Abstract

Localized heating in the focus of an optical trap operating in water can result in a temperature rise of several kelvins. We present spatially resolved measurements of the refractive-index distribution induced by the localized heating produced in an optical trap and infer the temperature distribution. We have determined a peak temperature rise in water of 4 K in the focus of a 985-nm-wavelength 55-mW laser beam. The localized heating is directly proportional to power and the absorption coefficient. The temperature distribution is in excellent agreement with a model based on the heat equation.

© 2000 Optical Society of America

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References

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  1. A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, S. Chu, “Observation of a single-beam gradient force optical trap for dielectric particles,” Opt. Lett. 11, 288–290 (1986).
    [CrossRef] [PubMed]
  2. A. Ashkin, J. M. Dziedzic, T. Yamane, “Optical trapping and manipulation of single cells using infrared laser beams,” Nature 330, 769–771 (1987).
    [CrossRef] [PubMed]
  3. S. M. Block, “Making light work with optical tweezers,” Nature 360, 493–495 (1992).
    [CrossRef] [PubMed]
  4. J. Conia, B. S. Edwards, S. Voelkel, “The micro-robotic laboratory: optical trapping and scissing for the biologist,” J. Clin. Lab. Anal. 11, 28–38 (1997).
    [CrossRef] [PubMed]
  5. S. C. Kuo, M. P. Sheetz, “Optical tweezers in cell biology,” Trends Cell Biol. 2, 116–118 (1992).
    [CrossRef] [PubMed]
  6. W. H. Wright, G. J. Sonek, Y. Tadir, M. W. Berns, “Laser trapping in cell biology,” IEEE J. Quantum Electron. 26, 2148–2157 (1990).
    [CrossRef]
  7. C. F. Chapman, Y. Liu, G. J. Sonek, B. J. Tromberg, “The use of exogenous fluorescent probes for temperature measurements in single living cells,” Photochem. Photobiol. 62, 416–425 (1995).
    [CrossRef] [PubMed]
  8. Y. Liu, D. K. Cheng, G. J. Sonek, M. W. Berns, B. J. Tromberg, “A microfluorometric technique for the determination of localized heating in organic particles,” Appl. Phys. Lett. 65, 919–921 (1994).
    [CrossRef]
  9. Y. Liu, D. K. Cheng, G. J. Sonek, M. W. Berns, C. F. Chapman, B. J. Tromberg, “Evidence for localized cell heating induced by infrared optical tweezers,” Biophys. J. 68, 2137–2144 (1995).
    [CrossRef] [PubMed]
  10. S. C. Kuo, “A simple assay for local heating by optical tweezers,” Methods Cell Biol. 55, 43–45 (1998).
    [CrossRef]
  11. M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, UK, 1980), p. 312.
  12. W. Lochte-Holtgreven, “Evaluation of plasma parameters,” in Plasma Diagnostics, W. Lochte-Holtgreven, ed. (North-Holland, Amsterdam, 1968), p. 184.
  13. W. R. Wing, R. V. Neidigh, “A rapid Abel inversion,” Am. J. Phys. 39, 760–764 (1971).
    [CrossRef]
  14. I. Thormählen, J. Straub, U. Grigul, “Refractive index of water and its dependence on wavelength, temperature and density,” J. Phys. Chem. Ref. Data 14, 933–945 (1985).
    [CrossRef]
  15. D. R. Lide, ed., Handbook of Chemistry and Physics, 77th ed. (CRC Press, Boca Raton, Fla., 1996), p. 6–10.
  16. A. Yariv, Quantum Electronics, 2nd ed. (Wiley, New York, 1975), Chap. 6.
  17. G. M. Hale, M. R. Querry, “Optical constants of water in the 200-nm to 200-µm wavelength region,” Appl. Opt. 12, 555–563 (1973).
    [CrossRef] [PubMed]
  18. W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U. Press, Cambridge, 1986), Chap. 17.
  19. J. P. Christiansen, D. E. T. F. Ashby, K. V. Roberts, “MEDUSA, a one-dimensional laser fusion code,” Comput. Phys. Commun. 7, 271–287 (1974).
    [CrossRef]
  20. Numerical solution of the heat equation in two dimensions was carried out by use of an alternating-direction-implicit numerical scheme (see Ref. 18) consisting of alternating one-dimensional passes along the z coordinate (planar geometry) and the ρ coordinate (cylindrical geometry). Each pass was solved implicitly with a Crank–Nicholson scheme (see Refs. 18 and 19). Details of Crank–Nicholson differencing schemes for one-dimensional planar, cylindrical, and spherical geometry can be found, for example, in Ref. 19.
  21. H. Liang, K. T. Vu, P. Krishnan, T. C. Trang, D. Shin, S. Kimel, M. W. Berns, “Wavelength dependence of cell cloning efficiency after optical trapping,” Biophys. J. 70, 1529–1533 (1996).
    [CrossRef] [PubMed]

