Abstract

This paper presents a theoretical study on propagation and scattering characteristics of a short optical pulse in a dense distribution of scatterers. Examples include pulse diffusion in whole blood and in a dense distribution of particulate matter in the atmosphere and the ocean. The parabolic equation technique is applicable to the forward-scatter region where the angular spread is confined within narrow forward angles. When the angular spread becomes comparable to the order of unit steradian, there is as much backscattering as forward scattering and diffusion phenomena take place. We start with the integral and differential equations for the two-frequency mutual coherence function under the first-order smoothing approximation, and a general diffusion equation and boundary conditions are obtained. As examples, we present solutions for diffusion of a pulse from a point source and a plane wave incident on a slab of scatterers.

© 1978 Optical Society of America

PDF Article

References

  • View by:
  • |
  • |
  • |

  1. V. I. Shishov, "Effect of refraction on scintillation characteristics and average pulse shape of pulsars," Sov. Astron. 17, 598–602 (1974).
  2. L. C. Lee and J. R. Jokipii, "Sontrong scintillations in astrophysics, II: A theory of temporal broadening of pulses," Astrophy. J. 201, 532–543 (1975).
  3. C. H. Liu, A. W. Weznik, and K. C. Yeh, "Propagation of pulse trains through a random medium," IEEE Trans. Antennas Propag. AP- 22, 524–627 (1974).
  4. A. Ishimaru and S. T. Hong, "Multiple scattering effects on coherent bandwidth and pulse distortion of a wave propagating in a random distribution of particles," Radio Sci. 10, 637–644 (1975).
  5. I. Sreenivasiah, A. Ishimaru, and S. T. Hong, "Two-frequency mutual coherence function and pulse propagation in a random medium: An analytical solution to plane wave case," Radio Sci. 11, 775–778 (1976).
  6. S. T. Hong and A. Ishimaru, "Two-frequency mutual coherence function, coherence bandwidth and coherence time of millimeter and optical waves in rain, fog and turbulence," Radio Sci. 11, 551–559 (1976).
  7. S. T. Hong, I. Sreenivasiah, and A. Ishimaru, "Plane wave pulse propagation through random media," IEEE Trans. Antennas Propag. AP-25, 822–827 (1977).
  8. B. J. Uscinski, "The propagation and broadening of pulses in weakly irregular media," Proc. R. Soc. Lond. A 336, 379–392 (1974).
  9. L. M. Erhukumov, I. G. Zarnitsina, and P. I. Kirsch, "Selective properties and the form of a signal passed through a statistically inhomogeneous arbitrary-thickness layer," Radiofiz. 16, 573–580 (1973).
  10. C. H. Liu and K. C. Yeh, "Frequency and spatial correlation function in a fading communication channel through the ionosphere," Radio Sci. 10, 1055–1061 (1975).
  11. E. A. Bucher and R. M. Lerner, "Experiments on light pulse communication and propagation through atmospheric clouds," Appl. Opt. 12, 2401–2414 (1973).
  12. L. Reynolds, C. C. Johnson, and A. Ishimaru, "Diffuse reflectance from a finite blood medium: applications to the modeling of fiberoptic catheters," Appl. Opt. 15, 2059–2067 (1976).
  13. B. J. Brinkworth, "Pulsed-Lidar reflectance of clouds," Appl. Opt. 12, 427–428 (1973).
  14. A. Ishimaru, "Theory and application of wave propagation and scattering in random media," Proc. IEEE 65, 1030–1061 (1977).
  15. A. Ishimaru, Wave propagation and scattering in random media, Volumes I and II (Academic, New York, 1978).
  16. P. M. Morse and H. Feshback, Methods of Theoretical Physics (McGraw-Hill, New York, 1953).

1977 (1)

S. T. Hong, I. Sreenivasiah, and A. Ishimaru, "Plane wave pulse propagation through random media," IEEE Trans. Antennas Propag. AP-25, 822–827 (1977).

1976 (3)

I. Sreenivasiah, A. Ishimaru, and S. T. Hong, "Two-frequency mutual coherence function and pulse propagation in a random medium: An analytical solution to plane wave case," Radio Sci. 11, 775–778 (1976).

S. T. Hong and A. Ishimaru, "Two-frequency mutual coherence function, coherence bandwidth and coherence time of millimeter and optical waves in rain, fog and turbulence," Radio Sci. 11, 551–559 (1976).

L. Reynolds, C. C. Johnson, and A. Ishimaru, "Diffuse reflectance from a finite blood medium: applications to the modeling of fiberoptic catheters," Appl. Opt. 15, 2059–2067 (1976).

1975 (3)

C. H. Liu and K. C. Yeh, "Frequency and spatial correlation function in a fading communication channel through the ionosphere," Radio Sci. 10, 1055–1061 (1975).

