Abstract

A method is presented for calculating and analyzing the angular distribution of fluorescent emission from randomly oriented anisotropic molecules embedded in small dielectric particles with the nonzero reorientation angle between absorption and emission moments suggested by physical considerations now taken into account. Calculations performed on the basis of this method are compared with some of the available experimental data for fluorescent dye molecules embedded in microspheres, and good quantitative agreement is found. It is shown how fitting the computed results to experimental data determines an effective reorientation angle between absorption and emission transition moments. A more definitive test to which the model could be subjected is described.

© 1983 Optical Society of America

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References

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  1. For a review, see P. J. McNulty, H. W. Chew, M. Kerker, in Aerosol Microphysics I. Topics in Current Physics, W. Marlow, Ed. (Springer, Berlin, 1980), Chap. 4.
  2. D. S. Wang, H. Chew, M. Kerker, Appl. Opt. 19, 2256 (1980).
    [CrossRef] [PubMed]
  3. S. L. McCall, P. M. Platzman, P. A. Wolff, Phys. Lett. A 77, 381 (1980).
    [CrossRef]
  4. P. J. McNulty, S. D. Druger, M. Kerker, H. W. Chew, Appl. Opt. 18, 1484 (1979).
    [CrossRef] [PubMed]
  5. D. S. Wang, M. Kerker, H. W. Chew, Appl. Opt. 19, 2315 (1980); the specific use made of these results is summarized briefly in the paragraph beginning with the words, “An analysis…” on p. 2321.
    [CrossRef] [PubMed]
  6. H. W. Chew, P. J. McNulty, M. Kerker, Phys. Rev. A 13, 396 (1976).
    [CrossRef]
  7. H. W. Chew, M. Kerker, P. J. McNulty, J. Opt. Soc. Am. 66, 44 (1976).
  8. W. Heitler, The Quantum Theory of Radiation (Oxford U.P., London, 1954), Chap. 5.
  9. H. Goldstein, Classical Mechanics (Addison-Wesley, Reading, Mass., 1950), p. 109; or 2nd Ed. (1980), p. 147.
  10. D. S. Wang, M. Kerker, H. W. Chew, Appl. Opt. 19, 2315 (1980).
    [CrossRef] [PubMed]
  11. We have also been able to show formally that this procedure is implied by assuming Eq. (2) to hold for elliptical polarization, but the physical argument given in the text is entirely adequate and more direct.
  12. J. P. Kratohvil, M.-P. Lee, M. Kerker, Appl. Opt. 17, 1978 (1978).
    [CrossRef] [PubMed]
  13. M.-P. Lee, “The Preparation and Optical Properties of Fluorescent Polymer Colloids,” Ph.D. Thesis, Clarkson College of Technology, Potsdam, New York (1977).
  14. E.-H. Lee, R. E. Benner, J. B. Fenn, R. K. Chang, Appl. Opt. 17, 1980 (1978).
    [CrossRef]
  15. E.-H. Lee, “Elastic and Inelastic Light Scattering from Small Spherical Particles with Plane Wave and Evanescent Wave Excitation,” Ph.D. Thesis, Yale University (1978).

1980

1979

1978

1976

H. W. Chew, P. J. McNulty, M. Kerker, Phys. Rev. A 13, 396 (1976).
[CrossRef]

H. W. Chew, M. Kerker, P. J. McNulty, J. Opt. Soc. Am. 66, 44 (1976).

Benner, R. E.

Chang, R. K.

Chew, H.

Chew, H. W.

D. S. Wang, M. Kerker, H. W. Chew, Appl. Opt. 19, 2315 (1980); the specific use made of these results is summarized briefly in the paragraph beginning with the words, “An analysis…” on p. 2321.
[CrossRef] [PubMed]

D. S. Wang, M. Kerker, H. W. Chew, Appl. Opt. 19, 2315 (1980).
[CrossRef] [PubMed]

P. J. McNulty, S. D. Druger, M. Kerker, H. W. Chew, Appl. Opt. 18, 1484 (1979).
[CrossRef] [PubMed]

H. W. Chew, P. J. McNulty, M. Kerker, Phys. Rev. A 13, 396 (1976).
[CrossRef]

H. W. Chew, M. Kerker, P. J. McNulty, J. Opt. Soc. Am. 66, 44 (1976).

For a review, see P. J. McNulty, H. W. Chew, M. Kerker, in Aerosol Microphysics I. Topics in Current Physics, W. Marlow, Ed. (Springer, Berlin, 1980), Chap. 4.

