Abstract

The action of a nanoscopic spherically symmetric refractive index profile on a focused Gaussian beam may easily be envisaged as the action of a phase-modifying element, i.e. a lens: Rays traversing the inhomogeneous refractive index field n(r) collect an additional phase along their trajectory which advances or retards their phase with respect to the unperturbed ray. This lens-like action has long been understood as being the mechanism behind the signal of thin sample photothermal absorption measurements [Appl. Opt. 34, 41–50 (1995)], [Jpn. J. Appl. Phys. 45, 7141–7151 (2006)], where a cylindrical symmetry and a different lengthscale is present. In photothermal single (nano-)particle microscopy, however, a complicated, though prediction-wise limited, electrodynamic scattering treatment was established [Phys. Rev. B 73, 045424 (2006)] during the emergence of this new technique. Our recent study [ACS Nano, DOI: 10.1021/nn300181h] extended this approach into a full ab-initio model and showed for the first time that the mechanism behind the signal, despite its nanoscopic origin, is also the lens-like action of the induced refractive index profile only hidden in the complicated guise of the theoretical generalized Mie-like framework. The diffraction model proposed here yields succinct analytical expressions for the axial photothermal signal shape and magnitude and its angular distribution, all showing the clear lens-signature. It is further demonstrated, that the Gouy-phase of a Gaussian beam does not contribute to the relative photothermal signal in forward direction, a fact which is not easily evident from the more rigorous EM treatment. The presented model may thus be used to estimate the signal shape and magnitude in photothermal single particle microscopy.

© 2012 OSA

Full Article  |  PDF Article

Errata

Markus Selmke, Marco Braun, and Frank Cichos, "Nano-lens diffraction around a single heated nano particle: errata," Opt. Express 21, 25344-25345 (2013)
https://www.osapublishing.org/oe/abstract.cfm?uri=oe-21-21-25344

References

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  1. X. S. Xie, S. J. Lu, W. Min, S. S. Chong, G. R. Holtom, “Label-free imaging of heme proteins with two-photon excited photothermal lens microscopy,” Appl. Phys. Lett. 96, 113701 (2010).
    [CrossRef]
  2. S. Sinha, A. Ray, K. Dasgupta, “Solvent dependent nonlinear refraction in organic dye solution,” J. Appl. Phys. 87, 3222–3226 (2000).
    [CrossRef]
  3. A. V. Brusnichkin, D. A. Nedosekin, M. A. Proskurnin, V. P. Zharov, “Photothermal lens detection of gold nanoparticles: Theory and experiments,” Appl. Spectrosc. 61, 1191–1201 (2007).
    [CrossRef] [PubMed]
  4. G. Battaglin, P. Calvelli, E. Cattaruzza, F. Gonella, R. Polloni, G. Mattei, P. Mazzoldi, “Z-scan study on the nonlinear refractive index of copper nanocluster composite silica glass,” Appl. Phys. Lett. 78, 3953–3955 (2001).
    [CrossRef]
  5. D. Rings, R. Schachoff, M. Selmke, F. Cichos, K. Kroy, “Hot Brownian Motion,” Phys. Rev. Lett. 105, 090604 (2010).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  13. K. Uchiyama, A. Hibara, H. Kimura, T. Sawada, T. Kitamori, “Thermal lens microscope,” Jpn. J. Appl. Phys. 39, 5316–5322 (2000).
    [CrossRef]
  14. A. Gaiduk, M. Yorulmaz, P. V. Ruijgrok, M. Orrit, “Room-temperature detection of a single molecule’s absorption by photothermal contrast,” Science 330, 353–356 (2010).
    [CrossRef] [PubMed]
  15. S. Berciaud, L. Cognet, G. Blab, B. Lounis, “Photothermal heterodyne imaging of individual nonfluorescent nanoclusters and nanocrystals,” Phys. Rev. Lett. 93, 257402 (2004).
    [CrossRef]
  16. D. Boyer, P. Tamarat, A. Maali, B. Lounis, M. Orrit, “Photothermal imaging of nanometer-sized metal particles among scatterers,” Science 297, 1160–1163 (2002).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  21. S. Berciaud, D. Lasne, G. Blab, L. Cognet, B. Lounis, “Photothermal heterodyne imaging of individual metallic nanoparticles: Theory versus experiment,” Phys. Rev. B 73, 045424 (2006).
    [CrossRef]
  22. Z. L. Horvath, Z. Bor, “Focusing of truncated gaussian beams,” Opt. Commun. 222, 51–68 (2003).
    [CrossRef]
  23. S. Teng, T. Zhou, C. Cheng, “Fresnel diffraction of truncated gaussian beam,” Optik 118, 435–439 (2007).
    [CrossRef]
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    [CrossRef]
  30. S. M. Mian, S. B. McGee, N. Melikechi, “Experimental and theoretical investigation of thermal lensing effects in mode-locked femtosecond z-scan experiments,” Opt. Commun. 207, 339–345 (2002).
    [CrossRef]
  31. A. Gnoli, L. Razzari, M. Righini, “Z-scan measurements using high repetition rate lasers: how to manage thermal effects,” Opt. Express 13, 7976–7981 (2005).
    [CrossRef] [PubMed]
  32. A. Gnoli, A. M. Paoletti, G. Pennesi, G. Rossi, M. Righini, “High-accuracy z-scan measurements of the optical nonlinearity of bis-phthalocyanines,” J. Porphyrins Phthalocyanines 11, 481–486 (2007).
    [CrossRef]
  33. R. Polloni, B. F. Scremin, P. Calvelli, E. Cattaruzza, G. Battaglin, G. Mattei, “Metal nanoparticles-silica composites: Z-scan determination of non-linear refractive index,” J. Non-Cryst. Solids 322, 300–305 (2003).
    [CrossRef]
  34. O. Pena, U. Pal, “Scattering of electromagnetic radiation by a multilayered sphere,” Comput. Phys. Commun. 180, 2348–2354 (2009).
    [CrossRef]
  35. F. Onofri, G. Grehan, G. Gouesbet, “Electromagnetic scattering from a multilayered sphere located in an arbitrary beam,” Appl. Opt. 34, 7113–7124 (1995).
    [CrossRef] [PubMed]
  36. G. Gouesbet, G. Grehan, B. Maheu, “Scattering of a gaussian-beam by a mie scatter center using a bromwich formalism,” J. Optics-Nouvelle Revue D Optique 16, 83–93 (1985).
  37. G. Gouesbet, B. Maheu, G. Grehan, “Light-scattering from a sphere arbitrarily located in a gaussian-beam, using a bromwich formulation,” J. Opt. Soc. Am. A 5, 1427–1443 (1988).
    [CrossRef]
  38. G. Gouesbet, J. Lock, G. Grehan, “Generalized lorenz-mie theories and description of electromagnetic arbitrary shaped beams: Localized approximations and localized beam models, a review,” J. Quant. Spectrosc. Radiat. Transfer 112, 1–27 (2011).
    [CrossRef]
  39. G. Gouesbet, J. A. Lock, G. Grehan, “Partial-wave representations of laser-beams for use in light-scattering calculations,” Appl. Opt. 34, 2133–2143 (1995).
    [CrossRef] [PubMed]
  40. G. H. Meeten, “Computation of s1–s2 in mie scattering-theory,” J. Phys. D: Appl. Phys. 17, L89–L91 (1984).
    [CrossRef]
  41. J. A. Lock, E. A. Hovenac, “Diffraction of a gaussian-beam by a spherical obstacle,” Am. J. Phys. 61, 698–707 (1993).
    [CrossRef]

