Abstract

We explore the intuitive lensing picture of laser-heated nanoparticles occurring in single particle photothermal (PT) microscopy. The effective focal length of the thermal lens (TL) is derived from a ray-optics treatment and used to transform the probing focused Gaussian beam with ABCD Gaussian matrix optics. The relative PT signal is obtained from the relative beam-waist change far from the TL. The analytical expression is semiquantitative, capable of describing the entire phenomenology of single particle PT microscopy, and shows that the signal is the product of the point-spread functions of the involved lasers times a linear function of the axial coordinate. The presented particularly simple and intuitive Gaussian beam lensing picture compares favorably to the experimental results for 60 nm gold nanoparticles and provides the prescription for optimum setup calibration.

© 2012 Optical Society of America

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  1. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley-VCH, 1998).
  2. S. Berciaud, L. Cognet, G. Blab, and B. Lounis, “Photothermal heterodyne imaging of individual nonfluorescent nanoclusters and nanocrystals,” Phys. Rev. Lett. 93, 257402 (2004).
    [CrossRef]
  3. S. Berciaud, L. Cognet, and B. Lounis, “Luminescence decay and the absorption cross section of individual single-walled carbon nanotubes,” Phys. Rev. Lett. 101, 077402 (2008).
    [CrossRef]
  4. A. Gaiduk, M. Yorulmaz, P. V. Ruijgrok, and M. Orrit, “Room-temperature detection of a single molecule’s absorption by photothermal contrast,” Science 330, 353–356 (2010).
    [CrossRef]
  5. S. Berciaud, L. Cognet, and B. Lounis, “Photothermal absorption spectroscopy of individual semiconductor nanocrystals,” Nano Lett. 5, 2160–2163 (2005).
    [CrossRef]
  6. D. Rings, R. Schachoff, M. Selmke, F. Cichos, and K. Kroy, “Hot Brownian motion,” Phys. Rev. Lett. 105, 090604(2010).
    [CrossRef]
  7. D. Rings, M. Selmke, F. Cichos, and K. Kroy, “Theory of hot Brownian motion,” Soft Matter 7, 3441–3452 (2011).
    [CrossRef]
  8. R. Radünz, D. Rings, K. Kroy, and F. Cichos, “Hot Brownian particles and photothermal correlation spectroscopy,” J. Phys. Chem. A 113, 1674–1677 (2009).
    [CrossRef]
  9. P. M. R. Paulo, A. Gaiduk, F. Kulzer, S. F. G. Krens, H. P. Spaink, T. Schmidt, and M. Orrit, “Photothermal correlation spectroscopy of gold nanoparticles in solution,” J. Phys. Chem. C 113, 11451–11457 (2009).
    [CrossRef]
  10. S. Berciaud, D. Lasne, G. Blab, L. Cognet, and B. Lounis, “Photothermal heterodyne imaging of individual metallic nanoparticles: theory versus experiment,” Phys. Rev. B 73, 045424 (2006).
    [CrossRef]
  11. M. Selmke, M. Braun, and F. Cichos, “Photothermal single particle microscopy, detection of a nano-lens,” ACS Nano 6, 2741–2749 (2012).
    [CrossRef]
  12. S. Bialcowski, Photothermal Spectroscopy Methods for Chemical Analysis (Wiley, 1996).
  13. J. Moreau and V. Loriette, “Confocal dual-beam thermal-lens microscope: model and experimental results,” Jpn. J. Appl. Phys. 1, 7141–7151 (2006).
    [CrossRef]
  14. B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, Wiley Series in Pure and Applied Optics (Wiley, 1991).
  15. J. Evans and M. Rosenquist “’F=ma’ optics,” Am. J. Phys. 54, 876–883 (1986).
    [CrossRef]
  16. J. Sivardière, “Perturbed elliptic motion,” Eur. J. Phys. 7, 283–286 (1986).
    [CrossRef]
  17. A. A. Rangwala, V. H. Kulkarni, and A. A. Rindani, “Laplace Runge Lenz vector for a light ray trajectory in r−1 media,” Am. J. Phys. 69, 803–809 (2001).
    [CrossRef]
  18. M. Selmke, R. Schachoff, M. Braun, and F. Cichos, “Twin-focus photothermal correlation spectroscopy,” RSC Adv. (submitted).
  19. M. Selmke, M. Braun, and F. Cichos, “Nano-lens diffraction around a single heated nano particle,” Opt. Express 20, 8055–8070 (2012).
    [CrossRef]
  20. G. Gouesbet, B. Maheu, and G. Gréhan, “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]
  21. K. Ren, G. Gréhan, and G. Gouesbet, “Localized approximation of generalized Lorenz Mie theory: faster algorithm for computations of beam shape coefficients, gnm,” Part. Part. Syst. Charact. 9, 144–150 (1992).
    [CrossRef]
  22. A. Gaiduk, P. V. Ruijgrok, M. Yorulmaz, and M. Orrit, “Making gold nanoparticles fluorescent for simultaneous absorption and fluorescence detection on the single particle level,” Phys. Chem. Chem. Phys. 13, 149–153 (2011).
    [CrossRef]

