## Coherence properties of nonstationary light wave fields

JOSA A, Vol. 15, Issue 3, pp. 695-705 (1998)

http://dx.doi.org/10.1364/JOSAA.15.000695

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### Abstract

A spectral approach to the theory of partial coherence of nonstationary light [BertolottiM., Pure Appl. Opt. 6, 153 (1997)] is applied to the study of spatial coherence properties of nonstationary wave fields on propagation in free space. Three types of nonstationary light sources are considered—a point source, a spatially incoherent source, and a uniformly coherent source, the last being perfectly coherent in both space–time and space–frequency domains. An example of the diffraction pattern from a slit with nonstationary partially coherent illumination is used to illustrate the general discussion.

© 1998 Optical Society of America

**OCIS Codes**

(030.1640) Coherence and statistical optics : Coherence

(050.0050) Diffraction and gratings : Diffraction and gratings

(320.0320) Ultrafast optics : Ultrafast optics

**History**

Original Manuscript: June 9, 1997

Revised Manuscript: October 3, 1997

Manuscript Accepted: October 3, 1997

Published: March 1, 1998

**Citation**

Leonid Sereda, Mario Bertolotti, and Aldo Ferrari, "Coherence properties of nonstationary light wave fields," J. Opt. Soc. Am. A **15**, 695-705 (1998)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-15-3-695

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### References

- M. Bertolotti, L. Sereda, A. Ferrari, “Application of the spectral representation of stochastic processes to the study of nonstationary light radiation: a tutorial,” Pure Appl. Opt. 6, 153–171 (1997). [CrossRef]
- M. Bertolotti, A. Ferrari, L. Sereda, “Coherence properties of nonstationary polychromatic light sources,” J. Opt. Soc. Am. B 12, 341–347 (1995). [CrossRef]
- M. Bertolotti, A. Ferrari, L. Sereda, “Far-zone diffraction of polychromatic and nonstationary plane waves from a slit,” J. Opt. Soc. Am. B 12, 1519–1526 (1995). [CrossRef]
- L. Sereda, A. Ferrari, M. Bertolotti, “On the partial coherence theory for nonstationary light,” in Coherence and Quantum Optics VII: J. H. Eberly, L. Mandel, E. Wolf, eds. (Plenum, New York, 1996), pp. 689–690.
- L. Sereda, A. Ferrari, M. Bertolotti, “Spectral and time evolution in diffraction from a slit of polychromatic and nonstationary plane waves,” J. Opt. Soc. Am. B 13, 1394–1402 (1996). [CrossRef]
- L. Sereda, A. Ferrari, M. Bertolotti, “Diffraction of a time Gaussian-shaped pulsed plane wave from a slit,” Pure Appl. Opt. 5, 349–353 (1996). [CrossRef]
- L. Sereda, A. Ferrari, M. Bertolotti, “Spectral and time evolution of nonstationary plane waves in diffraction from a slit,” in Coherence and Quantum Optics VII: J. H. Eberly, L. Mandel, E. Wolf, eds. (Plenum, New York, 1996), pp. 693–694.
- L. Sereda, A. Ferrari, M. Bertolotti, “Spectral and time evolution of non-stationary plane waves in a two-beam interference experiment,” J. Mod. Opt. 43, 2503–2522 (1996). [CrossRef]
- L. Sereda, A. Ferrari, M. Bertolotti, “Diffraction of a pulsed plane wave from an amplitude diffraction grating,” J. Mod. Opt. 44, 1321–1343 (1997). [CrossRef]
- L. Sereda, “The spectral theory of coherence, interference and diffraction of nonstationary light,” Ph.D. thesis (University of Rome “La Sapienza,”Rome, 1997).
- About the definitions of the source spectral composition and time intensity see also Refs. 1-3.
- L. Mandel, E. Wolf, “Some properties of coherent light,” J. Opt. Soc. Am. 51, 815–819 (1961). [CrossRef]
- L. Mandel, E. Wolf, “Complete coherence in the space–frequency domain,” Opt. Commun. 36, 247–249 (1981). [CrossRef]
- W. H. Carter, “Difference in the definitions of coherence in the space–time domain and in the space–frequency domain,” J. Mod. Opt. 39, 1461–1470 (1992). [CrossRef]
- As is shown in Refs. 5 and 6, the energy of a pulsed source is equal to the sum of intensities of the source monochromatic components—in our case given by Eq. (2.3), multiplied by the factor 2π, which constitutes a generalization of the Parceval theorem to pulsed stochastic processes of finite energy.
- L. Mandel, E. Wolf, “Spectral coherence and the concept of cross-spectral purity,” J. Opt. Soc. Am. 66, 529–535 (1976). [CrossRef]
- M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980).
- E. Wolf, “New spectral representation of random sources and of the partially coherent fields that they generate,” Opt. Commun. 38, 3–6 (1981). [CrossRef]
- An example of such a situation for a source, consisting of two partially correlated point sources, is given in Ref. 1.
- R. J. Adler, The Geometry of Random Fields (Wiley, New York, 1981).
- It means also that if a thin opaque screen with a small aperture is illuminated from a point source, the spatial coherence of light will not change across the aperture, forming in this way a secondary uniformly coherent source, as is defined by Eqs. (2.1) and (2.2).
- Considering the far-zone wave field, it is more exact to say that the normalized spectrum, time intensity, and energy remain unchanged in certain directions of observation, changing if this direction changes, as is shown in Refs. 3-10.
- M. Planck, The Theory of Heat Radiation (Dover, New York, 1959).

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