Abstract

We study in detail the effect of the anticorrelation of the polarization modes on the total intensity noise of a vertical-cavity surface-emitting laser. We show that small polarization-dependent losses can greatly improve the total intensity noise, and we determine and experimentally demonstrate the conditions necessary for optimal intensity noise reduction.

© 2004 Optical Society of America

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  1. E. Goobar, J. W. Scott, B. Thibeault, G. Robinson, Y. Akulova, and L. A. Coldren, Appl. Phys. Lett. 67, 3697 (1995).
    [CrossRef]
  2. M. P. van Exter, M. B. Willemsen, and J. P. Woerdman, Phys. Rev. A 58, 4191 (1998).
    [CrossRef]
  3. F. Prati, G. Giacomelli, and F. Marin, Phys. Rev. A 62, 033810 (2000).
    [CrossRef]
  4. J.-P. Hermier, A. Bramati, A. Z. Khoury, V. Josse, E. Giacobino, P. Schnitzer, R. Michalzik, and K. J. Ebeling, IEEE J. Quantum Electron. 37, 87 (2001).
    [CrossRef]
  5. J.-L. Vey, C. Degen, K. Auen, and W. Elsässer, Phys. Rev. A 60, 3284 (1999).
    [CrossRef]
  6. J. Kaiser, C. Degen, and W. Elsässer, Opt. Lett. 26, 1720 (2001).
    [CrossRef]
  7. J.-P. Hermier, M. I. Kolobov, I. Maurin, and E. Giacobino, Phys. Rev. A 65, 053825 (2002).
    [CrossRef]
  8. K. D. Choquette, D. A. Richie, and R. E. Leibenguth, Appl. Phys. Lett. 64, 2062 (1994).
    [CrossRef]
  9. J. E. Epler, S. Gehrsitz, K. H. Gulden, M. Moser, H. C. Sigg, and H. W. Lehmann, Appl. Phys. Lett. 69, 722 (1996).
    [CrossRef]
  10. A. Bramati, J.-P. Hermier, A. Z. Khoury, E. Giacobino, P. Schnitzer, R. Michalzik, K. J. Ebeling, J.-Ph. Poizat, and Ph. Grangier, Opt. Lett. 24, 893 (1999).
    [CrossRef]
  11. J.-P. Hermier, A. Bramati, A. Z. Khoury, E. Giacobino, J.-Ph. Poizat, T. J. Chang, and Ph. Grangier, J. Opt. Soc. Am. B 16, 2140 (1999).
    [CrossRef]
  12. N. Treps and C. Fabre, Phys. Rev. A 62, 033816 (2000).
    [CrossRef]
  13. D. Wiedenmann, P. Schnitzer, C. Jung, M. Grabherr, R. Jager, R. Michalzik, and K. J. Ebeling, Appl. Phys. Lett. 73, 717 (1998).
    [CrossRef]

2002 (1)

J.-P. Hermier, M. I. Kolobov, I. Maurin, and E. Giacobino, Phys. Rev. A 65, 053825 (2002).
[CrossRef]

2001 (2)

J. Kaiser, C. Degen, and W. Elsässer, Opt. Lett. 26, 1720 (2001).
[CrossRef]

J.-P. Hermier, A. Bramati, A. Z. Khoury, V. Josse, E. Giacobino, P. Schnitzer, R. Michalzik, and K. J. Ebeling, IEEE J. Quantum Electron. 37, 87 (2001).
[CrossRef]

2000 (2)

F. Prati, G. Giacomelli, and F. Marin, Phys. Rev. A 62, 033810 (2000).
[CrossRef]

N. Treps and C. Fabre, Phys. Rev. A 62, 033816 (2000).
[CrossRef]

1999 (3)

1998 (2)

