Abstract

A theoretical procedure in which a spheroidal coordinate separation-of-variables solution is used is developed for the determination of the internal and the near-surface electromagnetic fields for an arbitrary monochromatic field that is incident upon a homogeneous spheroidal particle. Calculations are presented for both the prolate and the oblate geometries, demonstrating the effects of particle size, particle axis ratio, and the orientation and character (plane-wave and focused Gaussian beam) of the incident field on the resultant internal and near-surface electromagnetic-field distributions.

© 1995 Optical Society of America

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References

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  1. 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]
  2. J. P. Barton, D. R. Alexander, “Electromagnetic fields for an irregularly-shaped, near-spherical particle illuminated by a focused laser beam,” J. Appl. Phys. 69, 7973–7986 (1991).
    [CrossRef]
  3. T. Oguchi, “Attenuation and phase rotation of radio waves due to rain: calculations at 19.3 and 34.8 GHz,” Radio Sci. 8, 31–38 (1973).
    [CrossRef]
  4. S. Asano, G. Yamamoto, “Light scattering by a spheroidal particle,” Appl. Opt. 14, 29–49 (1975).
    [PubMed]
  5. B. P. Sinha, R. H. MacPhie, “Electromagnetic scattering by prolate spheroids for plane waves with arbitrary polarization and angle of incidence,” Radio Sci. 12, 171–184 (1977).
    [CrossRef]
  6. C. Flammer, Spheroidal Wave Functions (Stanford U. Press, Stanford, Calif., 1957).
  7. J.A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).
  8. 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]

1991 (1)

J. P. Barton, D. R. Alexander, “Electromagnetic fields for an irregularly-shaped, near-spherical particle illuminated by a focused laser beam,” J. Appl. Phys. 69, 7973–7986 (1991).
[CrossRef]

1989 (1)

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]

1988 (1)

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]

1977 (1)

B. P. Sinha, R. H. MacPhie, “Electromagnetic scattering by prolate spheroids for plane waves with arbitrary polarization and angle of incidence,” Radio Sci. 12, 171–184 (1977).
[CrossRef]

1975 (1)

1973 (1)

T. Oguchi, “Attenuation and phase rotation of radio waves due to rain: calculations at 19.3 and 34.8 GHz,” Radio Sci. 8, 31–38 (1973).
[CrossRef]

Alexander, D. R.

J. P. Barton, D. R. Alexander, “Electromagnetic fields for an irregularly-shaped, near-spherical particle illuminated by a focused laser beam,” J. Appl. Phys. 69, 7973–7986 (1991).
[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]

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]

Asano, S.

Barton, J. P.

J. P. Barton, D. R. Alexander, “Electromagnetic fields for an irregularly-shaped, near-spherical particle illuminated by a focused laser beam,” J. Appl. Phys. 69, 7973–7986 (1991).
[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]

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]

Flammer, C.

C. Flammer, Spheroidal Wave Functions (Stanford U. Press, Stanford, Calif., 1957).

MacPhie, R. H.

B. P. Sinha, R. H. MacPhie, “Electromagnetic scattering by prolate spheroids for plane waves with arbitrary polarization and angle of incidence,” Radio Sci. 12, 171–184 (1977).
[CrossRef]

Oguchi, T.

T. Oguchi, “Attenuation and phase rotation of radio waves due to rain: calculations at 19.3 and 34.8 GHz,” Radio Sci. 8, 31–38 (1973).
[CrossRef]

Schaub, S. A.

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]

Sinha, B. P.

B. P. Sinha, R. H. MacPhie, “Electromagnetic scattering by prolate spheroids for plane waves with arbitrary polarization and angle of incidence,” Radio Sci. 12, 171–184 (1977).
[CrossRef]

Stratton, J.A.

J.A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).

Yamamoto, G.

Appl. Opt. (1)

J. Appl. Phys. (3)

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. P. Barton, D. R. Alexander, “Electromagnetic fields for an irregularly-shaped, near-spherical particle illuminated by a focused laser beam,” J. Appl. Phys. 69, 7973–7986 (1991).
[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]

Radio Sci. (2)

T. Oguchi, “Attenuation and phase rotation of radio waves due to rain: calculations at 19.3 and 34.8 GHz,” Radio Sci. 8, 31–38 (1973).
[CrossRef]

B. P. Sinha, R. H. MacPhie, “Electromagnetic scattering by prolate spheroids for plane waves with arbitrary polarization and angle of incidence,” Radio Sci. 12, 171–184 (1977).
[CrossRef]

Other (2)

C. Flammer, Spheroidal Wave Functions (Stanford U. Press, Stanford, Calif., 1957).

J.A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).

