Abstract

We present an experimental demonstration of the spectral interference phenomenon, using a spectrally broad white-light source in a Michelson interferometer configuration. We also present a theoretical analysis of the spectral interference law for the general case of amplitude-division interferometers. When a dispersive medium is introduced into one of the arms of the interferometer, the spectral interference pattern changes drastically, with a change in the frequency modulation corresponding to the dispersive nature of the medium. A zero-order fringe appears at a wavelength where the net path difference between the two arms of the interferometer is zero. We relate the thickness of the dispersive medium to the width of the zero-order fringe. From the experimental data over the entire visible region of the spectrum we obtain the refractive index n(λ) and the thickness t of the dispersive medium, calculated to an accuracy of the order of 10−5.

© 1995 Optical Society of America

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  1. E. Wolf, "New theory of partial coherence in the space-frequency domain. I: Spectra and cross spectra of steady state sources," J. Opt. Soc. Am. 72, 343 (1982).
    [CrossRef]
  2. D. F. V. James and E. Wolf, "Some new aspects of Young's interference experiment," Phys. Lett. A 157, 6 (1991).
    [CrossRef]
  3. M. Santarsiero and F. Gori, "Spectral changes in a Young's interference pattern," Phys. Lett. A 167, 123 (1992).
    [CrossRef]
  4. X. Y. Zou, T. P. Grayson, and L. Mandel, "Observation of quantum interference effects in the frequency domain," Phys. Rev. Lett. 69, 3041 (1992).
    [CrossRef] [PubMed]
  5. G. S. Agarwal, "Interference in complimentary spaces," Found. Phys. 25, 219 (1995).
    [CrossRef]
  6. L. Mandel and E. Wolf, "Spectral coherence and the concept of cross-spectral purity," J. Opt. Soc. Am. 66, 529 (1976).
    [CrossRef]
  7. K. Saxena, D. S. Mehta, H. C. Kandpal, J. S. Vaishya, and K. S. Joshi, "Experimental studies of field correlations using spectral interferometric technique," Opt. Commun. 111, 423 (1994).
    [CrossRef]
  8. D. N. Rao and V. N. Kumar, "Experimental demonstration of spectral modification in a Mach–Zehnder interferometer," J. Mod. Opt. 41, 1757 (1994).
    [CrossRef]
  9. D. F. V. James and E. Wolf, "Determination of field correlations from spectral measurements with application to synthetic aperture imaging," Radio Sci. 26, 1239 (1991).
    [CrossRef]
  10. E. Wolf, "Non-cosmological red shifts of spectral lines," Nature (London) 326, 363 (1987).
    [CrossRef]
  11. C. Sainz, J. Calatroni, and G. Tribillon, "Refractometry of liquid samples with spectrally resolved white light interferometry," Meas. Sci. Technol. 1, 356 (1990).
    [CrossRef]
  12. L. Guerrero, C. Sainz, H. Perrin, R. Castell, and J. Calatroni, "Refractive index distribution measurements by means of spectrally resolved white-light interferometry," Opt. Laser Technol. 24, 333 (1992).
    [CrossRef]
  13. X. D. Cao and D. D. Meyerhofer, "Frequency domain interferometer for the measurement of the polarization mode dispersion in single-mode optical fibers," Opt. Lett. 19, 1837 (1994).
    [CrossRef] [PubMed]
  14. C. Sainz, P. Jourdain, R. Escalona, and J. Calatroni, "Real time interferometric measurements of dispersion curves," Opt. Commun. 110, 381 (1994).
    [CrossRef]
  15. M. Nieto Vesperinas and E. Wolf, "Generalized Stokes reciprocity relations for scattering from dielectric objects of arbitrary shapes," J. Opt. Soc. Am. A 3, 2038 (1986).
    [CrossRef]
  16. V. N. Kumar and D. N. Rao, "Picosecond and sub picosecond relaxation studies in liquids using an incoherent nanosecond source," presented at the National Laser conference, Madras, India, 1993.

