Abstract

Using a theoretical semiclassical approach, we study in detail the amplitude fluctuations and correlations of a two-orthogonal polarization-mode semiconductor laser as obtained from a vertical-cavity surface-emitting laser (VCSEL). We demonstrate that there exists the possibility of squeezing in the two-mode regime besides sub-shot-noise emission in the well-known ideal single-mode operation regime. These theoretical results confirm a recent experimental demonstration of the generation of amplitude-squeezed light with VCSEL’s.

© 1998 Optical Society of America

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  1. Y. Yamamoto, S. Machida, and O. Nilsson, Phys. Rev. A 34, 4025 (1986).
    [CrossRef] [PubMed]
  2. S. Machida, Y. Yamamoto, and Y. Itaya, Phys. Rev. Lett. 58, 1000 (1987).
    [CrossRef] [PubMed]
  3. W. H. Richardson, S. Machida, and Y. Yamamoto, Phys. Rev. Lett. 66, 2867 (1991).
    [CrossRef] [PubMed]
  4. F. Marin, A. Bramati, E. Giacobino, T.-C. Zhang, J. Ph. Poizat, J. F. Roch, and P. Grangier, Phys. Rev. Lett. 75, 4606 (1995).
    [CrossRef] [PubMed]
  5. M. J. Freeman, H. Wang, D. G. Steel, R. Craig, and D. R. Scifres, Opt. Lett. 18, 2141 (1993).
    [CrossRef]
  6. T.-C. Zhang, J.-Ph. Poizat, P. Grelu, J.-F. Roch, P. Grangier, F. Marin, A. Bramati, V. Jost, M. D. Levenson, and E. Giacobino, Quantum Semiclass. Opt. 7, 601 (1995).
    [CrossRef]
  7. J. Kitching, A. Yariv, and Y. Shevy, Phys. Rev. Lett. 74, 3372 (1995).
    [CrossRef] [PubMed]
  8. J. L. Vey and P. Gallion, IEEE J. Quantum Electron. 33, 2097 (1997).
    [CrossRef]
  9. J. L. Vey and P. Gallion, IEEE J. Quantum Electron. 33, 2105 (1997).
    [CrossRef]
  10. B. Tromborg, H.-E. Lassen, and H. Olesen, IEEE J. Quantum Electron. 30, 939 (1994).
    [CrossRef]
  11. D. D. Marcenac and J. E. Carroll, IEEE J. Quantum Electron. 30, 2064 (1994).
    [CrossRef]
  12. G. Björk and Y. Yamamoto, IEEE J. Quantum Electron. 27, 2386 (1991).
    [CrossRef]
  13. J.-L. Vey and W. Elsässer, J. Opt. Soc. Am. B 14, 1299 (1997).
    [CrossRef]
  14. E. Goobar, J. W. Scott, B. Thibeault, G. Robinson, Y. Akulova, and L. A. Coldren, Appl. Phys. Lett. 67, 3697 (1995).
    [CrossRef]
  15. D. C. Kilper, P. A. Roos, J. L. Carsten, and K. L. Lear, Phys. Rev. A 55, 3323 (1997).
    [CrossRef]
  16. J. L. Vey and P. Gallion, Opt. Lett. 20, 2018 (1995).
    [CrossRef] [PubMed]
  17. J. L. Vey, K. Auen, and W. Elsässer, Proc. SPIE 2994, 178 (1997).
    [CrossRef]
  18. G. P. Agrawal, Phys. Rev. A 37, 2488 (1988).
    [CrossRef] [PubMed]
  19. J. Martin-Regalado, F. Prati, M. San Miguel, and N. B. Abraham, IEEE J. Quantum Electron. 33, 765 (1997).
    [CrossRef]
  20. K. J. Ebeling, U. Fiedler, R. Michalzik, G. Reiner, and B. Weigl, Int. J. Electron. Commun. 50, 316 (1996).