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Figures (18)

Fig. 1
Fig. 1

Normalized-source-function distribution in the xz plane for a plane wave that is incident upon a 2:1 axis ratio prolate spheroid with 0° angle of incidence. (hext = 8.00, n = 1.33, θbd = 0°, and ϕbd = 90°.)

Fig. 2
Fig. 2

Contour plot of the normalized-source-function distribution in the xz plane for a plane wave that is incident upon a 2:1 axis ratio prolate spheroid with 0° angle of incidence. (hext = 8.00, n = 1.33, θbd = 0°, and ϕbd = 90°.)

Fig. 3
Fig. 3

Normalized-source-function distribution in the xz plane for a plane wave that is incident upon a 2:1 axis ratio prolate spheroid with 45° angle of incidence. (hext = 8.00, n = 1.33, θbd = 45°, and ϕbd = 90°.)

Fig. 4
Fig. 4

Normalized-source-function distribution in the xz plane for a plane wave that is incident upon a 2:1 axis ratio prolate spheroid with 90° angle of incidence. (hext = 8.00, n = 1.33, θbd = 90°, and ϕbd = 90°.)

Fig. 5
Fig. 5

Normalized-source-function distribution in the xz plane for a plane wave that is incident upon a 2:1 axis ratio oblate spheroid with 0° angle of incidence. (hext = 8.00, n = 1.33, θbd = 0°, and ϕbd = 90°.)

Fig. 6
Fig. 6

Contour plot of the normalized-source-function distribution in the xz plane for a plane wave that is incident upon a 2:1 axis ratio oblate spheroid with 0° angle of incidence. (hext = 8.00, n = 1.33, θbd = 0°, and ϕbd = 90°.)

Fig. 7
Fig. 7

Normalized-source-function distribution in the xz plane for a plane wave that is incident upon a 2:1 axis ratio oblate spheroid with 45° angle of incidence. (hext = 8.00, n = 1.33, θbd = 45°, and ϕbd = 90°.)

Fig. 8
Fig. 8

Normalized-source-function distribution in the xz plane for a plane wave that is incident upon a 2:1 axis ratio oblate spheroid with 90° angle of incidence. (hext = 8.00, n = 1.33, θbd = 90°, and ϕbd = 90°.)

Fig. 9
Fig. 9

Normalized-source-function distribution in the xz plane for a focused Gaussian beam that is incident upon a 2:1 axis ratio prolate spheroid with 90° angle of incidence and focused on the backside spheroid focal point. (hext = 8.00, n = 1.33, θbd = 90°, ϕbd = 90°, w0 = 1.25, x0 = 0.0, y0 = 0.0, and z0 = 1.0.)

Fig. 10
Fig. 10

Contour plot of the normalized-source-function distribution in the xz plane for a focused Gaussian beam that is incident upon a 2:1 axis ratio prolate spheroid with 90° angle of incidence and focused on the backside spheroid focal point. (hext = 8.00, n = 1.33, θbd = 90°, ϕbd = 90°, w0 = 1.25, x0 = 0.0, y0 = 0.0, and z0 = 1.0.)

Fig. 11
Fig. 11

Normalized-source-function distribution in the xz plane for a focused Gaussian beam that is incident upon a 2:1 axis ratio oblate spheroid with 0° angle of incidence and focused on the upper spheroid focal point. (hext = 8.00, n = 1.33, θbd = 0°, ϕbd = 90°, w0 = 1.25, x0 = 1.0, y0 = 0.0, and z0 = 0.0.)

Fig. 12
Fig. 12

Contour plot of the normalized-source-function distribution in the xz plane for a focused Gaussian beam that is incident upon a 2:1 axis ratio oblate spheroid with 0° angle of incidence and focused on the upper spheroid focal point. (hext = 8.00, n = 1.33, θbd = 0°, ϕbd = 90°, w0 = 1.25, x0 = 1.0, y0 = 0.0, and z0 = 0.0.)