2011

G. Gouesbet, J. Lock, G. Grehan, “Generalized lorenz-mie theories and description of electromagnetic arbitrary shaped beams: Localized approximations and localized beam models, a review,” J. Quant. Spectrosc. Radiat. Transfer 112, 1–27 (2011).
[CrossRef]

2010

D. Rings, R. Schachoff, M. Selmke, F. Cichos, K. Kroy, “Hot Brownian Motion,” Phys. Rev. Lett. 105, 090604 (2010).
[CrossRef] [PubMed]

X. S. Xie, S. J. Lu, W. Min, S. S. Chong, G. R. Holtom, “Label-free imaging of heme proteins with two-photon excited photothermal lens microscopy,” Appl. Phys. Lett. 96, 113701 (2010).
[CrossRef]

A. Gaiduk, M. Yorulmaz, P. V. Ruijgrok, M. Orrit, “Room-temperature detection of a single molecule’s absorption by photothermal contrast,” Science 330, 353–356 (2010).
[CrossRef] [PubMed]

G. C. K. Chen, M. Andika, S. Vasudevan, “Excitation temporal pulse shape and probe beam size effect on pulsed photothermal lens of single particle,” J. Opt. Soc. Am. B 27, 796–805 (2010).
[CrossRef]

2009

O. Pena, U. Pal, “Scattering of electromagnetic radiation by a multilayered sphere,” Comput. Phys. Commun. 180, 2348–2354 (2009).
[CrossRef]

2008

R. Escalona, “Comparative study between interferometric and z-scan techniques for thermal lensing characterization,” Opt. Commun. 281, 1323–1330 (2008).
[CrossRef]

2007

A. Gnoli, A. M. Paoletti, G. Pennesi, G. Rossi, M. Righini, “High-accuracy z-scan measurements of the optical nonlinearity of bis-phthalocyanines,” J. Porphyrins Phthalocyanines 11, 481–486 (2007).
[CrossRef]

J. Hwang, W. E. Moerner, “Interferometry of a single nanoparticle using the gouy phase of a focused laser beam,” Opt. Commun. 280, 487–491 (2007).
[CrossRef]

S. Teng, T. Zhou, C. Cheng, “Fresnel diffraction of truncated gaussian beam,” Optik 118, 435–439 (2007).
[CrossRef]

A. V. Brusnichkin, D. A. Nedosekin, M. A. Proskurnin, V. P. Zharov, “Photothermal lens detection of gold nanoparticles: Theory and experiments,” Appl. Spectrosc. 61, 1191–1201 (2007).
[CrossRef] [PubMed]

2006

S. Berciaud, D. Lasne, G. Blab, L. Cognet, B. Lounis, “Photothermal heterodyne imaging of individual metallic nanoparticles: Theory versus experiment,” Phys. Rev. B 73, 045424 (2006).
[CrossRef]

J. Moreau, V. Loriette, “Confocal dual-beam thermal-lens microscope: Model and experimental results,” Jpn. J. Appl. Phys. 45, 7141–7151 (2006).
[CrossRef]

2005

2004

S. Berciaud, L. Cognet, G. Blab, B. Lounis, “Photothermal heterodyne imaging of individual nonfluorescent nanoclusters and nanocrystals,” Phys. Rev. Lett. 93, 257402 (2004).
[CrossRef]

J. Moreau, V. Loriette, “Confocal thermal-lens microscope,” Opt. Lett. 29, 1488–1490 (2004).
[CrossRef] [PubMed]

2003

R. Polloni, B. F. Scremin, P. Calvelli, E. Cattaruzza, G. Battaglin, G. Mattei, “Metal nanoparticles-silica composites: Z-scan determination of non-linear refractive index,” J. Non-Cryst. Solids 322, 300–305 (2003).
[CrossRef]

Z. L. Horvath, Z. Bor, “Focusing of truncated gaussian beams,” Opt. Commun. 222, 51–68 (2003).
[CrossRef]

2002

D. Boyer, P. Tamarat, A. Maali, B. Lounis, M. Orrit, “Photothermal imaging of nanometer-sized metal particles among scatterers,” Science 297, 1160–1163 (2002).
[CrossRef] [PubMed]

S. M. Mian, S. B. McGee, N. Melikechi, “Experimental and theoretical investigation of thermal lensing effects in mode-locked femtosecond z-scan experiments,” Opt. Commun. 207, 339–345 (2002).
[CrossRef]

2001

G. Battaglin, P. Calvelli, E. Cattaruzza, F. Gonella, R. Polloni, G. Mattei, P. Mazzoldi, “Z-scan study on the nonlinear refractive index of copper nanocluster composite silica glass,” Appl. Phys. Lett. 78, 3953–3955 (2001).
[CrossRef]

2000

S. Sinha, A. Ray, K. Dasgupta, “Solvent dependent nonlinear refraction in organic dye solution,” J. Appl. Phys. 87, 3222–3226 (2000).
[CrossRef]

K. Uchiyama, A. Hibara, H. Kimura, T. Sawada, T. Kitamori, “Thermal lens microscope,” Jpn. J. Appl. Phys. 39, 5316–5322 (2000).
[CrossRef]

1995

1993

M. Harada, K. Iwamotok, T. Kitamori, T. Sawada, “Photothermal microscopy with excitation and probe beams coaxial under the microscope and its application to microparticle ananlysis,” Anal. Chem. 65, 2938–2940 (1993).
[CrossRef]

M. Harada, T. Kitamori, T. Sawada, “Phase signal of optical beam deflection from single microparticles -theory and experiment,” J. Appl. Phys. 73, 2264–2271 (1993).
[CrossRef]

J. A. Lock, E. A. Hovenac, “Diffraction of a gaussian-beam by a spherical obstacle,” Am. J. Phys. 61, 698–707 (1993).
[CrossRef]

1991

J. Q. Wu, T. Kitamori, T. Sawada, “Theory of optical beam deflection for single microparticles,” J. of Appl. Phys. 69, 7015–7020 (1991).
[CrossRef]

1988

1985

G. Gouesbet, G. Grehan, B. Maheu, “Scattering of a gaussian-beam by a mie scatter center using a bromwich formalism,” J. Optics-Nouvelle Revue D Optique 16, 83–93 (1985).

1984

G. H. Meeten, “Computation of s1–s2 in mie scattering-theory,” J. Phys. D: Appl. Phys. 17, L89–L91 (1984).
[CrossRef]

1981

1977

A. A. Vigasin, “Diffraction of light by absorbing inclusions in solids,” Kvant. Elektron. (Moscow) [Sov. J. Quantum Electron.] 4, 662–666 (1977).

1973

Amer, N. M.

Andika, M.

Baffou, G.

G. Baffou, P. Bon, J. Savatier, J. Polleux, M. Zhu, M. Merlin, H. Rigneault, S. Monneret, “Thermal Imaging of Nanostructures by Quantitative Optical Phase Analysis,” ACS Nano, DOI:
[CrossRef] [PubMed]

Battaglin, G.