1997 (6)

J. L. Vey and P. Gallion, IEEE J. Quantum Electron. 33, 2097 (1997).
[CrossRef]

J. L. Vey and P. Gallion, IEEE J. Quantum Electron. 33, 2105 (1997).
[CrossRef]

J. L. Vey, K. Auen, and W. Elsässer, Proc. SPIE 2994, 178 (1997).
[CrossRef]

J. Martin-Regalado, F. Prati, M. San Miguel, and N. B. Abraham, IEEE J. Quantum Electron. 33, 765 (1997).
[CrossRef]

D. C. Kilper, P. A. Roos, J. L. Carsten, and K. L. Lear, Phys. Rev. A 55, 3323 (1997).
[CrossRef]

J.-L. Vey and W. Elsässer, J. Opt. Soc. Am. B 14, 1299 (1997).
[CrossRef]

1996 (1)

K. J. Ebeling, U. Fiedler, R. Michalzik, G. Reiner, and B. Weigl, Int. J. Electron. Commun. 50, 316 (1996).

1995 (5)

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

F. Marin, A. Bramati, E. Giacobino, T.-C. Zhang, J. Ph. Poizat, J. F. Roch, and P. Grangier, Phys. Rev. Lett. 75, 4606 (1995).
[CrossRef] [PubMed]

J. L. Vey and P. Gallion, Opt. Lett. 20, 2018 (1995).
[CrossRef] [PubMed]

T.-C. Zhang, J.-Ph. Poizat, P. Grelu, J.-F. Roch, P. Grangier, F. Marin, A. Bramati, V. Jost, M. D. Levenson, and E. Giacobino, Quantum Semiclass. Opt. 7, 601 (1995).
[CrossRef]

J. Kitching, A. Yariv, and Y. Shevy, Phys. Rev. Lett. 74, 3372 (1995).
[CrossRef] [PubMed]

1994 (2)

B. Tromborg, H.-E. Lassen, and H. Olesen, IEEE J. Quantum Electron. 30, 939 (1994).
[CrossRef]

D. D. Marcenac and J. E. Carroll, IEEE J. Quantum Electron. 30, 2064 (1994).
[CrossRef]

1993 (1)

1991 (2)

G. Björk and Y. Yamamoto, IEEE J. Quantum Electron. 27, 2386 (1991).
[CrossRef]

W. H. Richardson, S. Machida, and Y. Yamamoto, Phys. Rev. Lett. 66, 2867 (1991).
[CrossRef] [PubMed]

1988 (1)

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

1987 (1)

S. Machida, Y. Yamamoto, and Y. Itaya, Phys. Rev. Lett. 58, 1000 (1987).
[CrossRef] [PubMed]

1986 (1)

Y. Yamamoto, S. Machida, and O. Nilsson, Phys. Rev. A 34, 4025 (1986).
[CrossRef] [PubMed]

Abraham, N. B.

J. Martin-Regalado, F. Prati, M. San Miguel, and N. B. Abraham, IEEE J. Quantum Electron. 33, 765 (1997).
[CrossRef]

Agrawal, G. P.

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

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, K. Auen, and W. Elsässer, Proc. SPIE 2994, 178 (1997).
[CrossRef]

Björk, G.

G. Björk and Y. Yamamoto, IEEE J. Quantum Electron. 27, 2386 (1991).
[CrossRef]

Bramati, A.

F. Marin, A. Bramati, E. Giacobino, T.-C. Zhang, J. Ph. Poizat, J. F. Roch, and P. Grangier, Phys. Rev. Lett. 75, 4606 (1995).
[CrossRef] [PubMed]

T.-C. Zhang, J.-Ph. Poizat, P. Grelu, J.-F. Roch, P. Grangier, F. Marin, A. Bramati, V. Jost, M. D. Levenson, and E. Giacobino, Quantum Semiclass. Opt. 7, 601 (1995).
[CrossRef]

Carroll, J. E.

D. D. Marcenac and J. E. Carroll, IEEE J. Quantum Electron. 30, 2064 (1994).
[CrossRef]

Carsten, J. L.

D. C. Kilper, P. A. Roos, J. L. Carsten, and K. L. Lear, Phys. Rev. A 55, 3323 (1997).
[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]

Craig, R.

Ebeling, K. J.

K. J. Ebeling, U. Fiedler, R. Michalzik, G. Reiner, and B. Weigl, Int. J. Electron. Commun. 50, 316 (1996).

Elsässer, W.

J.-L. Vey and W. Elsässer, J. Opt. Soc. Am. B 14, 1299 (1997).
[CrossRef]

J. L. Vey, K. Auen, and W. Elsässer, Proc. SPIE 2994, 178 (1997).
[CrossRef]

Fiedler, U.

K. J. Ebeling, U. Fiedler, R. Michalzik, G. Reiner, and B. Weigl, Int. J. Electron. Commun. 50, 316 (1996).

Freeman, M. J.

Gallion, P.

