OSA's Digital Library

Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 41, Iss. 13 — May. 1, 2002
  • pp: 2494–2507

Trapping forces, force constants, and potential depths for dielectric spheres in the presence of spherical aberrations

Alexander Rohrbach and Ernst H. K. Stelzer  »View Author Affiliations


Applied Optics, Vol. 41, Issue 13, pp. 2494-2507 (2002)
http://dx.doi.org/10.1364/AO.41.002494


View Full Text Article

Enhanced HTML    Acrobat PDF (696 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We present and verify a theoretical model that predicts trapping forces (escape forces), force constants (trap stiffnesses), and trapping potential depths for dielectric spheres with diameters smaller than or equal to the wavelength of the trapping light. Optical forces can be calculated for arbitrary incident light distributions with a two-component approach that determines the gradient and the scattering force separately. We investigate the influence of spherical aberrations that are due to refractive-index mismatch on the maximum trapping force, the force constant, and the potential depth of a trap, which are important for optical tweezer applications. The relationships between the three parameters are explained and studied for different degrees of spherical aberration and various spheres (refractive indices n s = 1.39–1.57, radii a = 0.1–0.5 µm, λ0 = 1.064 µm). We find that all three parameters decrease when the distance to the coverslip increases. Effects that could make the interpretation of experimental results ambiguous are simulated and explained. Computational results are compared with the experimental data found in the literature. A good coincidence can be established.

© 2002 Optical Society of America

OCIS Codes
(070.2590) Fourier optics and signal processing : ABCD transforms
(140.7010) Lasers and laser optics : Laser trapping
(180.0180) Microscopy : Microscopy
(290.5850) Scattering : Scattering, particles

History
Original Manuscript: May 1, 2001
Revised Manuscript: November 13, 2001
Published: May 1, 2002

Citation
Alexander Rohrbach and Ernst H. K. Stelzer, "Trapping forces, force constants, and potential depths for dielectric spheres in the presence of spherical aberrations," Appl. Opt. 41, 2494-2507 (2002)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-41-13-2494