1998

S. C. Kuo, “A simple assay for local heating by optical tweezers,” Methods Cell Biol. 55, 43–45 (1998).
[CrossRef]

1997

J. Conia, B. S. Edwards, S. Voelkel, “The micro-robotic laboratory: optical trapping and scissing for the biologist,” J. Clin. Lab. Anal. 11, 28–38 (1997).
[CrossRef] [PubMed]

1996

H. Liang, K. T. Vu, P. Krishnan, T. C. Trang, D. Shin, S. Kimel, M. W. Berns, “Wavelength dependence of cell cloning efficiency after optical trapping,” Biophys. J. 70, 1529–1533 (1996).
[CrossRef] [PubMed]

1995

Y. Liu, D. K. Cheng, G. J. Sonek, M. W. Berns, C. F. Chapman, B. J. Tromberg, “Evidence for localized cell heating induced by infrared optical tweezers,” Biophys. J. 68, 2137–2144 (1995).
[CrossRef] [PubMed]

C. F. Chapman, Y. Liu, G. J. Sonek, B. J. Tromberg, “The use of exogenous fluorescent probes for temperature measurements in single living cells,” Photochem. Photobiol. 62, 416–425 (1995).
[CrossRef] [PubMed]

1994

Y. Liu, D. K. Cheng, G. J. Sonek, M. W. Berns, B. J. Tromberg, “A microfluorometric technique for the determination of localized heating in organic particles,” Appl. Phys. Lett. 65, 919–921 (1994).
[CrossRef]

1992

S. C. Kuo, M. P. Sheetz, “Optical tweezers in cell biology,” Trends Cell Biol. 2, 116–118 (1992).
[CrossRef] [PubMed]

S. M. Block, “Making light work with optical tweezers,” Nature 360, 493–495 (1992).
[CrossRef] [PubMed]

1990

W. H. Wright, G. J. Sonek, Y. Tadir, M. W. Berns, “Laser trapping in cell biology,” IEEE J. Quantum Electron. 26, 2148–2157 (1990).
[CrossRef]

1987

A. Ashkin, J. M. Dziedzic, T. Yamane, “Optical trapping and manipulation of single cells using infrared laser beams,” Nature 330, 769–771 (1987).
[CrossRef] [PubMed]

1986

1985

I. Thormählen, J. Straub, U. Grigul, “Refractive index of water and its dependence on wavelength, temperature and density,” J. Phys. Chem. Ref. Data 14, 933–945 (1985).
[CrossRef]

1974

J. P. Christiansen, D. E. T. F. Ashby, K. V. Roberts, “MEDUSA, a one-dimensional laser fusion code,” Comput. Phys. Commun. 7, 271–287 (1974).
[CrossRef]

1973

1971

W. R. Wing, R. V. Neidigh, “A rapid Abel inversion,” Am. J. Phys. 39, 760–764 (1971).
[CrossRef]

Ashby, D. E. T. F.

J. P. Christiansen, D. E. T. F. Ashby, K. V. Roberts, “MEDUSA, a one-dimensional laser fusion code,” Comput. Phys. Commun. 7, 271–287 (1974).
[CrossRef]

Ashkin, A.

