructure synthesis has triggered a need for advanced analytical tools suitable to interrogate nanostructures one at a time. The single-nanostructure sensitivity of optical microscopy has solidified the optical approach as a reliable technique for examining the electronic structure of materials at the nanoscale. By zooming in on the individual, optical microscopy has permitted detailed investigations of the linear optical response of nanomaterials such as semiconducting quantum dots and plasmon active nanometals. Besides studying the linear optical properties of nanostructures, optical microscopy has also been used to probe the nonlinear optical properties of nanoscale materials. FWM microscopy, a coherent third-order optical imaging technique, has shown great potential as a tool for investigating the nonlinear optical response of nanostructures. FWM microscopy not only permits the characterization of the nonlinear susceptibility of individual nanostructures, it also offers a route to explore the time-resolved dynamics of electronic and vibrational excitations on single structures. In addition, FWM produces strong signals from nanomaterials that are compatible with fast imaging applications, which holds promise for biological imaging studies based on nanoparticle labels that are not prone to photobleaching.

© 2010 Optical Society of America

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X. Liu, W. Rudolph, J. L. Thomas, “Characterization and application of femtosecond infrared stimulated parametric emission microscopy,” J. Opt. Soc. Am. B 27, 787–795 (2010).
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D. N. Christodoulides, I. C. Khoo, G. J. Salamo, G. I. Stegeman, E. W. Van Stryland, “Nonlinear refraction and absorption: mechanisms and magnitudes,” Adv. Opt. Photon. 2, 60–200 (2010).
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J. Renger, R. Quidant, N. v. Hulst, L. Novotny, “Surface-enhanced nonlinear four-wave-mixing,” Phys. Rev. Lett. 104, 046803 (2010).
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A. Jara, R. E. Arias, D. L. Mills, “Plasmon and the electromagnetic respons of nanowires,” Phys. Rev. B 81, 085422 (2010).
[CrossRef]

R. Ranav, S. Mukamel, “Stimulated coherent anti-Stokes Raman spectroscopy (CARS) resonances originate from double-slit interference of two-photon Stokes pathways,” Proc. Natl. Acad. Sci. U.S.A. 107, 4825–4829 (2010).
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2009 (18)

O. Roslyak, C. Marx, S. Mukamel, “Generalized Kramers–Heisenberg expressions for stimulated Raman scattering and two-photon absorption,” Phys. Rev. A 79, 063827 (2009).
[CrossRef]

J. Renger, R. Quidant, N. v. Hulst, S. Palomba, L. Novotny, “Free-space excitation of propagating surface plasmon polaritons by nonlinear four-wave-mixing,” Phys. Rev. Lett. 103, 266802 (2009).
[CrossRef]

S. Palomba, M. Danckwerts, L. Novotny, “Nonlinear plasmonics with gold nanoparticle antennas,” J. Opt. A, Pure Appl. Opt. 11, 114030 (2009).
[CrossRef]

W. Min, S. Lu, M. Rueckel, G. R. Holtom, X. S. Xie, “Near-degenerate four-wave-mixing microscopy,” Nano Lett. 9, 2423–2426 (2009).
[CrossRef] [PubMed]

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2008 (10)

J. Moger, B. D. Johnston, C. R. Tyler, “Imaging metal oxide nanoparticles in biological structures with CARS microscopy,” Opt. Express 16, 3408–3419 (2008).
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2006 (11)

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2004 (10)

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E. O. Potma, X. S. Xie, L. Muntean, J. Preusser, D. Jones, J. Ye, S. R. Leone, W. D. Hinsberg, W. Schade, “Chemical imaging of photoresists with coherent anti-Stokes Raman scattering (CARS) microscopy,” J. Phys. Chem. B 108, 1296–1301 (2004).
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2001 (8)

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R. Antoine, P. F. Brevet, H. H. Girault, D. Bethell, D. Schiffrin, “Surface plasmon enhanced non-linear optical response of gold nanoparticles at the air-toluene interface,” Chem. Commun. 1997(19), 1901–1902 (1997).
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Y. Barad, H. Eisenberg, M. Horowitz, Y. Silberberg, “Nonlinear scanning laser microscopy by third harmonic generation,” Appl. Phys. Lett. 70, 922–924 (1997).
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A. Voroshilov, C. Otto, J. Greve, “On the coherent vibrational phase in polarization sensitive resonance CARS spectroscopy of copper tetraphenylporphyrin,” J. Chem. Phys. 106, 2589–2598 (1997).
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1996 (5)

