Abstract

We experimentally study the transverse distribution of intensity noise in the far field of a single-mode semiconductor laser. We show that a large amount of noise is present in the higher-order nonlasing transverse modes (parallel to the diode junction). Furthermore, correlations between the TE00 and the TE10 modes are observed.

© 1998 Optical Society of America

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References

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  1. S. Machida, Y. Yamamoto, and Y. Itaya, “Observation of amplitude squeezing in a constant-current-driven semiconductor laser,” Phys. Rev. Lett. 58, 1000 (1987).
    [CrossRef] [PubMed]
  2. W. H. Richardson, S. Machida, and Y. Yamamoto, “Squeezed photon-number noise and sub-Poissonian electrical partition noise in a semiconductor laser,” Phys. Rev. Lett. 66, 2867 (1991).
    [CrossRef] [PubMed]
  3. M. J. Freeman, H. Wang, D. G. Steel, R. Craig, and D. R. Scifres, “Wavelength-tunable amplitude-squeezed light from a room-temperature quantum-well laser,” Opt. Lett. 18, 2141 (1993).
    [CrossRef] [PubMed]
  4. Yu. M. Golubev and I. V. Sokolov, Zh. Eksp. Teor. Fiz. 87, 804 (1984) [“Photon antibunching in a coherent light source and suppression of the photorecording noise,” Sov. Phys. JETP 60, 234 (1984)].
  5. Y. Yamamoto, S. Machida, and O. Nilsson, “Amplitude squeezing in a pump-noise-suppressed laser oscillator,” Phys. Rev. A 34, 4025 (1986).
    [CrossRef] [PubMed]
  6. A. W. Smith and J. A. Armstrong, “Intensity noise in multimode GaAs laser emission,” IBM J. Res. Dev. 10, 225 (1966).
    [CrossRef]
  7. S. Inoue, H. Ohzu, S. Machida, and Y. Yamamoto, “Quantum correlation between longitudinal-mode intensities in a multimode squeezed semiconductor laser,” Phys. Rev. A 46, 2757 (1992).
    [CrossRef] [PubMed]
  8. H. Wang, M. J. Freeman, and D. G. Steel, “Squeezed light from injection-locked quantum well lasers,” Phys. Rev. Lett. 71, 3951 (1993).
    [CrossRef] [PubMed]
  9. F. Marin, A. Bramati, E. Giacobino, T.-C. Zhang, J.-Ph. Poizat, J.-F. Roch, and P. Grangier, “Squeezing and intermode correlations in laser diodes,” Phys. Rev. Lett. 75, 4606 (1995).
    [CrossRef] [PubMed]
  10. D. C. Kilper and D. G. Steel, R. Craig, and D. R. Scifres, “Polarization-dependent noise in a photon-number squeezed light generated by quantum-well lasers,” Opt. Lett. 21, 1283 (1996).
    [CrossRef] [PubMed]
  11. D. C. Kilper, P. A. Roos, J. L. Carlsten, and K. L. Lear, “Squeezed light generated by a microcavity laser,” Phys. Rev. A 55, R3323 (1997).
    [CrossRef]
  12. C. C. Harb, T. C. Ralph, E. H. Huntington, D. E. McClelland, H.-A. Bachor, and I. Freitag, “Intensity-noise dependence of Nd:YAG lasers on their diode-laser pump source,” J. Opt. Soc. Am. B 14, 2936 (1997).
    [CrossRef]
  13. H. P. Yuen and V. W. S. Chan, “Noise in homodyne and heterodyne detection,” Opt. Lett. 8, 177 (1983).
    [CrossRef] [PubMed]
  14. Two photodiodes were used on each arm of the balanced detection in order to avoid saturation.
  15. M. D. Levenson, W. H. Richardson, and S. H. Perlmutter, “Stochastic noise in TEM00 laser beam position,” Opt. Lett. 14, 779 (1989); M. D. Levenson, S. H. Perlmutter, and W. H. Richardson, “Stochastic position noise, or why a laser beam can not go straight,” in Quantum Optics, V, J. D. Harvey and D. F. Walls, eds. (Springer-Verlag, Heidelberg, 1989).
    [CrossRef] [PubMed]
  16. M. J. Holland, M. J. Collett, D. F. Walls, and M. D. Levenson, “Nonideal quantum nondemolition measurements,” Phys. Rev. A 42, 2995 (1990).
    [CrossRef] [PubMed]
  17. K. Petermann, “Calculated spontaneous emission factor for double-heterostructure injection lasers with gain-induced waveguiding,” IEEE J. Quantum Electron. 15, 566 (1979).
    [CrossRef]
  18. H. A. Haus and S. Kawakami, “On the excess spontaneous emission factor in gain-guided laser amplifiers,” IEEE J. Quantum Electron. 21, 63 (1985).
    [CrossRef]
  19. A. E. Siegman, “Excess spontaneous emission in non-Hermitian optical system. I. Laser amplifiers,” Phys. Rev. A 39, 1253 (1989); “Excess spontaneous emission in non-Hermitian optical system. I. Laser oscillators,” Phys. Rev. A 39, 1264 (1989); see also A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986).
    [CrossRef] [PubMed]
  20. P. Grangier and J.-Ph. Poizat, “A simple quantum picture for the Petermann excess noise factor,” Eur. J. Phys. D 1, 97 (1998).
    [CrossRef]

