Abstract

Theoretical investigations of the generation of light with sub-shot-noise intensity fluctuations by vertical cavity surface-emitting lasers are performed with a semiclassical model. From these results we conclude that, because of their dimensions and structure, vertical cavity surface-emitting lasers are promising candidates for generation of amplitude squeezed states. Finally, the influence of internal loss, distributed reflection coefficients, and gain suppression is emphasized and discussed.

© 1997 Optical Society of America

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  1. K. Iga, F. Koyama, and S. Kinoshita, “Surface emitting semiconductor lasers,” IEEE J. Quantum Electron. 24, 1845–1855 (1988).
    [Crossref]
  2. J. L. Jewell and G. R. Olbright, “Surface-emitting lasers emerge from the laboratory,” Laser Focus World 28(5), 217–223 (1992).
  3. J. W. Scott, R. S. Geels, S. W. Corzine, and L. A. Coldren, “Modeling temperature effects and spatial hole burning to optimize vertical-cavity surface-emitting laser performance,” IEEE J. Quantum Electron. 29, 1295–1308 (1993).
    [Crossref]
  4. R. Michalzik and K. J. Ebeling, “Modeling and design of proton-implanted ultralow-threshold vertical-cavity laser diodes,” IEEE J. Quantum Electron. 29, 1963–1974 (1993).
    [Crossref]
  5. F. Jahnke and S. W. Koch, “Many-body theory for semiconductor microcavity lasers,” Phys. Rev. A 52, 1712–1727 (1995).
    [Crossref] [PubMed]
  6. G. Björk and Y. Yamamoto, “Analysis of semiconductor microcavity lasers using rate equations,” IEEE J. Quantum Electron. 27, 2386–2396 (1991).
    [Crossref]
  7. Y. Yamamoto, S. Machida, and G. Björk, “Micro-cavity semiconductor lasers with controlled spontaneous emission,” Opt. Quantum Electron. 24, 215–243 (1992).
    [Crossref]
  8. D. V. Kuksnkov, H. Temkin, and S. Swirhun, “Polarization instability and relative intensity noise in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 67, 2141–2143 (1995).
    [Crossref]
  9. D. M. Kutcha, J. Gamelin, J. D. Walker, J. Lin, K. Y. Lau, J. S. Smith, M. Hong, and J. P. Mannaerts, “Relative intensity noise of vertical cavity surface emitting lasers,” Appl. Phys. Lett. 62, 1194–1196 (1993).
    [Crossref]
  10. E. Goobar, J. W. Scott, B. Thibeault, G. Robinson, Y. Akulova, and L. A. Coldren, “Calibrated intensity noise measurements in microcavity laser diodes,” Appl. Phys. Lett. 67, 3697–3699 (1995).
    [Crossref]
  11. S. Machida, Y. Yamamoto, and Y. Itaya, “Observation of amplitude squeezing in a constant-current-driven semiconductor laser,” Phys. Rev. Lett. 58, 1000–1003 (1987).
    [Crossref] [PubMed]
  12. Y. Yamamoto, S. Machida, and O. Nilsson, “Amplitude squeezing in a pump-noise-suppressed laser oscillator,” Phys. Rev. A 14, 4025–4042 (1986).
    [Crossref]
  13. C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. Von Lehmen, L. T. Florez, and N. G. Stoffel, “Dynamic, polarization and transverse mode characteristics of vertical cavity surface emitting lasers,” IEEE J. Quantum Electron. 27, 1402–1409 (1991).
    [Crossref]
  14. J. L. Jewell, J. P. Harbison, A. Scherer, Y. H. Lee, and L. T. Florez, “Vertical-cavity surface-emitting lasers: design, growth, fabrication, characterization,” IEEE J. Quantum Electron. 27, 1332–1346 (1991).
    [Crossref]
  15. G. H. Duan, P. Gallion, and G. P. Agrawal, “Dynamic and noise properties of tunable multielectrode semiconductor lasers including spatial hole burning and non linear gain,” IEEE J. Quantum Electron. 29, 844 (1993).
    [Crossref]
  16. J. Arnaud, “Classical theory of laser noise,” Opt. Quantum Electron. 27, 63–89 (1995).
    [Crossref]
  17. D. D. Marcenac and J. E. Carroll, “Quantum-mechanical model for realistic Fabry–Perot lasers,” Proc. Inst. Electr. Eng. 140, 157–171 (1993).
  18. J. L. Vey and P. Gallion, “Amplitude noise squeezing with gain suppression: existence of optimum conditions,” Opt. Lett. 20, 2018–2020 (1995).
    [Crossref] [PubMed]
  19. B. Tromborg, H.-E. Lassen, and H. Olesen, “Traveling wave analysis of semiconductor lasers: modulation responses, mode stability and quantum mechanical treatment of noise spectra,” IEEE J. Quantum Electron. 30, 939–956 (1994).
    [Crossref]
  20. D. D. Marcenac and J. E. Carroll, “Modeling of intensity noise including squeezing in DFB and Fabry–Perot semiconductor laser diodes,” IEEE J. Quantum Electron. 30, 2064–2072 (1994).
    [Crossref]
  21. J. L. Vey, P. Gallion, and W. Elsässer, “Amplitude squeezing with complex laser structures” in International Quantum Electronics Conference, Vol. 16 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), pp. 43–44.
  22. J. L. Vey and W. Elsässer, “Amplitude noise squeezing with vertical cavity semiconductor lasers,” in Proceedings of the European Quantum Electronics Conference (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1996), p. 218.
  23. J. Arnaud, “Corpuscular theory of intensity noise with gain compression,” Phys. Rev. A. 45, 1775–1786 (1992).
    [Crossref] [PubMed]
  24. O. Nilsson, A. Karlsson, and E. Berglind, “Modulation and noise spectra of complicated laser structures” in Coherence, Amplification and Quantum Effects in Semiconductor Lasers, Y. Yamamoto, ed. (Wiley, New York, 1991), pp. 76–95.
  25. F. Girardin, G.-H. Duan, A. Talneau, and A. Ougazzaden, “Experimental investigation of the relative importance of carrier heating and spectral-hole-burning on nonlinear gain in bulk and strained multiquantum-well 1.55-µm lasers,” Appl. Phys. Lett. 67, 771–773 (1995).
    [Crossref]
  26. K. J. Ebeling, U. Fiedler, R. Michalzik, G. Reiner, and B. Weigel, “Efficient vertical cavity surface emitting laser diodes for high bit rate optical data transmission,” Int. J. Electron. Commun. 50, 316–326 (1996).