Druger, S. D.

Fenn, J. B.

Goldstein, H.

H. Goldstein, Classical Mechanics (Addison-Wesley, Reading, Mass., 1950), p. 109; or 2nd Ed. (1980), p. 147.

Heitler, W.

W. Heitler, The Quantum Theory of Radiation (Oxford U.P., London, 1954), Chap. 5.

Kerker, M.

Kratohvil, J. P.

Lee, E.-H.

E.-H. Lee, R. E. Benner, J. B. Fenn, R. K. Chang, Appl. Opt. 17, 1980 (1978).
[CrossRef]

E.-H. Lee, “Elastic and Inelastic Light Scattering from Small Spherical Particles with Plane Wave and Evanescent Wave Excitation,” Ph.D. Thesis, Yale University (1978).

Lee, M.-P.

J. P. Kratohvil, M.-P. Lee, M. Kerker, Appl. Opt. 17, 1978 (1978).
[CrossRef] [PubMed]

M.-P. Lee, “The Preparation and Optical Properties of Fluorescent Polymer Colloids,” Ph.D. Thesis, Clarkson College of Technology, Potsdam, New York (1977).

McCall, S. L.

S. L. McCall, P. M. Platzman, P. A. Wolff, Phys. Lett. A 77, 381 (1980).
[CrossRef]

McNulty, P. J.

P. J. McNulty, S. D. Druger, M. Kerker, H. W. Chew, Appl. Opt. 18, 1484 (1979).
[CrossRef] [PubMed]

H. W. Chew, P. J. McNulty, M. Kerker, Phys. Rev. A 13, 396 (1976).
[CrossRef]

H. W. Chew, M. Kerker, P. J. McNulty, J. Opt. Soc. Am. 66, 44 (1976).

For a review, see P. J. McNulty, H. W. Chew, M. Kerker, in Aerosol Microphysics I. Topics in Current Physics, W. Marlow, Ed. (Springer, Berlin, 1980), Chap. 4.

Platzman, P. M.

S. L. McCall, P. M. Platzman, P. A. Wolff, Phys. Lett. A 77, 381 (1980).
[CrossRef]

Wang, D. S.

Wolff, P. A.

S. L. McCall, P. M. Platzman, P. A. Wolff, Phys. Lett. A 77, 381 (1980).
[CrossRef]

Appl. Opt.

J. Opt. Soc. Am.

H. W. Chew, M. Kerker, P. J. McNulty, J. Opt. Soc. Am. 66, 44 (1976).

Phys. Lett. A

S. L. McCall, P. M. Platzman, P. A. Wolff, Phys. Lett. A 77, 381 (1980).
[CrossRef]

Phys. Rev. A

H. W. Chew, P. J. McNulty, M. Kerker, Phys. Rev. A 13, 396 (1976).
[CrossRef]

Other

For a review, see P. J. McNulty, H. W. Chew, M. Kerker, in Aerosol Microphysics I. Topics in Current Physics, W. Marlow, Ed. (Springer, Berlin, 1980), Chap. 4.

W. Heitler, The Quantum Theory of Radiation (Oxford U.P., London, 1954), Chap. 5.

H. Goldstein, Classical Mechanics (Addison-Wesley, Reading, Mass., 1950), p. 109; or 2nd Ed. (1980), p. 147.

We have also been able to show formally that this procedure is implied by assuming Eq. (2) to hold for elliptical polarization, but the physical argument given in the text is entirely adequate and more direct.

M.-P. Lee, “The Preparation and Optical Properties of Fluorescent Polymer Colloids,” Ph.D. Thesis, Clarkson College of Technology, Potsdam, New York (1977).

E.-H. Lee, “Elastic and Inelastic Light Scattering from Small Spherical Particles with Plane Wave and Evanescent Wave Excitation,” Ph.D. Thesis, Yale University (1978).