M. P. van Exter, M. B. Willemsen, and J. P. Woerdman, Phys. Rev. A 58, 4191 (1998).
[CrossRef]

D. Wiedenmann, P. Schnitzer, C. Jung, M. Grabherr, R. Jager, R. Michalzik, and K. J. Ebeling, Appl. Phys. Lett. 73, 717 (1998).
[CrossRef]

1996 (1)

J. E. Epler, S. Gehrsitz, K. H. Gulden, M. Moser, H. C. Sigg, and H. W. Lehmann, Appl. Phys. Lett. 69, 722 (1996).
[CrossRef]

1995 (1)

E. Goobar, J. W. Scott, B. Thibeault, G. Robinson, Y. Akulova, and L. A. Coldren, Appl. Phys. Lett. 67, 3697 (1995).
[CrossRef]

1994 (1)

K. D. Choquette, D. A. Richie, and R. E. Leibenguth, Appl. Phys. Lett. 64, 2062 (1994).
[CrossRef]

Akulova, Y.

E. Goobar, J. W. Scott, B. Thibeault, G. Robinson, Y. Akulova, and L. A. Coldren, Appl. Phys. Lett. 67, 3697 (1995).
[CrossRef]

Auen, K.

J.-L. Vey, C. Degen, K. Auen, and W. Elsässer, Phys. Rev. A 60, 3284 (1999).
[CrossRef]

Bramati, A.

Chang, T. J.

Choquette, K. D.

K. D. Choquette, D. A. Richie, and R. E. Leibenguth, Appl. Phys. Lett. 64, 2062 (1994).
[CrossRef]

Coldren, L. A.

E. Goobar, J. W. Scott, B. Thibeault, G. Robinson, Y. Akulova, and L. A. Coldren, Appl. Phys. Lett. 67, 3697 (1995).
[CrossRef]

Degen, C.

J. Kaiser, C. Degen, and W. Elsässer, Opt. Lett. 26, 1720 (2001).
[CrossRef]

J.-L. Vey, C. Degen, K. Auen, and W. Elsässer, Phys. Rev. A 60, 3284 (1999).
[CrossRef]

Ebeling, K. J.

J.-P. Hermier, A. Bramati, A. Z. Khoury, V. Josse, E. Giacobino, P. Schnitzer, R. Michalzik, and K. J. Ebeling, IEEE J. Quantum Electron. 37, 87 (2001).
[CrossRef]

A. Bramati, J.-P. Hermier, A. Z. Khoury, E. Giacobino, P. Schnitzer, R. Michalzik, K. J. Ebeling, J.-Ph. Poizat, and Ph. Grangier, Opt. Lett. 24, 893 (1999).
[CrossRef]

D. Wiedenmann, P. Schnitzer, C. Jung, M. Grabherr, R. Jager, R. Michalzik, and K. J. Ebeling, Appl. Phys. Lett. 73, 717 (1998).
[CrossRef]

Elsässer, W.

J. Kaiser, C. Degen, and W. Elsässer, Opt. Lett. 26, 1720 (2001).
[CrossRef]

J.-L. Vey, C. Degen, K. Auen, and W. Elsässer, Phys. Rev. A 60, 3284 (1999).
[CrossRef]

Epler, J. E.

J. E. Epler, S. Gehrsitz, K. H. Gulden, M. Moser, H. C. Sigg, and H. W. Lehmann, Appl. Phys. Lett. 69, 722 (1996).
[CrossRef]

Fabre, C.

N. Treps and C. Fabre, Phys. Rev. A 62, 033816 (2000).
[CrossRef]

Gehrsitz, S.

J. E. Epler, S. Gehrsitz, K. H. Gulden, M. Moser, H. C. Sigg, and H. W. Lehmann, Appl. Phys. Lett. 69, 722 (1996).
[CrossRef]

Giacobino, E.

