Abstract

We present measurements of the intensity autocorrelation function of the output of a free-running AlGaAs diode laser. To our knowledge these are the first such measurements performed on the output of a semiconductor laser. Our data display large structure at the relaxation oscillation frequency and reveal features that depend on the number of secondary modes lasing. This provides evidence that, even in so-called single-mode diode lasers, these side modes have a significant effect on the fluctuations of the total output of the laser. The autocorrelation function in fact can be used to measure how many modes contribute to the fluctuating intensity. The major features in the measured intensity autocorrelation function are in good agreement with the predictions of a simple multimode phase-diffusion model.

© 1993 Optical Society of America

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References

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  1. M. Osinski, J. Buus, IEEE J. Quantum Electron. QE-23, 9 (1987), Refs. 130–170 thereinY. Yamamoto, ed., Coherence, Amplification, and Quantum Effects in Semiconductor Lasers (Wiley, New York, 1991).
    [CrossRef]
  2. G. Gray, R. Roy, Phys. Rev. A 40, 2452 (1989).
    [CrossRef] [PubMed]
  3. G. P. Agrawal, Phys. Rev. A 37, 2488 (1988).
    [CrossRef] [PubMed]
  4. L. A. Westling, M. G. Raymer, M. G. Sceats, D. F. Coker, Opt. Commun. 47, 212 (1983); L. A. Westling, M. G. Raymer, J. Opt. Soc. Am. B 3, 911 (1986).
    [CrossRef]
  5. In fact, the form of the IAF changes significantly with feedback and provides an effective monitor for feedback. This will be a subject of further study in our laboratory.
  6. C. H. Henry, J. Lightwave Technol. LT-4, 298 (1986).
    [CrossRef]

1989 (1)

G. Gray, R. Roy, Phys. Rev. A 40, 2452 (1989).
[CrossRef] [PubMed]

1988 (1)

G. P. Agrawal, Phys. Rev. A 37, 2488 (1988).
[CrossRef] [PubMed]

1987 (1)

M. Osinski, J. Buus, IEEE J. Quantum Electron. QE-23, 9 (1987), Refs. 130–170 thereinY. Yamamoto, ed., Coherence, Amplification, and Quantum Effects in Semiconductor Lasers (Wiley, New York, 1991).
[CrossRef]

1986 (1)

C. H. Henry, J. Lightwave Technol. LT-4, 298 (1986).
[CrossRef]

1983 (1)

L. A. Westling, M. G. Raymer, M. G. Sceats, D. F. Coker, Opt. Commun. 47, 212 (1983); L. A. Westling, M. G. Raymer, J. Opt. Soc. Am. B 3, 911 (1986).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, Phys. Rev. A 37, 2488 (1988).
[CrossRef] [PubMed]

Buus, J.

M. Osinski, J. Buus, IEEE J. Quantum Electron. QE-23, 9 (1987), Refs. 130–170 thereinY. Yamamoto, ed., Coherence, Amplification, and Quantum Effects in Semiconductor Lasers (Wiley, New York, 1991).
[CrossRef]

Coker, D. F.

L. A. Westling, M. G. Raymer, M. G. Sceats, D. F. Coker, Opt. Commun. 47, 212 (1983); L. A. Westling, M. G. Raymer, J. Opt. Soc. Am. B 3, 911 (1986).
[CrossRef]

Gray, G.

G. Gray, R. Roy, Phys. Rev. A 40, 2452 (1989).
[CrossRef] [PubMed]

Henry, C. H.

C. H. Henry, J. Lightwave Technol. LT-4, 298 (1986).
[CrossRef]

Osinski, M.

M. Osinski, J. Buus, IEEE J. Quantum Electron. QE-23, 9 (1987), Refs. 130–170 thereinY. Yamamoto, ed., Coherence, Amplification, and Quantum Effects in Semiconductor Lasers (Wiley, New York, 1991).
[CrossRef]

Raymer, M. G.

L. A. Westling, M. G. Raymer, M. G. Sceats, D. F. Coker, Opt. Commun. 47, 212 (1983); L. A. Westling, M. G. Raymer, J. Opt. Soc. Am. B 3, 911 (1986).
[CrossRef]

Roy, R.