A. Ashkin, J. M. Dziedzic, T. Yamane, “Optical trapping and manipulation of single cells using infrared laser beams,” Nature 330, 769–771 (1987).
[CrossRef] [PubMed]

A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, S. Chu, “Observation of a single-beam gradient force optical trap for dielectric particles,” Opt. Lett. 11, 288–290 (1986).
[CrossRef] [PubMed]

Berns, M. W.

H. Liang, K. T. Vu, P. Krishnan, T. C. Trang, D. Shin, S. Kimel, M. W. Berns, “Wavelength dependence of cell cloning efficiency after optical trapping,” Biophys. J. 70, 1529–1533 (1996).
[CrossRef] [PubMed]

Y. Liu, D. K. Cheng, G. J. Sonek, M. W. Berns, C. F. Chapman, B. J. Tromberg, “Evidence for localized cell heating induced by infrared optical tweezers,” Biophys. J. 68, 2137–2144 (1995).
[CrossRef] [PubMed]

Y. Liu, D. K. Cheng, G. J. Sonek, M. W. Berns, B. J. Tromberg, “A microfluorometric technique for the determination of localized heating in organic particles,” Appl. Phys. Lett. 65, 919–921 (1994).
[CrossRef]

W. H. Wright, G. J. Sonek, Y. Tadir, M. W. Berns, “Laser trapping in cell biology,” IEEE J. Quantum Electron. 26, 2148–2157 (1990).
[CrossRef]

Bjorkholm, J. E.

Block, S. M.

S. M. Block, “Making light work with optical tweezers,” Nature 360, 493–495 (1992).
[CrossRef] [PubMed]

Born, M.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, UK, 1980), p. 312.

Chapman, C. F.

C. F. Chapman, Y. Liu, G. J. Sonek, B. J. Tromberg, “The use of exogenous fluorescent probes for temperature measurements in single living cells,” Photochem. Photobiol. 62, 416–425 (1995).
[CrossRef] [PubMed]

Y. Liu, D. K. Cheng, G. J. Sonek, M. W. Berns, C. F. Chapman, B. J. Tromberg, “Evidence for localized cell heating induced by infrared optical tweezers,” Biophys. J. 68, 2137–2144 (1995).
[CrossRef] [PubMed]

Cheng, D. K.

Y. Liu, D. K. Cheng, G. J. Sonek, M. W. Berns, C. F. Chapman, B. J. Tromberg, “Evidence for localized cell heating induced by infrared optical tweezers,” Biophys. J. 68, 2137–2144 (1995).
[CrossRef] [PubMed]

Y. Liu, D. K. Cheng, G. J. Sonek, M. W. Berns, B. J. Tromberg, “A microfluorometric technique for the determination of localized heating in organic particles,” Appl. Phys. Lett. 65, 919–921 (1994).
[CrossRef]

Christiansen, J. P.

J. P. Christiansen, D. E. T. F. Ashby, K. V. Roberts, “MEDUSA, a one-dimensional laser fusion code,” Comput. Phys. Commun. 7, 271–287 (1974).
[CrossRef]

Chu, S.

Conia, J.

J. Conia, B. S. Edwards, S. Voelkel, “The micro-robotic laboratory: optical trapping and scissing for the biologist,” J. Clin. Lab. Anal. 11, 28–38 (1997).
[CrossRef] [PubMed]

Dziedzic, J. M.

A. Ashkin, J. M. Dziedzic, T. Yamane, “Optical trapping and manipulation of single cells using infrared laser beams,” Nature 330, 769–771 (1987).
[CrossRef] [PubMed]

A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, S. Chu, “Observation of a single-beam gradient force optical trap for dielectric particles,” Opt. Lett. 11, 288–290 (1986).
[CrossRef] [PubMed]

Edwards, B. S.

J. Conia, B. S. Edwards, S. Voelkel, “The micro-robotic laboratory: optical trapping and scissing for the biologist,” J. Clin. Lab. Anal. 11, 28–38 (1997).
[CrossRef] [PubMed]

Flannery, B. P.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U. Press, Cambridge, 1986), Chap. 17.

Grigul, U.

I. Thormählen, J. Straub, U. Grigul, “Refractive index of water and its dependence on wavelength, temperature and density,” J. Phys. Chem. Ref. Data 14, 933–945 (1985).
[CrossRef]

Hale, G. M.