2012

M. Selmke, M. Braun, and F. Cichos, “Photothermal single particle microscopy, detection of a nano-lens,” ACS Nano 6, 2741–2749 (2012).
[CrossRef]

M. Selmke, M. Braun, and F. Cichos, “Nano-lens diffraction around a single heated nano particle,” Opt. Express 20, 8055–8070 (2012).
[CrossRef]

2011

D. Rings, M. Selmke, F. Cichos, and K. Kroy, “Theory of hot Brownian motion,” Soft Matter 7, 3441–3452 (2011).
[CrossRef]

A. Gaiduk, P. V. Ruijgrok, M. Yorulmaz, and M. Orrit, “Making gold nanoparticles fluorescent for simultaneous absorption and fluorescence detection on the single particle level,” Phys. Chem. Chem. Phys. 13, 149–153 (2011).
[CrossRef]

2010

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

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

2009

R. Radünz, D. Rings, K. Kroy, and F. Cichos, “Hot Brownian particles and photothermal correlation spectroscopy,” J. Phys. Chem. A 113, 1674–1677 (2009).
[CrossRef]

P. M. R. Paulo, A. Gaiduk, F. Kulzer, S. F. G. Krens, H. P. Spaink, T. Schmidt, and M. Orrit, “Photothermal correlation spectroscopy of gold nanoparticles in solution,” J. Phys. Chem. C 113, 11451–11457 (2009).
[CrossRef]

2008

S. Berciaud, L. Cognet, and B. Lounis, “Luminescence decay and the absorption cross section of individual single-walled carbon nanotubes,” Phys. Rev. Lett. 101, 077402 (2008).
[CrossRef]

2006

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

J. Moreau and V. Loriette, “Confocal dual-beam thermal-lens microscope: model and experimental results,” Jpn. J. Appl. Phys. 1, 7141–7151 (2006).
[CrossRef]

2005

S. Berciaud, L. Cognet, and B. Lounis, “Photothermal absorption spectroscopy of individual semiconductor nanocrystals,” Nano Lett. 5, 2160–2163 (2005).
[CrossRef]

2004

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

2001

A. A. Rangwala, V. H. Kulkarni, and A. A. Rindani, “Laplace Runge Lenz vector for a light ray trajectory in r−1 media,” Am. J. Phys. 69, 803–809 (2001).
[CrossRef]

1992

K. Ren, G. Gréhan, and G. Gouesbet, “Localized approximation of generalized Lorenz Mie theory: faster algorithm for computations of beam shape coefficients, gnm,” Part. Part. Syst. Charact. 9, 144–150 (1992).
[CrossRef]

1988

1986

J. Evans and M. Rosenquist “’F=ma’ optics,” Am. J. Phys. 54, 876–883 (1986).
[CrossRef]

J. Sivardière, “Perturbed elliptic motion,” Eur. J. Phys. 7, 283–286 (1986).
[CrossRef]

Berciaud, S.

S. Berciaud, L. Cognet, and B. Lounis, “Luminescence decay and the absorption cross section of individual single-walled carbon nanotubes,” Phys. Rev. Lett. 101, 077402 (2008).
[CrossRef]

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

S. Berciaud, L. Cognet, and B. Lounis, “Photothermal absorption spectroscopy of individual semiconductor nanocrystals,” Nano Lett. 5, 2160–2163 (2005).
[CrossRef]

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

Bialcowski, S.

S. Bialcowski, Photothermal Spectroscopy Methods for Chemical Analysis (Wiley, 1996).

Blab, G.

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

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley-VCH, 1998).

Braun, M.

M. Selmke, M. Braun, and F. Cichos, “Photothermal single particle microscopy, detection of a nano-lens,” ACS Nano 6, 2741–2749 (2012).
[CrossRef]

M. Selmke, M. Braun, and F. Cichos, “Nano-lens diffraction around a single heated nano particle,” Opt. Express 20, 8055–8070 (2012).
[CrossRef]

M. Selmke, R. Schachoff, M. Braun, and F. Cichos, “Twin-focus photothermal correlation spectroscopy,” RSC Adv. (submitted).

