Abstract

We analyze the distribution of the rf spectrum in optoelectronic oscillators due to the finite duration of the spectrum measurement. The distribution of the periodogram or the rf spectrum at a given frequency is calculated using a reduced model and is compared to a comprehensive numerical simulation. The model shows that the rf spectrum at a given frequency fluctuates from measurement to measurement with an exponential distribution.

© 2008 Optical Society of America

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References

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  1. X. S. Yao and L. Maleki, Opt. Lett. 21, 483 (1996).
    [CrossRef] [PubMed]
  2. X. S. Yao and L. Maleki, J. Opt. Soc. Am. B 13, 1725 (1996).
    [CrossRef]
  3. M. C. Li, IEEE Trans. Antennas Propag. 52, 3319 (2004).
    [CrossRef]
  4. E. C. Levy, M. Horowitz, and C. R. Menyuk, “Modeling optoelectronic oscillators,” J. Opt. Soc. Am. B (to be published).
  5. K. S. Trivedi, in Probability and Statistics with Reliability, Queueing and Computer Science Applications (Wiley, 2002), p. 637.

2004 (1)

M. C. Li, IEEE Trans. Antennas Propag. 52, 3319 (2004).
[CrossRef]

1996 (2)

Horowitz, M.

E. C. Levy, M. Horowitz, and C. R. Menyuk, “Modeling optoelectronic oscillators,” J. Opt. Soc. Am. B (to be published).

Levy, E. C.

E. C. Levy, M. Horowitz, and C. R. Menyuk, “Modeling optoelectronic oscillators,” J. Opt. Soc. Am. B (to be published).

Li, M. C.

M. C. Li, IEEE Trans. Antennas Propag. 52, 3319 (2004).
[CrossRef]

Maleki, L.

Menyuk, C. R.

E. C. Levy, M. Horowitz, and C. R. Menyuk, “Modeling optoelectronic oscillators,” J. Opt. Soc. Am. B (to be published).

Trivedi, K. S.

K. S. Trivedi, in Probability and Statistics with Reliability, Queueing and Computer Science Applications (Wiley, 2002), p. 637.

Yao, X. S.

IEEE Trans. Antennas Propag. (1)

M. C. Li, IEEE Trans. Antennas Propag. 52, 3319 (2004).
[CrossRef]

J. Opt. Soc. Am. B (1)

Opt. Lett. (1)

Other (2)

E. C. Levy, M. Horowitz, and C. R. Menyuk, “Modeling optoelectronic oscillators,” J. Opt. Soc. Am. B (to be published).

K. S. Trivedi, in Probability and Statistics with Reliability, Queueing and Computer Science Applications (Wiley, 2002), p. 637.

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Figures (4)

Fig. 1
Fig. 1

Radio frequency spectrum S rf ( f k ) as a function of the frequency offset from the carrier frequency. The spectrum was calculated from a single simulation run with a measurement duration of T = 2.8 ms (light gray curve). The rf spectral density (black curve) and the phase spectral density (dark gray curve) were calculated by averaging the results the over 350 runs.

Fig. 2
Fig. 2

Distribution of the real and the imaginary normalized Fourier coefficients, ξ rf ( f k ) , calculated from 30,000 simulation runs at three frequencies: f k τ = 1 10 (diamonds), f k τ = 1 20 (circles), and f k τ = 1 50 (triangles). The results are compared to a normal distribution with a variance σ 2 = 0.5 (dashed curve).

Fig. 3
Fig. 3

Distribution of the normalized rf spectrum, ξ rf ( f k ) 2 , at a frequency f k τ = 1 10 calculated from 30,000 runs. An exponential distribution with an average of 1 is added for comparison (dashed curve).

Fig. 4
Fig. 4

Cross correlation between the normalized Fourier coefficients ξ rf ( f k = 1 5 τ ) and ξ rf ( f m ) calculated for three different measurement durations: T = 1 f k (dotted triangles), T = 2 f k (dashed circles), and T = 20 f k (solid diamonds).

Equations (6)

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V ( t ) = a ( t ) cos [ ω c t + ϕ ( t ) ] = a ( t ) exp ( i ω c t ) 2 + c.c.
a ( t ) = k = a ̃ k exp ( i ω k t ) ,
S rf ( f k ) = a ̃ k 2 2 R P osc δ f ,
σ k 2 = R P osc S rf ( f k ) δ f ,
p ( x ) = 1 S rf ( f k ) exp [ x S rf ( f k ) ] ,
R f k , f m = ξ rf ( f k ) ξ rf * ( f m ) .

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