J. L. Vey and P. Gallion, IEEE J. Quantum Electron. 33, 2105 (1997).
[CrossRef]

J. L. Vey and P. Gallion, IEEE J. Quantum Electron. 33, 2097 (1997).
[CrossRef]

J. L. Vey and P. Gallion, Opt. Lett. 20, 2018 (1995).
[CrossRef] [PubMed]

Giacobino, E.

T.-C. Zhang, J.-Ph. Poizat, P. Grelu, J.-F. Roch, P. Grangier, F. Marin, A. Bramati, V. Jost, M. D. Levenson, and E. Giacobino, Quantum Semiclass. Opt. 7, 601 (1995).
[CrossRef]

F. Marin, A. Bramati, E. Giacobino, T.-C. Zhang, J. Ph. Poizat, J. F. Roch, and P. Grangier, Phys. Rev. Lett. 75, 4606 (1995).
[CrossRef] [PubMed]

Goobar, E.

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

Grangier, P.

F. Marin, A. Bramati, E. Giacobino, T.-C. Zhang, J. Ph. Poizat, J. F. Roch, and P. Grangier, Phys. Rev. Lett. 75, 4606 (1995).
[CrossRef] [PubMed]

T.-C. Zhang, J.-Ph. Poizat, P. Grelu, J.-F. Roch, P. Grangier, F. Marin, A. Bramati, V. Jost, M. D. Levenson, and E. Giacobino, Quantum Semiclass. Opt. 7, 601 (1995).
[CrossRef]

Grelu, P.

T.-C. Zhang, J.-Ph. Poizat, P. Grelu, J.-F. Roch, P. Grangier, F. Marin, A. Bramati, V. Jost, M. D. Levenson, and E. Giacobino, Quantum Semiclass. Opt. 7, 601 (1995).
[CrossRef]

Itaya, Y.

S. Machida, Y. Yamamoto, and Y. Itaya, Phys. Rev. Lett. 58, 1000 (1987).
[CrossRef] [PubMed]

Jost, V.

T.-C. Zhang, J.-Ph. Poizat, P. Grelu, J.-F. Roch, P. Grangier, F. Marin, A. Bramati, V. Jost, M. D. Levenson, and E. Giacobino, Quantum Semiclass. Opt. 7, 601 (1995).
[CrossRef]

Kilper, D. C.

D. C. Kilper, P. A. Roos, J. L. Carsten, and K. L. Lear, Phys. Rev. A 55, 3323 (1997).
[CrossRef]

Kitching, J.

J. Kitching, A. Yariv, and Y. Shevy, Phys. Rev. Lett. 74, 3372 (1995).
[CrossRef] [PubMed]

Lassen, H.-E.

B. Tromborg, H.-E. Lassen, and H. Olesen, IEEE J. Quantum Electron. 30, 939 (1994).
[CrossRef]

Lear, K. L.

D. C. Kilper, P. A. Roos, J. L. Carsten, and K. L. Lear, Phys. Rev. A 55, 3323 (1997).
[CrossRef]

Levenson, M. D.

T.-C. Zhang, J.-Ph. Poizat, P. Grelu, J.-F. Roch, P. Grangier, F. Marin, A. Bramati, V. Jost, M. D. Levenson, and E. Giacobino, Quantum Semiclass. Opt. 7, 601 (1995).
[CrossRef]

Machida, S.

W. H. Richardson, S. Machida, and Y. Yamamoto, Phys. Rev. Lett. 66, 2867 (1991).
[CrossRef] [PubMed]

S. Machida, Y. Yamamoto, and Y. Itaya, Phys. Rev. Lett. 58, 1000 (1987).
[CrossRef] [PubMed]

Y. Yamamoto, S. Machida, and O. Nilsson, Phys. Rev. A 34, 4025 (1986).
[CrossRef] [PubMed]

Marcenac, D. D.

D. D. Marcenac and J. E. Carroll, IEEE J. Quantum Electron. 30, 2064 (1994).
[CrossRef]

Marin, F.

T.-C. Zhang, J.-Ph. Poizat, P. Grelu, J.-F. Roch, P. Grangier, F. Marin, A. Bramati, V. Jost, M. D. Levenson, and E. Giacobino, Quantum Semiclass. Opt. 7, 601 (1995).
[CrossRef]

F. Marin, A. Bramati, E. Giacobino, T.-C. Zhang, J. Ph. Poizat, J. F. Roch, and P. Grangier, Phys. Rev. Lett. 75, 4606 (1995).
[CrossRef] [PubMed]

Martin-Regalado, J.