R. Polloni, B. F. Scremin, P. Calvelli, E. Cattaruzza, G. Battaglin, G. Mattei, “Metal nanoparticles-silica composites: Z-scan determination of non-linear refractive index,” J. Non-Cryst. Solids 322, 300–305 (2003).
[CrossRef]

G. Battaglin, P. Calvelli, E. Cattaruzza, F. Gonella, R. Polloni, G. Mattei, P. Mazzoldi, “Z-scan study on the nonlinear refractive index of copper nanocluster composite silica glass,” Appl. Phys. Lett. 78, 3953–3955 (2001).
[CrossRef]

Berciaud, S.

S. Berciaud, D. Lasne, G. Blab, L. Cognet, B. Lounis, “Photothermal heterodyne imaging of individual metallic nanoparticles: Theory versus experiment,” Phys. Rev. B 73, 045424 (2006).
[CrossRef]

S. Berciaud, L. Cognet, G. Blab, B. Lounis, “Photothermal heterodyne imaging of individual nonfluorescent nanoclusters and nanocrystals,” Phys. Rev. Lett. 93, 257402 (2004).
[CrossRef]

Blab, G.

S. Berciaud, D. Lasne, G. Blab, L. Cognet, B. Lounis, “Photothermal heterodyne imaging of individual metallic nanoparticles: Theory versus experiment,” Phys. Rev. B 73, 045424 (2006).
[CrossRef]

S. Berciaud, L. Cognet, G. Blab, B. Lounis, “Photothermal heterodyne imaging of individual nonfluorescent nanoclusters and nanocrystals,” Phys. Rev. Lett. 93, 257402 (2004).
[CrossRef]

Boccara, A. C.

Bon, P.

G. Baffou, P. Bon, J. Savatier, J. Polleux, M. Zhu, M. Merlin, H. Rigneault, S. Monneret, “Thermal Imaging of Nanostructures by Quantitative Optical Phase Analysis,” ACS Nano, DOI:
[CrossRef] [PubMed]

Bor, Z.

Z. L. Horvath, Z. Bor, “Focusing of truncated gaussian beams,” Opt. Commun. 222, 51–68 (2003).
[CrossRef]

Boyer, D.

D. Boyer, P. Tamarat, A. Maali, B. Lounis, M. Orrit, “Photothermal imaging of nanometer-sized metal particles among scatterers,” Science 297, 1160–1163 (2002).
[CrossRef] [PubMed]

Braun, M.

M. Selmke, M. Braun, F. Cichos, “Photothermal Single Particle Microscopy: Detection of a Nano-Lens,” ACS Nano, DOI:
[CrossRef] [PubMed]

M. Selmke, M. Braun, F. Cichos, “Photonic Rutherford Scattering,” in preparation (2012).

Brusnichkin, A. V.

Calvelli, P.

R. Polloni, B. F. Scremin, P. Calvelli, E. Cattaruzza, G. Battaglin, G. Mattei, “Metal nanoparticles-silica composites: Z-scan determination of non-linear refractive index,” J. Non-Cryst. Solids 322, 300–305 (2003).
[CrossRef]

G. Battaglin, P. Calvelli, E. Cattaruzza, F. Gonella, R. Polloni, G. Mattei, P. Mazzoldi, “Z-scan study on the nonlinear refractive index of copper nanocluster composite silica glass,” Appl. Phys. Lett. 78, 3953–3955 (2001).
[CrossRef]

Cattaruzza, E.

R. Polloni, B. F. Scremin, P. Calvelli, E. Cattaruzza, G. Battaglin, G. Mattei, “Metal nanoparticles-silica composites: Z-scan determination of non-linear refractive index,” J. Non-Cryst. Solids 322, 300–305 (2003).
[CrossRef]

G. Battaglin, P. Calvelli, E. Cattaruzza, F. Gonella, R. Polloni, G. Mattei, P. Mazzoldi, “Z-scan study on the nonlinear refractive index of copper nanocluster composite silica glass,” Appl. Phys. Lett. 78, 3953–3955 (2001).
[CrossRef]

Chen, G. C. K.

Cheng, C.

S. Teng, T. Zhou, C. Cheng, “Fresnel diffraction of truncated gaussian beam,” Optik 118, 435–439 (2007).
[CrossRef]

Chong, S. S.

X. S. Xie, S. J. Lu, W. Min, S. S. Chong, G. R. Holtom, “Label-free imaging of heme proteins with two-photon excited photothermal lens microscopy,” Appl. Phys. Lett. 96, 113701 (2010).
[CrossRef]

Cichos, F.

D. Rings, R. Schachoff, M. Selmke, F. Cichos, K. Kroy, “Hot Brownian Motion,” Phys. Rev. Lett. 105, 090604 (2010).
[CrossRef] [PubMed]

M. Selmke, M. Braun, F. Cichos, “Photothermal Single Particle Microscopy: Detection of a Nano-Lens,” ACS Nano, DOI:
[CrossRef] [PubMed]

M. Selmke, M. Braun, F. Cichos, “Photonic Rutherford Scattering,” in preparation (2012).

Cognet, L.

S. Berciaud, D. Lasne, G. Blab, L. Cognet, B. Lounis, “Photothermal heterodyne imaging of individual metallic nanoparticles: Theory versus experiment,” Phys. Rev. B 73, 045424 (2006).
[CrossRef]

S. Berciaud, L. Cognet, G. Blab, B. Lounis, “Photothermal heterodyne imaging of individual nonfluorescent nanoclusters and nanocrystals,” Phys. Rev. Lett. 93, 257402 (2004).
[CrossRef]

Dasgupta, K.

S. Sinha, A. Ray, K. Dasgupta, “Solvent dependent nonlinear refraction in organic dye solution,” J. Appl. Phys. 87, 3222–3226 (2000).
[CrossRef]

Escalona, R.

R. Escalona, “Comparative study between interferometric and z-scan techniques for thermal lensing characterization,” Opt. Commun. 281, 1323–1330 (2008).
[CrossRef]

Fournier, D.

Gaiduk, A.

A. Gaiduk, M. Yorulmaz, P. V. Ruijgrok, M. Orrit, “Room-temperature detection of a single molecule’s absorption by photothermal contrast,” Science 330, 353–356 (2010).
[CrossRef] [PubMed]

Gnoli, A.

A. Gnoli, A. M. Paoletti, G. Pennesi, G. Rossi, M. Righini, “High-accuracy z-scan measurements of the optical nonlinearity of bis-phthalocyanines,” J. Porphyrins Phthalocyanines 11, 481–486 (2007).
[CrossRef]

A. Gnoli, L. Razzari, M. Righini, “Z-scan measurements using high repetition rate lasers: how to manage thermal effects,” Opt. Express 13, 7976–7981 (2005).
[CrossRef] [PubMed]

Gonella, F.

G. Battaglin, P. Calvelli, E. Cattaruzza, F. Gonella, R. Polloni, G. Mattei, P. Mazzoldi, “Z-scan study on the nonlinear refractive index of copper nanocluster composite silica glass,” Appl. Phys. Lett. 78, 3953–3955 (2001).
[CrossRef]

Gouesbet, G.

