Abstract

When molecules which give rise to Raman and fluorescent light scattering are distributed within small dielectric particles, the signal is affected by the morphology and optical properties of the particle, and the distribution of molecules of interest within it. These effects are manifested by changes in the magnitude, in the angular distribution, and in the polarization of the scattered radiation. Furthermore, because the effects vary with the wavelengths of both the exciting and the emitted radiation, the emission spectrum for fluorescence may vary with the exciting wavelength, the morphology and optical properties of the particle, the distribution of the active molecules within the particle, and even the angle of observation. These phenomena must be considered in quantitative procedures for utilizing Raman and fluorescent scattering for determining the concentration of specific molecules in small particles such as aerosols or biological cells. The effects are illustrated here by a series of numerical calculations involving inelastic noncoherent scattering by molecules variously embedded in dielectric spheres.

© 1978 Optical Society of America

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Corrections

M. Kerker, P. J. McNulty, M. Sculley, H. Chew, and D. D. Cooke, "Errata," J. Opt. Soc. Am. 69, 1049-1049 (1979)
https://www.osapublishing.org/josa/abstract.cfm?uri=josa-69-7-1049

References

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  1. See, e.g., J. Histochem. Cytochem. 25, No. 7 (1977) in which issue, comprised of the Fifth Automated Cytology meeting, there are no fewer than 26 papers which utilize fluorescent signals for a variety of cytological studies including the estimation of the distribution of cells among the phases of the mitotic cycle.
  2. For recent efforts to develop Raman scattering for chemical analysis of aerosol particles, see G. J. Rosasco, E. S. Etz, and W. A. Cassatt, Appl. Spectrosc. 29, 396 (1975); M. Delhaye and P. Dhamelincourt, J. Raman Spectrosc. 3, 33(1975); J. Gelbwachs and M. Birnbaum, Appl. Opt. 12, 2442(1973); S. H. Melfi, J. D. Lawrence, and M. P. McCormack, Appl. Phys. Lett. 15, 295(1969); J. Cooney, J. Orr, and C. Tamasetti, Nature 224, 1098(1969).
    [Crossref] [PubMed]
  3. M. Kerker and D. D. Cooke, Appl. Opt. 12, 1378 (1973); P. W. Dusel, M. Kerker, and D. D. Cooke, J. Opt. Soc. Am. (to be published).
    [Crossref] [PubMed]
  4. H. Chew, P. J. McNulty, and M. Kerker, Phys. Rev. A 13, 396(1976).
    [Crossref]
  5. H. Chew, M. Kerker, and P. J. McNulty, J. Opt. Soc. Am. 66, 440 (1976).
    [Crossref]
  6. M. Kerker, Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969).

1977 (1)

See, e.g., J. Histochem. Cytochem. 25, No. 7 (1977) in which issue, comprised of the Fifth Automated Cytology meeting, there are no fewer than 26 papers which utilize fluorescent signals for a variety of cytological studies including the estimation of the distribution of cells among the phases of the mitotic cycle.

1976 (2)

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

H. Chew, M. Kerker, and P. J. McNulty, J. Opt. Soc. Am. 66, 440 (1976).
[Crossref]

1975 (1)

1973 (1)

Cassatt, W. A.

Chew, H.

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

H. Chew, M. Kerker, and P. J. McNulty, J. Opt. Soc. Am. 66, 440 (1976).
[Crossref]

Cooke, D. D.

Etz, E. S.

Kerker, M.

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

H. Chew, M. Kerker, and P. J. McNulty, J. Opt. Soc. Am. 66, 440 (1976).
[Crossref]

M. Kerker and D. D. Cooke, Appl. Opt. 12, 1378 (1973); P. W. Dusel, M. Kerker, and D. D. Cooke, J. Opt. Soc. Am. (to be published).
[Crossref] [PubMed]

M. Kerker, Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969).

McNulty, P. J.

H. Chew, M. Kerker, and P. J. McNulty, J. Opt. Soc. Am. 66, 440 (1976).
[Crossref]

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

Rosasco, G. J.

Appl. Opt. (1)

Appl. Spectrosc. (1)

J. Histochem. Cytochem. (1)

See, e.g., J. Histochem. Cytochem. 25, No. 7 (1977) in which issue, comprised of the Fifth Automated Cytology meeting, there are no fewer than 26 papers which utilize fluorescent signals for a variety of cytological studies including the estimation of the distribution of cells among the phases of the mitotic cycle.

J. Opt. Soc. Am. (1)

Phys. Rev. A (1)

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

Other (1)

M. Kerker, Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969).

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Figures (19)

FIG. 1
FIG. 1

Coordinate system with particle of radius a at center.

FIG. 2
FIG. 2

Inelastically scattered irradiances Iv and Ih for active molecule at x = 0.01a, y = z = 0 (dashed curves), and x = 0.7a, y = z = 0; α = 5, n1 = 1.5, λ = 1.5λ0.

FIG. 3
FIG. 3

Same as Fig. 2 for y = 0.01a, x = y = 0 (dashed curves), and y = 0.7a, x = z = 0.

FIG. 4
FIG. 4

Same as Fig. 2 for z = 0.01z, x = y = 0 (dashed curves), and z = 0.7a, x = y = 0.

FIG. 5
FIG. 5

Same as Fig. 2 for r = 0.25a, θ = 105°, ϕ = 66° (dashed curves), and r = 0.55a, θ = 195°, ϕ = 126°.

