Abstract

The use of the generalized Lorenz–Mie theory (GLMT) requires knowledge of beam-shape coefficients (BSC’s) that describe the beam illuminating a spherical scatterer. We theoretically demonstrated that these BSC’s can be determined from an actual beam in the laboratory. We demonstrate the effectiveness of our theoretical proposal by determining BSC’s for a He–Ne laser beam focused to a diameter of a few micrometers. Once these BSC’s are determined, the electromagnetic fields of the illuminating beam may be evaluated. By relying on the GLMT, we can also determine all properties of the interaction between beam and scatterer, including mechanical effects (radiation pressures and torques).

© 2001 Optical Society of America

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References

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  1. G. Gouesbet, G. Gréhan, “Generalized Lorenz–Mie theories, from past to future,” Atomization Sprays 10, 277–333 (2000).
  2. K. F. Ren, G. Gouesbet, G. Gréhan, “Integral localized approximation in generalized Lorenz–Mie theory,” Appl. Opt. 37, 4218–4225 (1998).
    [CrossRef]
  3. K. F. Ren, G. Gréhan, G. Gouesbet, “Prediction of reverse radiation pressure by generalized Lorenz–Mie theory,” Appl. Opt. 35, 2702–2710 (1996).
    [CrossRef] [PubMed]
  4. J. T. Hodges, G. Gréhan, G. Gouesbet, C. Presser, “Forward scattering of a Gaussian beam by a nonabsorbing sphere,” Appl. Opt. 34, 2120–2132 (1995).
    [CrossRef] [PubMed]
  5. J. A. Lock, J. T. Hodges, “Far-field scattering of an axisymmetric laser beam of arbitrary profile by an on-axis spherical particle,” Appl. Opt. 35, 4283–4290 (1996).
    [CrossRef] [PubMed]
  6. J. A. Lock, J. T. Hodges, “Far-field scattering of non-Gaussian off-axis axisymmetric laser beam by a spherical particle,” Appl. Opt. 35, 6605–6616 (1996).
    [CrossRef] [PubMed]
  7. G. Gouesbet, “On measurements of beam shape coefficients in generalized Lorenz–Mie theory and the density-matrix approach. I. Measurements,” Part. Part. Syst. Charact. 14, 12–20 (1997).
  8. G. Gouesbet, “On measurements of beam shape coefficients in generalized Lorenz–Mie theory and the density-matrix approach. II. The density-matrix approach,” Part. Part. Syst. Charact. 14, 88–92 (1997).
  9. H. Polaert, G. Gouesbet, G. Gréhan, “Measurement of beam-shape coefficients in the generalized Lorenz–Mie theory for the on-axis case,” Appl. Opt. 37, 5005–5013 (1998).
    [CrossRef]
  10. L. W. Davis, “Theory of electromagnetic beams,” Phys. Rev. A 19, 1177–1179 (1979).
    [CrossRef]
  11. G. Gouesbet, G. Gréhan, B. Maheu, “Computations of the coefficients gn in the generalized Lorenz–Mie theory using three different methods,” Appl. Opt. 27, 4874–4883 (1988).
    [CrossRef] [PubMed]
  12. G. Gouesbet, “Validity of the localized approximation for arbitrary shaped beams in generalized Lorenz–Mie theory for spheres,” J. Opt. Soc. Am. A 16, 1641–1650 (1999).
    [CrossRef]

2000 (1)

G. Gouesbet, G. Gréhan, “Generalized Lorenz–Mie theories, from past to future,” Atomization Sprays 10, 277–333 (2000).

1999 (1)

1998 (2)

1997 (2)

G. Gouesbet, “On measurements of beam shape coefficients in generalized Lorenz–Mie theory and the density-matrix approach. I. Measurements,” Part. Part. Syst. Charact. 14, 12–20 (1997).

G. Gouesbet, “On measurements of beam shape coefficients in generalized Lorenz–Mie theory and the density-matrix approach. II. The density-matrix approach,” Part. Part. Syst. Charact. 14, 88–92 (1997).

1996 (3)

1995 (1)

1988 (1)

1979 (1)

L. W. Davis, “Theory of electromagnetic beams,” Phys. Rev. A 19, 1177–1179 (1979).
[CrossRef]

Davis, L. W.

L. W. Davis, “Theory of electromagnetic beams,” Phys. Rev. A 19, 1177–1179 (1979).
[CrossRef]

Gouesbet, G.

G. Gouesbet, G. Gréhan, “Generalized Lorenz–Mie theories, from past to future,” Atomization Sprays 10, 277–333 (2000).

G. Gouesbet, “Validity of the localized approximation for arbitrary shaped beams in generalized Lorenz–Mie theory for spheres,” J. Opt. Soc. Am. A 16, 1641–1650 (1999).
[CrossRef]

H. Polaert, G. Gouesbet, G. Gréhan, “Measurement of beam-shape coefficients in the generalized Lorenz–Mie theory for the on-axis case,” Appl. Opt. 37, 5005–5013 (1998).
[CrossRef]

K. F. Ren, G. Gouesbet, G. Gréhan, “Integral localized approximation in generalized Lorenz–Mie theory,” Appl. Opt. 37, 4218–4225 (1998).
[CrossRef]

G. Gouesbet, “On measurements of beam shape coefficients in generalized Lorenz–Mie theory and the density-matrix approach. I. Measurements,” Part. Part. Syst. Charact. 14, 12–20 (1997).