1996 (1)

K. J. Ebeling, U. Fiedler, R. Michalzik, G. Reiner, and B. Weigel, “Efficient vertical cavity surface emitting laser diodes for high bit rate optical data transmission,” Int. J. Electron. Commun. 50, 316–326 (1996).

1995 (6)

F. Girardin, G.-H. Duan, A. Talneau, and A. Ougazzaden, “Experimental investigation of the relative importance of carrier heating and spectral-hole-burning on nonlinear gain in bulk and strained multiquantum-well 1.55-µm lasers,” Appl. Phys. Lett. 67, 771–773 (1995).
[Crossref]

J. L. Vey and P. Gallion, “Amplitude noise squeezing with gain suppression: existence of optimum conditions,” Opt. Lett. 20, 2018–2020 (1995).
[Crossref] [PubMed]

F. Jahnke and S. W. Koch, “Many-body theory for semiconductor microcavity lasers,” Phys. Rev. A 52, 1712–1727 (1995).
[Crossref] [PubMed]

D. V. Kuksnkov, H. Temkin, and S. Swirhun, “Polarization instability and relative intensity noise in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 67, 2141–2143 (1995).
[Crossref]

E. Goobar, J. W. Scott, B. Thibeault, G. Robinson, Y. Akulova, and L. A. Coldren, “Calibrated intensity noise measurements in microcavity laser diodes,” Appl. Phys. Lett. 67, 3697–3699 (1995).
[Crossref]

J. Arnaud, “Classical theory of laser noise,” Opt. Quantum Electron. 27, 63–89 (1995).
[Crossref]

1994 (2)

