Abstract

An experimental study is conducted to show the effect of the change in bandwidth of light on the spectral degree of coherence at a pair of points in the cross section of a beam. For this purpose a polychromatic source and a monochromator with variable entrance and exit slits were used to produce a variable bandwidth source. The classic Young’s interferometer was used to produce an interference pattern. The spectral measurements of the visibility of the interference fringes show that the spectral degree of coherence remains unaffected by the change in the frequency passband of the light.

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References

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  1. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge Univ. Press, 1995).
  2. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge Univ. Press, 1999), Chap. 4.
  3. L. Mandel and E. Wolf, J. Opt. Soc. Am. 66, 529 (1976).
    [CrossRef]
  4. E. Wolf and D. F. V. James, Rep. Prog. Phys. 59, 771 (1996).
    [CrossRef]
  5. E. Wolf, Opt. Lett. 8, 250 (1983).
    [CrossRef] [PubMed]
  6. L. Basano, P. Ottonello, G. Rottigni, and M. Vicari, Appl. Opt. 42, 6239 (2003).
    [CrossRef] [PubMed]
  7. E. Wolf, Introduction to Theory of Coherence and Polarization of Light (Cambridge Univ. Press, 2007), p. 76.
  8. A. T. Friberg and E. Wolf, Opt. Lett. 20, 623 (1995).
    [CrossRef] [PubMed]
  9. C. A. Parker, Photoluminescence of Solutions (Elsevier, 1968), Chap. 3.
  10. A. S. Marathay, Elements of Optical Coherence Theory (Wiley, 1982), p. 111.

2003 (1)

1996 (1)

E. Wolf and D. F. V. James, Rep. Prog. Phys. 59, 771 (1996).
[CrossRef]

1995 (1)

1983 (1)

1976 (1)

Basano, L.

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge Univ. Press, 1999), Chap. 4.

Friberg, A. T.

James, D. F. V.

E. Wolf and D. F. V. James, Rep. Prog. Phys. 59, 771 (1996).
[CrossRef]

Mandel, L.

L. Mandel and E. Wolf, J. Opt. Soc. Am. 66, 529 (1976).
[CrossRef]

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge Univ. Press, 1995).

Marathay, A. S.

A. S. Marathay, Elements of Optical Coherence Theory (Wiley, 1982), p. 111.

Ottonello, P.

Parker, C. A.

C. A. Parker, Photoluminescence of Solutions (Elsevier, 1968), Chap. 3.

Rottigni, G.

Vicari, M.

Wolf, E.

E. Wolf and D. F. V. James, Rep. Prog. Phys. 59, 771 (1996).
[CrossRef]

A. T. Friberg and E. Wolf, Opt. Lett. 20, 623 (1995).
[CrossRef] [PubMed]

E. Wolf, Opt. Lett. 8, 250 (1983).
[CrossRef] [PubMed]

L. Mandel and E. Wolf, J. Opt. Soc. Am. 66, 529 (1976).
[CrossRef]

E. Wolf, Introduction to Theory of Coherence and Polarization of Light (Cambridge Univ. Press, 2007), p. 76.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge Univ. Press, 1999), Chap. 4.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge Univ. Press, 1995).

Appl. Opt. (1)

J. Opt. Soc. Am. (1)

Opt. Lett. (2)

Rep. Prog. Phys. (1)

E. Wolf and D. F. V. James, Rep. Prog. Phys. 59, 771 (1996).
[CrossRef]

Other (5)

E. Wolf, Introduction to Theory of Coherence and Polarization of Light (Cambridge Univ. Press, 2007), p. 76.

C. A. Parker, Photoluminescence of Solutions (Elsevier, 1968), Chap. 3.

A. S. Marathay, Elements of Optical Coherence Theory (Wiley, 1982), p. 111.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge Univ. Press, 1995).

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge Univ. Press, 1999), Chap. 4.

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Figures (4)

Fig. 1
Fig. 1

Schematic of the experimental setup. Abbreviations are defined in the text.

Fig. 2
Fig. 2

(a) Plot of spectral density versus slit width of the monochromator. Curves are shown for slit widths (i) 2, (ii) 1.5, (iii) 1, (iv) 0.5, and (v) 0.1 mm . Dots show the data points connected by the solid curve. (b) FWHM of the spectra (after inserting SS) plotted with respect to the slit width. The trend line shows a linear fit. The error bars show the uncertainty in the mean value calculated at a 95% confidence level.

Fig. 3
Fig. 3

Two-slit diffraction patterns for different slit widths (a) without SS and (b) when SS is introduced (Fig. 1). In both the cases, the slit widths are (i) 2, (ii) 1.5, (iii) 1, (iv) 0.5, and (v) 0.1 mm .

Fig. 4
Fig. 4

Change in absolute value of the degree of spectral coherence (spectral visibility) with the bandwidth of light. The dashed line is a trend line showing a linear fit.

Equations (6)

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ν ( r ) = | μ ( r 1 , r 2 , ω ) | = S max S min S max + S min ,
W ( r 1 , r 2 , ω ) = U * ( r 1 , ω ) U ( r 2 , ω ) ,
W + ( r 1 , r 2 , ω ) = | T ( ω ) | 2 W ( r 1 , r 2 , ω ) .
μ ( r 1 , r 2 , ω 0 ) = W ( r 1 , r 2 , ω 0 ) [ W ( r 1 , r 1 , ω 0 ) ] 1 2 [ W ( r 2 , r 2 , ω 0 ) ] 1 2 .
μ + ( r 1 , r 2 , ω 0 ) = W + ( r 1 , r 2 , ω 0 ) [ W + ( r 1 , r 1 , ω 0 ) ] 1 2 [ W + ( r 2 , r 2 , ω 0 ) ] 1 2 .
μ + ( r 1 , r 2 , ω 0 ) = μ ( r 1 , r 2 , ω 0 ) ;

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