Cichos, F.

M. Selmke, M. Braun, and F. Cichos, “Nano-lens diffraction around a single heated nano particle,” Opt. Express 20, 8055–8070 (2012).
[CrossRef]

M. Selmke, M. Braun, and F. Cichos, “Photothermal single particle microscopy, detection of a nano-lens,” ACS Nano 6, 2741–2749 (2012).
[CrossRef]

D. Rings, M. Selmke, F. Cichos, and K. Kroy, “Theory of hot Brownian motion,” Soft Matter 7, 3441–3452 (2011).
[CrossRef]

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

R. Radünz, D. Rings, K. Kroy, and F. Cichos, “Hot Brownian particles and photothermal correlation spectroscopy,” J. Phys. Chem. A 113, 1674–1677 (2009).
[CrossRef]

M. Selmke, R. Schachoff, M. Braun, and F. Cichos, “Twin-focus photothermal correlation spectroscopy,” RSC Adv. (submitted).

Cognet, L.

S. Berciaud, L. Cognet, and B. Lounis, “Luminescence decay and the absorption cross section of individual single-walled carbon nanotubes,” Phys. Rev. Lett. 101, 077402 (2008).
[CrossRef]

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

S. Berciaud, L. Cognet, and B. Lounis, “Photothermal absorption spectroscopy of individual semiconductor nanocrystals,” Nano Lett. 5, 2160–2163 (2005).
[CrossRef]

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

Evans, J.

J. Evans and M. Rosenquist “’F=ma’ optics,” Am. J. Phys. 54, 876–883 (1986).
[CrossRef]

Gaiduk, A.

A. Gaiduk, P. V. Ruijgrok, M. Yorulmaz, and M. Orrit, “Making gold nanoparticles fluorescent for simultaneous absorption and fluorescence detection on the single particle level,” Phys. Chem. Chem. Phys. 13, 149–153 (2011).
[CrossRef]

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

P. M. R. Paulo, A. Gaiduk, F. Kulzer, S. F. G. Krens, H. P. Spaink, T. Schmidt, and M. Orrit, “Photothermal correlation spectroscopy of gold nanoparticles in solution,” J. Phys. Chem. C 113, 11451–11457 (2009).
[CrossRef]

Gouesbet, G.

K. Ren, G. Gréhan, and G. Gouesbet, “Localized approximation of generalized Lorenz Mie theory: faster algorithm for computations of beam shape coefficients, gnm,” Part. Part. Syst. Charact. 9, 144–150 (1992).
[CrossRef]

G. Gouesbet, B. Maheu, and G. Gréhan, “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]

Gréhan, G.

K. Ren, G. Gréhan, and G. Gouesbet, “Localized approximation of generalized Lorenz Mie theory: faster algorithm for computations of beam shape coefficients, gnm,” Part. Part. Syst. Charact. 9, 144–150 (1992).
[CrossRef]

G. Gouesbet, B. Maheu, and G. Gréhan, “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]

Huffman, D. R.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley-VCH, 1998).

Krens, S. F. G.

P. M. R. Paulo, A. Gaiduk, F. Kulzer, S. F. G. Krens, H. P. Spaink, T. Schmidt, and M. Orrit, “Photothermal correlation spectroscopy of gold nanoparticles in solution,” J. Phys. Chem. C 113, 11451–11457 (2009).
[CrossRef]

Kroy, K.

D. Rings, M. Selmke, F. Cichos, and K. Kroy, “Theory of hot Brownian motion,” Soft Matter 7, 3441–3452 (2011).
[CrossRef]

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

R. Radünz, D. Rings, K. Kroy, and F. Cichos, “Hot Brownian particles and photothermal correlation spectroscopy,” J. Phys. Chem. A 113, 1674–1677 (2009).
[CrossRef]

Kulkarni, V. H.

A. A. Rangwala, V. H. Kulkarni, and A. A. Rindani, “Laplace Runge Lenz vector for a light ray trajectory in r−1 media,” Am. J. Phys. 69, 803–809 (2001).
[CrossRef]

Kulzer, F.

P. M. R. Paulo, A. Gaiduk, F. Kulzer, S. F. G. Krens, H. P. Spaink, T. Schmidt, and M. Orrit, “Photothermal correlation spectroscopy of gold nanoparticles in solution,” J. Phys. Chem. C 113, 11451–11457 (2009).
[CrossRef]

Lasne, D.