J. Martin-Regalado, F. Prati, M. San Miguel, and N. B. Abraham, IEEE J. Quantum Electron. 33, 765 (1997).
[CrossRef]

Michalzik, R.

K. J. Ebeling, U. Fiedler, R. Michalzik, G. Reiner, and B. Weigl, Int. J. Electron. Commun. 50, 316 (1996).

Nilsson, O.

Y. Yamamoto, S. Machida, and O. Nilsson, Phys. Rev. A 34, 4025 (1986).
[CrossRef] [PubMed]

Olesen, H.

B. Tromborg, H.-E. Lassen, and H. Olesen, IEEE J. Quantum Electron. 30, 939 (1994).
[CrossRef]

Poizat, J. Ph.

F. Marin, A. Bramati, E. Giacobino, T.-C. Zhang, J. Ph. Poizat, J. F. Roch, and P. Grangier, Phys. Rev. Lett. 75, 4606 (1995).
[CrossRef] [PubMed]

Poizat, J.-Ph.

T.-C. Zhang, J.-Ph. Poizat, P. Grelu, J.-F. Roch, P. Grangier, F. Marin, A. Bramati, V. Jost, M. D. Levenson, and E. Giacobino, Quantum Semiclass. Opt. 7, 601 (1995).
[CrossRef]

Prati, F.

J. Martin-Regalado, F. Prati, M. San Miguel, and N. B. Abraham, IEEE J. Quantum Electron. 33, 765 (1997).
[CrossRef]

Reiner, G.

K. J. Ebeling, U. Fiedler, R. Michalzik, G. Reiner, and B. Weigl, Int. J. Electron. Commun. 50, 316 (1996).

Richardson, W. H.

W. H. Richardson, S. Machida, and Y. Yamamoto, Phys. Rev. Lett. 66, 2867 (1991).
[CrossRef] [PubMed]

Robinson, G.

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

Roch, J. F.

F. Marin, A. Bramati, E. Giacobino, T.-C. Zhang, J. Ph. Poizat, J. F. Roch, and P. Grangier, Phys. Rev. Lett. 75, 4606 (1995).
[CrossRef] [PubMed]

Roch, J.-F.

T.-C. Zhang, J.-Ph. Poizat, P. Grelu, J.-F. Roch, P. Grangier, F. Marin, A. Bramati, V. Jost, M. D. Levenson, and E. Giacobino, Quantum Semiclass. Opt. 7, 601 (1995).
[CrossRef]

Roos, P. A.

D. C. Kilper, P. A. Roos, J. L. Carsten, and K. L. Lear, Phys. Rev. A 55, 3323 (1997).
[CrossRef]

San Miguel, M.

J. Martin-Regalado, F. Prati, M. San Miguel, and N. B. Abraham, IEEE J. Quantum Electron. 33, 765 (1997).
[CrossRef]

Scifres, D. R.

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]

Shevy, Y.

J. Kitching, A. Yariv, and Y. Shevy, Phys. Rev. Lett. 74, 3372 (1995).
[CrossRef] [PubMed]

Steel, D. G.

Thibeault, B.

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

Tromborg, B.

B. Tromborg, H.-E. Lassen, and H. Olesen, IEEE J. Quantum Electron. 30, 939 (1994).
[CrossRef]

Vey, J. L.

J. L. Vey, K. Auen, and W. Elsässer, Proc. SPIE 2994, 178 (1997).
[CrossRef]

J. L. Vey and P. Gallion, IEEE J. Quantum Electron. 33, 2097 (1997).
[CrossRef]

J. L. Vey and P. Gallion, IEEE J. Quantum Electron. 33, 2105 (1997).
[CrossRef]

J. L. Vey and P. Gallion, Opt. Lett. 20, 2018 (1995).
[CrossRef] [PubMed]

Vey, J.-L.

Wang, H.

Weigl, B.

K. J. Ebeling, U. Fiedler, R. Michalzik, G. Reiner, and B. Weigl, Int. J. Electron. Commun. 50, 316 (1996).

Yamamoto, Y.

W. H. Richardson, S. Machida, and Y. Yamamoto, Phys. Rev. Lett. 66, 2867 (1991).
[CrossRef] [PubMed]

G. Björk and Y. Yamamoto, IEEE J. Quantum Electron. 27, 2386 (1991).
[CrossRef]

S. Machida, Y. Yamamoto, and Y. Itaya, Phys. Rev. Lett. 58, 1000 (1987).
[CrossRef] [PubMed]

Y. Yamamoto, S. Machida, and O. Nilsson, Phys. Rev. A 34, 4025 (1986).
[CrossRef] [PubMed]

Yariv, A.