T. Hashimoto, T. Yamada, T. Yoko, “Third order nonlinear optical properties of sol-gel derived α-Fe2O3, γ-Fe2O3, and Fe3O4 thin films.,” J. Appl. Phys. 80, 3184–3190 (1996).
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1995 (3)

S.-H. Kim, T. Yoko, "Nonlinear optical properties of TiO2-based glasses: MOx–TiO2 (M = Sc, Ti, V, Nb, Mo, Ta and W) binary glasses," J. Am. Ceram. Soc. 78, 1061–1065 (1995).
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T. Hashimoto, T. Yoko, “Third-order nonlinear optical properties of sol-gel derived V2O5, Nb2O5 and Ta2O3 thin films,” Appl. Opt. 34, 2941–2948 (1995).
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1994 (4)

1993 (3)

T. Hashimoto, T. Yoko, S. Sakka, “Third-order nonlinear optical susceptibility of α-Fe2O3 thin film prepared by the sol-gel method,” J. Ceram. Soc. Jpn. 101, 64–68 (1993).
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1992 (2)

Y. Kanemitsu, H. Uto, Y. Masumoto, Y. Maeda, “On the origin of visible photoluminescence in nanometer-size Ge crystallites,” Appl. Phys. Lett. 61, 2187–2189 (1992).
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1991 (5)

W. E. Torruellas, L. A. Weller-Brophy, R. Zanoni, G. I. Stegeman, Z. Osborne, B. J. J. Zelinski, “Third-harmonic generation measurement of nonlinearities in SiO2-TiO2 sol-gel films,” Appl. Phys. Lett. 58, 1128–1130 (1991).
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Y. Maeda, N. Tsukamoto, Y. Yazawa, Y. Kanemitsu, M. Yasuaki, “Visible photoluminescence of Ge microcrystals embedded in SiO2 glassy matrices,” Appl. Phys. Lett. 59, 3168–3170 (1991).
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L. Brus, “Quantum crystallites and nonlinear optics,” Appl. Phys. B 53, 465–474 (1991).
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1990 (2)

D. Ricard, P. Roussignol, F. Hache, C. Flytzanis, “Nonlinear optical properties of quantum confined semiconductor microcrystallites,” Phys. Status Solidi B 159, 275–284 (1990).
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1988 (2)

F. Hache, D. Ricard, C. Flytzanis, U. Kreibig, “The optical Kerr effect in small metal particles and metal colloids: the case of gold,” Appl. Phys. A 47, 347–357 (1988).
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D. McMorrow, W. T. Lotshaw, G. A. Kenney-Wallace, “Femtosecond optical Kerr effect studies on the origin of nonlinear optical response in simple liquids,” IEEE J. Quantum Electron. 24, 443–454 (1988).
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1987 (1)

S. Schmitt-Rink, D. A. B. Miller, D. S. Chemla, “Theory of the linear and nonlinear optical properties of semiconductor microcrystallites,” Phys. Rev. B 35, 8113–8125 (1987).
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1986 (2)

L. Bányai, S. W. Koch, “A simple theory for the effects of plasma screening on the optical spectra of highly excited semiconductors,” Z. Phys. B 63, 283–291 (1986).
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G. T. Boyd, Z. H. Yu, Y. R. Shen, “Photoinduced luminescence from the noble metals and its enhancement on roughened surfaces,” Phys. Rev. B 33, 7923–7936 (1986).
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1985 (5)

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M. Moskovits, “Surface-enhanced spectroscopy,” Rev. Mod. Phys. 57, 783–826 (1985).
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F. Kajzar, J. Messier, “Third-harmonic generation in liquids,” Phys. Rev. A 32, 2352–2363 (1985).
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T. Fujii, A. Kamata, M. Shimizu, Y. Adachi, S. Maeda, “Two-photon absorption study of 1,3,5-hexatriene by CARS and CSRS,” Chem. Phys. Lett. 115, 369–372 (1985).
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1984 (2)

