Abstract

We present a numerical technique to simulate the propagation characteristics of an on-off-keyed modulated optical signal through fog. The on-off-keyed modulated light (a square wave) is decomposed into a finite number of harmonic components, and a numerical solution for the vector radiative transfer equation is obtained for each harmonic that corresponds to the modulation frequency. With this method we study the distortion and the pulse spread in the received signal due to attenuation and scattering. We investigate the propagation characteristic of the modulated signal with different communication system parameters. This information can be used to study communication channel reliability.

© 2004 Optical Society of America

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References

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  1. A. Ishimaru, S. Jaruwatanadilok, Y. Kuga, “Polarized pulse waves in random discrete scatterers,” Appl. Opt. 40, 5495–5502 (2001).
    [CrossRef]
  2. A. Ishimaru, Wave Propagation and Scattering in Random Media (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1997).
  3. C. Davis, I. Smolyaninov, “The effect of atmospheric turbulence on bit-error rate in an on-off-keyed optical wireless system,” in Free-Space Laser Communication and Laser Imaging, D. G. Voelz, J. C. Ricklin, eds., Proc. SPIE4489, 129–131 (2002).
    [CrossRef]
  4. H. C. van de Hulst, Multiple Light Scattering, (Academic, New York, 1980), Vols. 1 and 2.
  5. R. L. Cheung, A. Ishimaru, “Transmission, backscattering, and depolarization of waves in randomly distributed spherical particles,” Appl. Opt. 21, 3792–3798 (1982).
    [CrossRef] [PubMed]
  6. S. Jaruwatanadilok, A. Ishimaru, Y. Kuga, “Photon density wave for imaging through random media,” Waves Random Media 12, 351–364 (2002).
    [CrossRef]
  7. L. W. Couch, Modern Communication Systems (Prentice-Hall, Englewood Cliffs, N.J., 1995).

2002 (1)

S. Jaruwatanadilok, A. Ishimaru, Y. Kuga, “Photon density wave for imaging through random media,” Waves Random Media 12, 351–364 (2002).
[CrossRef]

2001 (1)

1982 (1)

Cheung, R. L.

Couch, L. W.

L. W. Couch, Modern Communication Systems (Prentice-Hall, Englewood Cliffs, N.J., 1995).

Davis, C.

C. Davis, I. Smolyaninov, “The effect of atmospheric turbulence on bit-error rate in an on-off-keyed optical wireless system,” in Free-Space Laser Communication and Laser Imaging, D. G. Voelz, J. C. Ricklin, eds., Proc. SPIE4489, 129–131 (2002).
[CrossRef]

Ishimaru, A.

S. Jaruwatanadilok, A. Ishimaru, Y. Kuga, “Photon density wave for imaging through random media,” Waves Random Media 12, 351–364 (2002).
[CrossRef]

A. Ishimaru, S. Jaruwatanadilok, Y. Kuga, “Polarized pulse waves in random discrete scatterers,” Appl. Opt. 40, 5495–5502 (2001).
[CrossRef]

R. L. Cheung, A. Ishimaru, “Transmission, backscattering, and depolarization of waves in randomly distributed spherical particles,” Appl. Opt. 21, 3792–3798 (1982).
[CrossRef] [PubMed]

A. Ishimaru, Wave Propagation and Scattering in Random Media (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1997).

Jaruwatanadilok, S.

S. Jaruwatanadilok, A. Ishimaru, Y. Kuga, “Photon density wave for imaging through random media,” Waves Random Media 12, 351–364 (2002).
[CrossRef]

A. Ishimaru, S. Jaruwatanadilok, Y. Kuga, “Polarized pulse waves in random discrete scatterers,” Appl. Opt. 40, 5495–5502 (2001).
[CrossRef]

Kuga, Y.

S. Jaruwatanadilok, A. Ishimaru, Y. Kuga, “Photon density wave for imaging through random media,” Waves Random Media 12, 351–364 (2002).
[CrossRef]

A. Ishimaru, S. Jaruwatanadilok, Y. Kuga, “Polarized pulse waves in random discrete scatterers,” Appl. Opt. 40, 5495–5502 (2001).
[CrossRef]

Smolyaninov, I.

C. Davis, I. Smolyaninov, “The effect of atmospheric turbulence on bit-error rate in an on-off-keyed optical wireless system,” in Free-Space Laser Communication and Laser Imaging, D. G. Voelz, J. C. Ricklin, eds., Proc. SPIE4489, 129–131 (2002).
[CrossRef]

van de Hulst, H. C.

H. C. van de Hulst, Multiple Light Scattering, (Academic, New York, 1980), Vols. 1 and 2.

Appl. Opt. (2)

Waves Random Media (1)

S. Jaruwatanadilok, A. Ishimaru, Y. Kuga, “Photon density wave for imaging through random media,” Waves Random Media 12, 351–364 (2002).
[CrossRef]

Other (4)

L. W. Couch, Modern Communication Systems (Prentice-Hall, Englewood Cliffs, N.J., 1995).

A. Ishimaru, Wave Propagation and Scattering in Random Media (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1997).