G. Gouesbet, “On measurements of beam shape coefficients in generalized Lorenz–Mie theory and the density-matrix approach. II. The density-matrix approach,” Part. Part. Syst. Charact. 14, 88–92 (1997).

K. F. Ren, G. Gréhan, G. Gouesbet, “Prediction of reverse radiation pressure by generalized Lorenz–Mie theory,” Appl. Opt. 35, 2702–2710 (1996).
[CrossRef] [PubMed]

J. T. Hodges, G. Gréhan, G. Gouesbet, C. Presser, “Forward scattering of a Gaussian beam by a nonabsorbing sphere,” Appl. Opt. 34, 2120–2132 (1995).
[CrossRef] [PubMed]

G. Gouesbet, G. Gréhan, B. Maheu, “Computations of the coefficients gn in the generalized Lorenz–Mie theory using three different methods,” Appl. Opt. 27, 4874–4883 (1988).
[CrossRef] [PubMed]

Gréhan, G.

Hodges, J. T.

Lock, J. A.

Maheu, B.

Polaert, H.

Presser, C.

Ren, K. F.

Appl. Opt. (7)

Atomization Sprays (1)

G. Gouesbet, G. Gréhan, “Generalized Lorenz–Mie theories, from past to future,” Atomization Sprays 10, 277–333 (2000).

J. Opt. Soc. Am. A (1)

Part. Part. Syst. Charact. (2)

G. Gouesbet, “On measurements of beam shape coefficients in generalized Lorenz–Mie theory and the density-matrix approach. I. Measurements,” Part. Part. Syst. Charact. 14, 12–20 (1997).

G. Gouesbet, “On measurements of beam shape coefficients in generalized Lorenz–Mie theory and the density-matrix approach. II. The density-matrix approach,” Part. Part. Syst. Charact. 14, 88–92 (1997).

Phys. Rev. A (1)

L. W. Davis, “Theory of electromagnetic beams,” Phys. Rev. A 19, 1177–1179 (1979).
[CrossRef]

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Figures (13)

Fig. 1
Fig. 1

Geometrical configuration under study.

Fig. 2
Fig. 2

Fiber with a diameter equal to 0.1 µm. (a) Comparison between the measured longitudinal profile and the inverted longitudinal profile. (b) Comparison between the BSC’s extracted from the measurements and the theoretical values. (c) Comparison between the transverse intensity for the theoretical beam (Davis), the measured profile, and the inverted profile for z = 0. (d) Comparison between the transverse intensity for the theoretical beam (Davis), the measured profile, and the inverted profile for z = l 2.

Fig. 3
Fig. 3

Fiber with a diameter equal to 2 µm. (a) Comparison between the measured longitudinal profile and the inverted longitudinal profile. (b) Comparison between the BSC’s extracted from the measurements and the theoretical values. (c) Comparison between the transverse intensity for the theoretical beam (Davis), the measured profile, and the inverted profile for z = 0. (d) Comparison between the transverse intensity for the theoretical beam (Davis), the measured profile, and the inverted profile for z = l 2.

Fig. 4
Fig. 4

Fiber with a diameter equal to 4 µm. (a) Comparison between the measured longitudinal profile and the inverted longitudinal profile. (b) Comparison between the BSC’s extracted from the measurements and the theoretical values. (c) Comparison between the transverse intensity for the theoretical beam (Davis), the measured profile, and the inverted profile for z = 0. (d) Comparison between the transverse intensity for the theoretical beam (Davis), the measured profile, and the inverted profile for z = l 2.

Fig. 5
Fig. 5

Fiber with a diameter equal to 6 µm. (a) Comparison between the measured longitudinal profile and the inverted longitudinal profile. (b) Comparison between the BSC’s extracted from the measurements and the theoretical values. (c) Comparison between the transverse intensity for the theoretical beam (Davis), the measured profile, and the inverted profile for z = 0. (d) Comparison between the transverse intensity for the theoretical beam (Davis), the measured profile, and the inverted profile for z = l 2.

Fig. 6
Fig. 6

Measured longitudinal profile.

Fig. 7
Fig. 7

Transverse (x and y) locations of the fiber at the maximum of intensity versus the longitudinal fiber location z.

Fig. 8
Fig. 8

Comparison between the measured longitudinal data and the best fit for a Kogelnik beam.

Fig. 9
Fig. 9

Comparison between the measured longitudinal profile and the reconstructed longitudinal profile (one reconstruction origin point). Curve, experimental profile; pluses, reconstructed profile.

Fig. 10
Fig. 10

Comparison between the measured longitudinal profile and the reconstructed longitudinal profile (eight reconstruction origin points). Circles, measured; dotted curve, reconstructed; dashed curve, Gaussian.

Fig. 11
Fig. 11

Comparison between extracted BSC’s and filtered BSC’s: (a) Real part versus n. (b) Imaginary part versus n. Gray curve, reconstructed; dotted–dashed curve, measured.

Fig. 12
Fig. 12

Comparison between the measured longitudinal profile and the reconstructed longitudinal profile for one reconstruction origin point but with filtered BSC’s.

Fig. 13
Fig. 13

Comparison between the measured map and the reconstructed intensity map.

Equations (5)

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

Sz= Ren=1m=1 anmgngm*,
anm=1k2r2im-nn+12m+12n+m+1Dnm1+in+mDnm2,
Dnm1=drΨn1krdrdrΨm1krdr+k2r2Ψn1krΨm1kr,
Dnm2=krdrΨn1krdr Ψm1kr-drΨm1krdr Ψn1kr,
0μ0|E0|22=1,

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