1995

G. S. Agarwal, "Interference in complimentary spaces," Found. Phys. 25, 219 (1995).
[CrossRef]

1994

X. D. Cao and D. D. Meyerhofer, "Frequency domain interferometer for the measurement of the polarization mode dispersion in single-mode optical fibers," Opt. Lett. 19, 1837 (1994).
[CrossRef] [PubMed]

C. Sainz, P. Jourdain, R. Escalona, and J. Calatroni, "Real time interferometric measurements of dispersion curves," Opt. Commun. 110, 381 (1994).
[CrossRef]

K. Saxena, D. S. Mehta, H. C. Kandpal, J. S. Vaishya, and K. S. Joshi, "Experimental studies of field correlations using spectral interferometric technique," Opt. Commun. 111, 423 (1994).
[CrossRef]

D. N. Rao and V. N. Kumar, "Experimental demonstration of spectral modification in a Mach–Zehnder interferometer," J. Mod. Opt. 41, 1757 (1994).
[CrossRef]

1992

M. Santarsiero and F. Gori, "Spectral changes in a Young's interference pattern," Phys. Lett. A 167, 123 (1992).
[CrossRef]

X. Y. Zou, T. P. Grayson, and L. Mandel, "Observation of quantum interference effects in the frequency domain," Phys. Rev. Lett. 69, 3041 (1992).
[CrossRef] [PubMed]

L. Guerrero, C. Sainz, H. Perrin, R. Castell, and J. Calatroni, "Refractive index distribution measurements by means of spectrally resolved white-light interferometry," Opt. Laser Technol. 24, 333 (1992).
[CrossRef]

1991

D. F. V. James and E. Wolf, "Some new aspects of Young's interference experiment," Phys. Lett. A 157, 6 (1991).
[CrossRef]

D. F. V. James and E. Wolf, "Determination of field correlations from spectral measurements with application to synthetic aperture imaging," Radio Sci. 26, 1239 (1991).
[CrossRef]

1990

C. Sainz, J. Calatroni, and G. Tribillon, "Refractometry of liquid samples with spectrally resolved white light interferometry," Meas. Sci. Technol. 1, 356 (1990).
[CrossRef]

1987

E. Wolf, "Non-cosmological red shifts of spectral lines," Nature (London) 326, 363 (1987).
[CrossRef]

1986

1982

1976

Agarwal, G. S.

G. S. Agarwal, "Interference in complimentary spaces," Found. Phys. 25, 219 (1995).
[CrossRef]

Calatroni, J.

C. Sainz, P. Jourdain, R. Escalona, and J. Calatroni, "Real time interferometric measurements of dispersion curves," Opt. Commun. 110, 381 (1994).
[CrossRef]

L. Guerrero, C. Sainz, H. Perrin, R. Castell, and J. Calatroni, "Refractive index distribution measurements by means of spectrally resolved white-light interferometry," Opt. Laser Technol. 24, 333 (1992).
[CrossRef]

C. Sainz, J. Calatroni, and G. Tribillon, "Refractometry of liquid samples with spectrally resolved white light interferometry," Meas. Sci. Technol. 1, 356 (1990).
[CrossRef]

Cao, X. D.

Castell, R.

L. Guerrero, C. Sainz, H. Perrin, R. Castell, and J. Calatroni, "Refractive index distribution measurements by means of spectrally resolved white-light interferometry," Opt. Laser Technol. 24, 333 (1992).
[CrossRef]

Escalona, R.

C. Sainz, P. Jourdain, R. Escalona, and J. Calatroni, "Real time interferometric measurements of dispersion curves," Opt. Commun. 110, 381 (1994).
[CrossRef]

Gori, F.

M. Santarsiero and F. Gori, "Spectral changes in a Young's interference pattern," Phys. Lett. A 167, 123 (1992).
[CrossRef]

Grayson, T. P.

