New theory of partial coherence in the space-frequency domain. Part II: Steady-state fields and higher-order correlations

Journal of the Optical Society of America A: Optics and Image Science, and Vision

Volumn 3, Issue 1, 1986, Pages 76-85

  Wolf, Emil ^a  

^a UNIVERSITY OF ROCHESTER   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84975571278     PISSN: 10847529     EISSN: 15208532     Source Type: Journal    
DOI: 10.1364/JOSAA.3.000076     Document Type: Article

References (29)

1. 1/2.
2. E. Wolf, "A new description of second-order coherence phenomena in the space-frequency domain," AIP Conf. Proc. 65, 42-48 (1981).
3. E. Wolf, "New spectral representation of random sources and of the partially coherent fields that they generate," Opt. Commun. 38, 3-6 (1981).
4. A. Starikov and E. Wolf, "Coherent-mode representation of Gaussian Schell-model sources and of their radiation fields," J. Opt. Soc. Am. 72, 923-928 (1982).
5. A. Starikov, "Effective number of degrees of freedom of partially coherent sources," J. Opt. Soc. Am. 72, 1538-1544 (1982).
6. F. Gori, "Mode propagation of the field generated by Collett-Wolf Schell-model sources," Opt. Commun. 46, 149-154 (1983).
7. F. Gori and R. Grella, "Shape invariant propagation of polychromatic fields," Opt. Commun. 49, 173-177 (1984).
8. E. Wolf and G. S. Agarwal, "Coherence theory of laser resonator modes," J. Opt. Soc. Am. A 1, 541-546 (1984).
9. R. Martinez-Herrero and P. M. Mejias, "Radiometric definitions for partially coherent sources," J. Opt. Soc. Am. A 1, 556-558 (1984)
10. J. T. Foley and M. Nieto-Vesperinas, "Radiance functions that depend nonlinearly on the cross-spectral density," J. Opt. Soc. Am. A 2, 1446-1447 (1985).
11. I. J. LaHaie, "Inverse source problem for three-dimensional partially coherent sources and fields," J. Opt. Soc. Am. A 2, 35-45 (1985).
12. L. Mandel and E. Wolf, "Spectral coherence and the concept of cross-spectral purity," J. Opt. Soc. Am. 66, 529-535 (1976)
13. 2, ω), is discussed in E. Wolf, "Young's interference fringes with narrow-band light," Opt. Lett. 8, 250-252 (1983).
14. M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980), Sec. 10.3.1.
15. L. Mandel and E. Wolf, "Coherence properties of optical fields," Rev. Mod. Phys. 37, 231-287 (1965), Sec. 3.1.
16. C. H. Papas, Theory of Electromagnetic Wave Propagation (McGraw-Hill, New York, 1965), Sec. 2.1.
17. 2, τ) will not contain any negative frequency components (Ref. 12, Sec. 10.3.2), and the lower limits in the integrals in Eqs. (3.17) and (3.18) can then be replaced by zero.
18. Lord Rayleigh, The Theory of Sound (reprinted by Dover, New York, 1945), Vol. II, Sec. 278 [with a modification appropriate to time dependence exp(-iωt) used in the present paper].
19. Field correlations of arbitrary order appear to have been discussed first in the framework of the classical theory of stationary fields by L. Mandel, "Some coherence properties of non-Gaussian light," in Quantum Electronics III, P. Grivet and N. Bloembergen, eds. (Columbia U. Press, New York, 1964), Vol. I, pp. 101-109.
20. E. Wolf, "Basic concepts of optical coherence theory," in Proceedings of the Symposium on Optical Masers, J. Fox, ed. (Wiley, New York, 1963), pp. 29-42.
21. L. Mandel, "Some coherence properties of non-Gaussian light," in Quantum Electronics III, P. Grivet and N. Bloembergen, eds. (Columbia U. Press, New York, 1964), Vol. I, pp. 101-109.
22. It is implicitly assumed here that M > 1. When M = 1 one readily finds that the first product term (with the index j) in Eq. (4.10), and in all subsequent formulas where it appears, must be replaced by unity.
23. Cross-spectral density functions of arbitrary orders in classical wave fields were first considered by L. Mandel in Ref. 18. See also Refs. 21-23.
24. E. Wolf, "Light fluctuations as a new spectroscopic tool," Jpn. J. Appl. Phys. Suppl. 1 4, 1-14, (1965).
25. C. L. Mehta and L. Mandel, "Some properties of higher order coherence functions," in Electromagnetic Wave Theory, J. Brown, ed. (Pergamon, New York, 1967), Part 2, pp. 1069-1075.
26. L. Mandel, "Photoelectric correlations and fourth-order coherence properties of optical fields," AIP Conf. Proc. 65, 178-195 (1981).
27. Similar remarks apply here to those made in note 19 in connection with Eq. (4.10).
28. A preliminary account of this application of our theory was presented at the 1984 Annual Meeting of the Optical Society of America [J. Opt. Soc. Am. A 1, 1311 (A) (1984)].
29. Equation (A13) was obtained previously by a somewhat less rigorous argument by W. H. Carter and E. Wolf in "Correlation theory of wave-fields generated by fluctuating, three-dimensional, primary, scalar sources. I: General theory," Opt. Acta 28, 227-244 (1981), Sec. 2.