Abstract

Fluorescent and Raman scattering by molecules embedded in dielectric particles is strongly dependent on the morphology and optical properties of the particle, the distribution of active molecules within the particle, and, in the case of nonspherical particles, orientation. The model previously applied to spheres and cylinders is now extended to spheroids. The extended boundary condition method (EBCM) has been used to calculate the transmitted field at the incident frequency that stimulates the process. The equivalence principle underlying the EBCM has also been applied to calculate the fields at the shifted frequency. Numerical results are presented to illustrate some of the effects of refractive index, size, shape, and orientation of the particles for models representing two polarizabilities of active dipoles embedded inside the particles.

© 1980 Optical Society of America

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References

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  1. E. S. Etz, G. J. Rosasco, J. J. Blaha, in Environmental Pollutants, T. Toribara et al., Eds. (Plenum, New York, 1978), pp. 413ff.
  2. B. H. Mayall, B. L. Gledhill, Eds., J. Histochem. Cytochem. 27, 1 (1979).
    [CrossRef]
  3. J. A. Creighton, C. G. Blatchford, M. G. Albrecht, J. Chem. Soc. Faraday Trans. 75, 790 (1979).
    [CrossRef]
  4. H. Chew, P. J. McNulty, M. Kerker, Phys. Rev. A: 13, 396 (1976).
    [CrossRef]
  5. H. Chew, M. Kerker, P. J. McNulty, J. Opt. Soc. Am. 66, 440 (1976).
    [CrossRef]
  6. H. Chew, D. D. Cooke, M. Kerker, Appl. Opt. 19, 44 (1980).
    [CrossRef] [PubMed]
  7. M. Kerker, P. J. McNulty, M. Sculley, H. Chew, D. D. Cooke, J. Opt. Soc. Am. 68, 1676 (1978).
    [CrossRef]
  8. H. Chew, M. Sculley, M. Kerker, P. J. McNulty, D. D. Cooke, J. Opt. Soc. Am. 68, 1686 (1978).
    [CrossRef]
  9. M. Kerker, S. D. Druger, Appl. Opt. 18, 1180 (1979).
    [CrossRef] [PubMed]
  10. E.-H. Lee, R. E. Benner, J. B. Fenn, R. K. Chang, Appl. Opt. 17, 1980 (1978).
    [CrossRef]
  11. J. P. Kratohvil, M.-P. Lee, M. Kerker, Appl. Opt. 17, 1978 (1978).
    [CrossRef] [PubMed]
  12. P. J. McNulty, S. D. Druger, M. Kerker, H. W. Chew, Appl. Opt. 18, 1484 (1979).
    [CrossRef] [PubMed]
  13. M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969).
  14. S. Asano, G. Yamamoto, Appl. Opt. 14, 29 (1975).
    [PubMed]
  15. S. Asano, Appl. Opt. 18, 712 (1979).
    [CrossRef] [PubMed]
  16. P. C. Waterman, Proc. IEEE 53, 805 (1965).
    [CrossRef]
  17. P. C. Waterman, J. Appl. Phys. 50, 4550 (1979).
    [CrossRef]
  18. P. Barber, C. Yeh, Appl. Opt. 14, 2864 (1975).
    [CrossRef] [PubMed]
  19. D.-S. Wang, P. W. Barber, Appl. Opt. 18, 1190 (1979).
    [CrossRef] [PubMed]
  20. P. W. Barber, IEEE Trans. Microwave Theory Tech. MTT-25, 373 (1977).
    [CrossRef]
  21. S. A. Schelkunoff, Electromagnetic Waves (Van Nostrand, New York, 1943).

1980 (1)

1979 (7)

S. Asano, Appl. Opt. 18, 712 (1979).
[CrossRef] [PubMed]

M. Kerker, S. D. Druger, Appl. Opt. 18, 1180 (1979).
[CrossRef] [PubMed]

D.-S. Wang, P. W. Barber, Appl. Opt. 18, 1190 (1979).
[CrossRef] [PubMed]

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

B. H. Mayall, B. L. Gledhill, Eds., J. Histochem. Cytochem. 27, 1 (1979).
[CrossRef]

J. A. Creighton, C. G. Blatchford, M. G. Albrecht, J. Chem. Soc. Faraday Trans. 75, 790 (1979).
[CrossRef]

P. C. Waterman, J. Appl. Phys. 50, 4550 (1979).
[CrossRef]

1978 (4)

1977 (1)

P. W. Barber, IEEE Trans. Microwave Theory Tech. MTT-25, 373 (1977).
[CrossRef]

1976 (2)

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

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

1975 (2)

1965 (1)

P. C. Waterman, Proc. IEEE 53, 805 (1965).
[CrossRef]

Albrecht, M. G.