Fig. 13
Fig. 13

Normalized-source-function distribution in the xz plane for a plane wave that is incident upon a 2:1 axis ratio prolate spheroid with 0° angle of incidence. (hext = 12.00, n = 1.33, θbd = 0°, and ϕbd = 90°.)

Fig. 14
Fig. 14

Normalized-source-function distribution in the xz plane for a plane wave that is incident upon a 2:1 axis ratio oblate spheroid with 0° angle of incidence. (hext = 12.00, n = 1.33, θbd = 0°, and ϕbd = 90°.)

Fig. 15
Fig. 15

Normalized-source-function distribution in the xz plane for a plane wave that is incident upon a 3:1 axis ratio prolate spheroid with 0° angle of incidence. (hext = 8.00, n = 1.33, θbd = 0°, and ϕbd = 90°.)

Fig. 16
Fig. 16

Contour plot of the normalized-source-function distribution in the xz plane for a plane wave that is incident upon a 3:1 axis ratio prolate spheroid with 0° angle of incidence. (hext = 8.00, n = 1.33, θbd = 0°, and ϕbd = 90°.)

Fig. 17
Fig. 17

Normalized-source-function distribution in the xz plane for a plane wave that is incident upon a 3:1 axis ratio oblate spheroid with 0° angle of incidence. (hext = 8.00, n = 1.33, θbd = 0°, and ϕbd = 90°.)

Fig. 18
Fig. 18

Contour plot of the normalized-source-function distribution in the xz plane for a plane wave that is incident upon a 3:1 axis ratio oblate spheroid with 0° angle of incidence. (hext = 8.00, n = 1.33, θbd = 0°, and ϕbd = 90°.)

Equations (59)