J.-P. Hermier, M. I. Kolobov, I. Maurin, and E. Giacobino, Phys. Rev. A 65, 053825 (2002).
[CrossRef]

J.-P. Hermier, A. Bramati, A. Z. Khoury, V. Josse, E. Giacobino, P. Schnitzer, R. Michalzik, and K. J. Ebeling, IEEE J. Quantum Electron. 37, 87 (2001).
[CrossRef]

A. Bramati, J.-P. Hermier, A. Z. Khoury, E. Giacobino, P. Schnitzer, R. Michalzik, K. J. Ebeling, J.-Ph. Poizat, and Ph. Grangier, Opt. Lett. 24, 893 (1999).
[CrossRef]

J.-P. Hermier, A. Bramati, A. Z. Khoury, E. Giacobino, J.-Ph. Poizat, T. J. Chang, and Ph. Grangier, J. Opt. Soc. Am. B 16, 2140 (1999).
[CrossRef]

Giacomelli, G.

F. Prati, G. Giacomelli, and F. Marin, Phys. Rev. A 62, 033810 (2000).
[CrossRef]

Goobar, E.

E. Goobar, J. W. Scott, B. Thibeault, G. Robinson, Y. Akulova, and L. A. Coldren, Appl. Phys. Lett. 67, 3697 (1995).
[CrossRef]

Grabherr, M.

D. Wiedenmann, P. Schnitzer, C. Jung, M. Grabherr, R. Jager, R. Michalzik, and K. J. Ebeling, Appl. Phys. Lett. 73, 717 (1998).
[CrossRef]

Grangier, Ph.

Gulden, K. H.

J. E. Epler, S. Gehrsitz, K. H. Gulden, M. Moser, H. C. Sigg, and H. W. Lehmann, Appl. Phys. Lett. 69, 722 (1996).
[CrossRef]

Hermier, J.-P.

J.-P. Hermier, M. I. Kolobov, I. Maurin, and E. Giacobino, Phys. Rev. A 65, 053825 (2002).
[CrossRef]

J.-P. Hermier, A. Bramati, A. Z. Khoury, V. Josse, E. Giacobino, P. Schnitzer, R. Michalzik, and K. J. Ebeling, IEEE J. Quantum Electron. 37, 87 (2001).
[CrossRef]

J.-P. Hermier, A. Bramati, A. Z. Khoury, E. Giacobino, J.-Ph. Poizat, T. J. Chang, and Ph. Grangier, J. Opt. Soc. Am. B 16, 2140 (1999).
[CrossRef]

A. Bramati, J.-P. Hermier, A. Z. Khoury, E. Giacobino, P. Schnitzer, R. Michalzik, K. J. Ebeling, J.-Ph. Poizat, and Ph. Grangier, Opt. Lett. 24, 893 (1999).
[CrossRef]

Jager, R.

D. Wiedenmann, P. Schnitzer, C. Jung, M. Grabherr, R. Jager, R. Michalzik, and K. J. Ebeling, Appl. Phys. Lett. 73, 717 (1998).
[CrossRef]

Josse, V.

J.-P. Hermier, A. Bramati, A. Z. Khoury, V. Josse, E. Giacobino, P. Schnitzer, R. Michalzik, and K. J. Ebeling, IEEE J. Quantum Electron. 37, 87 (2001).
[CrossRef]

Jung, C.

D. Wiedenmann, P. Schnitzer, C. Jung, M. Grabherr, R. Jager, R. Michalzik, and K. J. Ebeling, Appl. Phys. Lett. 73, 717 (1998).
[CrossRef]

Kaiser, J.

Khoury, A. Z.

Kolobov, M. I.

J.-P. Hermier, M. I. Kolobov, I. Maurin, and E. Giacobino, Phys. Rev. A 65, 053825 (2002).
[CrossRef]

Lehmann, H. W.

J. E. Epler, S. Gehrsitz, K. H. Gulden, M. Moser, H. C. Sigg, and H. W. Lehmann, Appl. Phys. Lett. 69, 722 (1996).
[CrossRef]

Leibenguth, R. E.