G. Gouesbet, J. Lock, G. Grehan, “Generalized lorenz-mie theories and description of electromagnetic arbitrary shaped beams: Localized approximations and localized beam models, a review,” J. Quant. Spectrosc. Radiat. Transfer 112, 1–27 (2011).
[CrossRef]

G. Gouesbet, J. A. Lock, G. Grehan, “Partial-wave representations of laser-beams for use in light-scattering calculations,” Appl. Opt. 34, 2133–2143 (1995).
[CrossRef] [PubMed]

F. Onofri, G. Grehan, G. Gouesbet, “Electromagnetic scattering from a multilayered sphere located in an arbitrary beam,” Appl. Opt. 34, 7113–7124 (1995).
[CrossRef] [PubMed]

G. Gouesbet, B. Maheu, G. Grehan, “Light-scattering from a sphere arbitrarily located in a gaussian-beam, using a bromwich formulation,” J. Opt. Soc. Am. A 5, 1427–1443 (1988).
[CrossRef]

G. Gouesbet, G. Grehan, B. Maheu, “Scattering of a gaussian-beam by a mie scatter center using a bromwich formalism,” J. Optics-Nouvelle Revue D Optique 16, 83–93 (1985).

Grehan, G.

G. Gouesbet, J. Lock, G. Grehan, “Generalized lorenz-mie theories and description of electromagnetic arbitrary shaped beams: Localized approximations and localized beam models, a review,” J. Quant. Spectrosc. Radiat. Transfer 112, 1–27 (2011).
[CrossRef]

G. Gouesbet, J. A. Lock, G. Grehan, “Partial-wave representations of laser-beams for use in light-scattering calculations,” Appl. Opt. 34, 2133–2143 (1995).
[CrossRef] [PubMed]

F. Onofri, G. Grehan, G. Gouesbet, “Electromagnetic scattering from a multilayered sphere located in an arbitrary beam,” Appl. Opt. 34, 7113–7124 (1995).
[CrossRef] [PubMed]

G. Gouesbet, B. Maheu, G. Grehan, “Light-scattering from a sphere arbitrarily located in a gaussian-beam, using a bromwich formulation,” J. Opt. Soc. Am. A 5, 1427–1443 (1988).
[CrossRef]

G. Gouesbet, G. Grehan, B. Maheu, “Scattering of a gaussian-beam by a mie scatter center using a bromwich formalism,” J. Optics-Nouvelle Revue D Optique 16, 83–93 (1985).

Harada, M.

M. Harada, M. Shibata, T. Kitamori, T. Sawada, “Application of coaxial beam photothermal microscopy to the analysis of a single biological cell in water,” Anal. Chim. Acta. 299, 343–347 (1995).
[CrossRef]

M. Harada, T. Kitamori, T. Sawada, “Phase signal of optical beam deflection from single microparticles -theory and experiment,” J. Appl. Phys. 73, 2264–2271 (1993).
[CrossRef]

M. Harada, K. Iwamotok, T. Kitamori, T. Sawada, “Photothermal microscopy with excitation and probe beams coaxial under the microscope and its application to microparticle ananlysis,” Anal. Chem. 65, 2938–2940 (1993).
[CrossRef]

Hibara, A.

K. Uchiyama, A. Hibara, H. Kimura, T. Sawada, T. Kitamori, “Thermal lens microscope,” Jpn. J. Appl. Phys. 39, 5316–5322 (2000).
[CrossRef]

Holtom, G. R.

X. S. Xie, S. J. Lu, W. Min, S. S. Chong, G. R. Holtom, “Label-free imaging of heme proteins with two-photon excited photothermal lens microscopy,” Appl. Phys. Lett. 96, 113701 (2010).
[CrossRef]

Horvath, Z. L.

Z. L. Horvath, Z. Bor, “Focusing of truncated gaussian beams,” Opt. Commun. 222, 51–68 (2003).
[CrossRef]

Hovenac, E. A.

J. A. Lock, E. A. Hovenac, “Diffraction of a gaussian-beam by a spherical obstacle,” Am. J. Phys. 61, 698–707 (1993).
[CrossRef]

Hu, C.

Hwang, J.

J. Hwang, W. E. Moerner, “Interferometry of a single nanoparticle using the gouy phase of a focused laser beam,” Opt. Commun. 280, 487–491 (2007).
[CrossRef]

Iwamotok, K.

M. Harada, K. Iwamotok, T. Kitamori, T. Sawada, “Photothermal microscopy with excitation and probe beams coaxial under the microscope and its application to microparticle ananlysis,” Anal. Chem. 65, 2938–2940 (1993).
[CrossRef]

Jackson, W. B.

Jurgensen, F.

Kimura, H.

K. Uchiyama, A. Hibara, H. Kimura, T. Sawada, T. Kitamori, “Thermal lens microscope,” Jpn. J. Appl. Phys. 39, 5316–5322 (2000).
[CrossRef]

Kitamori, T.

K. Uchiyama, A. Hibara, H. Kimura, T. Sawada, T. Kitamori, “Thermal lens microscope,” Jpn. J. Appl. Phys. 39, 5316–5322 (2000).
[CrossRef]

M. Harada, M. Shibata, T. Kitamori, T. Sawada, “Application of coaxial beam photothermal microscopy to the analysis of a single biological cell in water,” Anal. Chim. Acta. 299, 343–347 (1995).
[CrossRef]

M. Harada, T. Kitamori, T. Sawada, “Phase signal of optical beam deflection from single microparticles -theory and experiment,” J. Appl. Phys. 73, 2264–2271 (1993).
[CrossRef]

M. Harada, K. Iwamotok, T. Kitamori, T. Sawada, “Photothermal microscopy with excitation and probe beams coaxial under the microscope and its application to microparticle ananlysis,” Anal. Chem. 65, 2938–2940 (1993).
[CrossRef]

J. Q. Wu, T. Kitamori, T. Sawada, “Theory of optical beam deflection for single microparticles,” J. of Appl. Phys. 69, 7015–7020 (1991).
[CrossRef]

Kroy, K.

D. Rings, R. Schachoff, M. Selmke, F. Cichos, K. Kroy, “Hot Brownian Motion,” Phys. Rev. Lett. 105, 090604 (2010).
[CrossRef] [PubMed]

Lasne, D.

S. Berciaud, D. Lasne, G. Blab, L. Cognet, B. Lounis, “Photothermal heterodyne imaging of individual metallic nanoparticles: Theory versus experiment,” Phys. Rev. B 73, 045424 (2006).
[CrossRef]

Lock, J.

G. Gouesbet, J. Lock, G. Grehan, “Generalized lorenz-mie theories and description of electromagnetic arbitrary shaped beams: Localized approximations and localized beam models, a review,” J. Quant. Spectrosc. Radiat. Transfer 112, 1–27 (2011).
[CrossRef]

Lock, J. A.

Loriette, V.

J. Moreau, V. Loriette, “Confocal dual-beam thermal-lens microscope: Model and experimental results,” Jpn. J. Appl. Phys. 45, 7141–7151 (2006).
[CrossRef]

J. Moreau, V. Loriette, “Confocal thermal-lens microscope,” Opt. Lett. 29, 1488–1490 (2004).
[CrossRef] [PubMed]

Lounis, B.

S. Berciaud, D. Lasne, G. Blab, L. Cognet, B. Lounis, “Photothermal heterodyne imaging of individual metallic nanoparticles: Theory versus experiment,” Phys. Rev. B 73, 045424 (2006).
[CrossRef]

S. Berciaud, L. Cognet, G. Blab, B. Lounis, “Photothermal heterodyne imaging of individual nonfluorescent nanoclusters and nanocrystals,” Phys. Rev. Lett. 93, 257402 (2004).
[CrossRef]

D. Boyer, P. Tamarat, A. Maali, B. Lounis, M. Orrit, “Photothermal imaging of nanometer-sized metal particles among scatterers,” Science 297, 1160–1163 (2002).
[CrossRef] [PubMed]

Lu, S. J.