1998 (1)

P. Grangier and J.-Ph. Poizat, “A simple quantum picture for the Petermann excess noise factor,” Eur. J. Phys. D 1, 97 (1998).
[CrossRef]

1997 (2)

1996 (1)

1995 (1)

F. Marin, A. Bramati, E. Giacobino, T.-C. Zhang, J.-Ph. Poizat, J.-F. Roch, and P. Grangier, “Squeezing and intermode correlations in laser diodes,” Phys. Rev. Lett. 75, 4606 (1995).
[CrossRef] [PubMed]

1993 (2)

1992 (1)

S. Inoue, H. Ohzu, S. Machida, and Y. Yamamoto, “Quantum correlation between longitudinal-mode intensities in a multimode squeezed semiconductor laser,” Phys. Rev. A 46, 2757 (1992).
[CrossRef] [PubMed]

1991 (1)

W. H. Richardson, S. Machida, and Y. Yamamoto, “Squeezed photon-number noise and sub-Poissonian electrical partition noise in a semiconductor laser,” Phys. Rev. Lett. 66, 2867 (1991).
[CrossRef] [PubMed]

1990 (1)

M. J. Holland, M. J. Collett, D. F. Walls, and M. D. Levenson, “Nonideal quantum nondemolition measurements,” Phys. Rev. A 42, 2995 (1990).
[CrossRef] [PubMed]

1987 (1)

S. Machida, Y. Yamamoto, and Y. Itaya, “Observation of amplitude squeezing in a constant-current-driven semiconductor laser,” Phys. Rev. Lett. 58, 1000 (1987).
[CrossRef] [PubMed]

1986 (1)

Y. Yamamoto, S. Machida, and O. Nilsson, “Amplitude squeezing in a pump-noise-suppressed laser oscillator,” Phys. Rev. A 34, 4025 (1986).
[CrossRef] [PubMed]

1985 (1)

H. A. Haus and S. Kawakami, “On the excess spontaneous emission factor in gain-guided laser amplifiers,” IEEE J. Quantum Electron. 21, 63 (1985).
[CrossRef]

1984 (1)

Yu. M. Golubev and I. V. Sokolov, Zh. Eksp. Teor. Fiz. 87, 804 (1984) [“Photon antibunching in a coherent light source and suppression of the photorecording noise,” Sov. Phys. JETP 60, 234 (1984)].

1983 (1)

1979 (1)

K. Petermann, “Calculated spontaneous emission factor for double-heterostructure injection lasers with gain-induced waveguiding,” IEEE J. Quantum Electron. 15, 566 (1979).
[CrossRef]

1966 (1)

A. W. Smith and J. A. Armstrong, “Intensity noise in multimode GaAs laser emission,” IBM J. Res. Dev. 10, 225 (1966).
[CrossRef]

Eur. J. Phys. D (1)

P. Grangier and J.-Ph. Poizat, “A simple quantum picture for the Petermann excess noise factor,” Eur. J. Phys. D 1, 97 (1998).
[CrossRef]

IBM J. Res. Dev. (1)

A. W. Smith and J. A. Armstrong, “Intensity noise in multimode GaAs laser emission,” IBM J. Res. Dev. 10, 225 (1966).
[CrossRef]

IEEE J. Quantum Electron. (2)

K. Petermann, “Calculated spontaneous emission factor for double-heterostructure injection lasers with gain-induced waveguiding,” IEEE J. Quantum Electron. 15, 566 (1979).
[CrossRef]

H. A. Haus and S. Kawakami, “On the excess spontaneous emission factor in gain-guided laser amplifiers,” IEEE J. Quantum Electron. 21, 63 (1985).
[CrossRef]

J. Opt. Soc. Am. B (1)

Opt. Lett. (3)

Phys. Rev. A (4)

M. J. Holland, M. J. Collett, D. F. Walls, and M. D. Levenson, “Nonideal quantum nondemolition measurements,” Phys. Rev. A 42, 2995 (1990).
[CrossRef] [PubMed]

S. Inoue, H. Ohzu, S. Machida, and Y. Yamamoto, “Quantum correlation between longitudinal-mode intensities in a multimode squeezed semiconductor laser,” Phys. Rev. A 46, 2757 (1992).
[CrossRef] [PubMed]

Y. Yamamoto, S. Machida, and O. Nilsson, “Amplitude squeezing in a pump-noise-suppressed laser oscillator,” Phys. Rev. A 34, 4025 (1986).
[CrossRef] [PubMed]

D. C. Kilper, P. A. Roos, J. L. Carlsten, and K. L. Lear, “Squeezed light generated by a microcavity laser,” Phys. Rev. A 55, R3323 (1997).
[CrossRef]

Phys. Rev. Lett. (4)

H. Wang, M. J. Freeman, and D. G. Steel, “Squeezed light from injection-locked quantum well lasers,” Phys. Rev. Lett. 71, 3951 (1993).
[CrossRef] [PubMed]