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  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, “Optical trapping and manipulation of viruses and bacteria,” Science 235, 1517–1520 (1987). [CrossRef] [PubMed]
  3. S. M. Block, D. F. Blair, H. C. Berg, “Compliance of bacterial flagella measured with optical tweezers,” Nature 338, 514–518 (1989). [CrossRef] [PubMed]
  4. S. M. Block, L. S. Goldstein, B. J. Schnapp, “Bead movement by single kinesin molecules studied with optical tweezers,” Nature 348, 348–352 (1990). [CrossRef] [PubMed]
  5. A. Ashkin, K. Schutze, J. M. Dziedzic, U. Euteneuer, M. Schliwa, “Force generation of organelle transport measured in vivo by an infrared laser trap,” Nature 348, 346–348 (1990). [CrossRef] [PubMed]
  6. S. C. Kuo, M. P. Sheetz, “Force of single kinesin molecules measured with optical tweezers,” Science 260, 232–234 (1993). [CrossRef] [PubMed]
  7. K. Svoboda, C. F. Schmidt, B. J. Schnapp, S. M. Block, “Direct observation of kinesin stepping by optical trapping interferometry,” Nature 365, 721–727 (1993). [CrossRef] [PubMed]
  8. R. W. Steubing, S. Cheng, W. H. Wright, Y. Numajiri, M. W. Berns, “Laser induced cell fusion in combination with optical tweezers: the laser cell fusion trap,” Cytometry 12, 505–510 (1991). [CrossRef] [PubMed]
  9. M. W. Berns, W. H. Wright, B. J. Tromberg, G. A. Profeta, J. J. Andrews, R. J. Walter, “Use of a laser-induced optical force trap to study chromosome movement on the mitotic spindle,” Proc. Natl. Acad. Sci. USA 86, 7914–7918 (1989). [CrossRef]
  10. S. Seeger, S. Monajembashi, K. J. Hutter, G. Futterman, J. Wolfrum, K. O. Greulich, “Application of laser optical tweezers in immunology and molecular genetics,” Cytometry 12, 497–504 (1991). [CrossRef] [PubMed]
  11. L. P. Ghislain, W. W. Webb, “Scanning-force microscope based on an optical trap,” Opt. Lett. 18, 1678–1680 (1993). [CrossRef] [PubMed]
  12. L. Ghislain, N. Switz, W. Webb, “Measurement of small forces using an optical trap,” Rev. Sci. Instrum. 65, 2762–2768 (1994). [CrossRef]
  13. E.-L. Florin, A. Pralle, J. K. H. Hörber, E. H. K. Stelzer, “Photonic force microscope (PFM) based on optical tweezers and two-photon excitation for biological applications,” J. Struct. Biol. 119, 202–211 (1997). [CrossRef] [PubMed]
  14. E.-L. Florin, A. Pralle, E. H. K. Stelzer, J. K. H. Hörber, “Photonic force microscope calibration by thermal noise analysis,” Appl. Phys. A 66, S75–S78 (1998). [CrossRef]
  15. A. Pralle, M. Prummer, E.-L. Florin, E. H. K. Stelzer, J. K. H. Hörber, “Three-dimensional position tracking for optical tweezers by forward scattered light,” Microsc. Res. Tech. 44, 378–386 (1999). [CrossRef] [PubMed]
  16. A. Ashkin, “Forces of a single-beam gradient laser trap on a dielectric sphere in the ray-optics regime,” Biophys. J. 61, 569–582 (1992). [CrossRef] [PubMed]
  17. R. Gussgard, T. Lindmo, I. Brevik, “Calculation of the trapping force in a strongly focused laser beam,” J. Opt. Soc. Am. B 9, 1922–1930 (1992). [CrossRef]
  18. T. Wohland, A. Rosin, E. H. K. Stelzer, “Theoretical determination of the influence of the polarization on forces exerted by optical tweezers,” Optik (Stuttgart) 102, 181–190 (1996).
  19. J. D. Jackson, Classial Electrodynamics, 2nd ed. (Wiley, New York, 1975).
  20. P. Mulser, “Radiation pressure on microscopic bodies,” J. Opt. Soc. Am. B 2, 1814–1829 (1985). [CrossRef]
  21. G. Mie, “Beitraege zur Optik trueber Medien speziell kolloidaler Metalloesungen,” Ann. Phys. 25, 377–445 (1908). [CrossRef]
  22. J. S. Kim, S. S. Lee, “Scattering of laser beams and the optical potential well for a homogeneous sphere,” J. Opt. Soc. Am. 73, 303–312 (1983). [CrossRef]
  23. J. P. Barton, D. R. Alexander, S. A. Schaub, “Theoretical determination of net radiation force and torque for a spherical particle illuminated by a focused laser beam,” J. Appl. Phys. 66, 4594–4602 (1989). [CrossRef]
  24. F. Ren, G. Gréhan, G. Gouesbet, “Radiation pressure forces exerted on a particle located arbitrarily in a Gaussian beam by using the generalized Lorentz–Mie theory and associated resonance effects,” Opt. Commun. 108, 343–354 (1994). [CrossRef]
  25. A. Rohrbach, H. K. Stelzer, “Optical trapping of dielectric particles in arbitrary fields,” J. Opt. Soc. Am. A 18, 839–853 (2001). [CrossRef]