X. S. Xie, S. J. Lu, W. Min, S. S. Chong, G. R. Holtom, “Label-free imaging of heme proteins with two-photon excited photothermal lens microscopy,” Appl. Phys. Lett. 96, 113701 (2010).
[CrossRef]

Maali, A.

D. Boyer, P. Tamarat, A. Maali, B. Lounis, M. Orrit, “Photothermal imaging of nanometer-sized metal particles among scatterers,” Science 297, 1160–1163 (2002).
[CrossRef] [PubMed]

Maheu, B.

G. Gouesbet, B. Maheu, G. Grehan, “Light-scattering from a sphere arbitrarily located in a gaussian-beam, using a bromwich formulation,” J. Opt. Soc. Am. A 5, 1427–1443 (1988).
[CrossRef]

G. Gouesbet, G. Grehan, B. Maheu, “Scattering of a gaussian-beam by a mie scatter center using a bromwich formalism,” J. Optics-Nouvelle Revue D Optique 16, 83–93 (1985).

Mattei, G.

R. Polloni, B. F. Scremin, P. Calvelli, E. Cattaruzza, G. Battaglin, G. Mattei, “Metal nanoparticles-silica composites: Z-scan determination of non-linear refractive index,” J. Non-Cryst. Solids 322, 300–305 (2003).
[CrossRef]

G. Battaglin, P. Calvelli, E. Cattaruzza, F. Gonella, R. Polloni, G. Mattei, P. Mazzoldi, “Z-scan study on the nonlinear refractive index of copper nanocluster composite silica glass,” Appl. Phys. Lett. 78, 3953–3955 (2001).
[CrossRef]

Mazzoldi, P.

G. Battaglin, P. Calvelli, E. Cattaruzza, F. Gonella, R. Polloni, G. Mattei, P. Mazzoldi, “Z-scan study on the nonlinear refractive index of copper nanocluster composite silica glass,” Appl. Phys. Lett. 78, 3953–3955 (2001).
[CrossRef]

McGee, S. B.

S. M. Mian, S. B. McGee, N. Melikechi, “Experimental and theoretical investigation of thermal lensing effects in mode-locked femtosecond z-scan experiments,” Opt. Commun. 207, 339–345 (2002).
[CrossRef]

Meeten, G. H.

G. H. Meeten, “Computation of s1–s2 in mie scattering-theory,” J. Phys. D: Appl. Phys. 17, L89–L91 (1984).
[CrossRef]

Melikechi, N.

S. M. Mian, S. B. McGee, N. Melikechi, “Experimental and theoretical investigation of thermal lensing effects in mode-locked femtosecond z-scan experiments,” Opt. Commun. 207, 339–345 (2002).
[CrossRef]

Merlin, M.

G. Baffou, P. Bon, J. Savatier, J. Polleux, M. Zhu, M. Merlin, H. Rigneault, S. Monneret, “Thermal Imaging of Nanostructures by Quantitative Optical Phase Analysis,” ACS Nano, DOI:
[CrossRef] [PubMed]

Mian, S. M.

S. M. Mian, S. B. McGee, N. Melikechi, “Experimental and theoretical investigation of thermal lensing effects in mode-locked femtosecond z-scan experiments,” Opt. Commun. 207, 339–345 (2002).
[CrossRef]

Min, W.

X. S. Xie, S. J. Lu, W. Min, S. S. Chong, G. R. Holtom, “Label-free imaging of heme proteins with two-photon excited photothermal lens microscopy,” Appl. Phys. Lett. 96, 113701 (2010).
[CrossRef]

Moerner, W. E.

J. Hwang, W. E. Moerner, “Interferometry of a single nanoparticle using the gouy phase of a focused laser beam,” Opt. Commun. 280, 487–491 (2007).
[CrossRef]

Monneret, S.

G. Baffou, P. Bon, J. Savatier, J. Polleux, M. Zhu, M. Merlin, H. Rigneault, S. Monneret, “Thermal Imaging of Nanostructures by Quantitative Optical Phase Analysis,” ACS Nano, DOI:
[CrossRef] [PubMed]

Moreau, J.

J. Moreau, V. Loriette, “Confocal dual-beam thermal-lens microscope: Model and experimental results,” Jpn. J. Appl. Phys. 45, 7141–7151 (2006).
[CrossRef]

J. Moreau, V. Loriette, “Confocal thermal-lens microscope,” Opt. Lett. 29, 1488–1490 (2004).
[CrossRef] [PubMed]

Nedosekin, D. A.

Onofri, F.

Orrit, M.

A. Gaiduk, M. Yorulmaz, P. V. Ruijgrok, M. Orrit, “Room-temperature detection of a single molecule’s absorption by photothermal contrast,” Science 330, 353–356 (2010).
[CrossRef] [PubMed]

D. Boyer, P. Tamarat, A. Maali, B. Lounis, M. Orrit, “Photothermal imaging of nanometer-sized metal particles among scatterers,” Science 297, 1160–1163 (2002).
[CrossRef] [PubMed]

Pal, U.

O. Pena, U. Pal, “Scattering of electromagnetic radiation by a multilayered sphere,” Comput. Phys. Commun. 180, 2348–2354 (2009).
[CrossRef]

Paoletti, A. M.

A. Gnoli, A. M. Paoletti, G. Pennesi, G. Rossi, M. Righini, “High-accuracy z-scan measurements of the optical nonlinearity of bis-phthalocyanines,” J. Porphyrins Phthalocyanines 11, 481–486 (2007).
[CrossRef]

Pena, O.

O. Pena, U. Pal, “Scattering of electromagnetic radiation by a multilayered sphere,” Comput. Phys. Commun. 180, 2348–2354 (2009).
[CrossRef]

Pennesi, G.

A. Gnoli, A. M. Paoletti, G. Pennesi, G. Rossi, M. Righini, “High-accuracy z-scan measurements of the optical nonlinearity of bis-phthalocyanines,” J. Porphyrins Phthalocyanines 11, 481–486 (2007).
[CrossRef]

Polleux, J.

G. Baffou, P. Bon, J. Savatier, J. Polleux, M. Zhu, M. Merlin, H. Rigneault, S. Monneret, “Thermal Imaging of Nanostructures by Quantitative Optical Phase Analysis,” ACS Nano, DOI:
[CrossRef] [PubMed]

Polloni, R.

R. Polloni, B. F. Scremin, P. Calvelli, E. Cattaruzza, G. Battaglin, G. Mattei, “Metal nanoparticles-silica composites: Z-scan determination of non-linear refractive index,” J. Non-Cryst. Solids 322, 300–305 (2003).
[CrossRef]

G. Battaglin, P. Calvelli, E. Cattaruzza, F. Gonella, R. Polloni, G. Mattei, P. Mazzoldi, “Z-scan study on the nonlinear refractive index of copper nanocluster composite silica glass,” Appl. Phys. Lett. 78, 3953–3955 (2001).
[CrossRef]

Proskurnin, M. A.

Ray, A.

S. Sinha, A. Ray, K. Dasgupta, “Solvent dependent nonlinear refraction in organic dye solution,” J. Appl. Phys. 87, 3222–3226 (2000).
[CrossRef]

Razzari, L.

Righini, M.