L. C. Lee and J. R. Jokipii, "Sontrong scintillations in astrophysics, II: A theory of temporal broadening of pulses," Astrophy. J. 201, 532–543 (1975).

A. Ishimaru and S. T. Hong, "Multiple scattering effects on coherent bandwidth and pulse distortion of a wave propagating in a random distribution of particles," Radio Sci. 10, 637–644 (1975).

1974 (3)

V. I. Shishov, "Effect of refraction on scintillation characteristics and average pulse shape of pulsars," Sov. Astron. 17, 598–602 (1974).

C. H. Liu, A. W. Weznik, and K. C. Yeh, "Propagation of pulse trains through a random medium," IEEE Trans. Antennas Propag. AP- 22, 524–627 (1974).

B. J. Uscinski, "The propagation and broadening of pulses in weakly irregular media," Proc. R. Soc. Lond. A 336, 379–392 (1974).

1973 (3)

L. M. Erhukumov, I. G. Zarnitsina, and P. I. Kirsch, "Selective properties and the form of a signal passed through a statistically inhomogeneous arbitrary-thickness layer," Radiofiz. 16, 573–580 (1973).

E. A. Bucher and R. M. Lerner, "Experiments on light pulse communication and propagation through atmospheric clouds," Appl. Opt. 12, 2401–2414 (1973).

B. J. Brinkworth, "Pulsed-Lidar reflectance of clouds," Appl. Opt. 12, 427–428 (1973).

Brinkworth, B. J.

Bucher, E. A.

Erhukumov, L. M.

L. M. Erhukumov, I. G. Zarnitsina, and P. I. Kirsch, "Selective properties and the form of a signal passed through a statistically inhomogeneous arbitrary-thickness layer," Radiofiz. 16, 573–580 (1973).

Feshback, H.

P. M. Morse and H. Feshback, Methods of Theoretical Physics (McGraw-Hill, New York, 1953).

Hong, S. T.

S. T. Hong, I. Sreenivasiah, and A. Ishimaru, "Plane wave pulse propagation through random media," IEEE Trans. Antennas Propag. AP-25, 822–827 (1977).

I. Sreenivasiah, A. Ishimaru, and S. T. Hong, "Two-frequency mutual coherence function and pulse propagation in a random medium: An analytical solution to plane wave case," Radio Sci. 11, 775–778 (1976).

S. T. Hong and A. Ishimaru, "Two-frequency mutual coherence function, coherence bandwidth and coherence time of millimeter and optical waves in rain, fog and turbulence," Radio Sci. 11, 551–559 (1976).

A. Ishimaru and S. T. Hong, "Multiple scattering effects on coherent bandwidth and pulse distortion of a wave propagating in a random distribution of particles," Radio Sci. 10, 637–644 (1975).

Ishimaru, A.

S. T. Hong, I. Sreenivasiah, and A. Ishimaru, "Plane wave pulse propagation through random media," IEEE Trans. Antennas Propag. AP-25, 822–827 (1977).

I. Sreenivasiah, A. Ishimaru, and S. T. Hong, "Two-frequency mutual coherence function and pulse propagation in a random medium: An analytical solution to plane wave case," Radio Sci. 11, 775–778 (1976).

L. Reynolds, C. C. Johnson, and A. Ishimaru, "Diffuse reflectance from a finite blood medium: applications to the modeling of fiberoptic catheters," Appl. Opt. 15, 2059–2067 (1976).

S. T. Hong and A. Ishimaru, "Two-frequency mutual coherence function, coherence bandwidth and coherence time of millimeter and optical waves in rain, fog and turbulence," Radio Sci. 11, 551–559 (1976).

A. Ishimaru and S. T. Hong, "Multiple scattering effects on coherent bandwidth and pulse distortion of a wave propagating in a random distribution of particles," Radio Sci. 10, 637–644 (1975).

A. Ishimaru, "Theory and application of wave propagation and scattering in random media," Proc. IEEE 65, 1030–1061 (1977).

A. Ishimaru, Wave propagation and scattering in random media, Volumes I and II (Academic, New York, 1978).

Johnson, C. C.

Jokipii, J. R.

L. C. Lee and J. R. Jokipii, "Sontrong scintillations in astrophysics, II: A theory of temporal broadening of pulses," Astrophy. J. 201, 532–543 (1975).

Kirsch, P. I.

L. M. Erhukumov, I. G. Zarnitsina, and P. I. Kirsch, "Selective properties and the form of a signal passed through a statistically inhomogeneous arbitrary-thickness layer," Radiofiz. 16, 573–580 (1973).

Lee, L. C.

L. C. Lee and J. R. Jokipii, "Sontrong scintillations in astrophysics, II: A theory of temporal broadening of pulses," Astrophy. J. 201, 532–543 (1975).