C. Davis, I. Smolyaninov, “The effect of atmospheric turbulence on bit-error rate in an on-off-keyed optical wireless system,” in Free-Space Laser Communication and Laser Imaging, D. G. Voelz, J. C. Ricklin, eds., Proc. SPIE4489, 129–131 (2002).
[CrossRef]

H. C. van de Hulst, Multiple Light Scattering, (Academic, New York, 1980), Vols. 1 and 2.

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Figures (11)

Fig. 1
Fig. 1

Top: simulated optical communication system and propagation channel. LHC, left-hand circular. Bottom: plane-parallel problem and definitions.

Fig. 2
Fig. 2

Block diagram of numerical simulations.

Fig. 4
Fig. 4

Received ac signal waveforms of 0.8-μm wavelength and 200-MHz modulation frequency for (a) τ0 = 1, FOV of 1 mrad; (b) τ0 = 1, FOV of 50 mrad; τ0 = 16, FOV of 1 mrad; (d) τ0 = 16, FOV of 50 mrad.

Fig. 6
Fig. 6

ac signal waveforms of 0.8-μm wavelength and 200-MHz modulation frequency with a FOV of 50 mrad for (a) τ0 = 30 and (b) τ0 = 40.

Fig. 11
Fig. 11

Received ac signal waveforms of 1.5-μm wavelength and 2-GHz modulation frequency with a FOV of 50 mrad for (a) τ0 = 1, (b) τ0 = 16, (c) τ0 = 30, (d) τ0 = 40.

Fig. 3
Fig. 3

Received (ac plus dc) signal waveforms of 0.8-μm wavelength and 200-MHz modulation frequency with a FOV of 50 mrad for (a) tau0 = 1, (b) tau0 = 16.

Fig. 5
Fig. 5

rms values of incoherent and coherent intensity of 0.8-μm wavelength and 200-MHz modulation frequency versus τ0 for (a) FOV of 1 mrad, (b) FOV of 10 mrad, (c) FOV of 50 mrad, (d) FOV of 100 mrad.

Fig. 7
Fig. 7

Eye diagram: received waveforms of 0.8-μm wavelength and 200-MHz modulation frequency with a FOV of 50 mrad for (a) τ0 = 1, (b) τ0 = 16, (c) τ0 = 30, (d) τ0 = 40.

Fig. 8
Fig. 8

rms values of incoherent and coherent intensity of 0.8-μm wavelength and 2-GHz modulation frequency with a FOV of 50 mrad versus τ0.

Fig. 9
Fig. 9

Received ac signal waveforms of 0.8-μm wavelength and 2-GHz modulation frequency with a FOV of 50 mrad for (a) τ0 = 1, (b) τ0 = 16, (c) τ0 = 30, (d) τ0 = 40.

Fig. 10
Fig. 10

rms values of incoherent and coherent intensity of 1.5-μm wavelength with a FOV of 50 mrad versus τ0 for (a) frequency of 200 MHz, (b) frequency of 2 GHz.

Tables (1)

Tables Icon

Table 1 Particle Size Distribution of the Fog

Equations (18)

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I=I1I2UVT=E1E1*E2E2*2 Re ×E1E2*2 ImE1E2*T,
μ τ+1+1τ0tnItn, τ, μ, ϕ=02π-11 Sμ, ϕ,μ, ϕItn, τ, μ, ϕdμdϕ +Jtn, τ, μ, ϕ, for 0ττ0.
S=1ρσtρ|f11|2ρ|f12|2ρ Ref11f12*-ρ Imf11f12*ρ|f21|2ρ|f22|2ρ Ref21f22*-ρ Imf21f22*ρ2 Ref11f21*ρ2 Ref12f22*ρ Ref11f22*+f12f21*-ρ Imf11f22*-f12f21*ρ2 Imf11f21*ρ2 Imf12f22*ρ Imf11f22*+f12f21*ρ Ref11f22*-f12f21*.
Itotalt=Iconstant+Itexp-iωmodt,
Itotalt=Itotal_reducedt+Itotal_diffusedt.
Itotal_reducedt=Iri_dc+Iri_ac,
Itotal_diffusedt=Id_dc+Id_ac,
Itotalt=Id_dc+Id_ac+Iri_dc+Iri_ac,
τ Iri=-Iri,
Irit, τ=I0ft, τexp-τδμ-1δϕ,
I0=1/2 1/2 0 1T,
ft, τ=exp-iωmt-ττ0,
μ τ+1+1τ0tnIdtn, τ, μ, ϕ=02π-11 Sμ, ϕ, μ, ϕIdtn, τ, μ,ϕdμdϕ +Eritn, τ, μ, ϕ, for 0ττ0.
Eri=02π-11 Sμ, ϕ, μ, ϕIrit, τ, μ, ϕdμdϕ =F0μ, ϕft, τexp-τ,
Idτ=0=0 for 0μ1,
Idτ=0=0 for -1μ0.
μ τ Idω, τ, μ1+μ-1i ω+ωmτ0Idω, τ, μ=02π-11 Sμ, ϕ, μ, ϕIdω, τ, μ, ϕdμdϕ +F0μ, ϕfω, τexp-τ,
fω, τ=2πδω.

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