K. C. Rustagi, C. Flytzanis, “Optical nonlinearities in semiconductor-doped glasses,” Opt. Lett. 9, 344–346 (1984).
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G. T. Boyd, T. Rasing, J. R. R. Leite, Y. R. Shen, “Local-field enhancement on rough surfaces of metals, semimetals, and semiconductors with the use of optical second-harmonic generation,” Phys. Rev. B 30, 519–525 (1984).
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1983 (4)

D. S. Chemla, J. P. Heritage, P. F. Liao, E. D. Isaacs, “Enhanced four-wave mixing from silver particles,” Phys. Rev. B 27, 4553–4558 (1983).
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G. R. Meredith, B. Buchalter, C. Hanzlik, “Third-order susceptibility determination by third harmonic generation. II,” J. Chem. Phys. 78, 1543–1551 (1983).
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1982 (4)

M. D. Duncan, J. Reintjes, T. J. Manuccia, “Scanning coherent anti-Stokes Raman microscope,” Opt. Lett. 7, 350–352 (1982).
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P. F. Liao, A. Wokaun, “Lightning rod effect in surface enhanced Raman scattering,” J. Chem. Phys. 76, 751–752 (1982).
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1981 (1)

S. A. J. Druet, J. P. E. Taran, “CARS spectroscopy,” Prog. Quantum Electron. 7, 1–72 (1981).
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1980 (2)

V. Kreminitskii, S. Odoulov, M. Soskin, “Backward degenerate four-wave mixing in CdTe,” Phys. Status Solidi A 57, K71–K74 (1980).
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J. Gersten, A. Nitzan, “Electromagnetic theory of enhanced Raman scattering by molecules adsorbed on rough surfaces,” J. Chem. Phys. 73, 3023–3037 (1980).
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1979 (4)

C. K. Chen, A. R. B. de Castro, Y. R. Shen, “Surface coherent anti-Stokes Raman spectroscopy,” Phys. Rev. Lett. 43, 946–949 (1979).
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J. L. Oudar, R. W. Smith, Y. R. Shen, “Polarization-sensitive coherent anti-Stokes Raman spectroscopy,” Appl. Phys. Lett. 34, 758–760 (1979).
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R. K. Jain, J. B. Klein, “Degenerate four-wave mixing near the band gap of semiconductors,” Appl. Phys. Lett. 35, 454–456 (1979).
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1978 (2)

M. L. Shand, R. R. Chance, “Third-order nonlinear mixing in polydiacetylene solutions,” J. Chem. Phys. 69, 4482–4486 (1978).
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1977 (4)

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H. J. Simon, R. E. Benner, J. G. Rako, “Optical second harmonic generation with surface plasmons in piezoelectric crystals,” Opt. Commun. 23, 245–248 (1977).
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1976 (3)

F. De Martini, Y. R. Shen, “Nonlinear excitations of surface polaritons,” Phys. Rev. Lett. 36, 216–219 (1976).
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F. De Martini, G. Giuliani, P. Mataloni, E. Palange, Y. R. Shen, “Study of surface polaritons in GaP by optical four-wave-mixing,” Phys. Rev. Lett. 37, 440–443 (1976).
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H. Lotem, R. T. Lynch, N. Bloembergen, “Interference between Raman resonances in four-wave difference mixing,” Phys. Rev. A 14, 1748–1755 (1976).
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1975 (3)

G. C. Bjorklund, “Effects of focusing on the third-order nonlinear process in isotropic media,” IEEE J. Quantum Electron. QE-11, 287–296 (1975).
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1974 (2)

H. J. Simon, D. E. Mitchell, J. G. Watson, “Optical second-harmonic generation with surface plasmons in silver films,” Phys. Rev. Lett. 33, 1531–1534 (1974).
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1971 (1)

W. K. Burns, N. Bloembergen, “Third-harmonic generation in absorbing media of cubic or isotropic symmetry.,” Phys. Rev. B 4, 3437–3450 (1971).
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1969 (3)

J. J. Wynne, “Optical third-order mixing in GaAS, Ge, Si and InAs,” Phys. Rev. 178, 1295–1303 (1969).
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1968 (3)

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1965 (1)

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1962 (1)

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1959 (1)

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1908 (1)

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1904 (1)

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1896 (1)

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1890 (1)

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H. S. Nalwa, S. Miyata, Nonlinear Optics of Organic Molecules and Polymers (CRC Press, 1997).