X. Y. Zou, T. P. Grayson, and L. Mandel, "Observation of quantum interference effects in the frequency domain," Phys. Rev. Lett. 69, 3041 (1992).
[CrossRef] [PubMed]

Guerrero, L.

L. Guerrero, C. Sainz, H. Perrin, R. Castell, and J. Calatroni, "Refractive index distribution measurements by means of spectrally resolved white-light interferometry," Opt. Laser Technol. 24, 333 (1992).
[CrossRef]

James, D. F. V.

D. F. V. James and E. Wolf, "Determination of field correlations from spectral measurements with application to synthetic aperture imaging," Radio Sci. 26, 1239 (1991).
[CrossRef]

D. F. V. James and E. Wolf, "Some new aspects of Young's interference experiment," Phys. Lett. A 157, 6 (1991).
[CrossRef]

Joshi, K. S.

K. Saxena, D. S. Mehta, H. C. Kandpal, J. S. Vaishya, and K. S. Joshi, "Experimental studies of field correlations using spectral interferometric technique," Opt. Commun. 111, 423 (1994).
[CrossRef]

Jourdain, P.

C. Sainz, P. Jourdain, R. Escalona, and J. Calatroni, "Real time interferometric measurements of dispersion curves," Opt. Commun. 110, 381 (1994).
[CrossRef]

Kandpal, H. C.

K. Saxena, D. S. Mehta, H. C. Kandpal, J. S. Vaishya, and K. S. Joshi, "Experimental studies of field correlations using spectral interferometric technique," Opt. Commun. 111, 423 (1994).
[CrossRef]

Kumar, V. N.

D. N. Rao and V. N. Kumar, "Experimental demonstration of spectral modification in a Mach–Zehnder interferometer," J. Mod. Opt. 41, 1757 (1994).
[CrossRef]

V. N. Kumar and D. N. Rao, "Picosecond and sub picosecond relaxation studies in liquids using an incoherent nanosecond source," presented at the National Laser conference, Madras, India, 1993.

Mandel, L.

X. Y. Zou, T. P. Grayson, and L. Mandel, "Observation of quantum interference effects in the frequency domain," Phys. Rev. Lett. 69, 3041 (1992).
[CrossRef] [PubMed]

L. Mandel and E. Wolf, "Spectral coherence and the concept of cross-spectral purity," J. Opt. Soc. Am. 66, 529 (1976).
[CrossRef]

Mehta, D. S.

K. Saxena, D. S. Mehta, H. C. Kandpal, J. S. Vaishya, and K. S. Joshi, "Experimental studies of field correlations using spectral interferometric technique," Opt. Commun. 111, 423 (1994).
[CrossRef]

Meyerhofer, D. D.

Perrin, H.

L. Guerrero, C. Sainz, H. Perrin, R. Castell, and J. Calatroni, "Refractive index distribution measurements by means of spectrally resolved white-light interferometry," Opt. Laser Technol. 24, 333 (1992).
[CrossRef]

Rao, D. N.

D. N. Rao and V. N. Kumar, "Experimental demonstration of spectral modification in a Mach–Zehnder interferometer," J. Mod. Opt. 41, 1757 (1994).
[CrossRef]

V. N. Kumar and D. N. Rao, "Picosecond and sub picosecond relaxation studies in liquids using an incoherent nanosecond source," presented at the National Laser conference, Madras, India, 1993.

Sainz, C.

C. Sainz, P. Jourdain, R. Escalona, and J. Calatroni, "Real time interferometric measurements of dispersion curves," Opt. Commun. 110, 381 (1994).
[CrossRef]

L. Guerrero, C. Sainz, H. Perrin, R. Castell, and J. Calatroni, "Refractive index distribution measurements by means of spectrally resolved white-light interferometry," Opt. Laser Technol. 24, 333 (1992).
[CrossRef]

C. Sainz, J. Calatroni, and G. Tribillon, "Refractometry of liquid samples with spectrally resolved white light interferometry," Meas. Sci. Technol. 1, 356 (1990).
[CrossRef]

Santarsiero, M.