K. D. Choquette, D. A. Richie, and R. E. Leibenguth, Appl. Phys. Lett. 64, 2062 (1994).
[CrossRef]

Marin, F.

F. Prati, G. Giacomelli, and F. Marin, Phys. Rev. A 62, 033810 (2000).
[CrossRef]

Maurin, I.

J.-P. Hermier, M. I. Kolobov, I. Maurin, and E. Giacobino, Phys. Rev. A 65, 053825 (2002).
[CrossRef]

Michalzik, R.

J.-P. Hermier, A. Bramati, A. Z. Khoury, V. Josse, E. Giacobino, P. Schnitzer, R. Michalzik, and K. J. Ebeling, IEEE J. Quantum Electron. 37, 87 (2001).
[CrossRef]

A. Bramati, J.-P. Hermier, A. Z. Khoury, E. Giacobino, P. Schnitzer, R. Michalzik, K. J. Ebeling, J.-Ph. Poizat, and Ph. Grangier, Opt. Lett. 24, 893 (1999).
[CrossRef]

D. Wiedenmann, P. Schnitzer, C. Jung, M. Grabherr, R. Jager, R. Michalzik, and K. J. Ebeling, Appl. Phys. Lett. 73, 717 (1998).
[CrossRef]

Moser, M.

J. E. Epler, S. Gehrsitz, K. H. Gulden, M. Moser, H. C. Sigg, and H. W. Lehmann, Appl. Phys. Lett. 69, 722 (1996).
[CrossRef]

Poizat, J.-Ph.

Prati, F.

F. Prati, G. Giacomelli, and F. Marin, Phys. Rev. A 62, 033810 (2000).
[CrossRef]

Richie, D. A.

K. D. Choquette, D. A. Richie, and R. E. Leibenguth, Appl. Phys. Lett. 64, 2062 (1994).
[CrossRef]

Robinson, G.

E. Goobar, J. W. Scott, B. Thibeault, G. Robinson, Y. Akulova, and L. A. Coldren, Appl. Phys. Lett. 67, 3697 (1995).
[CrossRef]

Schnitzer, P.

J.-P. Hermier, A. Bramati, A. Z. Khoury, V. Josse, E. Giacobino, P. Schnitzer, R. Michalzik, and K. J. Ebeling, IEEE J. Quantum Electron. 37, 87 (2001).
[CrossRef]

A. Bramati, J.-P. Hermier, A. Z. Khoury, E. Giacobino, P. Schnitzer, R. Michalzik, K. J. Ebeling, J.-Ph. Poizat, and Ph. Grangier, Opt. Lett. 24, 893 (1999).
[CrossRef]

D. Wiedenmann, P. Schnitzer, C. Jung, M. Grabherr, R. Jager, R. Michalzik, and K. J. Ebeling, Appl. Phys. Lett. 73, 717 (1998).
[CrossRef]

Scott, J. W.

E. Goobar, J. W. Scott, B. Thibeault, G. Robinson, Y. Akulova, and L. A. Coldren, Appl. Phys. Lett. 67, 3697 (1995).
[CrossRef]

Sigg, H. C.

J. E. Epler, S. Gehrsitz, K. H. Gulden, M. Moser, H. C. Sigg, and H. W. Lehmann, Appl. Phys. Lett. 69, 722 (1996).
[CrossRef]

Thibeault, B.

E. Goobar, J. W. Scott, B. Thibeault, G. Robinson, Y. Akulova, and L. A. Coldren, Appl. Phys. Lett. 67, 3697 (1995).
[CrossRef]

Treps, N.

N. Treps and C. Fabre, Phys. Rev. A 62, 033816 (2000).
[CrossRef]

van Exter, M. P.

M. P. van Exter, M. B. Willemsen, and J. P. Woerdman, Phys. Rev. A 58, 4191 (1998).
[CrossRef]

Vey, J.-L.