Kimel, S.

H. Liang, K. T. Vu, P. Krishnan, T. C. Trang, D. Shin, S. Kimel, M. W. Berns, “Wavelength dependence of cell cloning efficiency after optical trapping,” Biophys. J. 70, 1529–1533 (1996).
[CrossRef] [PubMed]

Krishnan, P.

H. Liang, K. T. Vu, P. Krishnan, T. C. Trang, D. Shin, S. Kimel, M. W. Berns, “Wavelength dependence of cell cloning efficiency after optical trapping,” Biophys. J. 70, 1529–1533 (1996).
[CrossRef] [PubMed]

Kuo, S. C.

S. C. Kuo, “A simple assay for local heating by optical tweezers,” Methods Cell Biol. 55, 43–45 (1998).
[CrossRef]

S. C. Kuo, M. P. Sheetz, “Optical tweezers in cell biology,” Trends Cell Biol. 2, 116–118 (1992).
[CrossRef] [PubMed]

Liang, H.

H. Liang, K. T. Vu, P. Krishnan, T. C. Trang, D. Shin, S. Kimel, M. W. Berns, “Wavelength dependence of cell cloning efficiency after optical trapping,” Biophys. J. 70, 1529–1533 (1996).
[CrossRef] [PubMed]

Liu, Y.

Y. Liu, D. K. Cheng, G. J. Sonek, M. W. Berns, C. F. Chapman, B. J. Tromberg, “Evidence for localized cell heating induced by infrared optical tweezers,” Biophys. J. 68, 2137–2144 (1995).
[CrossRef] [PubMed]

C. F. Chapman, Y. Liu, G. J. Sonek, B. J. Tromberg, “The use of exogenous fluorescent probes for temperature measurements in single living cells,” Photochem. Photobiol. 62, 416–425 (1995).
[CrossRef] [PubMed]

Y. Liu, D. K. Cheng, G. J. Sonek, M. W. Berns, B. J. Tromberg, “A microfluorometric technique for the determination of localized heating in organic particles,” Appl. Phys. Lett. 65, 919–921 (1994).
[CrossRef]

Lochte-Holtgreven, W.

W. Lochte-Holtgreven, “Evaluation of plasma parameters,” in Plasma Diagnostics, W. Lochte-Holtgreven, ed. (North-Holland, Amsterdam, 1968), p. 184.

Neidigh, R. V.

W. R. Wing, R. V. Neidigh, “A rapid Abel inversion,” Am. J. Phys. 39, 760–764 (1971).
[CrossRef]

Press, W. H.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U. Press, Cambridge, 1986), Chap. 17.

Querry, M. R.

Roberts, K. V.

J. P. Christiansen, D. E. T. F. Ashby, K. V. Roberts, “MEDUSA, a one-dimensional laser fusion code,” Comput. Phys. Commun. 7, 271–287 (1974).
[CrossRef]

Sheetz, M. P.

S. C. Kuo, M. P. Sheetz, “Optical tweezers in cell biology,” Trends Cell Biol. 2, 116–118 (1992).
[CrossRef] [PubMed]

Shin, D.

H. Liang, K. T. Vu, P. Krishnan, T. C. Trang, D. Shin, S. Kimel, M. W. Berns, “Wavelength dependence of cell cloning efficiency after optical trapping,” Biophys. J. 70, 1529–1533 (1996).
[CrossRef] [PubMed]

Sonek, G. J.

Y. Liu, D. K. Cheng, G. J. Sonek, M. W. Berns, C. F. Chapman, B. J. Tromberg, “Evidence for localized cell heating induced by infrared optical tweezers,” Biophys. J. 68, 2137–2144 (1995).
[CrossRef] [PubMed]

C. F. Chapman, Y. Liu, G. J. Sonek, B. J. Tromberg, “The use of exogenous fluorescent probes for temperature measurements in single living cells,” Photochem. Photobiol. 62, 416–425 (1995).
[CrossRef] [PubMed]

Y. Liu, D. K. Cheng, G. J. Sonek, M. W. Berns, B. J. Tromberg, “A microfluorometric technique for the determination of localized heating in organic particles,” Appl. Phys. Lett. 65, 919–921 (1994).
[CrossRef]

W. H. Wright, G. J. Sonek, Y. Tadir, M. W. Berns, “Laser trapping in cell biology,” IEEE J. Quantum Electron. 26, 2148–2157 (1990).
[CrossRef]

Straub, J.

