Abstract

We demonstrate a simple, adjustment-insensitive technique for measuring the temporal coherence function of cw multimode and monomode semiconductor lasers, using two-beam coupling in photorefractive InP and CdTe crystals. The emission spectra of the diodes are measured independently. The coherence functions are also calculated from these spectra and agree with the photorefractive measurements. Coupling of two partially coherent waves in low-speed photorefractive media is described theoretically. The range of the experimental parameters in which the method of coherence measurement is correct is given.

© 1999 Optical Society of America

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  1. D. Velaskas, K. Jarashiunas, P. Baltrameiunas, J. Vaitkeus, “Coherence length measurement of laser pulses,” Appl. Pis’ma Zh. Teor. Fiz. 1, 708–711 (1975).
  2. H. J. Eichler, U. Klein, D. Langhans, “Coherence time measurement of picosecond pulses by a light-induced grating method,” Appl. Phys. 21, 215–219 (1980).
    [CrossRef]
  3. H. J. Eichler, P. Günter, D. W. Pohl, Laser-Induced Dynamic Gratings (Springer-Verlag, Berlin, 1986).
    [CrossRef]
  4. R. Trebino, E. Gustafson, A. E. Siegman, “Fourth-order partial-coherence effects in the formation of integrated-intensity gratings with pulsed light sources,” J. Opt. Soc. Am. B 3, 1295–1304 (1986).
    [CrossRef]
  5. W. L. Nighan, T. Gong, L. Liou, P. M. Fauchet, “Self-diffraction: a new method for characterization of ultrashort pulses,” Opt. Commun. 69, 339–344 (1989).
    [CrossRef]
  6. V. Dominic, X. S. Yao, R. M. Pierce, J. Feinberg, “Measuring the coherence length of mode-locked laser pulses in real time,” Appl. Phys. Lett. 56, 521–523 (1990).
    [CrossRef]
  7. N. V. Bogodaev, L. I. Ivleva, A. S. Korshunov, N. M. Polozkov, V. V. Shkunov, “Increase of light-beam coherence by two-wave-mixing in photorefractive crystals,” J. Opt. Soc. Am. B 10, 2287–2289 (1993).
    [CrossRef]
  8. N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetski, “Holographic storage in electrooptic crystals. II. Beam coupling–light amplification,” Ferroelectrics 22, 961–964 (1979).
    [CrossRef]
  9. M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1970).
  10. H.-J. Eichler, “Dispersion and absorption of light,” in Optik, Vol. 3 of Lehrbuck der Experimentalphysik, L. Bergmann, C. Schaefer, eds. (deGruyter, Berlin, 1993), pp. 234–237.
  11. X. Yi, P. Yeh, “Two-wave mixing with partially coherent waves in high-speed photorefractive media,” J. Opt. Soc. Am. B 14, 2885–2894 (1997).
    [CrossRef]

1997 (1)

1993 (1)

1990 (1)

V. Dominic, X. S. Yao, R. M. Pierce, J. Feinberg, “Measuring the coherence length of mode-locked laser pulses in real time,” Appl. Phys. Lett. 56, 521–523 (1990).
[CrossRef]

1989 (1)

W. L. Nighan, T. Gong, L. Liou, P. M. Fauchet, “Self-diffraction: a new method for characterization of ultrashort pulses,” Opt. Commun. 69, 339–344 (1989).
[CrossRef]

1986 (1)

1980 (1)

H. J. Eichler, U. Klein, D. Langhans, “Coherence time measurement of picosecond pulses by a light-induced grating method,” Appl. Phys. 21, 215–219 (1980).
[CrossRef]

1979 (1)

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetski, “Holographic storage in electrooptic crystals. II. Beam coupling–light amplification,” Ferroelectrics 22, 961–964 (1979).
[CrossRef]

1975 (1)

D. Velaskas, K. Jarashiunas, P. Baltrameiunas, J. Vaitkeus, “Coherence length measurement of laser pulses,” Appl. Pis’ma Zh. Teor. Fiz. 1, 708–711 (1975).

Baltrameiunas, P.

D. Velaskas, K. Jarashiunas, P. Baltrameiunas, J. Vaitkeus, “Coherence length measurement of laser pulses,” Appl. Pis’ma Zh. Teor. Fiz. 1, 708–711 (1975).

Bogodaev, N. V.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1970).

Dominic, V.

V. Dominic, X. S. Yao, R. M. Pierce, J. Feinberg, “Measuring the coherence length of mode-locked laser pulses in real time,” Appl. Phys. Lett. 56, 521–523 (1990).
[CrossRef]

Eichler, H. J.

