Abstract

The scattering properties of active particles are studied and compared with those of particles with a complex conjugate (passive) index of refraction. It is shown that the extinction cross section of active particles is zero at certain frequencies and that only at certain frequency bands it is amplified. For most frequencies, the interference between diffracted and refracted waves causes the extinction cross section to behave like that of passive particles. A comparison of backscattered and forwardscattered intensities between active and passive particles with na = np* shows that as ±Im(n) → + ∞ the intensities converge to the same value. For nonsymmetric scatterers, such as cylindrical fibers of elliptic cross section, it is shown that in the resonance region the major portion of the scattered field is not in the forward direction. In addition, the ratio of back-scattered to forward scattered intensity is found to be greater than unity for active media for certain frequencies beyond the low frequency region.

© 1978 Optical Society of America

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References

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  1. M. Kerker, The Scattering of Light (Academic, New York, 1969).
  2. R. G. Newton, Scattering Theory of Waves and Particles (McGraw-Hill, New York, 1966).
  3. J. A. Morrison, M. J. Cross, Bell Syst. Tech. J. 53, 955 (1974).
  4. A. Nelson, L. Eyges, J. Opt. Soc. Am. 66, 254 (1976).
    [CrossRef]
  5. N. Uzunoglu, B. G. Evans, A. R. Holt, Electron. Lett. 12, 312 (1976).
    [CrossRef]
  6. N. K. Uzunoglu, A. R. Holt, J. Phys. A( 00, 000) (March1977).
  7. A. R. Holt, N. K. Uzunoglu, B. G. Evans, “The Scattering of Electromagnetic Radiation by Precipitation Particles: Fredholm Integral Equation Theory,” submitted for publication to IEEE Trans. Antenna Propag.
  8. N. G. Alexopoulos, G. A. Tadler, F. W. Schott, IEEE Trans. Antenna Propag. AP-22, 132 (1974).
    [CrossRef]
  9. N. G. Alexopoulos, P. L. Uslenghi, G. A. Tadler, IEEE Trans. Antenna Propag. AP-22, 722 (1974).
    [CrossRef]
  10. N. G. Alexopoulos, G. A. Tadler, J. Appl. Phys. 46, 3326 (1975).
    [CrossRef]
  11. M. Kerker, J. Opt. Soc. Am. 65, 375 (1975).
  12. C. Yeh, J. Opt. Soc. Am. 55, 309 (1963).
    [CrossRef]

1977 (1)

N. K. Uzunoglu, A. R. Holt, J. Phys. A( 00, 000) (March1977).

1976 (2)

A. Nelson, L. Eyges, J. Opt. Soc. Am. 66, 254 (1976).
[CrossRef]

N. Uzunoglu, B. G. Evans, A. R. Holt, Electron. Lett. 12, 312 (1976).
[CrossRef]

1975 (2)

N. G. Alexopoulos, G. A. Tadler, J. Appl. Phys. 46, 3326 (1975).
[CrossRef]

M. Kerker, J. Opt. Soc. Am. 65, 375 (1975).

1974 (3)

J. A. Morrison, M. J. Cross, Bell Syst. Tech. J. 53, 955 (1974).

N. G. Alexopoulos, G. A. Tadler, F. W. Schott, IEEE Trans. Antenna Propag. AP-22, 132 (1974).
[CrossRef]

N. G. Alexopoulos, P. L. Uslenghi, G. A. Tadler, IEEE Trans. Antenna Propag. AP-22, 722 (1974).
[CrossRef]

1963 (1)

Alexopoulos, N. G.

N. G. Alexopoulos, G. A. Tadler, J. Appl. Phys. 46, 3326 (1975).
[CrossRef]

N. G. Alexopoulos, P. L. Uslenghi, G. A. Tadler, IEEE Trans. Antenna Propag. AP-22, 722 (1974).
[CrossRef]

N. G. Alexopoulos, G. A. Tadler, F. W. Schott, IEEE Trans. Antenna Propag. AP-22, 132 (1974).
[CrossRef]

Cross, M. J.

J. A. Morrison, M. J. Cross, Bell Syst. Tech. J. 53, 955 (1974).

Evans, B. G.

N. Uzunoglu, B. G. Evans, A. R. Holt, Electron. Lett. 12, 312 (1976).
[CrossRef]

A. R. Holt, N. K. Uzunoglu, B. G. Evans, “The Scattering of Electromagnetic Radiation by Precipitation Particles: Fredholm Integral Equation Theory,” submitted for publication to IEEE Trans. Antenna Propag.

Eyges, L.

Holt, A. R.

N. K. Uzunoglu, A. R. Holt, J. Phys. A( 00, 000) (March1977).

N. Uzunoglu, B. G. Evans, A. R. Holt, Electron. Lett. 12, 312 (1976).
[CrossRef]

A. R. Holt, N. K. Uzunoglu, B. G. Evans, “The Scattering of Electromagnetic Radiation by Precipitation Particles: Fredholm Integral Equation Theory,” submitted for publication to IEEE Trans. Antenna Propag.

Kerker, M.

M. Kerker, J. Opt. Soc. Am. 65, 375 (1975).

M. Kerker, The Scattering of Light (Academic, New York, 1969).

Morrison, J. A.

J. A. Morrison, M. J. Cross, Bell Syst. Tech. J. 53, 955 (1974).

Nelson, A.

Newton, R. G.

R. G. Newton, Scattering Theory of Waves and Particles (McGraw-Hill, New York, 1966).

Schott, F. W.

