Abstract

Light undergoing phase diffusion displays a Lorentzian line shape: Here, electrical filtering techniques are used to examine the correlations among different spectral regions under this line shape. The experiment involves delayed self-heterodyne measurements of the output from a single-mode semiconductor laser. Two filters are tuned to isolate the signal contributions from opposite wings of the spectrum, and the transmitted intensities are shown to be strongly correlated in some regimes and strongly anticorrelated in others.

© 1998 Optical Society of America

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References

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  1. A. L. Schawlow and C. H. Townes, Phys. Rev. 112, 1940 (1958).
    [CrossRef]
  2. R. C. Neelen, D. M. Boersma, M. P. van Exter, G. Nienhuis, and J. P. Woerdman, Phys. Rev. Lett. 69, 593 (1992).
    [CrossRef]
  3. R. C. Neelen, D. M. Boersma, M. P. van Exter, G. Nienhuis, and J. P. Woerdman, Opt. Commun. 100, 289 (1993).
    [CrossRef]
  4. M. Harris, G. N. Pearson, and J. M. Vaughan, Electron. Lett. 30, 1678 (1994).
    [CrossRef]
  5. S. Nilsson, T. Kjellberg, T. Klinga, R. Schatz, J. Wallin, and K. Streubel, J. Lightwave Technol. 13, 434 (1995).
    [CrossRef]
  6. T. Okoshi, K. Kikuchi, and A. Nakayama, Electron. Lett. 16, 630 (1980).
    [CrossRef]
  7. M. Harris, Contemp. Phys. 36, 215 (1995).
    [CrossRef]
  8. G. N. Pearson, M. Harris, E. Jakeman, and D. Letalick, J. Mod. Opt. 41, 2067 (1994).
    [CrossRef]
  9. M. Harris, G. N. Pearson, C. A. Hill, and J. M. Vaughan, Appl. Opt. 33, 7226 (1994).
    [CrossRef] [PubMed]
  10. P. R. Tapster, Laser and Photonics Department, Defence Evaluation Research Agency, Malvern, Worcestershire WR14 3PS UK (personal communication, 1997).
  11. J. M. Vaughan, The Fabry–Perot Interferometer (Hilger, Bristol, UK, 1989).

1995 (2)

S. Nilsson, T. Kjellberg, T. Klinga, R. Schatz, J. Wallin, and K. Streubel, J. Lightwave Technol. 13, 434 (1995).
[CrossRef]

M. Harris, Contemp. Phys. 36, 215 (1995).
[CrossRef]

1994 (3)

G. N. Pearson, M. Harris, E. Jakeman, and D. Letalick, J. Mod. Opt. 41, 2067 (1994).
[CrossRef]

M. Harris, G. N. Pearson, C. A. Hill, and J. M. Vaughan, Appl. Opt. 33, 7226 (1994).
[CrossRef] [PubMed]

M. Harris, G. N. Pearson, and J. M. Vaughan, Electron. Lett. 30, 1678 (1994).
[CrossRef]

1993 (1)

R. C. Neelen, D. M. Boersma, M. P. van Exter, G. Nienhuis, and J. P. Woerdman, Opt. Commun. 100, 289 (1993).
[CrossRef]

1992 (1)

R. C. Neelen, D. M. Boersma, M. P. van Exter, G. Nienhuis, and J. P. Woerdman, Phys. Rev. Lett. 69, 593 (1992).
[CrossRef]

1980 (1)

T. Okoshi, K. Kikuchi, and A. Nakayama, Electron. Lett. 16, 630 (1980).
[CrossRef]

1958 (1)

A. L. Schawlow and C. H. Townes, Phys. Rev. 112, 1940 (1958).
[CrossRef]

Boersma, D. M.

R. C. Neelen, D. M. Boersma, M. P. van Exter, G. Nienhuis, and J. P. Woerdman, Opt. Commun. 100, 289 (1993).
[CrossRef]

R. C. Neelen, D. M. Boersma, M. P. van Exter, G. Nienhuis, and J. P. Woerdman, Phys. Rev. Lett. 69, 593 (1992).
[CrossRef]

Harris, M.

