Correlation dependent, propagation-induced shifts in the generalized spectra of cyclostationary, random fields are predicted. This result generalizes the Wolf shift for stationary fields and is applicable to periodic trains of fast pulses such as might be generated in comb spectroscopy or other mode-locked pulsed systems. Examples illustrate these shifts for intrinsically stationary fields and the fields generated by a mode-locked laser.

© 2009 Optical Society of America

1. E. Wolf, Introduction to the Theory of Coherence and Polarization (Cambridge University Press, 2007).
2. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, 1995).
3. P. Corkum and Z. Chang, "The Attosecond Revolution," Opt. Photon. News 19, 24-29 (2008). [CrossRef]
4. W. Gardner, A. Napolitano, and L. Paura, "Cyclostationarity: Half a Century of Research," Signal Process. 86, 639-697 (2006). [CrossRef]
5. B. Davis, "Measurable Coherence Theory for Statistically Periodic Fields," Phys. Rev. A 76, 043,843 (2007). [CrossRef]
6. E. Wolf, "Invariance of the Spectrum of Light on Propagation," Phys. Rev. Lett. 56, 1370-1372 (1986). [CrossRef] [PubMed]
7. E. Wolf, "Noncosmological Redshifts of Spectral Lines," Nature (London) 326, 363-365 (1987). [CrossRef]
8. S. Ponomarenko, G. Agrawal, and E. Wolf, "Energy Spectrum of a Nonstationary Ensemble of Pulses," Opt. Lett. 29, 394-396 (2004). [CrossRef] [PubMed]
9. H. Lajunen, P. Vahimaa, and J. Tervo, "Theory of Spatially and Spectrally Partially Coherent Pulses," J. Opt. Soc. Am. A 22, 1536-1545 (2005). [CrossRef]
10. R. Gase and M. Schubert, "On the Determination of Spectral Properties of Non-stationary Radiation," J. Mod. Opt. 29, 1331-1347 (1982).
11. R. Schoonover, B. Davis, R. Bartels, and P. Carney, "Optical Interferometry with Pulsed Fields," J. Mod. Opt. 55, 1541-1556 (2008). [CrossRef]
12. A. Kubo, K. Onda, H. Petek, Z. Sun, Y. Jung, and H. Kim, "Femtosecond Imaging of Surface Plasmon Dynamics in a Nanostructured Silver Film," Nano Lett 5, 1123-1127 (2005). [CrossRef] [PubMed]
13. Y. Liau, A. Unterreiner, Q. Chang, and N. Scherer, "Ultrafast Dephasing of Single Nanoparticles Studied by Two-pulse Second-order Interferometry," J. Phys. Chem. B 105, 2135-2142 (2001). [CrossRef]
14. T. Stievater, X. Li, D. Steel, D. Gammon, D. Katzer, D. Park, C. Piermarocchi, and L. Sham, "Rabi Oscillations of Excitons in Single Quantum Dots," Phys. Rev. Lett. 87, 133,603 (2001). [CrossRef]
15. J. Reichert, R. Holzwarth, T. Udem, and T. H¨ansch,"Measuring the Frequency of Light with Mode-locked Lasers," Opt. Commun. 172, 59-68 (1999). [CrossRef]
16. D. Jones, S. Diddams, J. Ranka, A. Stentz, R. Windeler, J. Hall, and S. Cundiff, "Carrier-Envelope Phase Control of Femtosecond Mode-Locked Lasers and Direct Optical Frequency Synthesis," Science (London) 288, 635 (2000).
17. B. Saleh and M. Teich, Fundamentals of Photonics (New York: Wiley-Interscience, 1991). [CrossRef]
18. S. Jacobs, "The Optical Heterodyne," Electronics 36, 29 (1963).
19. A. Siegman, S. Harris, and B. McMurtry, "Optical Heterodyning and Optical Demodulation at Microwave Frequencies," Optical Masers pp. 511-527 (1963).
20. T. Young, "The Bakerian Lecture. Experiments and Calculations Relative to Physical Optics," Phil. Trans. R. Soc. Lond 94 (1804).

Agrawal, G.
Bartels, R.
Carney, P.
Chang, Q.
Chang, Z.
Corkum, P.
Cundiff, S.
Davis, B.
Diddams, S.
Gammon, D.
Gardner, W.
Gase, R.
H¨ansch, T.
Hall, J.
Holzwarth, R.
Jacobs, S.
Jones, D.
Jung, Y.
Katzer, D.
Kim, H.
Kubo, A.
Lajunen, H.
Li, X.
Liau, Y.
Napolitano, A.
Onda, K.
Park, D.
Paura, L.
Petek, H.
Piermarocchi, C.
Ponomarenko, S.
Ranka, J.
Reichert, J.
Scherer, N.
Schoonover, R.
Schubert, M.
Sham, L.
Steel, D.
Stentz, A.
Stievater, T.
Sun, Z.
Tervo, J.
Udem, T.
Unterreiner, A.
Vahimaa, P.
Windeler, R.
Wolf, E.
Young, T.

