Abstract

We introduce a new definition of the energy spectrum of a nonstationary ensemble of pulses that reduces to the usual ones in the limit of statistically stationary ensembles of signals and of fully temporarily coherent ensembles.

© 2004 Optical Society of America

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References

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  1. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, 1995).
    [CrossRef]
  2. W. A. Gardner and L. E. Franks, IEEE Trans. Inf. Theory 21, 4 (1975).
    [CrossRef]
  3. For an application of cyclostationary processes to optics, see, for example, S. B. Cavalcanti, New J. Phys. 4, 19.1 (2002).
    [CrossRef]
  4. D. Marcuse, Light Transmission in Optics, 2nd ed. (Van Nostrand Reinhold, New York, 1982), Sec. 12.3.
  5. C. H. Page, J. Appl. Phys. 23, 103 (1952).
    [CrossRef]
  6. D. G. Lampard, J. Appl. Phys. 25, 803 (1954).
    [CrossRef]
  7. W. D. Mark, J. Sound Vib. 11, 19 (1970).
    [CrossRef]
  8. J. H. Eberly and K. Wódkievicz, J. Opt. Soc. Am. 67, 1552 (1977).
  9. M. Bertolotti, A. Ferrari, and L. Sereda, J. Opt. Soc. Am. B 15, 341 (1995).
    [CrossRef]
  10. L. Sereda, M. Bertolotti, and A. Ferrari, J. Opt. Soc. Am. A 15, 695 (1998) and references therein.
    [CrossRef]
  11. G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, San Diego, Calif., 2001).
  12. For an excellent review on the behavior of optical signals in complementary spaces see G. S. Agarwal, Found. Phys. 25, 219 (1995).
    [CrossRef]
  13. F. W. Buron and R. W. Fuller, Mathematics of Classical and Quantum Physics (Dover, New York, 1992) p. 248.
  14. R. A. Silverman, Proc. IRE Trans. Inf. Theory 3, 182 (1957).
    [CrossRef]
  15. E. Wolf, Opt. Lett. 28, 5 (2003).
    [CrossRef] [PubMed]
  16. Such a definition of the spectrum of light was employed in a theoretical analysis of strong-field resonance fluorescence in B. Renaud, R. M. Whitley, and C. R. Stroud, J. Phys. B 10, 19 (1977).
    [CrossRef]

2003 (1)

2002 (1)

For an application of cyclostationary processes to optics, see, for example, S. B. Cavalcanti, New J. Phys. 4, 19.1 (2002).
[CrossRef]

1998 (1)

1995 (2)

M. Bertolotti, A. Ferrari, and L. Sereda, J. Opt. Soc. Am. B 15, 341 (1995).
[CrossRef]

For an excellent review on the behavior of optical signals in complementary spaces see G. S. Agarwal, Found. Phys. 25, 219 (1995).
[CrossRef]

1977 (2)

J. H. Eberly and K. Wódkievicz, J. Opt. Soc. Am. 67, 1552 (1977).

Such a definition of the spectrum of light was employed in a theoretical analysis of strong-field resonance fluorescence in B. Renaud, R. M. Whitley, and C. R. Stroud, J. Phys. B 10, 19 (1977).
[CrossRef]

1975 (1)

W. A. Gardner and L. E. Franks, IEEE Trans. Inf. Theory 21, 4 (1975).
[CrossRef]

1970 (1)

W. D. Mark, J. Sound Vib. 11, 19 (1970).
[CrossRef]

1957 (1)

R. A. Silverman, Proc. IRE Trans. Inf. Theory 3, 182 (1957).
[CrossRef]

1954 (1)

D. G. Lampard, J. Appl. Phys. 25, 803 (1954).
[CrossRef]

1952 (1)

C. H. Page, J. Appl. Phys. 23, 103 (1952).
[CrossRef]

Agarwal, G. S.

For an excellent review on the behavior of optical signals in complementary spaces see G. S. Agarwal, Found. Phys. 25, 219 (1995).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, San Diego, Calif., 2001).

Bertolotti, M.

Buron, F. W.

F. W. Buron and R. W. Fuller, Mathematics of Classical and Quantum Physics (Dover, New York, 1992) p. 248.

Cavalcanti, S. B.

For an application of cyclostationary processes to optics, see, for example, S. B. Cavalcanti, New J. Phys. 4, 19.1 (2002).
[CrossRef]

Eberly, J. H.

J. H. Eberly and K. Wódkievicz, J. Opt. Soc. Am. 67, 1552 (1977).

Ferrari, A.

Franks, L. E.

W. A. Gardner and L. E. Franks, IEEE Trans. Inf. Theory 21, 4 (1975).
[CrossRef]

Fuller, R. W.

F. W. Buron and R. W. Fuller, Mathematics of Classical and Quantum Physics (Dover, New York, 1992) p. 248.

Gardner, W. A.