M. Harris, Contemp. Phys. 36, 215 (1995).
[CrossRef]

M. Harris, G. N. Pearson, and J. M. Vaughan, Electron. Lett. 30, 1678 (1994).
[CrossRef]

G. N. Pearson, M. Harris, E. Jakeman, and D. Letalick, J. Mod. Opt. 41, 2067 (1994).
[CrossRef]

M. Harris, G. N. Pearson, C. A. Hill, and J. M. Vaughan, Appl. Opt. 33, 7226 (1994).
[CrossRef] [PubMed]

Hill, C. A.

Jakeman, E.

G. N. Pearson, M. Harris, E. Jakeman, and D. Letalick, J. Mod. Opt. 41, 2067 (1994).
[CrossRef]

Kikuchi, K.

T. Okoshi, K. Kikuchi, and A. Nakayama, Electron. Lett. 16, 630 (1980).
[CrossRef]

Kjellberg, T.

S. Nilsson, T. Kjellberg, T. Klinga, R. Schatz, J. Wallin, and K. Streubel, J. Lightwave Technol. 13, 434 (1995).
[CrossRef]

Klinga, T.

S. Nilsson, T. Kjellberg, T. Klinga, R. Schatz, J. Wallin, and K. Streubel, J. Lightwave Technol. 13, 434 (1995).
[CrossRef]

Letalick, D.

G. N. Pearson, M. Harris, E. Jakeman, and D. Letalick, J. Mod. Opt. 41, 2067 (1994).
[CrossRef]

Nakayama, A.

T. Okoshi, K. Kikuchi, and A. Nakayama, Electron. Lett. 16, 630 (1980).
[CrossRef]

Neelen, R. C.

R. C. Neelen, D. M. Boersma, M. P. van Exter, G. Nienhuis, and J. P. Woerdman, Opt. Commun. 100, 289 (1993).
[CrossRef]

R. C. Neelen, D. M. Boersma, M. P. van Exter, G. Nienhuis, and J. P. Woerdman, Phys. Rev. Lett. 69, 593 (1992).
[CrossRef]

Nienhuis, G.

R. C. Neelen, D. M. Boersma, M. P. van Exter, G. Nienhuis, and J. P. Woerdman, Opt. Commun. 100, 289 (1993).
[CrossRef]

R. C. Neelen, D. M. Boersma, M. P. van Exter, G. Nienhuis, and J. P. Woerdman, Phys. Rev. Lett. 69, 593 (1992).
[CrossRef]

Nilsson, S.

S. Nilsson, T. Kjellberg, T. Klinga, R. Schatz, J. Wallin, and K. Streubel, J. Lightwave Technol. 13, 434 (1995).
[CrossRef]

Okoshi, T.

T. Okoshi, K. Kikuchi, and A. Nakayama, Electron. Lett. 16, 630 (1980).
[CrossRef]

Pearson, G. N.

M. Harris, G. N. Pearson, and J. M. Vaughan, Electron. Lett. 30, 1678 (1994).
[CrossRef]

G. N. Pearson, M. Harris, E. Jakeman, and D. Letalick, J. Mod. Opt. 41, 2067 (1994).
[CrossRef]

M. Harris, G. N. Pearson, C. A. Hill, and J. M. Vaughan, Appl. Opt. 33, 7226 (1994).
[CrossRef] [PubMed]

Schatz, R.

S. Nilsson, T. Kjellberg, T. Klinga, R. Schatz, J. Wallin, and K. Streubel, J. Lightwave Technol. 13, 434 (1995).
[CrossRef]

Schawlow, A. L.

A. L. Schawlow and C. H. Townes, Phys. Rev. 112, 1940 (1958).
[CrossRef]

Streubel, K.

S. Nilsson, T. Kjellberg, T. Klinga, R. Schatz, J. Wallin, and K. Streubel, J. Lightwave Technol. 13, 434 (1995).
[CrossRef]

Tapster, P. R.

P. R. Tapster, Laser and Photonics Department, Defence Evaluation Research Agency, Malvern, Worcestershire WR14 3PS UK (personal communication, 1997).

Townes, C. H.

A. L. Schawlow and C. H. Townes, Phys. Rev. 112, 1940 (1958).
[CrossRef]

van Exter, M. P.

R. C. Neelen, D. M. Boersma, M. P. van Exter, G. Nienhuis, and J. P. Woerdman, Opt. Commun. 100, 289 (1993).
[CrossRef]

R. C. Neelen, D. M. Boersma, M. P. van Exter, G. Nienhuis, and J. P. Woerdman, Phys. Rev. Lett. 69, 593 (1992).
[CrossRef]

Vaughan, J. M.