J. Kitching, A. Yariv, and Y. Shevy, Phys. Rev. Lett. 74, 3372 (1995).
[CrossRef] [PubMed]

Zhang, T.-C.

F. Marin, A. Bramati, E. Giacobino, T.-C. Zhang, J. Ph. Poizat, J. F. Roch, and P. Grangier, Phys. Rev. Lett. 75, 4606 (1995).
[CrossRef] [PubMed]

T.-C. Zhang, J.-Ph. Poizat, P. Grelu, J.-F. Roch, P. Grangier, F. Marin, A. Bramati, V. Jost, M. D. Levenson, and E. Giacobino, Quantum Semiclass. Opt. 7, 601 (1995).
[CrossRef]

Appl. Phys. Lett. (1)

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

IEEE J. Quantum Electron. (6)

J. Martin-Regalado, F. Prati, M. San Miguel, and N. B. Abraham, IEEE J. Quantum Electron. 33, 765 (1997).
[CrossRef]

J. L. Vey and P. Gallion, IEEE J. Quantum Electron. 33, 2097 (1997).
[CrossRef]

J. L. Vey and P. Gallion, IEEE J. Quantum Electron. 33, 2105 (1997).
[CrossRef]

B. Tromborg, H.-E. Lassen, and H. Olesen, IEEE J. Quantum Electron. 30, 939 (1994).
[CrossRef]

D. D. Marcenac and J. E. Carroll, IEEE J. Quantum Electron. 30, 2064 (1994).
[CrossRef]

G. Björk and Y. Yamamoto, IEEE J. Quantum Electron. 27, 2386 (1991).
[CrossRef]

Int. J. Electron. Commun. (1)

K. J. Ebeling, U. Fiedler, R. Michalzik, G. Reiner, and B. Weigl, Int. J. Electron. Commun. 50, 316 (1996).

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

Opt. Lett. (2)

Phys. Rev. A (3)

D. C. Kilper, P. A. Roos, J. L. Carsten, and K. L. Lear, Phys. Rev. A 55, 3323 (1997).
[CrossRef]

Y. Yamamoto, S. Machida, and O. Nilsson, Phys. Rev. A 34, 4025 (1986).
[CrossRef] [PubMed]

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

Phys. Rev. Lett. (4)

S. Machida, Y. Yamamoto, and Y. Itaya, Phys. Rev. Lett. 58, 1000 (1987).
[CrossRef] [PubMed]

W. H. Richardson, S. Machida, and Y. Yamamoto, Phys. Rev. Lett. 66, 2867 (1991).
[CrossRef] [PubMed]

F. Marin, A. Bramati, E. Giacobino, T.-C. Zhang, J. Ph. Poizat, J. F. Roch, and P. Grangier, Phys. Rev. Lett. 75, 4606 (1995).
[CrossRef] [PubMed]

J. Kitching, A. Yariv, and Y. Shevy, Phys. Rev. Lett. 74, 3372 (1995).
[CrossRef] [PubMed]

Proc. SPIE (1)

J. L. Vey, K. Auen, and W. Elsässer, Proc. SPIE 2994, 178 (1997).
[CrossRef]

Quantum Semiclass. Opt. (1)

T.-C. Zhang, J.-Ph. Poizat, P. Grelu, J.-F. Roch, P. Grangier, F. Marin, A. Bramati, V. Jost, M. D. Levenson, and E. Giacobino, Quantum Semiclass. Opt. 7, 601 (1995).
[CrossRef]

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Figures (2)

Fig. 1
Fig. 1

Amplitude noise of the total emitted field at low frequency ω0 normalized by the shot-noise level (top, left-hand scale) and normalized correlation between the amplitude fluctuation of the two polarization modes at low frequency ω0 (bottom, right-hand scale) as a function of M for various total photon numbers in the cavity, P0=103 1, 104, 5×104, 105, 5×105, 106 5.

Fig. 2
Fig. 2

Amplitude noise of the total emitted field ω0 normalized by the shot-noise level as a function of the photon number inside the cavity for M=10-4, 10-2, 10-1, 1.

Equations (3)

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

dPdt=νgg1P-PτP1+FP, dSdt=νgg2S-SτP2+FS, dNdt=IeV-Nτe-νgg1P+g2S+FN,
g1=gdN-N0-β11P-θ12S, g2=gdN-N0-β22S-θ21P,
Corω=SS+Pω-SPω-SSω2SPωSSω.

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