R. Saito, G. Dresselhaus, M. S. Dresselhaus, Physical Properties of Carbon Nanotubes (Imperial, 1998).

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Figures (18)

Fig. 1
Fig. 1

Energy diagrams of several representative FWM processes. In these diagrams, a | is the ground state, b | and t | are intermediate states, and n | , n | are higher-energy states in the material. Note that all of these states, except for the ground state, can represent either eigenstates of the material or virtual states. (a) CARS excitation scheme. If b | is a vibrational state, then this scheme corresponds to vibrational CARS. (b) TPA-enhanced difference-frequency mixing, an electronically resonant scheme. This scheme has also been referred to as stimulated parametric emission (SPE). The t | level corresponds to a two-photon accessible eigenstate of the material. (c) TPA-enhanced sum-frequency mixing. (d) SRS excitation scheme. If b | is a vibrational state, then this scheme corresponds to vibrational SRS. The emitted field is at the same frequency as one of the incident beams ( ω 2 ) . (e) TPA-enhanced difference-frequency mixing. Like SRS, this scheme results in emission at ω 2 . (f) THG. The t | level corresponds to a one- or three-photon accessible eigenstate of the material.

Fig. 2
Fig. 2

Focal fields of a high-numerical-aperture lens (NA 1.1, water immersion). (a) Focal field amplitude of a 800 nm laser beam. (b) Phase profile of the focal field given in (a). The propagation phase has been subtracted for clarity. (c) Amplitude of the CARS excitation field E 1 2 E 2 * with λ 1 = 800 nm and λ 2 = 1064 nm . (d) Phase profile of the excitation field given in (c).

Fig. 3
Fig. 3

Far-field emission pattern of the FWM CARS response from a 50 nm nanocube in the focus of a NA 1.1 water immersion lens. The CARS excitation volume is given in Figs. 2(c), 2(d). Note that because of their small size relative to an optical wavelength, the FWM emission from nanoscale objects resembles the emission of a Hertzian dipole, resulting in comparable amounts of radiation in the forward direction and epi-direction.

Fig. 4
Fig. 4

Schematic of a dual-color FWM microscope based on a synchronously pumped optical parametric oscillator (OPO) light source. Two detector channels are used, one in the forward (F) propagating direction and one in the epi-direction (E). M, mirror; DM, dichroic mirror; SM, galvanometric scanning mirrors; Obj, microscope objective lens; S, sample; L, lens; PMT, photomultiplier tube.

Fig. 5
Fig. 5

Interference effects in epi-detection of FWM radiation from nanostructures on a glass substrate. The nonresonant FWM in the glass substrate is reflected at the glass/air and glass/nanostructure interface, resulting in a background signal in the epi-channel (large arrow). The FWM field from the nanostructure itself can mix coherently with the background FWM radiation. If the background signal is large, the weak FWM response from nanostructures can be enhanced in a homodyne manner.

Fig. 6
Fig. 6

Lateral cross section of a 1 μ m silica bead measured with nonresonant CARS (solid curve) and optical Kerr effect microscopy (dots). Both FWM techniques produce good microscopic contrast from a nonresonant (transparent) material with a low nonlinear susceptibility.

Fig. 7
Fig. 7

Electronic CARS FWM of liquid crystals. (a) Schematic of the director fields in a smectic A phase of an octylcyano-biphenyl (8CB) liquid crystal. The liquid crystal molecules have a highly anisotropic electronic response, resulting in orientation sensitive FWM images. The conical morphology is known as the focal conic domain (FCD). (b), (c) Horizontally sectioned FWM images of the FCD, indicating highly oriented liquid crystal domains. White arrows represent the laser polarization direction. Reprinted in part with permission from [95]. Copyright 2009, American Institute of Physics.