N. G. Alexopoulos, G. A. Tadler, F. W. Schott, IEEE Trans. Antenna Propag. AP-22, 132 (1974).
[CrossRef]

Tadler, G. A.

N. G. Alexopoulos, G. A. Tadler, J. Appl. Phys. 46, 3326 (1975).
[CrossRef]

N. G. Alexopoulos, P. L. Uslenghi, G. A. Tadler, IEEE Trans. Antenna Propag. AP-22, 722 (1974).
[CrossRef]

N. G. Alexopoulos, G. A. Tadler, F. W. Schott, IEEE Trans. Antenna Propag. AP-22, 132 (1974).
[CrossRef]

Uslenghi, P. L.

N. G. Alexopoulos, P. L. Uslenghi, G. A. Tadler, IEEE Trans. Antenna Propag. AP-22, 722 (1974).
[CrossRef]

Uzunoglu, N.

N. Uzunoglu, B. G. Evans, A. R. Holt, Electron. Lett. 12, 312 (1976).
[CrossRef]

Uzunoglu, N. K.

N. K. Uzunoglu, A. R. Holt, J. Phys. A( 00, 000) (March1977).

A. R. Holt, N. K. Uzunoglu, B. G. Evans, “The Scattering of Electromagnetic Radiation by Precipitation Particles: Fredholm Integral Equation Theory,” submitted for publication to IEEE Trans. Antenna Propag.

Yeh, C.

Bell Syst. Tech. J. (1)

J. A. Morrison, M. J. Cross, Bell Syst. Tech. J. 53, 955 (1974).

Electron. Lett. (1)

N. Uzunoglu, B. G. Evans, A. R. Holt, Electron. Lett. 12, 312 (1976).
[CrossRef]

IEEE Trans. Antenna Propag. (2)

N. G. Alexopoulos, G. A. Tadler, F. W. Schott, IEEE Trans. Antenna Propag. AP-22, 132 (1974).
[CrossRef]

N. G. Alexopoulos, P. L. Uslenghi, G. A. Tadler, IEEE Trans. Antenna Propag. AP-22, 722 (1974).
[CrossRef]

J. Appl. Phys. (1)

N. G. Alexopoulos, G. A. Tadler, J. Appl. Phys. 46, 3326 (1975).
[CrossRef]

J. Opt. Soc. Am. (3)

J. Phys. A (1)

N. K. Uzunoglu, A. R. Holt, J. Phys. A( 00, 000) (March1977).

Other (3)

A. R. Holt, N. K. Uzunoglu, B. G. Evans, “The Scattering of Electromagnetic Radiation by Precipitation Particles: Fredholm Integral Equation Theory,” submitted for publication to IEEE Trans. Antenna Propag.

M. Kerker, The Scattering of Light (Academic, New York, 1969).

R. G. Newton, Scattering Theory of Waves and Particles (McGraw-Hill, New York, 1966).

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Figures (11)

Fig. 1
Fig. 1

Qext vs koa for active (— – —) and passive (—) scatterers for n = (2)1/2 ± i.

Fig. 2
Fig. 2

Backscattering intensity vs ni = Im(n) for active (— – – —) and passive (—) scatterers with Re(n) = (2)1/2 and koa = 2.

Fig. 3
Fig. 3

Forward intensity vs ni = Im(n) for active (– —) and passive (—) scatterers with Re(n) = (2)1/2 and koa = 2.

Fig. 4
Fig. 4

Backscattered intensity vs koa for n = (2)1/2i.

Fig. 5
Fig. 5

Backscattered intensity vs koa for n = (2)1/2 + i.

Fig. 6
Fig. 6

Forward intensity vs koa for n = (2)1/2i.

Fig. 7
Fig. 7

Forward intensity vs koa for n = (2)1/2 + i.

Fig. 8
Fig. 8

i1(θ),i2(θ) intensity functions dependence to zenithal angle θ for an active and passive scatterer with n = (2)1/2 ± i and koa = 3.

Fig. 9
Fig. 9

Angular variation of intensity function for three elliptical cross section fiber scatterers with koa ≅ 1.9 and kob ≅ 2.8.

Fig. 10
Fig. 10

Comparison of scattered intensities for active and passive scatterers with n = (2)1/2 ± i,ϕo = 90°,koa = 0.5, and kob = 3.0.

Fig. 11
Fig. 11

Scattered wave intensity for an elliptic cross-section fiber for n = (2)1/2i,ϕo = 45°, koa = 2.0, and kob = 4.0.

Equations (7)

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Q scatt = π a 2 2 x 2 t = 1 ( 2 t + 1 ) { | S e t 1 | 2 + | S m t 1 | 2 }
Q abs , amp = π a 2 x 2 t = 1 ( 2 t + 1 ) { 1 | S e t | 2 + | S m t | 2 2 } ,
Q ext = Q abs , amp + Q scatt .
( Q ext ) p , a = 24 x ( π a 2 ) ± n r n i ( n r 2 n i 2 + 2 ) 2 + 4 n r 2 n i 2 ,
( Q ext ) p , a 2 π a 2
E ( r ) exp [ i k 0 r cos ( ϕ s ϕ 0 ) ] + f ( ϕ s ) exp ( i k 0 r ) ( r ) 1 / 2 ,
[ ( x 2 ) / ( a 2 ) ] + [ ( y 2 ) / ( b 2 ) ] = 1 ,

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