H. J. Eichler, U. Klein, D. Langhans, “Coherence time measurement of picosecond pulses by a light-induced grating method,” Appl. Phys. 21, 215–219 (1980).
[CrossRef]

H. J. Eichler, P. Günter, D. W. Pohl, Laser-Induced Dynamic Gratings (Springer-Verlag, Berlin, 1986).
[CrossRef]

Eichler, H.-J.

H.-J. Eichler, “Dispersion and absorption of light,” in Optik, Vol. 3 of Lehrbuck der Experimentalphysik, L. Bergmann, C. Schaefer, eds. (deGruyter, Berlin, 1993), pp. 234–237.

Fauchet, P. M.

W. L. Nighan, T. Gong, L. Liou, P. M. Fauchet, “Self-diffraction: a new method for characterization of ultrashort pulses,” Opt. Commun. 69, 339–344 (1989).
[CrossRef]

Feinberg, J.

V. Dominic, X. S. Yao, R. M. Pierce, J. Feinberg, “Measuring the coherence length of mode-locked laser pulses in real time,” Appl. Phys. Lett. 56, 521–523 (1990).
[CrossRef]

Gong, T.

W. L. Nighan, T. Gong, L. Liou, P. M. Fauchet, “Self-diffraction: a new method for characterization of ultrashort pulses,” Opt. Commun. 69, 339–344 (1989).
[CrossRef]

Günter, P.

H. J. Eichler, P. Günter, D. W. Pohl, Laser-Induced Dynamic Gratings (Springer-Verlag, Berlin, 1986).
[CrossRef]

Gustafson, E.

Ivleva, L. I.

Jarashiunas, K.

D. Velaskas, K. Jarashiunas, P. Baltrameiunas, J. Vaitkeus, “Coherence length measurement of laser pulses,” Appl. Pis’ma Zh. Teor. Fiz. 1, 708–711 (1975).

Klein, U.

H. J. Eichler, U. Klein, D. Langhans, “Coherence time measurement of picosecond pulses by a light-induced grating method,” Appl. Phys. 21, 215–219 (1980).
[CrossRef]

Korshunov, A. S.

Kukhtarev, N. V.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetski, “Holographic storage in electrooptic crystals. II. Beam coupling–light amplification,” Ferroelectrics 22, 961–964 (1979).
[CrossRef]

Langhans, D.

H. J. Eichler, U. Klein, D. Langhans, “Coherence time measurement of picosecond pulses by a light-induced grating method,” Appl. Phys. 21, 215–219 (1980).
[CrossRef]

Liou, L.

W. L. Nighan, T. Gong, L. Liou, P. M. Fauchet, “Self-diffraction: a new method for characterization of ultrashort pulses,” Opt. Commun. 69, 339–344 (1989).
[CrossRef]

Markov, V. B.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetski, “Holographic storage in electrooptic crystals. II. Beam coupling–light amplification,” Ferroelectrics 22, 961–964 (1979).
[CrossRef]

Nighan, W. L.

W. L. Nighan, T. Gong, L. Liou, P. M. Fauchet, “Self-diffraction: a new method for characterization of ultrashort pulses,” Opt. Commun. 69, 339–344 (1989).
[CrossRef]

Odulov, S. G.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetski, “Holographic storage in electrooptic crystals. II. Beam coupling–light amplification,” Ferroelectrics 22, 961–964 (1979).
[CrossRef]

Pierce, R. M.

V. Dominic, X. S. Yao, R. M. Pierce, J. Feinberg, “Measuring the coherence length of mode-locked laser pulses in real time,” Appl. Phys. Lett. 56, 521–523 (1990).
[CrossRef]

Pohl, D. W.

H. J. Eichler, P. Günter, D. W. Pohl, Laser-Induced Dynamic Gratings (Springer-Verlag, Berlin, 1986).
[CrossRef]

Polozkov, N. M.

Shkunov, V. V.

Siegman, A. E.

Soskin, M. S.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetski, “Holographic storage in electrooptic crystals. II. Beam coupling–light amplification,” Ferroelectrics 22, 961–964 (1979).
[CrossRef]

Trebino, R.

Vaitkeus, J.

D. Velaskas, K. Jarashiunas, P. Baltrameiunas, J. Vaitkeus, “Coherence length measurement of laser pulses,” Appl. Pis’ma Zh. Teor. Fiz. 1, 708–711 (1975).

Velaskas, D.

D. Velaskas, K. Jarashiunas, P. Baltrameiunas, J. Vaitkeus, “Coherence length measurement of laser pulses,” Appl. Pis’ma Zh. Teor. Fiz. 1, 708–711 (1975).

Vinetski, V. L.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetski, “Holographic storage in electrooptic crystals. II. Beam coupling–light amplification,” Ferroelectrics 22, 961–964 (1979).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1970).