J. A. Creighton, C. G. Blatchford, M. G. Albrecht, J. Chem. Soc. Faraday Trans. 75, 790 (1979).
[CrossRef]

Asano, S.

Barber, P.

Barber, P. W.

D.-S. Wang, P. W. Barber, Appl. Opt. 18, 1190 (1979).
[CrossRef] [PubMed]

P. W. Barber, IEEE Trans. Microwave Theory Tech. MTT-25, 373 (1977).
[CrossRef]

Benner, R. E.

Blaha, J. J.

E. S. Etz, G. J. Rosasco, J. J. Blaha, in Environmental Pollutants, T. Toribara et al., Eds. (Plenum, New York, 1978), pp. 413ff.

Blatchford, C. G.

J. A. Creighton, C. G. Blatchford, M. G. Albrecht, J. Chem. Soc. Faraday Trans. 75, 790 (1979).
[CrossRef]

Chang, R. K.

Chew, H.

Chew, H. W.

Cooke, D. D.

Creighton, J. A.

J. A. Creighton, C. G. Blatchford, M. G. Albrecht, J. Chem. Soc. Faraday Trans. 75, 790 (1979).
[CrossRef]

Druger, S. D.

Etz, E. S.

E. S. Etz, G. J. Rosasco, J. J. Blaha, in Environmental Pollutants, T. Toribara et al., Eds. (Plenum, New York, 1978), pp. 413ff.

Fenn, J. B.

Kerker, M.

Kratohvil, J. P.

Lee, E.-H.

Lee, M.-P.

McNulty, P. J.

Rosasco, G. J.

E. S. Etz, G. J. Rosasco, J. J. Blaha, in Environmental Pollutants, T. Toribara et al., Eds. (Plenum, New York, 1978), pp. 413ff.

Schelkunoff, S. A.

S. A. Schelkunoff, Electromagnetic Waves (Van Nostrand, New York, 1943).

Sculley, M.

Wang, D.-S.

Waterman, P. C.

P. C. Waterman, J. Appl. Phys. 50, 4550 (1979).
[CrossRef]

P. C. Waterman, Proc. IEEE 53, 805 (1965).
[CrossRef]

Yamamoto, G.

Yeh, C.

Appl. Opt. (9)

IEEE Trans. Microwave Theory Tech. (1)

P. W. Barber, IEEE Trans. Microwave Theory Tech. MTT-25, 373 (1977).
[CrossRef]

J. Appl. Phys. (1)

P. C. Waterman, J. Appl. Phys. 50, 4550 (1979).
[CrossRef]

J. Chem. Soc. Faraday Trans. (1)

J. A. Creighton, C. G. Blatchford, M. G. Albrecht, J. Chem. Soc. Faraday Trans. 75, 790 (1979).
[CrossRef]

J. Histochem. Cytochem. (1)

B. H. Mayall, B. L. Gledhill, Eds., J. Histochem. Cytochem. 27, 1 (1979).
[CrossRef]

J. Opt. Soc. Am. (3)

Phys. Rev. A: (1)

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

Proc. IEEE (1)

P. C. Waterman, Proc. IEEE 53, 805 (1965).
[CrossRef]

Other (3)

S. A. Schelkunoff, Electromagnetic Waves (Van Nostrand, New York, 1943).

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

E. S. Etz, G. J. Rosasco, J. J. Blaha, in Environmental Pollutants, T. Toribara et al., Eds. (Plenum, New York, 1978), pp. 413ff.

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Figures (15)

Fig. 1
Fig. 1

Elastic scattering problem for particle with surface s; dielectric constants 1 and 2 for particle and medium, respectively; incident fields E0.H0; transmitted fields Et,Ht; and scattered fields Es and Hs.

Fig. 2
Fig. 2

Inelastic scattering problem. Fields inside and outside, respectively, are E1.H1 and E2,H2. Dipole fields can be attributed to current sources. J dip, Mdip.

Fig. 3
Fig. 3

(a) Continuous medium 1, μ0 in which current sources Jdie,Mdie generate Edie,Hdie throughout space. (b) Equivalent problem for creation of Edie,Hdie within S and zero fields outside S by surface currents J3,M3.

Fig. 4
Fig. 4

(a) Continuous medium 1, μ0 in which current sources J4,M4 generate −Edip,−Hdip throughout space. (b) Equivalent problem for creation of −Edip,−Hdip outside S and zero fields inside S by surface currents J5,M5.