Fig. 8
Fig. 8

Electronic CARS FWM emission from silicon. (a) FWM from nanowires. The emission maximum from a 40 nm diameter silicon nanowire, illuminated with incident waves ω 1 ( λ 1 = 790 nm ) and ω 2 ( λ 2 = 1018 nm ) , coincides with the expected ( ω 4 = 2 ω 1 ω 2 , λ 4 = 645 nm ) FWM frequency. The inset shows a FWM image of several silicon nanowires acquired in 0.5 s . Scale bar is 2 μ m . Reprinted in part with permission from [115]. Copyright 2009, American Chemical Society. (b) FWM from a 30 nm diameter silicon nanoparticle ( λ 1 = 817 nm and λ 2 = 1064 nm ). The particle size is much smaller than the focal volume of the 1.1 NA water immersion lens, enabling an effective point spread function measurement, which provides information about the size and shape of the focal spot. Scale bar is 0.5 μ m . (c) One-dimensional cross section of the measurement in (b). The width of the profile is 0.40 μ m .

Fig. 9
Fig. 9

Dispersion of χ ( 3 ) of several metal oxides as a function of the bandgap energy. The solid curve corresponds to a fit based on a phenomenological model for THG generation, as detailed in [127].

Fig. 10
Fig. 10

Electronic CARS FWM imaging of Ti O 2 nanoparticles in fish gill tissue. Fish gills were exposed to Ti O 2 nanoparticles for a period of one week, resulting in localized clusters of nanoparticles. (a) Three-dimensional projection of the FWM signal from a 150 μ m deep stack in a region of gill tissue containing a large nanoparticles aggregate (white arrow). Detection was in the forward direction. (b) Identical image stack obtained in the epi-direction. Combined laser power of the λ 1 ( 924 nm ) and λ 2 ( 1255 nm ) beam was 100 mW . Reprinted in part with permission from [139]. Copyright 2009, Optical Society of America.

Fig. 11
Fig. 11

Electronic CARS FWM imaging of semiconducting CdSe nanowires using ps laser pulses. CdSe wires are 330 nm wide, 60 nm high and were lithographically fabricated on a glass cover slip. Details on fabrication can be found in [155]. FWM signals were detected in the epi-direction. The combined laser power of the λ 1 ( 817 nm ) and λ 2 ( 1064 nm ) beam was 10 mW .

Fig. 12
Fig. 12

Illuminating a thin metal film with a high-numerical-aperture lens in an inverted microscope configuration. (a) Schematic for low-NA illumination conditions. The incident light is normal to the metal surface and is partially backreflected at the glass/metal interface. In the metal, the electromagnetic field is nonpropagating, and the field amplitude is exponentially decaying along the axial dimension. If the metal film is thinner than the skin depth, part of the light will be transmitted through the film. (b) Schematic for high-NA illumination conditions. If the cone angle of the lens includes the angle needed for coupling to the SPP, counterpropagating surface waves will be launched that will interfere depending on the defocus from the interface.

Fig. 13
Fig. 13

Frequency mixing at a rectangular gold nanowire. Emission spectrum of a single gold nanowire ( 180 nm wide, 25 nm high) when illuminated with two ps pulses at λ 1 ( 817 nm ) and λ 2 ( 1064 nm ) . Electronic CARS, SHG and SGF are clearly observed. The blue curve is measured when the laser beams are polarized perpendicular to the long axis of the nanowire (parallel to the traverse surface plasmon mode). The red curve is obtained when the excitation beams are polarized orthogonal to the transverse surface plasmon mode.

Fig. 14
Fig. 14

Electronic CARS FWM imaging of gold nanowire structures. (a) FWM image of a zig-zag gold nanowire. Dimensions of the image are 10 μ m × 10    μ m . (b) Atomic force microscopy image of the zig-zag wire. The tall plateaus are 80 nm high, and the shallow plateaus are 20 nm high. Note that the strongest FWM signals are obtained from the shallow plateaus, indicating much stronger local fields in those areas.

Fig. 15
Fig. 15

Images of cells (HepG2) in which the Golgi apparatus is stained with an Alexa488 fluorescent immunostain, and a secondary antibody with gold nanoparticles. (a) Epifluorescence image overlaid with a phase contrast image of a cell labeled with 10 nm diameter gold nanoparticles. (b) Close up of the Golgi apparatus based on electronic FWM contrast of the gold nanoparticle of the dashed square area in (a). (c) Epifluorescence image overlaid with a phase contrast image of a cell labeled with 5 nm diameter gold nanoparticles. (d) Close up of the Golgi apparatus based on electronic FWM contrast of the gold nanoparticle of the dashed square area in (c). (e) y z image taken at the dashed line in (d). Reprinted with permission from [83]. Copyright 2009, Optical Society of America.