B. Tromborg, H.-E. Lassen, and H. Olesen, “Traveling wave analysis of semiconductor lasers: modulation responses, mode stability and quantum mechanical treatment of noise spectra,” IEEE J. Quantum Electron. 30, 939–956 (1994).
[Crossref]

D. D. Marcenac and J. E. Carroll, “Modeling of intensity noise including squeezing in DFB and Fabry–Perot semiconductor laser diodes,” IEEE J. Quantum Electron. 30, 2064–2072 (1994).
[Crossref]

1993 (5)

D. D. Marcenac and J. E. Carroll, “Quantum-mechanical model for realistic Fabry–Perot lasers,” Proc. Inst. Electr. Eng. 140, 157–171 (1993).

G. H. Duan, P. Gallion, and G. P. Agrawal, “Dynamic and noise properties of tunable multielectrode semiconductor lasers including spatial hole burning and non linear gain,” IEEE J. Quantum Electron. 29, 844 (1993).
[Crossref]

D. M. Kutcha, J. Gamelin, J. D. Walker, J. Lin, K. Y. Lau, J. S. Smith, M. Hong, and J. P. Mannaerts, “Relative intensity noise of vertical cavity surface emitting lasers,” Appl. Phys. Lett. 62, 1194–1196 (1993).
[Crossref]

J. W. Scott, R. S. Geels, S. W. Corzine, and L. A. Coldren, “Modeling temperature effects and spatial hole burning to optimize vertical-cavity surface-emitting laser performance,” IEEE J. Quantum Electron. 29, 1295–1308 (1993).
[Crossref]

R. Michalzik and K. J. Ebeling, “Modeling and design of proton-implanted ultralow-threshold vertical-cavity laser diodes,” IEEE J. Quantum Electron. 29, 1963–1974 (1993).
[Crossref]

1992 (3)

J. L. Jewell and G. R. Olbright, “Surface-emitting lasers emerge from the laboratory,” Laser Focus World 28(5), 217–223 (1992).

Y. Yamamoto, S. Machida, and G. Björk, “Micro-cavity semiconductor lasers with controlled spontaneous emission,” Opt. Quantum Electron. 24, 215–243 (1992).
[Crossref]

J. Arnaud, “Corpuscular theory of intensity noise with gain compression,” Phys. Rev. A. 45, 1775–1786 (1992).
[Crossref] [PubMed]

1991 (3)

C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. Von Lehmen, L. T. Florez, and N. G. Stoffel, “Dynamic, polarization and transverse mode characteristics of vertical cavity surface emitting lasers,” IEEE J. Quantum Electron. 27, 1402–1409 (1991).
[Crossref]

J. L. Jewell, J. P. Harbison, A. Scherer, Y. H. Lee, and L. T. Florez, “Vertical-cavity surface-emitting lasers: design, growth, fabrication, characterization,” IEEE J. Quantum Electron. 27, 1332–1346 (1991).
[Crossref]

G. Björk and Y. Yamamoto, “Analysis of semiconductor microcavity lasers using rate equations,” IEEE J. Quantum Electron. 27, 2386–2396 (1991).
[Crossref]

1988 (1)

K. Iga, F. Koyama, and S. Kinoshita, “Surface emitting semiconductor lasers,” IEEE J. Quantum Electron. 24, 1845–1855 (1988).
[Crossref]

1987 (1)

S. Machida, Y. Yamamoto, and Y. Itaya, “Observation of amplitude squeezing in a constant-current-driven semiconductor laser,” Phys. Rev. Lett. 58, 1000–1003 (1987).
[Crossref] [PubMed]

1986 (1)

Y. Yamamoto, S. Machida, and O. Nilsson, “Amplitude squeezing in a pump-noise-suppressed laser oscillator,” Phys. Rev. A 14, 4025–4042 (1986).
[Crossref]

Agrawal, G. P.

G. H. Duan, P. Gallion, and G. P. Agrawal, “Dynamic and noise properties of tunable multielectrode semiconductor lasers including spatial hole burning and non linear gain,” IEEE J. Quantum Electron. 29, 844 (1993).
[Crossref]

Akulova, Y.