FIG. 6
FIG. 6

Inelastically scattered intensity Ih at scattering angle 180° as a function of position of active molecule along the z axis; α = 5, n1 = 1.5, λ = 1.5 λ0. Also plotted is the power associated with internal field at the exciting wavelength at each site (dotted curve) and Ih when the internal field is replaced by unperturbed incident field (dashed curve).

FIG. 7
FIG. 7

Inelastically scattered intensity Ih at scattering angles 180° and 30° as a function of position of active molecule along the x axis; α = 5, n1 = 1.5, λ = 1.5 λ0. Also plotted is power associated with the internal field at λ0 at each site (dotted curve).

FIG. 8
FIG. 8

Inelastically scattered intensity Ih for two active molecules separating along the y axis; α = 50, n1 = 1.05, λ = 1.5 λ0. Distances from the origin: (1) 0.05 a; (2) 0.20 a; (3) 0.65a, (4) 0.70a.

FIG. 9
FIG. 9

Same as Fig. 8 except Iv.

FIG. 10
FIG. 10

Inelastically scattered intensity Ih at scattering angle 30° for two active molecules separating along the z axis (case I) and x axis (case 2, scale multiplied by 10−2) as a function of distances from the origin; α = 50, n = 1.05, λ = 1.5 λ0. Dashed curves represents power associated with exciting field at each pair of sites.

FIG. 11
FIG. 11

Inelastically scattered intensities Ih and Iv for arrays of active molecules uniformly distributed over spherical surfaces at radial distances a, 0. 166a (dashed curves), 0.5a (dotted curves), and for a molecule at the origin (dashed-dotted curves); α = 5, n1 = 1.5, λ = 1.5 λ0.

FIGURE 12
FIGURE 12

Inelastically scattered intensity Ih at scattering angles 0°, 30°, 90°, and 180° as a function of radial distance of the array of active molecules uniformly distributed over a spherical surface. α = 5, n = 1.5, λ = 1.5 λ0. Dashed curve represents power associated with exciting field over the spherical surfaces.

FIG. 13
FIG. 13

Inelastically scattered intensity Ih and Iv for spheres uniformly filled with active molecules α = 5, α = 3 (dotted curves), α = 1 (dashed curves); n = 1.5, λ = 1.5 λ0.

FIG. 14
FIG. 14

Inelastically scattered intensities Ih and Iv for sphere with active molecules uniformly distributed within a core with radius 0.2a, and with this core into 38 (dashed curves) and 126 (dotted curves) small grains uniformly dispersed through the particles; α = 5, n1 = 1.5, λ = 1.5 λ0.

FIG. 15
FIG. 15

Inelastically scattered intensities Ih and Iv for sphere with active molecules uniformly distributed within a core with radius 0.4a and with this core deformed into equivolume prolate spheroids with figure axis on the z axis equal to 0.7a (dashed curve) and a (dotted curve); α = 5, n1 = 1.5, λ = 1.5 λ0.

FIG. 16
FIG. 16

Correction factor for Ih at scattering angle θ = 0° for uniform distribution of active molecules; α = 1, λ0 = 300 nm; α = 3, λ0 = 300 nm; α = 5, λ0 = 300 nm; α = 6, λ0 = 300 nm; α = 3, λ0 = 250 nm; also n1 = 1.50.

FIG. 17
FIG. 17

Correction factor for Ih for uniform distribution of active molecules at scattering angles θ = 30°, 50°, and 180° for α = 5, n1 = 1.5, λ0 = 300 nm.

FIG. 18
FIG. 18

Correction factor for Ih at scattering angle θ = 0° for a single active molecule located at (a) x = y = z = 0; (b) x = 0.5a, y = z = 0; (c) y = 0.5a, x = z = 0; (d) z = 0.5a, x = y = 0, α = 5, n = 1.5, λ0 = 300nm; (e) is the same as (c) except θ = 90°; α = 5, n1 = 1.50, λ0 = 300 nm.

FIG. 19
FIG. 19

Fraction depolarized, Vh/Ih, for arrays of active molecules uniformly distributed over spherical surfaces at radial distances (a) 0.166a, (b) 0.333a, (c) 0.5a, (d) a, and (e) for a uniform distribution of active molecules; α = 5.0, n1 = 1.5, λ = 1.5 λ0.

Equations (8)

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E 2 ( r ) = l , m { ( i c / n 2 2 ω ) C E ( l , m ) × [ h l ( 1 ) ( k 2 r ) Y l l m ( r ˆ ) + C M ( l , m ) h l ( 1 ) ( k 2 r ) Y l l m ( r ˆ ) ] }
B 2 ( r ) = l , m { C E ( l , m ) h l ( 1 ) ( k 2 r ) Y l l m ( r ˆ ) - ( i c / ω ) C M ( l , m ) × [ h l ( 1 ) ( k 2 r ) Y l l m ( r ˆ ) ] } .
B 2 ( r ) = e i k 2 r k 2 r l , m ( - i ) l + 1 { C E ( l , m ) Y l l m ( r ˆ ) + n 2 C M ( l , m ) r ˆ × Y l l m ( r ˆ ) }
E 2 ( r ) = ( 1 / n 2 ) B 2 ( r ) × r ˆ ,
( d P ( r ) d r ) j = c r 2 8 π n 2 2 B 2 j ( r ) 2 .
d P ( r ) d r = j = 1 N ( d P ( r ) d r ) j .
d P ( r ) d r = c r 2 8 π n 2 2 | j = 1 N B 2 ( r ) | 2 .
l > 2 π a / λ = α ,