I. Thormählen, J. Straub, U. Grigul, “Refractive index of water and its dependence on wavelength, temperature and density,” J. Phys. Chem. Ref. Data 14, 933–945 (1985).
[CrossRef]

Tadir, Y.

W. H. Wright, G. J. Sonek, Y. Tadir, M. W. Berns, “Laser trapping in cell biology,” IEEE J. Quantum Electron. 26, 2148–2157 (1990).
[CrossRef]

Teukolsky, S. A.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U. Press, Cambridge, 1986), Chap. 17.

Thormählen, I.

I. Thormählen, J. Straub, U. Grigul, “Refractive index of water and its dependence on wavelength, temperature and density,” J. Phys. Chem. Ref. Data 14, 933–945 (1985).
[CrossRef]

Trang, T. C.

H. Liang, K. T. Vu, P. Krishnan, T. C. Trang, D. Shin, S. Kimel, M. W. Berns, “Wavelength dependence of cell cloning efficiency after optical trapping,” Biophys. J. 70, 1529–1533 (1996).
[CrossRef] [PubMed]

Tromberg, B. J.

Y. Liu, D. K. Cheng, G. J. Sonek, M. W. Berns, C. F. Chapman, B. J. Tromberg, “Evidence for localized cell heating induced by infrared optical tweezers,” Biophys. J. 68, 2137–2144 (1995).
[CrossRef] [PubMed]

C. F. Chapman, Y. Liu, G. J. Sonek, B. J. Tromberg, “The use of exogenous fluorescent probes for temperature measurements in single living cells,” Photochem. Photobiol. 62, 416–425 (1995).
[CrossRef] [PubMed]

Y. Liu, D. K. Cheng, G. J. Sonek, M. W. Berns, B. J. Tromberg, “A microfluorometric technique for the determination of localized heating in organic particles,” Appl. Phys. Lett. 65, 919–921 (1994).
[CrossRef]

Vetterling, W. T.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U. Press, Cambridge, 1986), Chap. 17.

Voelkel, S.

J. Conia, B. S. Edwards, S. Voelkel, “The micro-robotic laboratory: optical trapping and scissing for the biologist,” J. Clin. Lab. Anal. 11, 28–38 (1997).
[CrossRef] [PubMed]

Vu, K. T.

H. Liang, K. T. Vu, P. Krishnan, T. C. Trang, D. Shin, S. Kimel, M. W. Berns, “Wavelength dependence of cell cloning efficiency after optical trapping,” Biophys. J. 70, 1529–1533 (1996).
[CrossRef] [PubMed]

Wing, W. R.

W. R. Wing, R. V. Neidigh, “A rapid Abel inversion,” Am. J. Phys. 39, 760–764 (1971).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, UK, 1980), p. 312.

Wright, W. H.

W. H. Wright, G. J. Sonek, Y. Tadir, M. W. Berns, “Laser trapping in cell biology,” IEEE J. Quantum Electron. 26, 2148–2157 (1990).
[CrossRef]

Yamane, T.

A. Ashkin, J. M. Dziedzic, T. Yamane, “Optical trapping and manipulation of single cells using infrared laser beams,” Nature 330, 769–771 (1987).
[CrossRef] [PubMed]

Yariv, A.

A. Yariv, Quantum Electronics, 2nd ed. (Wiley, New York, 1975), Chap. 6.

Am. J. Phys.

W. R. Wing, R. V. Neidigh, “A rapid Abel inversion,” Am. J. Phys. 39, 760–764 (1971).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

Y. Liu, D. K. Cheng, G. J. Sonek, M. W. Berns, B. J. Tromberg, “A microfluorometric technique for the determination of localized heating in organic particles,” Appl. Phys. Lett. 65, 919–921 (1994).
[CrossRef]

Biophys. J.

Y. Liu, D. K. Cheng, G. J. Sonek, M. W. Berns, C. F. Chapman, B. J. Tromberg, “Evidence for localized cell heating induced by infrared optical tweezers,” Biophys. J. 68, 2137–2144 (1995).
[CrossRef] [PubMed]

H. Liang, K. T. Vu, P. Krishnan, T. C. Trang, D. Shin, S. Kimel, M. W. Berns, “Wavelength dependence of cell cloning efficiency after optical trapping,” Biophys. J. 70, 1529–1533 (1996).
[CrossRef] [PubMed]

Comput. Phys. Commun.

J. P. Christiansen, D. E. T. F. Ashby, K. V. Roberts, “MEDUSA, a one-dimensional laser fusion code,” Comput. Phys. Commun. 7, 271–287 (1974).
[CrossRef]

IEEE J. Quantum Electron.

W. H. Wright, G. J. Sonek, Y. Tadir, M. W. Berns, “Laser trapping in cell biology,” IEEE J. Quantum Electron. 26, 2148–2157 (1990).
[CrossRef]

J. Clin. Lab. Anal.

J. Conia, B. S. Edwards, S. Voelkel, “The micro-robotic laboratory: optical trapping and scissing for the biologist,” J. Clin. Lab. Anal. 11, 28–38 (1997).
[CrossRef] [PubMed]

J. Phys. Chem. Ref. Data

I. Thormählen, J. Straub, U. Grigul, “Refractive index of water and its dependence on wavelength, temperature and density,” J. Phys. Chem. Ref. Data 14, 933–945 (1985).
[CrossRef]

Methods Cell Biol.

S. C. Kuo, “A simple assay for local heating by optical tweezers,” Methods Cell Biol. 55, 43–45 (1998).
[CrossRef]

Nature

A. Ashkin, J. M. Dziedzic, T. Yamane, “Optical trapping and manipulation of single cells using infrared laser beams,” Nature 330, 769–771 (1987).
[CrossRef] [PubMed]

S. M. Block, “Making light work with optical tweezers,” Nature 360, 493–495 (1992).
[CrossRef] [PubMed]

Opt. Lett.

Photochem. Photobiol.

C. F. Chapman, Y. Liu, G. J. Sonek, B. J. Tromberg, “The use of exogenous fluorescent probes for temperature measurements in single living cells,” Photochem. Photobiol. 62, 416–425 (1995).
[CrossRef] [PubMed]

Trends Cell Biol.

S. C. Kuo, M. P. Sheetz, “Optical tweezers in cell biology,” Trends Cell Biol. 2, 116–118 (1992).
[CrossRef] [PubMed]

Other

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, UK, 1980), p. 312.

W. Lochte-Holtgreven, “Evaluation of plasma parameters,” in Plasma Diagnostics, W. Lochte-Holtgreven, ed. (North-Holland, Amsterdam, 1968), p. 184.

Numerical solution of the heat equation in two dimensions was carried out by use of an alternating-direction-implicit numerical scheme (see Ref. 18) consisting of alternating one-dimensional passes along the z coordinate (planar geometry) and the ρ coordinate (cylindrical geometry). Each pass was solved implicitly with a Crank–Nicholson scheme (see Refs. 18 and 19). Details of Crank–Nicholson differencing schemes for one-dimensional planar, cylindrical, and spherical geometry can be found, for example, in Ref. 19.

D. R. Lide, ed., Handbook of Chemistry and Physics, 77th ed. (CRC Press, Boca Raton, Fla., 1996), p. 6–10.

A. Yariv, Quantum Electronics, 2nd ed. (Wiley, New York, 1975), Chap. 6.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U. Press, Cambridge, 1986), Chap. 17.

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Figures (10)

Fig. 1
Fig. 1

Sketch showing the measurement principle. A probe laser illuminates a sample from below, with wave fronts indicated schematically. The index of refraction in the sample volume deviates from the ambient value and produces a distribution of optical path delays on the probe beam after it passes through.

Fig. 2
Fig. 2

Change in index of refraction of water as a function of temperature rise in water at 1-atm pressure for light at wavelength 543 nm.

Fig. 3
Fig. 3

Details of the experimental layout (see text explanation).

Fig. 4
Fig. 4

Oscilloscope recording of the laser pulse train, the mirror scan ramp, and the data-collection trigger. Data collection begins on the rising edge of the trigger and lasts for a duration of 250 ms. Each measurement scan required data collection during two consecutive mirror ramp scans: one with the laser toggled off and one with it toggled on.

Fig. 5
Fig. 5

Phase shift scans in water at 8.5-, 17-, 40-, and 55-mW power and in a culture medium at 48.5-mW power. Quadratic curve fits to these data are shown and are also summarized in Table 1.

Fig. 6
Fig. 6

Temperature distributions inferred from data for the 55-mW power case. Broken curves indicate temperature inferred from direct Abel inversion of the raw data out to r max = 100 µm (dotted–dashed curve) and 200 µm (dashed curve). The solid curve indicates the temperature distribution inferred from a fit to a calculated two-dimensional refractive-index distribution (see Section 9 in text).

Fig. 7
Fig. 7

Temperature as a function of distance from focus at 1, 10, 100, and 1000 ms for a heating power of 10 mW at 985 nm. The curves show calculated temperatures for a 1.25-NA objective along the beam axis (dotted curves), perpendicular to the beam axis (dashed curves), and spherically averaged (solid curves, as a function of radius) as well as for a spherically symmetric deposition of the same power (solid curves, indistinguishable from the spherically averaged case on this scale).

Fig. 8
Fig. 8

Heating distribution owing to a pulsed laser sequence with 10-mW laser power. The gray scale represents a snapshot of the temperature distribution at 11.86 s in the calculation. Grey levels are distributed on a logarithmic scale, as are contours of constant temperature. Temperature contours (from the right) are 0.002, 0.005, 0.01, 0.02, 0.05, … K.

Fig. 9
Fig. 9

Heating as a function of time at varius positions relative to the focus of the optical trap: 1 µm along the z axis (solid curve), 1 µm along the ρ axis (short-dashed curve), 100 µm along the z axis (dotted curve), and 100 µm along the ρ axis (long-and-short-dashed curve). The curves show several cycles in the middle of the 50-cycle calculation with 55-mW peak power at 985 nm.

Fig. 10
Fig. 10

Calculated phase-shift distributions corresponding the measurements at 55-mW power for spherical deposition (solid curve) and deposition from the 1.25-NA objective (dashed curve) in comparison with the observations (open circles).

Tables (2)

Tables Icon

Table 1 Coefficients for Quadratic Curve Fits to the Measurements of Phase Shift at 543 nm As a Function of Positiona

Tables Icon

Table 2 Peak Temperature Rises for 985-nm Laser Light Focused in Water with a 1.25-NA Objective Inferred from the Experiment for Heating Time t = 250 ms and Estimated with Expression (9) for t = 250 ms and 1, 10, and 100 sa

Equations (12)

Equations on this page are rendered with MathJax. Learn more.

δz=L δnzdz,
dϕ=2π δzλ=2πλL δnzdz.
dϕ=2πLδn/ΔTΔT/λ2π20 μm-0.0001 K-13 K/0.543 μm-70 mrad.
δϕy=4πλyrmaxrδnrr2-y2dr.
δnr=-λ2π2rrmaxδϕyy2-r2dy,
2ΔT-1κΔTt=-qK,
q=qsr=αP/2πr2,
q=qcρ, z=αP/2πρ2+z21-cos θtan-1ρ/z<θ0tan-1ρ/z>θ,
ΔTr, t=0dr αP4πκρcrr4κtπexp-|r-r|24κt-exp-r+r24κt-|r-r|erfc|r-r|4κt+r+rerfcr+r4κt.
ΔTr, tαPT0+β logt/t0r0/r2,
q=qρ, z, t=qcρ, zn=049Ut-nτ-Ut-nτ/2,
δϕρ=all cycles2πλtonton+250 msdt×- δnΔTρ, z, tdz-tofftoff+250 msdt - δnΔTρ, z, tdz.

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