Lerner, R. M.

Liu, C. H.

C. H. Liu and K. C. Yeh, "Frequency and spatial correlation function in a fading communication channel through the ionosphere," Radio Sci. 10, 1055–1061 (1975).

C. H. Liu, A. W. Weznik, and K. C. Yeh, "Propagation of pulse trains through a random medium," IEEE Trans. Antennas Propag. AP- 22, 524–627 (1974).

Morse, P. M.

P. M. Morse and H. Feshback, Methods of Theoretical Physics (McGraw-Hill, New York, 1953).

Reynolds, L.

Shishov, V. I.

V. I. Shishov, "Effect of refraction on scintillation characteristics and average pulse shape of pulsars," Sov. Astron. 17, 598–602 (1974).

Sreenivasiah, I.

S. T. Hong, I. Sreenivasiah, and A. Ishimaru, "Plane wave pulse propagation through random media," IEEE Trans. Antennas Propag. AP-25, 822–827 (1977).

I. Sreenivasiah, A. Ishimaru, and S. T. Hong, "Two-frequency mutual coherence function and pulse propagation in a random medium: An analytical solution to plane wave case," Radio Sci. 11, 775–778 (1976).

Uscinski, B. J.

B. J. Uscinski, "The propagation and broadening of pulses in weakly irregular media," Proc. R. Soc. Lond. A 336, 379–392 (1974).

Weznik, A. W.

C. H. Liu, A. W. Weznik, and K. C. Yeh, "Propagation of pulse trains through a random medium," IEEE Trans. Antennas Propag. AP- 22, 524–627 (1974).

Yeh, K. C.

C. H. Liu and K. C. Yeh, "Frequency and spatial correlation function in a fading communication channel through the ionosphere," Radio Sci. 10, 1055–1061 (1975).

C. H. Liu, A. W. Weznik, and K. C. Yeh, "Propagation of pulse trains through a random medium," IEEE Trans. Antennas Propag. AP- 22, 524–627 (1974).

Zarnitsina, I. G.

L. M. Erhukumov, I. G. Zarnitsina, and P. I. Kirsch, "Selective properties and the form of a signal passed through a statistically inhomogeneous arbitrary-thickness layer," Radiofiz. 16, 573–580 (1973).

Appl. Opt. (3)

Astrophy. J. (1)

L. C. Lee and J. R. Jokipii, "Sontrong scintillations in astrophysics, II: A theory of temporal broadening of pulses," Astrophy. J. 201, 532–543 (1975).

IEEE Trans. Antennas Propag. (2)

C. H. Liu, A. W. Weznik, and K. C. Yeh, "Propagation of pulse trains through a random medium," IEEE Trans. Antennas Propag. AP- 22, 524–627 (1974).

S. T. Hong, I. Sreenivasiah, and A. Ishimaru, "Plane wave pulse propagation through random media," IEEE Trans. Antennas Propag. AP-25, 822–827 (1977).

Proc. R. Soc. Lond. (1)

B. J. Uscinski, "The propagation and broadening of pulses in weakly irregular media," Proc. R. Soc. Lond. A 336, 379–392 (1974).

Radio Sci. (4)

C. H. Liu and K. C. Yeh, "Frequency and spatial correlation function in a fading communication channel through the ionosphere," Radio Sci. 10, 1055–1061 (1975).

A. Ishimaru and S. T. Hong, "Multiple scattering effects on coherent bandwidth and pulse distortion of a wave propagating in a random distribution of particles," Radio Sci. 10, 637–644 (1975).

I. Sreenivasiah, A. Ishimaru, and S. T. Hong, "Two-frequency mutual coherence function and pulse propagation in a random medium: An analytical solution to plane wave case," Radio Sci. 11, 775–778 (1976).

S. T. Hong and A. Ishimaru, "Two-frequency mutual coherence function, coherence bandwidth and coherence time of millimeter and optical waves in rain, fog and turbulence," Radio Sci. 11, 551–559 (1976).

Radiofiz. (1)

L. M. Erhukumov, I. G. Zarnitsina, and P. I. Kirsch, "Selective properties and the form of a signal passed through a statistically inhomogeneous arbitrary-thickness layer," Radiofiz. 16, 573–580 (1973).

Sov. Astron. (1)

V. I. Shishov, "Effect of refraction on scintillation characteristics and average pulse shape of pulsars," Sov. Astron. 17, 598–602 (1974).

Other (3)

A. Ishimaru, "Theory and application of wave propagation and scattering in random media," Proc. IEEE 65, 1030–1061 (1977).

A. Ishimaru, Wave propagation and scattering in random media, Volumes I and II (Academic, New York, 1978).

P. M. Morse and H. Feshback, Methods of Theoretical Physics (McGraw-Hill, New York, 1953).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.