  26. Y. Harada, T. Asakura, “Radiation forces on a dielectric sphere in the Rayleigh scattering regime,” Opt. Commun. 124, 529–541 (1996). [CrossRef]
  27. A. L. Stout, D. Axelrod, “Evanescent field excitation of fluorescence by epiillumination microscopy,” Appl. Opt. 28, 5237–5242 (1989). [CrossRef] [PubMed]
  28. S. Hell, G. Reiner, C. Cremer, E. H. K. Stelzer, “Aberrations in confocal fluorescence microscopy induced by mismatches in refractive index,” J. Microsc. 169, 391–405 (1993). [CrossRef]
  29. P. Török, P. Varga, Z. Laczik, G. R. Booker, “Electromagnetic diffraction of light focused through a planar interface between materials of mismatched refractive indices: an integral representation,” J. Opt. Soc. Am. A 12, 325–332 (1995). [CrossRef]
  30. W. H. Wright, G. J. Sonek, M. W. Berns, “Radiation trapping forces on microspheres with optical tweezers,” Appl. Phys. Lett. 63, 715–717 (1993). [CrossRef]
  31. K. Svoboda, S. M. Block, “Biological applications of optical forces,” Ann. Rev. Biophys. Biomol. Struct. 23, 247–285 (1994). [CrossRef]
  32. H. Felgner, O. Müller, M. Schliwa, “Calibration of light forces in optical tweezers,” Appl. Opt. 34, 977–982 (1995). [CrossRef] [PubMed]
  33. W. H. Wright, G. J. Sonek, M. W. Berns, “Parametric study of the forces on microspheres held by optical tweezers,” Appl. Opt. 33, 1735–1748 (1994). [CrossRef] [PubMed]
  34. M. E. J. Friese, H. Rubinsztein-Dunlop, N. R. Heckenberg, E. W. Dearden, “Determination of the force constant of a single-beam gradient trap by measurement of backscattered light,” Appl. Opt. 35, 7112–7116 (1996). [CrossRef] [PubMed]
  35. P. C. Ke, M. Gu, “Characterization of trapping force in the presence of spherical aberration,” J. Mod. Opt. 45, 2159–2168 (1998). [CrossRef]
  36. A. C. Dogariu, R. Rajagopalan, “Optical traps as force transducers: the effects of focusing the trapping beam through a dielectric interface,” Langmuir 16, 2770–2778 (2000). [CrossRef]
  37. C. W. McCutchen, “Generalized aperture and the three-dimensional diffraction image,” J. Opt. Soc. Am 54, 240–244 (1964). [CrossRef]
  38. J. W. Goodman, Introduction to Fourier Optics, 1st ed. (McGraw-Hill, San Francisco, 1968), pp. 48–56.
  39. M. Mansuripur, “Distribution of light at and near the focus of high-numerical-aperture objectives,” J. Opt. Soc. Am. A 3, 2086–2093 (1986). [CrossRef]
  40. M. Mansuripur, “Certain computational aspects of vector diffraction problems,” J. Opt. Soc. Am. A 6, 786–805 (1989). [CrossRef]
  41. C. J. R. Sheppard, K. G. Larkin, “Vectorial pupil functions and vectorial transfer functions,” Optik (Stuttgart) 107, 79–87 (1997).
  42. W. Singer, K.-H. Brenner, “Transition of a scalar field at a refracting surface in the generalized Kirchhoff diffraction theory,” J. Opt. Soc. Am. A 12, 1913–1919 (1995). [CrossRef]
  43. A. Rohrbach, W. Singer, “Scattering of a scalar field at dielectric surfaces by Born series expansion,” J. Opt. Soc. Am. A 15, 2651–2659 (1998). [CrossRef]
  44. J. P. Gordon, “Radiation forces and momenta in dielectric media,” Phys. Rev. 8, 14–21 (1973). [CrossRef]
  45. H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1957).
  46. R. M. Simmons, J. T. Finer, S. Chu, J. A. Spudich, “Quantitative measurement of force and displacement using an optical trap,” Biophys. J. 70, 1813–1822 (1996). [CrossRef] [PubMed]
  47. T. D. Parsons, J. R. Coorssen, H. Horstmann, W. Almers, “Docked granules, the exocytotic burst, and the need for ATP hydrolysis in endocrine cells,” Neuron 15, 1085–1096 (1995). [CrossRef] [PubMed]
  48. R. Drezek, A. Dunn, R. Richards-Kortum, “Light scattering from cells: finite-difference time-domain simulations and goniometric measurements,” Appl. Opt. 38, 3651–3661 (1999). [CrossRef]
  49. T. D. Visser, G. J. Brakenhoff, F. C. A. Groen, “The one-point fluorescence response in confocal microscopy,” Optik (Stuttgart) 87, 39–40 (1991).
  50. C. Tischer, European Molecular Biology Laboratory, Meyerhofstrasse 1, Heidelberg D-69117, Germany (personal communication, 2000).
  51. F. Reif, Fundamentals of Statistical and Thermal Physics (McGraw-Hill, Auckland, New Zealand, 1985), pp.560–565.
  52. A. Rohrbach, H. K. Stelzer, “Three-dimensional position detection of optically trapped dielectric particles,” J. Appl. Phys. 91, 5474–5488 (2002). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited