## Calculation of the radiation trapping force for laser tweezers by use of generalized Lorenz-Mie theory. I. Localized model description of an on-axis tightly focused laser beam with spherical aberration

Applied Optics, Vol. 43, Issue 12, pp. 2532-2544 (2004)

http://dx.doi.org/10.1364/AO.43.002532

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### Abstract

Calculation of the radiation trapping force in laser tweezers by use of generalized Lorenz-Mie theory requires knowledge of the shape coefficients of the incident laser beam. The localized version of these coefficients has been developed and justified only for a moderately focused Gaussian beam polarized in the *x* direction and traveling in the positive *z* direction. Here the localized model is extended to a beam tightly focused and truncated by a high-numerical-aperture lens, aberrated by its transmission through the wall of the sample cell, and incident upon a spherical particle whose center is on the beam axis. We also consider polarization of the beam in the *y* direction and propagation in the negative *z* direction to be able to describe circularly polarized beams and reflected beams.

© 2004 Optical Society of America

**OCIS Codes**

(140.7010) Lasers and laser optics : Laser trapping

(290.4020) Scattering : Mie theory

**History**

Original Manuscript: August 4, 2003

Revised Manuscript: January 26, 2004

Published: April 20, 2004

**Citation**

James A. Lock, "Calculation of the radiation trapping force for laser tweezers by use of generalized Lorenz-Mie theory. I. Localized model description of an on-axis tightly focused laser beam with spherical aberration," Appl. Opt. **43**, 2532-2544 (2004)

http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-43-12-2532

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### References

- 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]
- R. C. Gauthier, “Theoretical investigation of the optical trapping force and torque on cylindrical micro-objects,” J. Opt. Soc. Am. B 14, 3323–3333 (1997). [CrossRef]
- 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]
- 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]
- Y. Harada, T. Asakura, “Radiation forces on a dielectric sphere in the Rayleigh scattering regime,” Opt. Commun. 124, 529–541 (1996). [CrossRef]
- P. C. Chaumet, M. Nieto-Vesperinas, “Time-averaged total force on a polar sphere in an electromagnetic field,” Opt. Lett. 25, 1065–1067 (2000). [CrossRef]
- T. Tlusty, A. Meller, R. Bar-Ziv, “Optical gradient forces of strongly localized fields,” Phys. Rev. Lett. 81, 1738–1741 (1998). [CrossRef]
- 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]
- A. Rohrbach, E. H. K. Stelzer, “Optical trapping of dielectric particles in arbitrary fields,” J. Opt. Soc. Am. A 18, 839–853 (2001). [CrossRef]
- A. Rohrbach, E. 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). [CrossRef] [PubMed]
- 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]
- 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]
- S. Nemoto, H. Togo, “Axial force acting on a dielectric sphere in a focused laser beam,” Appl. Opt. 37, 6386–6394 (1998). [CrossRef]
- M. Gu, P. C. Ke, X. S. Gan, “Trapping force by a high numerical-aperture microscope objective obeying the sine condition,” Rev. Sci. Instrum. 68, 3666–3668 (1997). [CrossRef]
- T. Wohland, A. Rosin, E. H. K. Stelzer, “Theoretical determination of the influence of polarization on forces exerted by optical tweezers,” Optik (Stuttgart) 102, 181–190 (1996).
- 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]
- 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]
- 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]
- J. P. Barton, D. R. Alexander, S. A. Schaub, “Internal and near-surface electromagnetic fields for a spherical particle irradiated by a focused laser beam,” J. Appl. Phys. 64, 1632–1639 (1988). [CrossRef]
- J. A. Lock, “Contribution of high-order rainbows to the scattering of a Gaussian laser beam by a spherical particle,” J. Opt. Soc. Am. A 10, 693–706 (1993). [CrossRef]
- B. Maheu, G. Grehan, G. Gouesbet, “Ray localization in Gaussian beams,” Opt. Commun. 70, 259–262 (1989). [CrossRef]
- H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981), pp. 208–209.
- G. Gouesbet, G. Grehan, B. Maheu, “Localized interpretation to compute all the coefficients gnm in the generalized Lorenz-Mie theory,” J. Opt. Soc. Am. A 7, 998–1007 (1990). [CrossRef]
- J. A. Lock, “Improved Gaussian beam scattering algorithm,” Appl. Opt. 34, 559–570 (1995). [CrossRef] [PubMed]
- B. Maheu, G. Grehan, G. Gouesbet, “Generalized Lorenz-Mie theory: first exact values and comparisons with the localized approximation,” Appl. Opt. 26, 23–25 (1987). [CrossRef] [PubMed]
- G. Grehan, B. Maheu, G. Gouesbet, “Scattering of laser beams from Mie scatter centers: numerical results using a localized approximation,” Appl. Opt. 25, 3539–3548 (1986). [CrossRef] [PubMed]
- J. A. Lock, G. Gouesbet, “Rigorous justification of the localized approximation to the beam-shape coefficients in generalized Lorenz-Mie theory. I. On-axis beams,” J. Opt. Soc. Am. A 11, 2503–2515 (1994). [CrossRef]
- G. Gouesbet, J. A. Lock, “Rigorous justification of the localized approximation to the beam-shape coefficients in generalized Lorenz-Mie theory. II. Off-axis beams,” J. Opt. Soc. Am. A 11, 2516–2525 (1994). [CrossRef]
- K. F. Ren, G. Grehan, G. Gouesbet, “Radiation pressure forces exerted on a particle arbitrarily located in a Gaussian beam using the generalized Lorenz-Mie theory, and associated resonance effects,” Opt. Commun. 108, 343–354 (1994). [CrossRef]
- G. Martinot-Lagarde, B. Pouligny, M. I. Angelova, G. Grehan, G. Gouesbet, “Trapping and levitation of a dielectric sphere with off-centered Gaussian beams. II. GLMT analysis,” Pure Appl. Opt. 4, 571–585 (1995). [CrossRef]
- K. F. Ren, G. Grehan, G. Gouesbet, “Prediction of reverse radiation pressure by generalized Lorenz-Mie theory,” Appl. Opt. 35, 2702–2710 (1996). [CrossRef] [PubMed]
- H. Polaert, G. Grehan, G. Gouesbet, “Improved standard beams with application to reverse radiation pressure,” Appl. Opt. 37, 2435–2440 (1998). [CrossRef]
- J. A. Lock, “Calculation of the radiation trapping force for laser tweezers by use of generalized Lorenz-Mie theory. II. On-axis trapping force,” Appl. Opt. 43, 2545–2554 (2004). [CrossRef] [PubMed]
- H. Felgner, O. Muller, M. Schliwa, “Calibration of light forces in optical tweezers,” Appl. Opt. 34, 977–982 (1995). [CrossRef] [PubMed]
- P. L. Marston, J. H. Crichton, “Radiation torque on a sphere caused by a circularly-polarized electromagnetic wave,” Phys. Rev. A 30, 2508–2516 (1984). [CrossRef]
- S. Chang, S. S. Lee, “Optical torque exerted on a homogeneous sphere levitated in the circularly polarized fundamental-mode laser beam,” J. Opt. Soc. Am. B 2, 1853–1860 (1985). [CrossRef]
- G. Arfken, Mathematical Methods for Physicists, 3rd ed. (Academic, New York, 1985), p. 668, Eqs. (12.81) and (12.81a) and footnote 2.
- 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]
- G. Gouesbet, “Partial-wave expansions and properties of axisymmetric beams,” Appl. Opt. 35, 1543–1555 (1996). [CrossRef] [PubMed]
- S. A. Schaub, J. P. Barton, D. R. Alexander, “Simplified scattering coefficient expressions for a spherical particle located on the propagation axis of a fifth-order Gaussian beam,” Appl. Phys. Lett. 55, 2709–2711 (1989). [CrossRef]
- L. W. Davis, “Theory of electromagnetic beams,” Phys. Rev. A 19, 1177–1179 (1979). [CrossRef]
- J. P. Barton, D. R. Alexander, “Fifth-order corrected electromagnetic field components for a fundamental Gaussian beam,” J. Appl. Phys. 66, 2800–2802 (1989). [CrossRef]
- E. Wolf, “Electromagnetic diffraction in optical systems. I. An integral representation of the image field,” Proc. R. Soc. London Ser. A 253, 349–357 (1959). [CrossRef]
- R. Richards, E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system,” Proc. R. Soc. London Ser. A 253, 358–379 (1959). [CrossRef]
- P. Torok, 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]
- P. Torok, 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 (errata),” J. Opt. Soc. Am. A 12, 1605 (1995). [CrossRef]
- P. Torok, P. Varga, G. R. Booker, “Electromagnetic diffraction of light focused through a planar interface between materials of mismatched refractive indices: structure of the electromagnetic field. I,” J. Opt. Soc. Am. A 12, 2136–2144 (1995). [CrossRef]
- I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, New York, 1965), p. 634, Eq. (5.52.1).
- Ref. 48, p. 692, Eq. (6.574.2).

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