M. Santarsiero and F. Gori, "Spectral changes in a Young's interference pattern," Phys. Lett. A 167, 123 (1992).
[CrossRef]

Saxena, K.

K. Saxena, D. S. Mehta, H. C. Kandpal, J. S. Vaishya, and K. S. Joshi, "Experimental studies of field correlations using spectral interferometric technique," Opt. Commun. 111, 423 (1994).
[CrossRef]

Tribillon, G.

C. Sainz, J. Calatroni, and G. Tribillon, "Refractometry of liquid samples with spectrally resolved white light interferometry," Meas. Sci. Technol. 1, 356 (1990).
[CrossRef]

Vaishya, J. S.

K. Saxena, D. S. Mehta, H. C. Kandpal, J. S. Vaishya, and K. S. Joshi, "Experimental studies of field correlations using spectral interferometric technique," Opt. Commun. 111, 423 (1994).
[CrossRef]

Vesperinas, M. Nieto

Wolf, E.

D. F. V. James and E. Wolf, "Some new aspects of Young's interference experiment," Phys. Lett. A 157, 6 (1991).
[CrossRef]

D. F. V. James and E. Wolf, "Determination of field correlations from spectral measurements with application to synthetic aperture imaging," Radio Sci. 26, 1239 (1991).
[CrossRef]

E. Wolf, "Non-cosmological red shifts of spectral lines," Nature (London) 326, 363 (1987).
[CrossRef]

M. Nieto Vesperinas and E. Wolf, "Generalized Stokes reciprocity relations for scattering from dielectric objects of arbitrary shapes," J. Opt. Soc. Am. A 3, 2038 (1986).
[CrossRef]

E. Wolf, "New theory of partial coherence in the space-frequency domain. I: Spectra and cross spectra of steady state sources," J. Opt. Soc. Am. 72, 343 (1982).
[CrossRef]

L. Mandel and E. Wolf, "Spectral coherence and the concept of cross-spectral purity," J. Opt. Soc. Am. 66, 529 (1976).
[CrossRef]

Zou, X. Y.

X. Y. Zou, T. P. Grayson, and L. Mandel, "Observation of quantum interference effects in the frequency domain," Phys. Rev. Lett. 69, 3041 (1992).
[CrossRef] [PubMed]

Found. Phys.

G. S. Agarwal, "Interference in complimentary spaces," Found. Phys. 25, 219 (1995).
[CrossRef]

J. Mod. Opt.

D. N. Rao and V. N. Kumar, "Experimental demonstration of spectral modification in a Mach–Zehnder interferometer," J. Mod. Opt. 41, 1757 (1994).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Meas. Sci. Technol.

C. Sainz, J. Calatroni, and G. Tribillon, "Refractometry of liquid samples with spectrally resolved white light interferometry," Meas. Sci. Technol. 1, 356 (1990).
[CrossRef]

Nature

E. Wolf, "Non-cosmological red shifts of spectral lines," Nature (London) 326, 363 (1987).
[CrossRef]

Opt. Commun.

C. Sainz, P. Jourdain, R. Escalona, and J. Calatroni, "Real time interferometric measurements of dispersion curves," Opt. Commun. 110, 381 (1994).
[CrossRef]

K. Saxena, D. S. Mehta, H. C. Kandpal, J. S. Vaishya, and K. S. Joshi, "Experimental studies of field correlations using spectral interferometric technique," Opt. Commun. 111, 423 (1994).
[CrossRef]

Opt. Laser Technol.

L. Guerrero, C. Sainz, H. Perrin, R. Castell, and J. Calatroni, "Refractive index distribution measurements by means of spectrally resolved white-light interferometry," Opt. Laser Technol. 24, 333 (1992).
[CrossRef]

Opt. Lett.