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

Loriette, V.

J. Moreau and V. Loriette, “Confocal dual-beam thermal-lens microscope: model and experimental results,” Jpn. J. Appl. Phys. 1, 7141–7151 (2006).
[CrossRef]

Lounis, B.

S. Berciaud, L. Cognet, and B. Lounis, “Luminescence decay and the absorption cross section of individual single-walled carbon nanotubes,” Phys. Rev. Lett. 101, 077402 (2008).
[CrossRef]

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

S. Berciaud, L. Cognet, and B. Lounis, “Photothermal absorption spectroscopy of individual semiconductor nanocrystals,” Nano Lett. 5, 2160–2163 (2005).
[CrossRef]

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

Maheu, B.

Moreau, J.

J. Moreau and V. Loriette, “Confocal dual-beam thermal-lens microscope: model and experimental results,” Jpn. J. Appl. Phys. 1, 7141–7151 (2006).
[CrossRef]

Orrit, M.

A. Gaiduk, P. V. Ruijgrok, M. Yorulmaz, and M. Orrit, “Making gold nanoparticles fluorescent for simultaneous absorption and fluorescence detection on the single particle level,” Phys. Chem. Chem. Phys. 13, 149–153 (2011).
[CrossRef]

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

P. M. R. Paulo, A. Gaiduk, F. Kulzer, S. F. G. Krens, H. P. Spaink, T. Schmidt, and M. Orrit, “Photothermal correlation spectroscopy of gold nanoparticles in solution,” J. Phys. Chem. C 113, 11451–11457 (2009).
[CrossRef]

Paulo, P. M. R.

P. M. R. Paulo, A. Gaiduk, F. Kulzer, S. F. G. Krens, H. P. Spaink, T. Schmidt, and M. Orrit, “Photothermal correlation spectroscopy of gold nanoparticles in solution,” J. Phys. Chem. C 113, 11451–11457 (2009).
[CrossRef]

Radünz, R.

R. Radünz, D. Rings, K. Kroy, and F. Cichos, “Hot Brownian particles and photothermal correlation spectroscopy,” J. Phys. Chem. A 113, 1674–1677 (2009).
[CrossRef]

Rangwala, A. A.

A. A. Rangwala, V. H. Kulkarni, and A. A. Rindani, “Laplace Runge Lenz vector for a light ray trajectory in r−1 media,” Am. J. Phys. 69, 803–809 (2001).
[CrossRef]

Ren, K.

K. Ren, G. Gréhan, and G. Gouesbet, “Localized approximation of generalized Lorenz Mie theory: faster algorithm for computations of beam shape coefficients, gnm,” Part. Part. Syst. Charact. 9, 144–150 (1992).
[CrossRef]

Rindani, A. A.

A. A. Rangwala, V. H. Kulkarni, and A. A. Rindani, “Laplace Runge Lenz vector for a light ray trajectory in r−1 media,” Am. J. Phys. 69, 803–809 (2001).
[CrossRef]

Rings, D.

D. Rings, M. Selmke, F. Cichos, and K. Kroy, “Theory of hot Brownian motion,” Soft Matter 7, 3441–3452 (2011).
[CrossRef]

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

R. Radünz, D. Rings, K. Kroy, and F. Cichos, “Hot Brownian particles and photothermal correlation spectroscopy,” J. Phys. Chem. A 113, 1674–1677 (2009).
[CrossRef]

Rosenquist, M.

J. Evans and M. Rosenquist “’F=ma’ optics,” Am. J. Phys. 54, 876–883 (1986).
[CrossRef]

Ruijgrok, P. V.

A. Gaiduk, P. V. Ruijgrok, M. Yorulmaz, and M. Orrit, “Making gold nanoparticles fluorescent for simultaneous absorption and fluorescence detection on the single particle level,” Phys. Chem. Chem. Phys. 13, 149–153 (2011).
[CrossRef]

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

Saleh, B. E. A.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, Wiley Series in Pure and Applied Optics (Wiley, 1991).

Schachoff, R.

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

M. Selmke, R. Schachoff, M. Braun, and F. Cichos, “Twin-focus photothermal correlation spectroscopy,” RSC Adv. (submitted).

Schmidt, T.