A. Gnoli, A. M. Paoletti, G. Pennesi, G. Rossi, M. Righini, “High-accuracy z-scan measurements of the optical nonlinearity of bis-phthalocyanines,” J. Porphyrins Phthalocyanines 11, 481–486 (2007).
[CrossRef]

A. Gnoli, L. Razzari, M. Righini, “Z-scan measurements using high repetition rate lasers: how to manage thermal effects,” Opt. Express 13, 7976–7981 (2005).
[CrossRef] [PubMed]

Rigneault, H.

G. Baffou, P. Bon, J. Savatier, J. Polleux, M. Zhu, M. Merlin, H. Rigneault, S. Monneret, “Thermal Imaging of Nanostructures by Quantitative Optical Phase Analysis,” ACS Nano, DOI:
[CrossRef] [PubMed]

Rings, D.

D. Rings, R. Schachoff, M. Selmke, F. Cichos, K. Kroy, “Hot Brownian Motion,” Phys. Rev. Lett. 105, 090604 (2010).
[CrossRef] [PubMed]

Rossi, G.

A. Gnoli, A. M. Paoletti, G. Pennesi, G. Rossi, M. Righini, “High-accuracy z-scan measurements of the optical nonlinearity of bis-phthalocyanines,” J. Porphyrins Phthalocyanines 11, 481–486 (2007).
[CrossRef]

Ruijgrok, P. V.

A. Gaiduk, M. Yorulmaz, P. V. Ruijgrok, M. Orrit, “Room-temperature detection of a single molecule’s absorption by photothermal contrast,” Science 330, 353–356 (2010).
[CrossRef] [PubMed]

Saleh, B. E. A.

B. E. A. Saleh, M. C. Teich, Fundamentals of Photonics (John Wiley and Sons, Inc., 1991).
[CrossRef]

Savatier, J.

G. Baffou, P. Bon, J. Savatier, J. Polleux, M. Zhu, M. Merlin, H. Rigneault, S. Monneret, “Thermal Imaging of Nanostructures by Quantitative Optical Phase Analysis,” ACS Nano, DOI:
[CrossRef] [PubMed]

Sawada, T.

K. Uchiyama, A. Hibara, H. Kimura, T. Sawada, T. Kitamori, “Thermal lens microscope,” Jpn. J. Appl. Phys. 39, 5316–5322 (2000).
[CrossRef]

M. Harada, M. Shibata, T. Kitamori, T. Sawada, “Application of coaxial beam photothermal microscopy to the analysis of a single biological cell in water,” Anal. Chim. Acta. 299, 343–347 (1995).
[CrossRef]

M. Harada, T. Kitamori, T. Sawada, “Phase signal of optical beam deflection from single microparticles -theory and experiment,” J. Appl. Phys. 73, 2264–2271 (1993).
[CrossRef]

M. Harada, K. Iwamotok, T. Kitamori, T. Sawada, “Photothermal microscopy with excitation and probe beams coaxial under the microscope and its application to microparticle ananlysis,” Anal. Chem. 65, 2938–2940 (1993).
[CrossRef]

J. Q. Wu, T. Kitamori, T. Sawada, “Theory of optical beam deflection for single microparticles,” J. of Appl. Phys. 69, 7015–7020 (1991).
[CrossRef]

Schachoff, R.

D. Rings, R. Schachoff, M. Selmke, F. Cichos, K. Kroy, “Hot Brownian Motion,” Phys. Rev. Lett. 105, 090604 (2010).
[CrossRef] [PubMed]

Schroer, W.

Scremin, B. F.

R. Polloni, B. F. Scremin, P. Calvelli, E. Cattaruzza, G. Battaglin, G. Mattei, “Metal nanoparticles-silica composites: Z-scan determination of non-linear refractive index,” J. Non-Cryst. Solids 322, 300–305 (2003).
[CrossRef]

Selmke, M.

D. Rings, R. Schachoff, M. Selmke, F. Cichos, K. Kroy, “Hot Brownian Motion,” Phys. Rev. Lett. 105, 090604 (2010).
[CrossRef] [PubMed]

M. Selmke, M. Braun, F. Cichos, “Photothermal Single Particle Microscopy: Detection of a Nano-Lens,” ACS Nano, DOI:
[CrossRef] [PubMed]

M. Selmke, M. Braun, F. Cichos, “Photonic Rutherford Scattering,” in preparation (2012).

Shibata, M.

M. Harada, M. Shibata, T. Kitamori, T. Sawada, “Application of coaxial beam photothermal microscopy to the analysis of a single biological cell in water,” Anal. Chim. Acta. 299, 343–347 (1995).
[CrossRef]

Sinha, S.

S. Sinha, A. Ray, K. Dasgupta, “Solvent dependent nonlinear refraction in organic dye solution,” J. Appl. Phys. 87, 3222–3226 (2000).
[CrossRef]

Tamarat, P.

D. Boyer, P. Tamarat, A. Maali, B. Lounis, M. Orrit, “Photothermal imaging of nanometer-sized metal particles among scatterers,” Science 297, 1160–1163 (2002).
[CrossRef] [PubMed]

Teich, M. C.

B. E. A. Saleh, M. C. Teich, Fundamentals of Photonics (John Wiley and Sons, Inc., 1991).
[CrossRef]

Teng, S.

S. Teng, T. Zhou, C. Cheng, “Fresnel diffraction of truncated gaussian beam,” Optik 118, 435–439 (2007).
[CrossRef]

Uchiyama, K.

K. Uchiyama, A. Hibara, H. Kimura, T. Sawada, T. Kitamori, “Thermal lens microscope,” Jpn. J. Appl. Phys. 39, 5316–5322 (2000).
[CrossRef]

Vasudevan, S.

Vigasin, A. A.

A. A. Vigasin, “Diffraction of light by absorbing inclusions in solids,” Kvant. Elektron. (Moscow) [Sov. J. Quantum Electron.] 4, 662–666 (1977).

Whinnery, J. R.

Wu, J. Q.

J. Q. Wu, T. Kitamori, T. Sawada, “Theory of optical beam deflection for single microparticles,” J. of Appl. Phys. 69, 7015–7020 (1991).
[CrossRef]

Xie, X. S.

X. S. Xie, S. J. Lu, W. Min, S. S. Chong, G. R. Holtom, “Label-free imaging of heme proteins with two-photon excited photothermal lens microscopy,” Appl. Phys. Lett. 96, 113701 (2010).
[CrossRef]

Yorulmaz, M.

A. Gaiduk, M. Yorulmaz, P. V. Ruijgrok, M. Orrit, “Room-temperature detection of a single molecule’s absorption by photothermal contrast,” Science 330, 353–356 (2010).
[CrossRef] [PubMed]

Zharov, V. P.

Zhou, T.

S. Teng, T. Zhou, C. Cheng, “Fresnel diffraction of truncated gaussian beam,” Optik 118, 435–439 (2007).
[CrossRef]

Zhu, M.

G. Baffou, P. Bon, J. Savatier, J. Polleux, M. Zhu, M. Merlin, H. Rigneault, S. Monneret, “Thermal Imaging of Nanostructures by Quantitative Optical Phase Analysis,” ACS Nano, DOI:
[CrossRef] [PubMed]

ACS Nano

G. Baffou, P. Bon, J. Savatier, J. Polleux, M. Zhu, M. Merlin, H. Rigneault, S. Monneret, “Thermal Imaging of Nanostructures by Quantitative Optical Phase Analysis,” ACS Nano, DOI:
[CrossRef] [PubMed]

Am. J. Phys.

J. A. Lock, E. A. Hovenac, “Diffraction of a gaussian-beam by a spherical obstacle,” Am. J. Phys. 61, 698–707 (1993).
[CrossRef]

Anal. Chem.

M. Harada, K. Iwamotok, T. Kitamori, T. Sawada, “Photothermal microscopy with excitation and probe beams coaxial under the microscope and its application to microparticle ananlysis,” Anal. Chem. 65, 2938–2940 (1993).
[CrossRef]

Anal. Chim. Acta.

M. Harada, M. Shibata, T. Kitamori, T. Sawada, “Application of coaxial beam photothermal microscopy to the analysis of a single biological cell in water,” Anal. Chim. Acta. 299, 343–347 (1995).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

X. S. Xie, S. J. Lu, W. Min, S. S. Chong, G. R. Holtom, “Label-free imaging of heme proteins with two-photon excited photothermal lens microscopy,” Appl. Phys. Lett. 96, 113701 (2010).
[CrossRef]

G. Battaglin, P. Calvelli, E. Cattaruzza, F. Gonella, R. Polloni, G. Mattei, P. Mazzoldi, “Z-scan study on the nonlinear refractive index of copper nanocluster composite silica glass,” Appl. Phys. Lett. 78, 3953–3955 (2001).
[CrossRef]

Appl. Spectrosc.

Comput. Phys. Commun.

O. Pena, U. Pal, “Scattering of electromagnetic radiation by a multilayered sphere,” Comput. Phys. Commun. 180, 2348–2354 (2009).
[CrossRef]

J. Appl. Phys.

S. Sinha, A. Ray, K. Dasgupta, “Solvent dependent nonlinear refraction in organic dye solution,” J. Appl. Phys. 87, 3222–3226 (2000).
[CrossRef]

M. Harada, T. Kitamori, T. Sawada, “Phase signal of optical beam deflection from single microparticles -theory and experiment,” J. Appl. Phys. 73, 2264–2271 (1993).
[CrossRef]

J. Non-Cryst. Solids

R. Polloni, B. F. Scremin, P. Calvelli, E. Cattaruzza, G. Battaglin, G. Mattei, “Metal nanoparticles-silica composites: Z-scan determination of non-linear refractive index,” J. Non-Cryst. Solids 322, 300–305 (2003).
[CrossRef]

J. of Appl. Phys.

J. Q. Wu, T. Kitamori, T. Sawada, “Theory of optical beam deflection for single microparticles,” J. of Appl. Phys. 69, 7015–7020 (1991).
[CrossRef]

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

J. Optics-Nouvelle Revue D Optique

G. Gouesbet, G. Grehan, B. Maheu, “Scattering of a gaussian-beam by a mie scatter center using a bromwich formalism,” J. Optics-Nouvelle Revue D Optique 16, 83–93 (1985).

J. Phys. D: Appl. Phys.

G. H. Meeten, “Computation of s1–s2 in mie scattering-theory,” J. Phys. D: Appl. Phys. 17, L89–L91 (1984).
[CrossRef]

J. Porphyrins Phthalocyanines

A. Gnoli, A. M. Paoletti, G. Pennesi, G. Rossi, M. Righini, “High-accuracy z-scan measurements of the optical nonlinearity of bis-phthalocyanines,” J. Porphyrins Phthalocyanines 11, 481–486 (2007).
[CrossRef]

J. Quant. Spectrosc. Radiat. Transfer

G. Gouesbet, J. Lock, G. Grehan, “Generalized lorenz-mie theories and description of electromagnetic arbitrary shaped beams: Localized approximations and localized beam models, a review,” J. Quant. Spectrosc. Radiat. Transfer 112, 1–27 (2011).
[CrossRef]

Jpn. J. Appl. Phys.

K. Uchiyama, A. Hibara, H. Kimura, T. Sawada, T. Kitamori, “Thermal lens microscope,” Jpn. J. Appl. Phys. 39, 5316–5322 (2000).
[CrossRef]

J. Moreau, V. Loriette, “Confocal dual-beam thermal-lens microscope: Model and experimental results,” Jpn. J. Appl. Phys. 45, 7141–7151 (2006).
[CrossRef]

Kvant. Elektron. (Moscow) [Sov. J. Quantum Electron.]

A. A. Vigasin, “Diffraction of light by absorbing inclusions in solids,” Kvant. Elektron. (Moscow) [Sov. J. Quantum Electron.] 4, 662–666 (1977).

Opt. Commun.

R. Escalona, “Comparative study between interferometric and z-scan techniques for thermal lensing characterization,” Opt. Commun. 281, 1323–1330 (2008).
[CrossRef]

S. M. Mian, S. B. McGee, N. Melikechi, “Experimental and theoretical investigation of thermal lensing effects in mode-locked femtosecond z-scan experiments,” Opt. Commun. 207, 339–345 (2002).
[CrossRef]

J. Hwang, W. E. Moerner, “Interferometry of a single nanoparticle using the gouy phase of a focused laser beam,” Opt. Commun. 280, 487–491 (2007).
[CrossRef]

Z. L. Horvath, Z. Bor, “Focusing of truncated gaussian beams,” Opt. Commun. 222, 51–68 (2003).
[CrossRef]

Opt. Express

Opt. Lett.

Optik

S. Teng, T. Zhou, C. Cheng, “Fresnel diffraction of truncated gaussian beam,” Optik 118, 435–439 (2007).
[CrossRef]

Phys. Rev. B

S. Berciaud, D. Lasne, G. Blab, L. Cognet, B. Lounis, “Photothermal heterodyne imaging of individual metallic nanoparticles: Theory versus experiment,” Phys. Rev. B 73, 045424 (2006).
[CrossRef]

Phys. Rev. Lett.

S. Berciaud, L. Cognet, G. Blab, B. Lounis, “Photothermal heterodyne imaging of individual nonfluorescent nanoclusters and nanocrystals,” Phys. Rev. Lett. 93, 257402 (2004).
[CrossRef]

D. Rings, R. Schachoff, M. Selmke, F. Cichos, K. Kroy, “Hot Brownian Motion,” Phys. Rev. Lett. 105, 090604 (2010).
[CrossRef] [PubMed]

Science

A. Gaiduk, M. Yorulmaz, P. V. Ruijgrok, M. Orrit, “Room-temperature detection of a single molecule’s absorption by photothermal contrast,” Science 330, 353–356 (2010).
[CrossRef] [PubMed]

D. Boyer, P. Tamarat, A. Maali, B. Lounis, M. Orrit, “Photothermal imaging of nanometer-sized metal particles among scatterers,” Science 297, 1160–1163 (2002).
[CrossRef] [PubMed]

Other

M. Selmke, M. Braun, F. Cichos, “Photothermal Single Particle Microscopy: Detection of a Nano-Lens,” ACS Nano, DOI:
[CrossRef] [PubMed]

B. E. A. Saleh, M. C. Teich, Fundamentals of Photonics (John Wiley and Sons, Inc., 1991).
[CrossRef]

M. Selmke, M. Braun, F. Cichos, “Photonic Rutherford Scattering,” in preparation (2012).

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Figures (6)

Fig. 1
Fig. 1

a) Geometry for the computation of the phase advance iχ (ρ), Eq. (4). b) Geometry for the diffraction integral, Eq. (3). The shading in the image-plane corresponds to the difference in intensities between the diffraction of a cold and a hot nano-particle, Eq. 8, and shows the configuration for a negative detected rel. PT signal Φ, Eq. (6).