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f = a [ 1 ( b / a ) 2 ] 1 / 2 .
( 2 + h 2 ) = 0 ,
lm = S lm ( h , η ) R lm ( h , ξ ) exp ( im ϕ ) ,
( 2 + h 2 ) E = 0 ,
( 2 + h 2 ) H = 0 .
M lm = × ( r lm ) ,
N lm = 1 h × M lm .
E ( s ) = l , m [ a lm N lm ( s ) + b lm M lm ( s ) ] ,
H ( s ) = i ext l , m [ a lm M lm ( s ) + b lm N lm ( s ) ] ,
lm ( s ) = S lm ( h ext , η ) R lm ( 3 ) ( h ext , ξ ) exp ( im ϕ ) .
E ( w ) = l , m [ c lm N lm ( w ) + d lm M lm ( w ) ] ,
H ( w ) = i ext n l , m [ c lm M lm ( w ) + d lm N lm ( w ) ] ,
lm ( w ) = S lm ( h int , η ) R lm ( 1 ) ( h int , ξ ) exp ( im ϕ ) .
E η ( i ) + E η ( s ) = E η ( w ) ,
E ϕ ( i ) + E ϕ ( s ) = E ϕ ( w ) ,
H η ( i ) + H η ( s ) = H η ( w ) ,
H ϕ ( i ) + H ϕ ( s ) = H ϕ ( w ) .
l = | m | L ( I lm l 1 a lm I lm l 2 b lm + I lm l 3 c lm + I lm l 4 d lm ) = 1 2 π A l m η ,
l = | m | L ( I lm l 5 a lm I lm l 6 b lm + I lm l 7 c lm + I lm l 8 d lm ) = 1 2 π A l m ϕ ,
l = | m | L ( I lm l 2 a lm I lm l 1 b lm + n int I lm l 4 c lm + n int I lm l 3 d lm ) = i 2 π ext B l m η ,
l = | m | L ( I lm l 6 a lm I lm l 5 b lm + n I lm l 8 c lm + n I lm l 7 d lm ) = i 2 π ext B l m ϕ ,
A l m η = 0 2 π 1 1 E η ( i ) ( ξ 0 , η , ϕ ) S l m ( h ext , η ) exp ( im ϕ ) d η d ϕ ,
A l m ϕ = 0 2 π 1 1 E ϕ ( i ) ( ξ 0 , η , ϕ ) S l m ( h ext , η ) exp ( im ϕ ) d η d ϕ ,
B l m η = 0 2 π 1 1 H η ( i ) ( ξ 0 , η , ϕ ) S l m ( h ext , η ) exp ( im ϕ ) d η d ϕ ,
B l m ϕ = 0 2 π 1 1 H ϕ ( i ) ( ξ 0 , η , ϕ ) S l m ( h ext , η ) exp ( im ϕ ) d η d ϕ .
l = 0 L ( I l 0 l 1 a l 0 + I l 0 l 3 c l 0 ) = 1 2 π A l 0 η ,
l = 0 L ( I l 0 l 6 b l 0 + I l 0 l 8 d l 0 ) = 1 2 π A l 0 ϕ ,
l = 0 L ( I l 0 l 1 b l 0 + n I l 0 l 3 d l 0 ) = i 2 π ext B l 0 η ,
l = 0 L ( I l 0 l 6 a l 0 + n I l 0 l 8 c l 0 ) = i 2 π ext B l 0 ϕ ,
x = [ ( ξ 2 1 ) ( 1 η 2 ) ] 1 / 2 cos ϕ ,
y = [ ( ξ 2 1 ) ( 1 η 2 ) ] 1 / 2 sin ϕ ,
z = ξ η .
( a / b ) = ξ 0 ( ξ 0 2 1 ) 1 / 2 .
M lm , ξ = im η [ ( ξ 2 η 2 ) ( ξ 2 1 ) ] 1 / 2 R lm ( h , ξ ) S lm ( h , η ) exp ( im ϕ ) ,
M lm , η = im ξ [ ( ξ 2 η 2 ) ( 1 η 2 ) ] 1 / 2 R lm ( h , ξ ) S lm ( h , η ) exp ( im ϕ ) ,
M lm , ϕ = [ ( ξ 2 1 ) ( 1 η 2 ) ] 1 / 2 ( ξ 2 η 2 ) [ ξ R lm ( h , ξ ) S lm ( h , η ) η R lm ( h , ξ ) S lm ( h , η ) ] exp ( im ϕ ) ,
N lm , ξ = ( ξ 2 1 ) 1 / 2 h ( ξ 2 η 2 ) 3 / 2 × { ξ [ λ lm h 2 η 2 + m 2 ( ξ 2 1 ) ] S lm ( h , η ) R lm ( h , ξ ) 2 ξ η ( 1 η 2 ) ( ξ 2 η 2 ) S lm ( h , η ) R lm ( h , ξ ) + η ( 1 η 2 ) S lm ( h , η ) R lm ( h , ξ ) + [ ξ 2 ( 1 3 η 2 ) + η 2 ( η 2 + 1 ) ( ξ 2 η 2 ) ] S lm ( h , η ) R lm ( h , ξ ) } × exp ( im ϕ ) ,