M. Harris, G. N. Pearson, C. A. Hill, and J. M. Vaughan, Appl. Opt. 33, 7226 (1994).
[CrossRef] [PubMed]

M. Harris, G. N. Pearson, and J. M. Vaughan, Electron. Lett. 30, 1678 (1994).
[CrossRef]

J. M. Vaughan, The Fabry–Perot Interferometer (Hilger, Bristol, UK, 1989).

Wallin, J.

S. Nilsson, T. Kjellberg, T. Klinga, R. Schatz, J. Wallin, and K. Streubel, J. Lightwave Technol. 13, 434 (1995).
[CrossRef]

Woerdman, J. P.

R. C. Neelen, D. M. Boersma, M. P. van Exter, G. Nienhuis, and J. P. Woerdman, Opt. Commun. 100, 289 (1993).
[CrossRef]

R. C. Neelen, D. M. Boersma, M. P. van Exter, G. Nienhuis, and J. P. Woerdman, Phys. Rev. Lett. 69, 593 (1992).
[CrossRef]

Appl. Opt. (1)

Contemp. Phys. (1)

M. Harris, Contemp. Phys. 36, 215 (1995).
[CrossRef]

Electron. Lett. (2)

T. Okoshi, K. Kikuchi, and A. Nakayama, Electron. Lett. 16, 630 (1980).
[CrossRef]

M. Harris, G. N. Pearson, and J. M. Vaughan, Electron. Lett. 30, 1678 (1994).
[CrossRef]

J. Lightwave Technol. (1)

S. Nilsson, T. Kjellberg, T. Klinga, R. Schatz, J. Wallin, and K. Streubel, J. Lightwave Technol. 13, 434 (1995).
[CrossRef]

J. Mod. Opt. (1)

G. N. Pearson, M. Harris, E. Jakeman, and D. Letalick, J. Mod. Opt. 41, 2067 (1994).
[CrossRef]

Opt. Commun. (1)

R. C. Neelen, D. M. Boersma, M. P. van Exter, G. Nienhuis, and J. P. Woerdman, Opt. Commun. 100, 289 (1993).
[CrossRef]

Phys. Rev. (1)

A. L. Schawlow and C. H. Townes, Phys. Rev. 112, 1940 (1958).
[CrossRef]

Phys. Rev. Lett. (1)

R. C. Neelen, D. M. Boersma, M. P. van Exter, G. Nienhuis, and J. P. Woerdman, Phys. Rev. Lett. 69, 593 (1992).
[CrossRef]

Other (2)

P. R. Tapster, Laser and Photonics Department, Defence Evaluation Research Agency, Malvern, Worcestershire WR14 3PS UK (personal communication, 1997).

J. M. Vaughan, The Fabry–Perot Interferometer (Hilger, Bristol, UK, 1989).

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Figures (4)

Fig. 1
Fig. 1

Experimental delayed self-heterodyne fiber interferometer: OI, optical isolator; FC's, fiber couplers; AOM, acousto-optic modulator; FPC, fiber polarization controller. BPF1 and PBF2 are the two bandpass filters; cross correlation of their outputs is subsequently evaluated.

Fig. 2
Fig. 2

Double filtering of the laser spectrum. The filters have a roughly Gaussian-shaped transmission function and are positioned symmetrically on either side of the Lorentzian-shaped laser profile. Note that the laser width Γ appears doubled in the delayed self-heterodyne spectrum.4 The two transmitted signals are individually processed to give two separate power/intensity time series. The cross correlation between these is then calculated, and the experiment is carried out for a range of filter widths and spacings.

Fig. 3
Fig. 3

(a) Portion of the two experimental intensity time series I1t and I2t obtained for zero detuning (Δ=1 MHz, δ=0). The two traces should then be identical, and are indeed seen to lie almost one on top of the other. (b) Time series I1t and I2t measured close to the minimum (peak anticorrelation) of Fig.  4 (Δ=1 MHz, δ=2 MHz). The anticorrelation is dramatically obvious, with the peaks of one trace clearly tending to coincide with the troughs of the other.

Fig. 4
Fig. 4

Plot of experimentally determined cross correlation versus filter separation for a range of filter widths. At larger detuning, the outputs become highly anticorrelated. At very large detuning, a small positive correlation is apparent for the two largest filter widths.

Equations (1)

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C12=I1tI2tI1tI2t,

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