Fig. 2
Fig. 2

a) z p -Scan of the rel. photothermal signal Φ for on-axis detection, i.e. θ = 0°, Eq. (7). The chosen laser-offset of Δz f = 0 results in a symmetric shape. b) Angular pattern of the photothermal signal for z p = {0, −z R , −2z R , −3z R }, i.e. Φ(θ,z p ), Eq. (8). The plot has been normalized to 1.0 on the optical axis. The following parameters have been used for the calculations: R = 10 nm, ΔT0 = 100K, n0 = 1.46, dn/dT = −3.6 × 10−3, λ = 635 nm, ω0 = 281 nm, λ h = 532 nm, ω0 ,h = 233 nm, defining a beam divergence angle θdiv = arctan (ω0/z R ) ≈ 26° determining the approximate angular extent of the feature.

Fig. 3
Fig. 3

a) Schematic of the Poynting-vector integration within the GLMT framework. b) Discretization of the refractive index profile n(r) into concentric spherical shells for the computation of the multilayer Mie scatter coefficients [34].

Fig. 4
Fig. 4

Comparison of the diffraction (black) and Gaussian GLMT model (red). Parameters used for calculations are detailed in the caption of Fig. 2. The diffraction model results have been scaled by a constant factor of 1.5 except for (d) where the factor is 0.8. a) PT signal angular distribution with positive (blue) and negative (red) signal. b) On-axis z-scan (NA = 0, θ = 0°) of PT signal. The black dotted curve is the unscaled prediction of the diffraction model. c) On-axis z p -scan for a finite NA detection. d) On-axis z p -scan with central beam stop (inverse aperture). The grey curve corresponds to no central beam-stop (NA = 0.75 from (c)).

Fig. 5
Fig. 5

On-axis scans of the rel. PT signal Φ (z p ) for a finite detection numerical aperture NA for Δz f = −3z R,d , −2z R,d ,..., 3z R,d (red to blue). a) Comparison of the diffraction (dashed-solid) and Gaussian GLMT model (solid). The diffraction model results have been scaled by a constant factor of 1.6 (thick dashed-solid). The unscaled prediction of the diffraction model is thin dashed-solid. Insets: PT signal angular distribution Φ (θ)/Φ (0) for GLMT and diffraction model for decreasing z p < 0. b) Peak amplitudes of the PT signal versus axial beam displacement Δz f . c) Axial position of the peaks.

Fig. 6
Fig. 6

Normalized photothermal single particle signal z p -scan (left) and xz-scan (right) of a gold-nanoparticle (R = 30 nm) measured (a) and computed (b) with the exact beam shape co-efficients in the GLMT framework for a full NA = 0.75 detection (black curve on the left and upper pictures on the right) and with a inverse aperture up to an detection angle of θmax = 31° (dashed blue on the left and lower pictures on the right). The parameters used in the calculation are the same as those in our reference [17].

Equations (21)

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n ( r ) = n 0 + d n d T Δ T ( r ) = n 0 + Δ n R r ,
Δ n = σ abs I h ( z p , Δ z f ) 4 π κ R ( d n d T ) = σ abs I h , 0 4 π κ R ( d n d T ) 1 1 + ( z p Δ z f ) 2 / z R , h 2 .
U ( r , z ) = k i z exp ( i k r 2 2 z i k z ) R U a ( ρ ) exp ( i k ρ 2 2 z ) J 0 ( k ρ r z ) exp ( i Δ χ ( ρ ) ) ρ d ρ
Δ χ ( ρ ) = k 0 L L [ n 0 + R Δ n z 2 + ρ 2 ] d z 2 k 0 [ L n 0 R Δ n ln ( ρ 2 L ) ] ,
U a ( ρ ) = U 0 ω 0 ω ( z p ) exp ( ρ 2 ω 2 ( z p ) ) exp ( i k z p i k ρ 2 2 R C ( z p ) + i ζ G ( z p ) ) ,
Φ ( r , z ) = [ | U ( r , z ) | Δ n ( Δ T ( z p ) ) 2 | U ( r , z ) | Δ n = 0 2 ] / | U ( r = 0 , z ) | Δ n = 0 2
Φ ( z p ) = exp ( 2 R Δ n k 0 arg ( Ω ) ) | Γ ( 1 + i R Δ n k 0 ) | 2 1 ,
Φ ( θ , z p ) = exp ( k 2 tan 2 ( θ ) Re ( Ω 1 ) 2 ) × [ exp ( 2 R Δ n k 0 arg ( Ω ) ) | Γ ( 1 + i R Δ n k 0 ) F 1 1 ( i R Δ n k 0 , 1 , k 2 tan 2 ( θ ) 4 Ω ) | 2 1 ] .
Φ ( θ min , θ max , z p ) = F × 2 π θ min θ max Φ ( θ , z p ) sin ( θ ) cos 3 ( θ ) d θ ,
F = 1 A sphc 𝒫 d , I 0 𝒫 d , I = 2 z R 2 π ω 0 2 [ exp ( 2 tan 2 ( θ min ) z R 2 / ω 0 2 ) exp ( 2 tan 2 ( θ max ) z R 2 / ω 0 2 ) ] 1
d 𝒫 d ( θ , ϕ ) = S t d A = S t d A .
S 1 2 = n = 1 2 n + 1 n ( n + 1 ) g n [ a n Π n ( cos θ ) τ n ( cos θ ) + b n τ n ( cos θ ) Π n ( cos θ ) ] ,
2 S t = Re ( E θ i H ϕ i * E ϕ i H θ i * ) ( incidence field   flux ) + Re ( E θ s H ϕ s * E ϕ s H θ s * ) ( scattered field flux ) + Re ( E θ i H ϕ s * + E θ s H ϕ i * E ϕ i H θ s * E ϕ s H θ i * ) ( interference flux ) .
g n ( z p ) = Q exp ( Q s 2 ( n 1 ) ( n + 2 ) ) exp ( i γ s 1 / 2 ) .
d σ sca ( θ ) = π k 2 ( | S 1 ( θ ) | 2 + | S 2 ( θ ) | 2 ) ,
d σ ext ( θ ) = π k 2 [ Re ( M ) Re ( S 12 ) + Im ( M ) Im ( S 12 ) ] .
M ( θ ) = n = 1 2 n + 1 n ( n + 1 ) g n [ Π n ( cos θ ) + τ n ( cos θ ) ] .
σ sca = 2 π k 2 n = 1 ( 2 n + 1 ) | g n | 2 ( | a n | 2 + | b n | 2 ) , σ ext = 2 π k 2 n = 1 ( 2 n + 1 ) | g n | 2 Re ( a n + b n ) .
σ inc , n = m = 1 n N m g m N n m + 1 g n m + 1 * 0 θ max [ m n m + 1 ( 1 ) n Δ m Δ n m + 1 ] sin θ d θ ,
Φ ( θ ) = d 𝒫 d hot d 𝒫 d cold d 𝒫 inc cold
= [ d σ sca ( θ ) d σ ext ( θ ) ] a n L + 1 , b n L + 1 n ( r ) , n Au [ d σ sca ( θ ) d σ ext ( θ ) ] a n , b n n 0 , n Au d σ inc d ( θ )

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