W. A. Gardner and L. E. Franks, IEEE Trans. Inf. Theory 21, 4 (1975).
[CrossRef]

Lampard, D. G.

D. G. Lampard, J. Appl. Phys. 25, 803 (1954).
[CrossRef]

Mandel, L.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, 1995).
[CrossRef]

Marcuse, D.

D. Marcuse, Light Transmission in Optics, 2nd ed. (Van Nostrand Reinhold, New York, 1982), Sec. 12.3.

Mark, W. D.

W. D. Mark, J. Sound Vib. 11, 19 (1970).
[CrossRef]

Page, C. H.

C. H. Page, J. Appl. Phys. 23, 103 (1952).
[CrossRef]

Renaud, B.

Such a definition of the spectrum of light was employed in a theoretical analysis of strong-field resonance fluorescence in B. Renaud, R. M. Whitley, and C. R. Stroud, J. Phys. B 10, 19 (1977).
[CrossRef]

Sereda, L.

Silverman, R. A.

R. A. Silverman, Proc. IRE Trans. Inf. Theory 3, 182 (1957).
[CrossRef]

Stroud, C. R.

Such a definition of the spectrum of light was employed in a theoretical analysis of strong-field resonance fluorescence in B. Renaud, R. M. Whitley, and C. R. Stroud, J. Phys. B 10, 19 (1977).
[CrossRef]

Whitley, R. M.

Such a definition of the spectrum of light was employed in a theoretical analysis of strong-field resonance fluorescence in B. Renaud, R. M. Whitley, and C. R. Stroud, J. Phys. B 10, 19 (1977).
[CrossRef]

Wódkievicz, K.

J. H. Eberly and K. Wódkievicz, J. Opt. Soc. Am. 67, 1552 (1977).

Wolf, E.

E. Wolf, Opt. Lett. 28, 5 (2003).
[CrossRef] [PubMed]

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, 1995).
[CrossRef]

Found. Phys. (1)

For an excellent review on the behavior of optical signals in complementary spaces see G. S. Agarwal, Found. Phys. 25, 219 (1995).
[CrossRef]

IEEE Trans. Inf. Theory (1)

W. A. Gardner and L. E. Franks, IEEE Trans. Inf. Theory 21, 4 (1975).
[CrossRef]

J. Appl. Phys. (2)

C. H. Page, J. Appl. Phys. 23, 103 (1952).
[CrossRef]

D. G. Lampard, J. Appl. Phys. 25, 803 (1954).
[CrossRef]

J. Opt. Soc. Am. (1)

J. H. Eberly and K. Wódkievicz, J. Opt. Soc. Am. 67, 1552 (1977).

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

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

M. Bertolotti, A. Ferrari, and L. Sereda, J. Opt. Soc. Am. B 15, 341 (1995).
[CrossRef]

J. Phys. B (1)

Such a definition of the spectrum of light was employed in a theoretical analysis of strong-field resonance fluorescence in B. Renaud, R. M. Whitley, and C. R. Stroud, J. Phys. B 10, 19 (1977).
[CrossRef]

J. Sound Vib. (1)

W. D. Mark, J. Sound Vib. 11, 19 (1970).
[CrossRef]

New J. Phys. (1)

For an application of cyclostationary processes to optics, see, for example, S. B. Cavalcanti, New J. Phys. 4, 19.1 (2002).
[CrossRef]

Opt. Lett. (1)

Proc. IRE Trans. Inf. Theory (1)

R. A. Silverman, Proc. IRE Trans. Inf. Theory 3, 182 (1957).
[CrossRef]

Other (4)

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, 1995).
[CrossRef]

D. Marcuse, Light Transmission in Optics, 2nd ed. (Van Nostrand Reinhold, New York, 1982), Sec. 12.3.

G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, San Diego, Calif., 2001).

F. W. Buron and R. W. Fuller, Mathematics of Classical and Quantum Physics (Dover, New York, 1992) p. 248.

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Equations (17)

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U˜ω-+dtUtexp-iωt,
SωU˜ω2,
Sω=-+-+dt1dt2Γt1,t2expiωt1-t2,
Γt1,t2=U*t1Ut2
-+dωSω=-+dtUt2.
Γt1,t2=Φt1+t22ξt1-t2,
τc=-+-+dt1dt2t1-t22γt1,t22-+-+dt1dt2γt1,t221/2.
γt1,t2Γt1,t2It1It2,
γt1,t2=expiϕt1,t2.
γt1,t2=expiψt1-ψt2.
Γt1,t2=Ψ*t1Ψt2,
Rt=UDt2.
UDt=-+dtHt-tUtexp-iωft-t,
Rt,ωf=-+dt-+dt H*t-t Ht-t×Γt1,t2exp-iωft-t .
Ht=2γfθtexp-γft,
S¯ωf=-T0T0dtRt,ωf.
σωf=-+dωπγfγf2+ω-ωf2Sω.

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