P. M. R. Paulo, A. Gaiduk, F. Kulzer, S. F. G. Krens, H. P. Spaink, T. Schmidt, and M. Orrit, “Photothermal correlation spectroscopy of gold nanoparticles in solution,” J. Phys. Chem. C 113, 11451–11457 (2009).
[CrossRef]

Selmke, M.

M. Selmke, M. Braun, and F. Cichos, “Nano-lens diffraction around a single heated nano particle,” Opt. Express 20, 8055–8070 (2012).
[CrossRef]

M. Selmke, M. Braun, and F. Cichos, “Photothermal single particle microscopy, detection of a nano-lens,” ACS Nano 6, 2741–2749 (2012).
[CrossRef]

D. Rings, M. Selmke, F. Cichos, and K. Kroy, “Theory of hot Brownian motion,” Soft Matter 7, 3441–3452 (2011).
[CrossRef]

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

M. Selmke, R. Schachoff, M. Braun, and F. Cichos, “Twin-focus photothermal correlation spectroscopy,” RSC Adv. (submitted).

Sivardière, J.

J. Sivardière, “Perturbed elliptic motion,” Eur. J. Phys. 7, 283–286 (1986).
[CrossRef]

Spaink, H. P.

P. M. R. Paulo, A. Gaiduk, F. Kulzer, S. F. G. Krens, H. P. Spaink, T. Schmidt, and M. Orrit, “Photothermal correlation spectroscopy of gold nanoparticles in solution,” J. Phys. Chem. C 113, 11451–11457 (2009).
[CrossRef]

Teich, M. C.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, Wiley Series in Pure and Applied Optics (Wiley, 1991).

Yorulmaz, M.

A. Gaiduk, P. V. Ruijgrok, M. Yorulmaz, and M. Orrit, “Making gold nanoparticles fluorescent for simultaneous absorption and fluorescence detection on the single particle level,” Phys. Chem. Chem. Phys. 13, 149–153 (2011).
[CrossRef]

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

ACS Nano

M. Selmke, M. Braun, and F. Cichos, “Photothermal single particle microscopy, detection of a nano-lens,” ACS Nano 6, 2741–2749 (2012).
[CrossRef]

Am. J. Phys.

J. Evans and M. Rosenquist “’F=ma’ optics,” Am. J. Phys. 54, 876–883 (1986).
[CrossRef]

A. A. Rangwala, V. H. Kulkarni, and A. A. Rindani, “Laplace Runge Lenz vector for a light ray trajectory in r−1 media,” Am. J. Phys. 69, 803–809 (2001).
[CrossRef]

Eur. J. Phys.

J. Sivardière, “Perturbed elliptic motion,” Eur. J. Phys. 7, 283–286 (1986).
[CrossRef]

J. Opt. Soc. Am. A

J. Phys. Chem. A

R. Radünz, D. Rings, K. Kroy, and F. Cichos, “Hot Brownian particles and photothermal correlation spectroscopy,” J. Phys. Chem. A 113, 1674–1677 (2009).
[CrossRef]

J. Phys. Chem. C

P. M. R. Paulo, A. Gaiduk, F. Kulzer, S. F. G. Krens, H. P. Spaink, T. Schmidt, and M. Orrit, “Photothermal correlation spectroscopy of gold nanoparticles in solution,” J. Phys. Chem. C 113, 11451–11457 (2009).
[CrossRef]

Jpn. J. Appl. Phys.

J. Moreau and V. Loriette, “Confocal dual-beam thermal-lens microscope: model and experimental results,” Jpn. J. Appl. Phys. 1, 7141–7151 (2006).
[CrossRef]

Nano Lett.

S. Berciaud, L. Cognet, and B. Lounis, “Photothermal absorption spectroscopy of individual semiconductor nanocrystals,” Nano Lett. 5, 2160–2163 (2005).
[CrossRef]

Opt. Express

Part. Part. Syst. Charact.

K. Ren, G. Gréhan, and G. Gouesbet, “Localized approximation of generalized Lorenz Mie theory: faster algorithm for computations of beam shape coefficients, gnm,” Part. Part. Syst. Charact. 9, 144–150 (1992).
[CrossRef]

Phys. Chem. Chem. Phys.

A. Gaiduk, P. V. Ruijgrok, M. Yorulmaz, and M. Orrit, “Making gold nanoparticles fluorescent for simultaneous absorption and fluorescence detection on the single particle level,” Phys. Chem. Chem. Phys. 13, 149–153 (2011).
[CrossRef]

Phys. Rev. B

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

Phys. Rev. Lett.