Phys. Lett. A

D. F. V. James and E. Wolf, "Some new aspects of Young's interference experiment," Phys. Lett. A 157, 6 (1991).
[CrossRef]

M. Santarsiero and F. Gori, "Spectral changes in a Young's interference pattern," Phys. Lett. A 167, 123 (1992).
[CrossRef]

Phys. Rev. Lett.

X. Y. Zou, T. P. Grayson, and L. Mandel, "Observation of quantum interference effects in the frequency domain," Phys. Rev. Lett. 69, 3041 (1992).
[CrossRef] [PubMed]

Radio Sci.

D. F. V. James and E. Wolf, "Determination of field correlations from spectral measurements with application to synthetic aperture imaging," Radio Sci. 26, 1239 (1991).
[CrossRef]

Other

V. N. Kumar and D. N. Rao, "Picosecond and sub picosecond relaxation studies in liquids using an incoherent nanosecond source," presented at the National Laser conference, Madras, India, 1993.

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Figures (5)

Fig. 1
Fig. 1

Schematic of the experimental setup used to study the spectral interference by using a white light (a) in a MI: M1, M2, mirrors; BS, beam splitter; CP, compensating plate; DM, dispersive medium, and (b) in a MZI: M1, M2, mirrors; BS1, BS2, beam splitters.

Fig. 2
Fig. 2

Spectral recordings of the output of the MI. (a) Spectrum of the lamp used when either one of the arms of the interferometer is closed. (b) Spectral interference with the compensating plate introduced into arm 1 of the MI. (c) Spectral interference pattern with the dispersive medium introduced into arm 1 of the MI.

Fig. 3
Fig. 3

Experimental recordings of the spectral interference pattern with the theoretical fit [by Eq. (8)] for four different thicknesses t of the dispersive medium kept in arm 1 of the MI. Experimental data are represented by dotted curves, and the continuous curves are theoretical fits: (a) one micro slide, (b) two slides, (c) three slides, (d) 1.5-mm slide.

Fig. 4
Fig. 4

Plot of the phase |ϕ| as a function of λ for the four different thicknesses of the dispersive medium with the stationary phase point (zero-order fringe) at different λ values.

Fig. 5
Fig. 5

Refractive index n of the dispersive medium as a function of λ for the best theoretical fit of the entire visible region of the spectral interference pattern.

Tables (1)

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Table 1 Summary of n(λ) and t Measured from the Theoretical Fit

Equations (11)

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( ω ) = a ( ω ) 1 ( ω ) + b ( ω ) 2 ( ω ) exp ( - i ω Δ / c ) ,
( ω 1 ) * ( ω 2 ) = S ( ω 1 ) δ ( ω 1 - ω 2 ) ,
S ( ω ) = a 2 S 1 ( ω ) + b 2 S 2 ( ω ) + [ a * b S 12 ( ω ) exp ( - i ω Δ / c ) + c . c . ] .
1 ( ω 1 ) 2 ( ω 2 ) = S 12 ( ω 1 ) δ ( ω 1 - ω 2 ) .
S ( ω ) = S 0 ( ω ) { a 2 + b 2 + 2 Re [ a * b μ 12 ( ω ) exp ( - i ω Δ / c ) ] } .
μ 12 ( ω ) = μ 12 ( ω ) exp [ i β 12 ( ω ) ] .
a 2 + b 2 = 1 / 2 ,             a * b = 1 / 4.
S ( ω ) = ( 1 / 2 ) S 0 ( ω ) { 1 + Re [ μ 12 ( ω ) ] cos ( ω Δ / c + ϑ ) } ,
S ( λ ) = ( 1 / 2 ) S 0 ( λ ) { 1 + Re [ μ 12 ( λ ) ] cos ( 2 π Δ / λ + ϑ ) } .
Δ = n ( λ ) 2 t - L 0             ( MI ) ,
Δ = n ( λ ) t - L 0             ( MZI ) ,

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