Electronics

• S. Jacobs, "The Optical Heterodyne," Electronics 36, 29 (1963).

J. Mod. Opt.

• R. Gase and M. Schubert, "On the Determination of Spectral Properties of Non-stationary Radiation," J. Mod. Opt. 29, 1331-1347 (1982).
• R. Schoonover, B. Davis, R. Bartels, and P. Carney, "Optical Interferometry with Pulsed Fields," J. Mod. Opt. 55, 1541-1556 (2008). [CrossRef]

J. Opt. Soc. Am. A

• H. Lajunen, P. Vahimaa, and J. Tervo, "Theory of Spatially and Spectrally Partially Coherent Pulses," J. Opt. Soc. Am. A 22, 1536-1545 (2005). [CrossRef]

J. Phys. Chem. B

• Y. Liau, A. Unterreiner, Q. Chang, and N. Scherer, "Ultrafast Dephasing of Single Nanoparticles Studied by Two-pulse Second-order Interferometry," J. Phys. Chem. B 105, 2135-2142 (2001). [CrossRef]

Nano Lett

• A. Kubo, K. Onda, H. Petek, Z. Sun, Y. Jung, and H. Kim, "Femtosecond Imaging of Surface Plasmon Dynamics in a Nanostructured Silver Film," Nano Lett 5, 1123-1127 (2005). [CrossRef] [PubMed]

Nature (London)

• E. Wolf, "Noncosmological Redshifts of Spectral Lines," Nature (London) 326, 363-365 (1987). [CrossRef]

Opt. Commun.

• J. Reichert, R. Holzwarth, T. Udem, and T. H¨ansch,"Measuring the Frequency of Light with Mode-locked Lasers," Opt. Commun. 172, 59-68 (1999). [CrossRef]

Opt. Lett.

• S. Ponomarenko, G. Agrawal, and E. Wolf, "Energy Spectrum of a Nonstationary Ensemble of Pulses," Opt. Lett. 29, 394-396 (2004). [CrossRef] [PubMed]

Opt. Photon. News

• P. Corkum and Z. Chang, "The Attosecond Revolution," Opt. Photon. News 19, 24-29 (2008). [CrossRef]

Phil. Trans. R. Soc. Lond

• T. Young, "The Bakerian Lecture. Experiments and Calculations Relative to Physical Optics," Phil. Trans. R. Soc. Lond 94 (1804).

Phys. Rev. A

• B. Davis, "Measurable Coherence Theory for Statistically Periodic Fields," Phys. Rev. A 76, 043,843 (2007). [CrossRef]

Phys. Rev. Lett.

• E. Wolf, "Invariance of the Spectrum of Light on Propagation," Phys. Rev. Lett. 56, 1370-1372 (1986). [CrossRef] [PubMed]
• T. Stievater, X. Li, D. Steel, D. Gammon, D. Katzer, D. Park, C. Piermarocchi, and L. Sham, "Rabi Oscillations of Excitons in Single Quantum Dots," Phys. Rev. Lett. 87, 133,603 (2001). [CrossRef]

Science (London)

• D. Jones, S. Diddams, J. Ranka, A. Stentz, R. Windeler, J. Hall, and S. Cundiff, "Carrier-Envelope Phase Control of Femtosecond Mode-Locked Lasers and Direct Optical Frequency Synthesis," Science (London) 288, 635 (2000).

Signal Process.

• W. Gardner, A. Napolitano, and L. Paura, "Cyclostationarity: Half a Century of Research," Signal Process. 86, 639-697 (2006). [CrossRef]

Other

• E. Wolf, Introduction to the Theory of Coherence and Polarization (Cambridge University Press, 2007).
• L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, 1995).
• B. Saleh and M. Teich, Fundamentals of Photonics (New York: Wiley-Interscience, 1991). [CrossRef]
• A. Siegman, S. Harris, and B. McMurtry, "Optical Heterodyning and Optical Demodulation at Microwave Frequencies," Optical Masers pp. 511-527 (1963).

2008, Corkum, Opt. Photon. News
2008, Schoonover, J. Mod. Opt.
2007, Davis, Phys. Rev. A
2006, Gardner, Signal Process.
2005, Lajunen, J. Opt. Soc. Am. A
2005, Kubo, Nano Lett
2004, Ponomarenko, Opt. Lett.
2001, Liau, J. Phys. Chem. B
2001, Stievater, Phys. Rev. Lett.
2000, Jones, Science (London)
1999, Reichert, Opt. Commun.
1987, Wolf, Nature (London)
1986, Wolf, Phys. Rev. Lett.
1982, Gase, J. Mod. Opt.
1963, Jacobs, Electronics
1804, Young, Phil. Trans. R. Soc. Lond

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