G. Gray, R. Roy, Phys. Rev. A 40, 2452 (1989).
[CrossRef] [PubMed]

Sceats, M. G.

L. A. Westling, M. G. Raymer, M. G. Sceats, D. F. Coker, Opt. Commun. 47, 212 (1983); L. A. Westling, M. G. Raymer, J. Opt. Soc. Am. B 3, 911 (1986).
[CrossRef]

Westling, L. A.

L. A. Westling, M. G. Raymer, M. G. Sceats, D. F. Coker, Opt. Commun. 47, 212 (1983); L. A. Westling, M. G. Raymer, J. Opt. Soc. Am. B 3, 911 (1986).
[CrossRef]

IEEE J. Quantum Electron. (1)

M. Osinski, J. Buus, IEEE J. Quantum Electron. QE-23, 9 (1987), Refs. 130–170 thereinY. Yamamoto, ed., Coherence, Amplification, and Quantum Effects in Semiconductor Lasers (Wiley, New York, 1991).
[CrossRef]

J. Lightwave Technol. (1)

C. H. Henry, J. Lightwave Technol. LT-4, 298 (1986).
[CrossRef]

Opt. Commun. (1)

L. A. Westling, M. G. Raymer, M. G. Sceats, D. F. Coker, Opt. Commun. 47, 212 (1983); L. A. Westling, M. G. Raymer, J. Opt. Soc. Am. B 3, 911 (1986).
[CrossRef]

Phys. Rev. A (2)

G. Gray, R. Roy, Phys. Rev. A 40, 2452 (1989).
[CrossRef] [PubMed]

G. P. Agrawal, Phys. Rev. A 37, 2488 (1988).
[CrossRef] [PubMed]

Other (1)

In fact, the form of the IAF changes significantly with feedback and provides an effective monitor for feedback. This will be a subject of further study in our laboratory.

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Figures (4)

Fig. 1
Fig. 1

Intensity autocorrelator consists of a plate beam splitter, two corner-cube retroreflectors, a LiIO3 crystal, and a photomultiplier tube (PMT) detector. The output of the diode laser is split into two beams. One of these beams undergoes a variable delay T before the two are recombined with a lens in the crystal. The light at twice the laser frequency, which is due to the mixing of the fields of the two beams in the crystal, is detected as a function of delay, then amplified, collected, and stored in a computer.

Fig. 2
Fig. 2

Measured IAF of a Sharp LTO21 diode laser with a 59.5-mA operating current. The dc offset, which is due to the average intensity, has been removed. Large-scale structure is due to relaxation oscillations; small spikes occur because of mode beating between the main mode with many tiny side modes. The inset shows the figure in detail.

Fig. 3
Fig. 3

Fourier transform of the measured IAF shown in Fig. 2. The spikes occur at integer multiples of the laser’s longitudinal mode spacing. The number of spikes reveals that six modes on either side of the main mode contribute significantly to the laser’s intensity variations.

Fig. 4
Fig. 4

Modeled IAF. The widths of the spikes are determined by the number of modes and hence by the number of frequencies contributing to the laser output. Here the number of side modes is six on each side. ΩR, relaxation oscillation frequency; ΓR, damping rate of the relaxation oscillations; R, spontaneous emission rate; ΓN, damping rate of the carrier fluctuations; ΓS, damping rate of the sidemode intensity fluctuations; α, linewidth enhancement factor; Np, number of photons in the laser cavity. The inset shows the figure in detail.

Equations (4)

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E ( t ) = n E n ( t ) exp { i [ ( ω + n Δ ω ) t + ϕ n ( t ) ] } ,
I ( t ) I ( t + T ) = n = 0 N I n ( t ) I n ( t + T ) + n , m = 0 n m N I m ( t ) I n ( t + T ) + n , m = 1 n m N E n ( t ) E m ( t + T ) E n * ( t + T ) × E m * ( t ) exp { i [ ( n - m ) Δ ω T + Ψ n - Ψ 0 ] } ,
E n ( t ) E 0 ( t + T ) E n * ( t + T ) E 0 * ( t ) 2 n I 0 I n 2 cos ( n Δ ω T ) ,
2 n = 1 N [ 2 I n I 0 cos ( n Δ ω T ) ] exp { - [ 1 2 ( Ψ n 2 - Ψ 0 2 ) ] } .

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