J.-L. Vey, C. Degen, K. Auen, and W. Elsässer, Phys. Rev. A 60, 3284 (1999).
[CrossRef]

Wiedenmann, D.

D. Wiedenmann, P. Schnitzer, C. Jung, M. Grabherr, R. Jager, R. Michalzik, and K. J. Ebeling, Appl. Phys. Lett. 73, 717 (1998).
[CrossRef]

Willemsen, M. B.

M. P. van Exter, M. B. Willemsen, and J. P. Woerdman, Phys. Rev. A 58, 4191 (1998).
[CrossRef]

Woerdman, J. P.

M. P. van Exter, M. B. Willemsen, and J. P. Woerdman, Phys. Rev. A 58, 4191 (1998).
[CrossRef]

Appl. Phys. Lett. (4)

E. Goobar, J. W. Scott, B. Thibeault, G. Robinson, Y. Akulova, and L. A. Coldren, Appl. Phys. Lett. 67, 3697 (1995).
[CrossRef]

K. D. Choquette, D. A. Richie, and R. E. Leibenguth, Appl. Phys. Lett. 64, 2062 (1994).
[CrossRef]

J. E. Epler, S. Gehrsitz, K. H. Gulden, M. Moser, H. C. Sigg, and H. W. Lehmann, Appl. Phys. Lett. 69, 722 (1996).
[CrossRef]

D. Wiedenmann, P. Schnitzer, C. Jung, M. Grabherr, R. Jager, R. Michalzik, and K. J. Ebeling, Appl. Phys. Lett. 73, 717 (1998).
[CrossRef]

IEEE J. Quantum Electron. (1)

J.-P. Hermier, A. Bramati, A. Z. Khoury, V. Josse, E. Giacobino, P. Schnitzer, R. Michalzik, and K. J. Ebeling, IEEE J. Quantum Electron. 37, 87 (2001).
[CrossRef]

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

Opt. Lett. (2)

Phys. Rev. A (5)

J.-P. Hermier, M. I. Kolobov, I. Maurin, and E. Giacobino, Phys. Rev. A 65, 053825 (2002).
[CrossRef]

J.-L. Vey, C. Degen, K. Auen, and W. Elsässer, Phys. Rev. A 60, 3284 (1999).
[CrossRef]

M. P. van Exter, M. B. Willemsen, and J. P. Woerdman, Phys. Rev. A 58, 4191 (1998).
[CrossRef]

F. Prati, G. Giacomelli, and F. Marin, Phys. Rev. A 62, 033810 (2000).
[CrossRef]

N. Treps and C. Fabre, Phys. Rev. A 62, 033816 (2000).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Experimental setup for polarization-selective attenuation: The two orthogonal linear polarizations are separated with a polarizing beam splitter (PBS) and then superimposed again after suitable attenuation of the polarization exhibiting the higher noise.

Fig. 2
Fig. 2

Absolute intensity noise of polarization 1 (lower trace) and polarization 2 (upper trace). The traces are recorded at a noise frequency of 6 MHz.

Fig. 3
Fig. 3

Solid curve, normalized intensity noise ST as a function of intensity transmission T, as calculated from Eq. (1). The measured parameters are q=1.162, v1=21,519, v2=30,512, and C=-0.999. Dots, experimental data. The noise of the unfiltered beam is 21.2 dB. Optimal noise reduction leads to a 14.4-dB noise level for Topt=0.908.

Fig. 4
Fig. 4

Normalized intensity noise of the total beam (upper trace) and of the beam after optimal polarization-selective attenuation (lower trace) for T=Topt=0.908.

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

ST=1+qv1+T2v22TCq1+v11+v21/2q+T=1+ET,
ET<0,
C<-qv1+T2v22Tq1+v11+v21/2.
C2>qv1-T2v224T2q1+v11+v2+v1v21+v11+v2.
qv1=Topt2v2.
C2>v1v21+v11+v2.

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