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

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

S. Berciaud, L. Cognet, and B. Lounis, “Luminescence decay and the absorption cross section of individual single-walled carbon nanotubes,” Phys. Rev. Lett. 101, 077402 (2008).
[CrossRef]

Science

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

Soft Matter

D. Rings, M. Selmke, F. Cichos, and K. Kroy, “Theory of hot Brownian motion,” Soft Matter 7, 3441–3452 (2011).
[CrossRef]

Other

S. Bialcowski, Photothermal Spectroscopy Methods for Chemical Analysis (Wiley, 1996).

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley-VCH, 1998).

M. Selmke, R. Schachoff, M. Braun, and F. Cichos, “Twin-focus photothermal correlation spectroscopy,” RSC Adv. (submitted).

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, Wiley Series in Pure and Applied Optics (Wiley, 1991).

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Figures (5)

Fig. 1.
Fig. 1.

Heated nanoparticle creates a refractive index profile n ( r ) , which constitutes the thermal lens. A ray-optics treatment delivers a focal length when probed by a confined Gaussian beam (see text). For typical material parameters, the focal lengths are large as compared to the particle dimension, i.e., f R .

Fig. 2.
Fig. 2.

Probing Gaussian beam is focused at a distance z p to the lens (first optical element). An interface from a medium with refractive index n 0 to air with n 1 and free space propagation by a distance d follow. (Top) Beam transformation through the optical system with a lens present. (Bottom) Beam transformation without the lens.

Fig. 3.
Fig. 3.

(Top) Lorentzian profile of the power P abs ( z p ) absorbed by the particle for an axial laser offset Δ z f = 2.1 z R . (Bottom) Axial scans of the relative PT signal, Eq. (10) ( × F ), for Δ z f / z R = { 2.1 , 1.4 , 0.7 , 0.7 , 1.4 , 2.1 } (blue to red). Parameters: R = 30 nm , Δ T = 200 K corresponding to the experimental parameters ω 0 , h = 0.380 μm , ω 0 = 0.315 μm , σ abs ( λ h ) = 1.16 × 10 14 m 2 , and P h = 225 μW .

Fig. 4.
Fig. 4.

(Top) The left two images show theoretical R = 30 nm AuNP x z scans of transmitted powers computed within GLMT (probing, λ = 0.635 μm , ω 0 = 0.315 μm ; heating beam, λ h = 0.532 μm , ω 0 , h = 0.330 μm ; both in PDMS n 0 = 1.46 ). The left and right contours show incident intensities I d and I h , respectively. The right two images show the corresponding scans recorded with a photodiode. (Bottom) Theoretical axial scans (black, along white dashed lines) and Φ ( z p ) for Δ z f = 0 (blue; gray solid in print). Also shown are the axial Lorentzian heating beam profiles (in arbitrary units, solid-dashed, colored).

Fig. 5.
Fig. 5.

(a) Experimental axial signal scans Φ ( z p ) . (b) Extrema positions versus axial displacement of heating and detection foci. (c) Extrema values of relative PT signal. (d) Dependence of the finite angle correction factor F = Φ ( θ ) / Φ ( 0 ) on the numerical aperture NA = n 0 sin ( θ ) at z p = 0.5 μm . Parameters as in Fig. 3. Top axes for axial coordinates have been scaled by z R .

Equations (10)

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Φ = ( P th P 0 ) / P 0 .
r = ( 1 2 n 2 ( r ) ) , | r | = n ( r ) ,
Δ n = [ d n d T ] P abs 4 π κ R .
r ( ϕ , b ) = p ϵ cos ( γ [ ϕ ϕ 0 ] ) 1 .
ξ = n 0 / R Δ n p = ( b 2 ξ 2 1 ) / ξ γ 2 = 1 b 2 ξ 2 ϵ = b ξ ϕ 0 = π γ 1 arccos ( 1 / ϵ ) π / 2 + b 1 ξ 1 + O ( b 2 ξ 2 ) } .
f ( b ) b 2 n 0 / [ 2 Δ n R ] ,
f eff ( z p ) n 0 Δ n ω 0 2 4 R [ z p 2 z R 2 + 1 ] .
q in 1 = 1 R C ( z p ) i λ / n π ω 2 ( z p ) , q out = A q in + B C q in + D .
Φ ( z p ) = 2 z p / f .
Φ = 4 P h σ abs [ d n d T ] π 2 κ n 0 ω 0 , h 2 ω 0 2 [ ( z p Δ z f ) 2 z R , h 2 + 1 ] 1 z p [ z p 2 z R 2 + 1 ] 1 .

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