Fig. 5
Fig. 5

(a) Superposition of fields and sources in Figs. 3(b) and 4(b). (b) Equivalent problem to Fig. 2 obtained by addition of Jdip,Mdip to construction in Fig. 5(a).

Fig. 6
Fig. 6

Geometry. Incident angles are θii; scattering angles are θs(ϕs = 0); incident direction is i; directions parallel and perpendicular to the x-z plane are h and υ.

Fig. 7
Fig. 7

Differential scattering cross sections for spheres vs scattering angle θs. With reference to the text, KA is k 2 a = α; M is m; other notations are the same as in the text.

Fig. 8
Fig. 8

Differential scattering cross sections for spheroids, m = 1.150, volume corresponding to sphere with α = 1, IPFD.

Fig. 9
Fig. 9

Same as Fig. 8 for ROFA.

Fig. 10
Fig. 10

Same as Fig. 8 for sphere α = 3.

Fig. 11
Fig. 11

Same as Fig. 10 for ROFA.

Fig. 12
Fig. 12

Same as Fig. 8 for m = 2.

Fig. 13
Fig. 13

Same as Fig. 9 for m = 2.

Fig. 14
Fig. 14

Same as Fig. 10 for m = 2.

Fig. 15
Fig. 15

Same as Fig. 11 for m = 2.

Equations (42)