F. Marin, A. Bramati, E. Giacobino, T.-C. Zhang, J.-Ph. Poizat, J.-F. Roch, and P. Grangier, “Squeezing and intermode correlations in laser diodes,” Phys. Rev. Lett. 75, 4606 (1995).
[CrossRef] [PubMed]

S. Machida, Y. Yamamoto, and Y. Itaya, “Observation of amplitude squeezing in a constant-current-driven semiconductor laser,” Phys. Rev. Lett. 58, 1000 (1987).
[CrossRef] [PubMed]

W. H. Richardson, S. Machida, and Y. Yamamoto, “Squeezed photon-number noise and sub-Poissonian electrical partition noise in a semiconductor laser,” Phys. Rev. Lett. 66, 2867 (1991).
[CrossRef] [PubMed]

Sov. Phys. JETP (1)

Yu. M. Golubev and I. V. Sokolov, Zh. Eksp. Teor. Fiz. 87, 804 (1984) [“Photon antibunching in a coherent light source and suppression of the photorecording noise,” Sov. Phys. JETP 60, 234 (1984)].

Other (3)

Two photodiodes were used on each arm of the balanced detection in order to avoid saturation.

M. D. Levenson, W. H. Richardson, and S. H. Perlmutter, “Stochastic noise in TEM00 laser beam position,” Opt. Lett. 14, 779 (1989); M. D. Levenson, S. H. Perlmutter, and W. H. Richardson, “Stochastic position noise, or why a laser beam can not go straight,” in Quantum Optics, V, J. D. Harvey and D. F. Walls, eds. (Springer-Verlag, Heidelberg, 1989).
[CrossRef] [PubMed]

A. E. Siegman, “Excess spontaneous emission in non-Hermitian optical system. I. Laser amplifiers,” Phys. Rev. A 39, 1253 (1989); “Excess spontaneous emission in non-Hermitian optical system. I. Laser oscillators,” Phys. Rev. A 39, 1264 (1989); see also A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986).
[CrossRef] [PubMed]

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Figures (4)

Fig. 1
Fig. 1

Simplified experimental setup. The external grating is not shown, for the sake of clarity. B.S., beam splitter; P.D., photodiode; S.A., spectrum analyzer.

Fig. 2
Fig. 2

Razor-blade scan along x (with w=1). Trace (S) is the SQL (proportional to the intensity). Trace (L) [or (R)] corresponds to the razor blade entering the beam from the left (right). Trace (R) is flipped over in order to be compared conveniently with trace (L). The two traces are almost superimposed, which is the signature for a vanishing correlation. For each trace the thin solid curve is the best fit. The fitting parameters are v0=-0.16±0.02, v1=14.3±0.2, v2=4±1, and C=0.00±0.02.

Fig. 3
Fig. 3

Razor-blade scan along x (with w=1). Trace (S) is the SQL (proportional to the intensity). The results of this figure are obtained with a slightly different fine adjustment of the orientation of the grating compared with the results of Fig. 2. Trace (L) [or (R)] corresponds to the razor blade entering the beam from the left (right). For each trace the thin solid curve is the best fit. Trace (R) is flipped over in order to be compared conveniently with trace (L). The fitting parameters are v0=-0.10±0.02, v1=14.9±0.2, v2=1±0.5, and C=0.23±0.02. The inset is a zoom of the SQL-normalized noise of trace (L), showing that the maximum squeezing is obtained when part of the beam is screened. For each trace the thin solid curve is the best fit.

Fig. 4
Fig. 4

Correlation experimental setup. D1 is a two-quadrant photodiode. D2 and D2 are ordinary photodiodes.14 The transmission of beam splitter BS1 is 70%. BS2 is the 50/50 beam splitter of the balanced detection. S1,2,3 are RF switchable (+/-) power combiners. L.D., laser diode; S.A., spectrum analyzer.

Equations (11)

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V(X)=E02Xu02(x)dx+v0Xu02(x)dx2+v1Xu0(x)u1(x)dx2+2c01Xu02(x)dxXu0(x)u1(x)dx,
u0(x)=(2/π)1/41/w exp(-x2/w2),
u1(x)=(2/π)1/41/w2(x/w) exp(-x2/w2),
X+u0(x)u1(x)dx=---Xu0(x)u1(x)dx.
E(x)=E0u0(x)+i=0+δEiui(x),
I(X)=E02Xu02(x)dx+i=0+E0δPiXu0(x)ui(x)dx,
δI2(X)=i,jE02δPiδPj×Xu0(x)ui(x)dxXu0(x)uj(x)dx.
ΘX(x)=0forx<X,
ΘX(x)=1forxX,
ui|ΘX|uj=-+ΘX(x)ui(x)uj(x)dx=Xui(x)uj(x)dx.
δI2(X)=E02i,jδPiδPju0|ΘX|ujui|ΘX|u0=E02u0|ΘX|u0+i=0+(δPi2-1)|ui|ΘX|u0|2+ijδPiδPjui|ΘX|u0u0|ΘX|uj,

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