Fig. 16
Fig. 16

Photothermal heating of gold nanorods when illuminated with femtosecond radiation. (a) Modification of the two-photon excited fluorescence emission spectra of a single gold nanorod (aspect ratio 3.3) with increasing average excitation power. (b) Shift in the photoluminescence with increasing excitation power for the same nanorod, indicating a change in the morphological shape of the particle as shown in the series of AFM images. Reprinted with permission from [205]. Copyright 2005, the American Physical Society (http://prl.aps.org/abstract/PRL/v95/i26/e267405).

Fig. 17
Fig. 17

Electronically resonant FWM imaging of red blood cells. A broad continuum was used for excitation, which was truncated at the blue side of the spectrum. Difference-frequency mixing components within the band induce electronic CARS-type blueshifted components that can be spectrally isolated and detected. Strong signals are observed when the laser spectrum in this (nondegenerate) FWM scheme is tuned to near-resonance with the Q band of (de-)oxyhemoglobin. The donut shape of red blood cells is clearly illustrated. Reprinted in part with permission from [220]. Copyright 2009, American Chemical Society.

Fig. 18
Fig. 18

Electronically resonant FWM imaging of carbon nanotubes. (a) FWM image of an individual carbon nanotube of a 3.9 nm multiwalled nanotube. The polarization direction of the incident beams is indicated by the white arrow. A strong signal is observed when the polarization of the excitation beams is aligned with the enhanced electronic excitations along the long axis of the nanotube. (b) FWM image of the same nanotube when the beam polarization is orthogonal to the long axis of the nanotube. Without direct excitation of the enhanced electronic transitions in the nanotube, no discernible FWM signal is observed.

Tables (5)

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Table 1 Third-Order Susceptibility of Several Common Materials and Organic Liquids a

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Table 2 Third-Order Nonlinear Susceptibility of Elemental Semiconducting Materials a

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Table 3 Third-Order Susceptibility of Several Metal Oxides a

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Table 4 Third-Order Nonlinear Susceptibility of Types II–VI and III–V Semiconducting Materials a

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Table 5 Third-Order Nonlinear Susceptibility of Metals a

Equations (19)

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P i ( 3 ) ( ω 4 = ω 1 + ω 2 + ω 3 ; r ) = ϵ 0 χ i j k l ( 3 ) ( ω 4 ; ω 1 , ω 2 , ω 3 ; r ) E j ( ω 1 , r ) E k ( ω 2 , r ) E l ( ω 3 , r ) ,
χ i j k l ( 3 ) ( ω 4 ; ω 1 , ω 2 , ω 3 ) = g i l ( ω 4 , ω 3 ) f j k ( ω 1 , ω 2 ) ω b a ( ω 1 + ω 2 ) i Γ b a + f j k * ( ω 1 , ω 2 ) g i l * ( ω 4 , ω 3 ) ω b a + ( ω 1 + ω 2 ) + i Γ b a + g i k ( ω 4 , ω 2 ) f j l ( ω 1 , ω 3 ) ω b a ( ω 1 + ω 3 ) i Γ b a + f j l * ( ω 1 , ω 3 ) g i k * ( ω 4 , ω 2 ) ω b a + ( ω 1 + ω 3 ) + i Γ b a + g i j ( ω 4 , ω 1 ) f k l ( ω 2 , ω 3 ) ω b a ( ω 2 + ω 3 ) i Γ b a + f k l * ( ω 2 , ω 3 ) g i j * ( ω 4 , ω 1 ) ω b a + ( ω 2 + ω 3 ) + i Γ b a
g x y ( ω i , ω j ) = ( N 3 ) 1 2 n ( μ a n x μ n b y ω n a ω i i Γ n a + μ a n x μ n b y ω n a + ω j + i Γ n b ) ,
f x y ( ω i , ω j ) = ( N 3 ) 1 2 n ( μ b n x μ n a y ω n a ω i i Γ n a + μ b n x μ n a y ω n a ω j i Γ n a ) .
χ ( 3 ) ( ω 4 ; ω 1 , ω 1 , ω 2 ) = χ NR ( 3 ) + t [ A t ω t 2 ω 1 i Γ t + A t