N lm , η = ( 1 η 2 ) 1 / 2 h ( ξ 2 η 2 ) 3 / 2 { ξ ( ξ 2 1 ) R lm ( h , ξ ) S lm ( h , η ) + ξ 2 ( ξ 2 1 ) + η 2 ( 1 3 ξ 2 ) ( ξ 2 η 2 ) R lm ( h , ξ ) S lm ( h , η ) η [ λ lm ξ 2 h 2 m 2 ( 1 η 2 ) ] R lm ( h , ξ ) S lm ( h , η ) + 2 ξ η ( ξ 2 1 ) ( ξ 2 η 2 ) R lm ( h , ξ ) S lm ( h , η ) } exp ( im ϕ ) ,
N lm , ϕ = im [ ( ξ 2 1 ) ( 1 η 2 ) ] 1 / 2 h ( ξ 2 η 2 ) [ η ( ξ 2 1 ) S lm ( h , η ) × R lm ( h , ξ ) + ξ ( 1 η 2 ) R lm ( h , ξ ) S lm ( h , η ) + ( ξ 2 η 2 ) ( ξ 2 1 ) ( 1 η 2 ) S lm ( h , η ) R lm ( h , ξ ) ] exp ( im ϕ ) .
x = [ ( ξ 2 + 1 ) ( 1 η 2 ) ] 1 / 2 cos ϕ ,
y = [ ( ξ 2 + 1 ) ( 1 η 2 ) ] 1 / 2 sin ϕ ,
z = ξ η .
( a / b ) = [ 1 + ( 1 / ξ 0 2 ) ] 1 / 2 .
M lm , ξ = im η [ ( ξ 2 + η 2 ) ( ξ 2 + 1 ) ] 1 / 2 R lm ( h , ξ ) S lm ( h , η ) exp ( im ϕ ) ,
M lm , η = im ξ [ ( ξ 2 + η 2 ) ( 1 η 2 ) ] 1 / 2 R lm ( h , ξ ) S lm ( h , η ) exp ( im ϕ ) ,
M lm , ϕ = [ ( ξ 2 + 1 ) ( 1 η 2 ) ] 1 / 2 ( ξ 2 + η 2 ) [ ξ R lm ( h , ξ ) S lm ( h , η ) + η R lm ( h , ξ ) S lm ( h , η ) exp ( im ϕ ) ,
N lm , ξ = ( ξ 2 + 1 ) 1 / 2 h ( ξ 2 + η 2 ) 3 / 2 × { ξ [ λ lm + h 2 η 2 m 2 ( ξ 2 1 ) ] S lm ( h , η ) R lm ( h , ξ ) + 2 ξ η ( 1 η 2 ) ( ξ 2 + η 2 ) S lm ( h , η ) R lm ( h , ξ ) η ( 1 η 2 ) S lm ( h , η ) R lm ( h , ξ ) [ ξ 2 ( 1 3 η 2 ) η 2 ( η 2 + 1 ) ( ξ 2 + η 2 ) ] S lm ( h , η ) R lm ( h , ξ ) } × exp ( im ϕ ) ,
N lm , η = ( 1 η 2 ) 1 / 2 h ( ξ 2 + η 2 ) 3 / 2 { ξ ( ξ 2 + 1 ) R lm ( h , ξ ) S lm ( h , η ) + ξ 2 ( ξ 2 1 ) + η 2 ( 1 + 3 ξ 2 ) ( ξ 2 + η 2 ) R lm ( h , ξ ) S lm ( h , η ) + η [ λ lm ξ 2 h 2 m 2 ( 1 η 2 ) ] R lm ( h , ξ ) S lm ( h , η ) 2 ξ η ( ξ 2 + 1 ) ( ξ 2 + η 2 ) R lm ( h , ξ ) S lm ( h , η ) } exp ( im ϕ ) ,
N lm , ϕ = im [ ( ξ 2 + 1 ) ( 1 η 2 ) ] 1 / 2 h ( ξ 2 + η 2 ) × [ η ( ξ 2 + 1 ) S lm ( h , η ) R lm ( h , ξ ) + ξ ( 1 η 2 ) R lm ( h , ξ ) S lm ( h , η ) + ( ξ 2 + η 2 ) ( ξ 2 + 1 ) ( 1 η 2 ) S lm ( h , η ) R lm ( h , ξ ) ] exp ( im ϕ ) ,
E ξ ( i ) + E ξ ( s ) = n 2 E ξ ( w ) ,
H ξ ( i ) + H ξ ( s ) = H ξ ( w ) .
I lm l l = 2 0 1 N lm , η ( s ) ( ξ 0 , η , 0 ) S l m ( h ext , η ) d η ,
I lm l 2 = 2 0 1 M lm , η ( s ) ( ξ 0 , η , 0 ) S l m ( h ext , η ) d η ,
I lm l 3 = 2 0 1 N lm , η ( w ) ( ξ 0 , η , 0 ) S l m ( h ext , η ) d η ,
I lm l 4 = 2 0 1 M lm , η ( w ) ( ξ 0 , η , 0 ) S l m ( h ext , η ) d η ,
I lm l 5 = 2 0 1 N lm , ϕ ( s ) ( ξ 0 , η , 0 ) S l m ( h ext , η ) d η ,
I lm l 6 = 2 0 1 M lm , ϕ ( s ) ( ξ 0 , η , 0 ) S l m ( h ext , η ) d η ,
I lm l 7 = 2 0 1 N lm , ϕ ( w ) ( ξ 0 , η , 0 ) S l m ( h ext , η ) d η ,
I lm l 8 = 2 0 1 M lm , ϕ ( w ) ( ξ 0 , η , 0 ) S l m ( h ext , η ) d η .

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