Yao, X. S.

V. Dominic, X. S. Yao, R. M. Pierce, J. Feinberg, “Measuring the coherence length of mode-locked laser pulses in real time,” Appl. Phys. Lett. 56, 521–523 (1990).
[CrossRef]

Yeh, P.

Yi, X.

Appl. Phys. (1)

H. J. Eichler, U. Klein, D. Langhans, “Coherence time measurement of picosecond pulses by a light-induced grating method,” Appl. Phys. 21, 215–219 (1980).
[CrossRef]

Appl. Phys. Lett. (1)

V. Dominic, X. S. Yao, R. M. Pierce, J. Feinberg, “Measuring the coherence length of mode-locked laser pulses in real time,” Appl. Phys. Lett. 56, 521–523 (1990).
[CrossRef]

Appl. Pis’ma Zh. Teor. Fiz. (1)

D. Velaskas, K. Jarashiunas, P. Baltrameiunas, J. Vaitkeus, “Coherence length measurement of laser pulses,” Appl. Pis’ma Zh. Teor. Fiz. 1, 708–711 (1975).

Ferroelectrics (1)

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetski, “Holographic storage in electrooptic crystals. II. Beam coupling–light amplification,” Ferroelectrics 22, 961–964 (1979).
[CrossRef]

J. Opt. Soc. Am. B (3)

Opt. Commun. (1)

W. L. Nighan, T. Gong, L. Liou, P. M. Fauchet, “Self-diffraction: a new method for characterization of ultrashort pulses,” Opt. Commun. 69, 339–344 (1989).
[CrossRef]

Other (3)

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1970).

H.-J. Eichler, “Dispersion and absorption of light,” in Optik, Vol. 3 of Lehrbuck der Experimentalphysik, L. Bergmann, C. Schaefer, eds. (deGruyter, Berlin, 1993), pp. 234–237.

H. J. Eichler, P. Günter, D. W. Pohl, Laser-Induced Dynamic Gratings (Springer-Verlag, Berlin, 1986).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Experimental setup for measurement of the coherence function: HR, highly reflecting.

Fig. 2
Fig. 2

Measured coherence function of (a) a monomode distributed-feedback and (b) a multimode laser diode.

Fig. 3
Fig. 3

Highly resolved part of the squared coherence function of two different multimode laser diodes. Squares, measured values; solid curves, calculated from the spectra shown at the right.

Fig. 4
Fig. 4

Squared mutual coherence Φ(L) behind the crystal as a function of the signal intensity increment for equal-input beam intensities. The curves from top to bottom are for initial coherence values Φ0 = Φ(ΔI S = 0) = 0.9, 0.7, 0.5, 0.3, 0.1.

Equations (18)

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Γτ=limT12T-T+T ER*tESt+τdtlimT12T-T+T ER*tEStdt=ER*tES5+τIRIS,
dUdz=-ΓPR2 V,  U=IR-ISIR+IS,  dVdz=ΓPRUV,  V=4 |ER*tES5+τ|2IR+IS2,
V=4Φ IRISIR+IS2,  Φ=|Γτ|2=|ER*tESt+τ|2IRIS,
dΦdIS=1-ΦIR-ISIRIS.
dISdz=ΓPRΦ0IRISIR+IS,  dIRdz=-ΓPRΦ0IRISIR+IS.
ΔISββ+1 IS0Φ0ΓPRL=1/2Φ0ΓPRL,
Φτ=ΔISτΔISmax
Gf=- Γτexpi2πfτdτ.
exp-τ2/2τc2,
Gfg0δf0+kgkδf0+kΔf+g-kδf0-kΔf, k=1, 2, 3,.
Γτ=g0 expi2πf0τ+kgk expi2πf0+kΔfτ+g-k expi2πf0-kΔfτg0+kgk+g-k.
Φτ=ΓτΓ*τ=c0+k ck cos2πkΔfτ,  c0=g02+kgk2+g-k2/g,  ck=2 lglgl+k+g-lg-l-k/g, l=0, 1, 2, ,  g=g0+kgk+g-k2.
ΦL=1-1-Φ0IR0IS0IRLISL,
ΔΦβ=1=-1-Φ0ΔISIS0211+ΔIS/IS01-ΔIS/IS0
ΔΦβ=1-1-Φ0ΔISIS02.
|ΔΦβ=1Φ0|141-Φ0Φ0ΓPRL2116ΓPRL2.
ΔΦβ11-Φ0ΔISIS0,  IS0  IR0,ΔΦβ1-1-Φ0ΔISIR0,  IR0  IS0,
λΔλ=2smaxλ.

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