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E 2 = E 0 + E s , H 2 = H 0 + H s .
E 2 ( r ) 0 } = E 0 + × S ( n × E t ) G ( k 2 R ) ds + × S 1 j ω 0 2 ( n × H t ) G ( k 2 R ) ds for r { outside S , inside S .
E 0 ( r ) = × S ( n × E t ) G ( k 2 R ) ds + × S 1 j ω 0 2 ( n × H t ) G ( k 2 R ) ds .
E 0 = ν D ν [ α ν M ν 1 ( k 2 r ) + β ν N ν 1 ( k 2 r ) ] , E t = μ D μ [ c μ M μ 1 ( k 1 r ) + d μ N μ 1 ( k 1 r ) ] , H t = k 1 j ω 0 μ 1 μ D μ [ c μ N μ 1 ( k 1 r ) + d μ M μ 1 ( k 1 r ) ] , G ( k 2 R ) = j k 2 π ν D ν [ M ν 3 ( k 2 r ) M ν 1 ( k 2 r ) + N ν 3 ( k 2 r ) N ν 1 ( k 2 r ) ] ,
D ν = m ( 2 n + 1 ) ( n m ) ! 4 n ( n + 1 ) ( n + m ) ! , m = { 1 , m = 0 2 , m > 0 ν = σ = even odd m = 0 n n = 1 N .
j α ν = μ [ D μ ( K + r J ) c μ + D μ ( L + r I ) d μ ] ,
j β ν = μ [ D μ ( I + r L ) c μ + D μ ( J + r K ) d μ ] ,
I = k 2 2 π S n [ M ν 3 ( k 2 r ) × M μ 1 ( k 1 r ) ] ds , J = k 2 2 π S n [ M ν 3 ( k 2 r ) × N μ 1 ( k 1 r ) ] ds , K = k 2 2 π S n [ N ν 3 ( k 2 r ) × M μ 1 ( k 1 r ) ] ds , L = k 2 2 π S n [ N ν 3 ( k 2 r ) × N μ 1 ( k 1 r ) ] ds .
( c d ) = j [ D ] 1 [ Q 31 ] 1 ( α β ) ,
[ Q 31 ] = ( K + r J L + r I I + r L J + r K ) ,
E dip = 1 j ω 1 ( × × A dip ) ,
A dip = j k 1 exp ( j k 1 | r r | ) | r r | P ,
A dip = 4 π j k 1 G ( k 1 R ) P ,
E dip = 4 π k 1 ω 1 × × [ G ( k 1 R ) P ] .
E dip = ν D ν [ a ν M ν 3 ( k 1 r ) + b ν N ν 3 ( k 1 r ) ] , G ( k 1 R ) = ν D ν [ M ν 3 ( k 1 r ) M ν 1 ( k 1 r ) + N ν 3 ( k 1 r ) N ν 1 ( k 1 r ) ] .
ν D ν [ a ν M ν 3 ( k 1 r ) + b ν N ν 3 ( k 1 r ) ] = 4 j k 1 3 μ 0 1 × { ν D ν [ M ν 3 ( k 1 r ) M ν 1 ( k 1 r ) × P + N ν 3 ( k 1 r ) N ν 1 ( k 1 r ) P ] } .
× × M 3 = k 1 2 M 3 , × × N 3 = k 1 2 N 3 .
a ν ( r ) = 4 j k 1 3 ( μ 0 1 ) 1 / 2 M 1 ( k 1 r ) P ,
b ν ( r ) = 4 j k 1 3 ( μ 0 1 ) 1 / 2 N ν 1 ( k 1 r ) P ,
E 1 ( r ) 0 } = E die + × S ( n 1 × E 1 ) G ( k 1 R ) ds × × S 1 j ω 1 ( n 1 × H 1 ) G ( k 1 R ) ds for r { inside S , outside S .
E dip = × S ( n 1 × E 1 ) G ( k 1 R ) ds × × S 1 j ω 1 ( n 1 × H 1 ) G ( k 1 R ) ds .
n 1 × E 1 = n 1 × E 2 ,
n 1 × H 1 = n 1 × H 2 .
E dip = × S ( n 1 × E 2 ) G ( k 1 R ) ds × × S 1 j ω 1 ( n 1 × H 2 ) G ( k 1 R ) ds .
E dip = ν D ν [ a ν M ν 3 ( k 1 r ) + b ν N ν 3 ( k 1 r ) ] ,
E 2 = μ D μ [ f μ M μ 3 ( k 2 r ) + g μ N μ 3 ( k 2 r ) ] ,
H 2 = j ( 2 μ 0 ) 1 / 2 μ [ f μ N μ 3 ( k 2 r ) + g μ M μ 3 ( k 2 r ) ] ,
G ( k 1 R ) = j k 1 π ν D ν [ M ν 3 ( k 1 r ) M ν 1 ( k 1 r ) + N ν 3 ( k 1 r ) N ν 1 ( k 1 r ) ] .
ν D ν [ a ν M ν 3 ( k 1 r ) + b ν N ν 3 ( k 1 r ) ] = ν D ν j k 1 2 π { S [ N ν 3 ( k 1 r ) M ν 1 ( k 1 r ) + M ν 3 ( k 1 r ) N ν 1 ( k 1 r ) ] ( n 1 × E 2 ) ds + j ( μ 0 1 ) 1 / 2 S [ M ν 3 ( k 1 r ) M ν 1 ( k 1 r ) + N ν 3 ( k 1 r ) N ν 1 ( k 1 r ) ] ( n 1 × H 2 ) ds . }
× M = k 1 N , × N = k 1 M , × × M = k 1 2 M , × × N = k 1 2 N .
a ν = j k 1 2 π S [ N ν 1 ( k 1 r ) ( n 1 × E 2 ) + j ( μ 0 1 ) 1 / 2 M ν 1 ( k 1 r ) ( n 1 × H 2 ) ] ds ,
b ν = j k 1 2 π S [ M ν 1 ( k 1 r ) ( n 1 × E 2 ) + j ( μ 0 1 ) 1 / 2 N ν 1 ( k 1 r ) ( n 1 × H 2 ) ] ds .
j a ν = k 1 2 π S { n 1 N ν 1 ( k 1 r ) × μ D μ [ f μ M μ 3 ( k 2 r ) + g μ N μ 3 ( k 2 r ) ] + ( 2 1 ) 1 / 2 M ν 1 ( k 2 r ) × μ D μ [ f μ N μ 3 ( k 2 r ) + g μ M μ 2 ( k 2 r ) ] } ds ,
j a ν = D μ [ ( K + η J ) f μ + ( L + η I ) g μ ] ,
I = k 1 2 π S n 1 [ M ν 1 ( k 1 r ) × M μ 3 ( k 2 r ) ] ds , J = k 1 2 π S n 1 [ M ν 1 ( k 1 r ) × N μ 3 ( k 2 r ) ] ds , K = k 1 2 π S n 1 [ N ν 1 ( k 1 r ) × M μ 3 ( k 2 r ) ] ds , L = k 1 2 π S n 1 [ N ν 1 ( k 1 r ) × N μ 3 ( k 2 r ) ] ds .
j b ν = μ D μ [ ( I + η L ) f μ + ( J + η K ) g μ ] .
( ja jb ) = [ Q 13 ] [ D ] ( f g ) ,
[ Q 13 ] = ( K + η J L + η I I + η L J + η K ) ,
( f g ) = [ D ] 1 [ Q 13 ] 1 ( ja jb ) .
( f g ) = { [ Q 13 ] [ D ] [ T ] [ Q 33 ] [ D ] } ( ja jb ) ,
F ( θ s , ϕ s / θ i , ϕ i ) = E 2 ( k 2 r ) r exp ( j k 2 r ) k 2 r .
σ D ( θ s , ϕ s / θ i , ϕ i ) = 4 π | F ( θ s , ϕ s / θ i , ϕ i ) | 2 .

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