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Figures (6)

Fig. 1
Fig. 1

Coordinate systems used in describing the fluorescent emission from randomly oriented molecules for the (unrealistic) case of a linearly polarized driving field E0. The (xyz′) axes are fixed in the molecule with the z′ direction chosen parallel to pe, while the (x,y,z) axes are chosen at each molecular site so as to have the z axis parallel to E0.

Fig. 2
Fig. 2

Calculated parallel moment and perpendicular moment angular distribution for fluorescent emission from randomly oriented molecules embedded uniformly throughout a dielectric sphere (based on parameters applicable to the data of Kratohvil et al., Table XXIII of Ref. 13).

Fig. 3
Fig. 3

Fit between theory and experiment for the data of Kratohvil et al. (See Table I.)

Fig. 4
Fig. 4

Fit between theory and experiment for the data of Lee, Benner, Fenn, and Chang obtained for 0.806-μm diam particles. (See Table I.)

Fig. 5
Fig. 5

Fit between theory and experiment for the data of Lee, Benner, Fenn, and Chang obtained for 0.460-μm diam particles. (See Table I.)

Fig. 6
Fig. 6

Dependence of the fluorescent angular distribution on the reorientation angle Ө for Hh polarization.

Tables (1)

Tables Icon

Table I Summary of Results for the Fit to Experimental Data

Equations (28)

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[ E 0 ] = [ A ] [ E 0 ] ,
p e = α n e ( n a · E 0 ) ,
n e = ( sin Ө , 0 , cos Ө ) .
[ p e ] = { α [ n a ] T [ A ] [ E 0 ] } { [ A ] T [ n e ] } .
{ } = α E 0 cos θ .
p e = ( α E 0 ) [ m (par)cosӨ + m (per)sinӨ ] = p (par)cosӨ + p (per)sinӨ ,
[ m (par) ] = ( sin θ cos θ sin ϕ sin θ cos θ cos ϕ cos 2 θ ) ,
[ m ( per ) ] = ( cos θ cos ψ cos ϕ cos 2 θ sin ϕ sin ψ cos θ cos ψ sin ϕ + cos 2 θ cos ϕ sin ψ sin θ cos θ sin ψ ) .
E ξ ( scatt ) = η F ξ η p e , η ,
I = | ˆ · E ( scatt ) | 2 = | η ξ ˆ ξ F ξ η p e , η | 2 .
I avg = | η ( ξ ˆ ξ F ξ η ) p η ( par ) | 2 cos 2 Ө + | η ( ξ ˆ ξ F ξ η ) p η ( per ) | 2 sin 2 Ө + ( cross term ) × sin Ө cos Ө ,
I avg = ( cos 2 Ө ) I par + ( sin 2 Ө ) I per ,
I par = η ( | ξ ˆ ξ F ξ η | 2 ) [ p η ( par ) ] 2 ,
cos 2 θ = 1 3 , sin 2 θ = 2 3 , cos 4 θ = 1 5 , sin 2 ϕ = cos 2 ϕ = sin 2 ψ = cos 2 ψ = 1 2 , sin 2 θ cos 2 θ = 2 15 ,
I par = 1 15 [ 3 I z + ( I x + I y ) ] ,
I per = 1 15 [ I z + 2 ( I x + I y ) ] ,
I η = ( α E 0 ) 2 | ξ ˆ ξ F ξ η | 2
I z = ( α E 0 ) 2 | ξ ˆ ξ F ξ z | 2
1 2 ( | E 1 · n α | 2 + | E 2 · n α | 2 ) ,
I = { I par cos 2 Ө } avg + { I par sin 2 Ө } avg ,
I = { cos 2 Ө } avg I par + { sin 2 Ө } avg I per .
{ cos 2 Ө } avg = 1 3 , { sin 2 Ө } avg = 2 3 ,
I ROUE = 1 3 I par + 2 3 I per = 1 3 ( I x + I y + I z ) ,
I par = 1 15 ( 1 + 2 cos 2 θ s )
I per = 1 15 ( 2 cos 2 θ s )
L = j = 1 2 { i = 1 N [ I exp ( j ) ( θ s , i ) λ 1 I par ( j ) ( θ s , i ) λ 2 I per ( j ) ( θ s , i ) ] 2 } ,
cos 2 Ө = λ 1 / ( λ 1 + λ 2 ) ,
I z = 1 2 ( I x + I y )

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