E. Goobar, J. W. Scott, B. Thibeault, G. Robinson, Y. Akulova, and L. A. Coldren, “Calibrated intensity noise measurements in microcavity laser diodes,” Appl. Phys. Lett. 67, 3697–3699 (1995).
[Crossref]

Arnaud, J.

J. Arnaud, “Classical theory of laser noise,” Opt. Quantum Electron. 27, 63–89 (1995).
[Crossref]

J. Arnaud, “Corpuscular theory of intensity noise with gain compression,” Phys. Rev. A. 45, 1775–1786 (1992).
[Crossref] [PubMed]

Berglind, E.

O. Nilsson, A. Karlsson, and E. Berglind, “Modulation and noise spectra of complicated laser structures” in Coherence, Amplification and Quantum Effects in Semiconductor Lasers, Y. Yamamoto, ed. (Wiley, New York, 1991), pp. 76–95.

Björk, G.

Y. Yamamoto, S. Machida, and G. Björk, “Micro-cavity semiconductor lasers with controlled spontaneous emission,” Opt. Quantum Electron. 24, 215–243 (1992).
[Crossref]

G. Björk and Y. Yamamoto, “Analysis of semiconductor microcavity lasers using rate equations,” IEEE J. Quantum Electron. 27, 2386–2396 (1991).
[Crossref]

Carroll, J. E.

D. D. Marcenac and J. E. Carroll, “Modeling of intensity noise including squeezing in DFB and Fabry–Perot semiconductor laser diodes,” IEEE J. Quantum Electron. 30, 2064–2072 (1994).
[Crossref]

D. D. Marcenac and J. E. Carroll, “Quantum-mechanical model for realistic Fabry–Perot lasers,” Proc. Inst. Electr. Eng. 140, 157–171 (1993).

Chang-Hasnain, C. J.

C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. Von Lehmen, L. T. Florez, and N. G. Stoffel, “Dynamic, polarization and transverse mode characteristics of vertical cavity surface emitting lasers,” IEEE J. Quantum Electron. 27, 1402–1409 (1991).
[Crossref]

Coldren, L. A.

E. Goobar, J. W. Scott, B. Thibeault, G. Robinson, Y. Akulova, and L. A. Coldren, “Calibrated intensity noise measurements in microcavity laser diodes,” Appl. Phys. Lett. 67, 3697–3699 (1995).
[Crossref]

J. W. Scott, R. S. Geels, S. W. Corzine, and L. A. Coldren, “Modeling temperature effects and spatial hole burning to optimize vertical-cavity surface-emitting laser performance,” IEEE J. Quantum Electron. 29, 1295–1308 (1993).
[Crossref]

Corzine, S. W.

J. W. Scott, R. S. Geels, S. W. Corzine, and L. A. Coldren, “Modeling temperature effects and spatial hole burning to optimize vertical-cavity surface-emitting laser performance,” IEEE J. Quantum Electron. 29, 1295–1308 (1993).
[Crossref]

Duan, G. H.

G. H. Duan, P. Gallion, and G. P. Agrawal, “Dynamic and noise properties of tunable multielectrode semiconductor lasers including spatial hole burning and non linear gain,” IEEE J. Quantum Electron. 29, 844 (1993).
[Crossref]

Duan, G.-H.

F. Girardin, G.-H. Duan, A. Talneau, and A. Ougazzaden, “Experimental investigation of the relative importance of carrier heating and spectral-hole-burning on nonlinear gain in bulk and strained multiquantum-well 1.55-µm lasers,” Appl. Phys. Lett. 67, 771–773 (1995).
[Crossref]

Ebeling, K. J.

K. J. Ebeling, U. Fiedler, R. Michalzik, G. Reiner, and B. Weigel, “Efficient vertical cavity surface emitting laser diodes for high bit rate optical data transmission,” Int. J. Electron. Commun. 50, 316–326 (1996).

R. Michalzik and K. J. Ebeling, “Modeling and design of proton-implanted ultralow-threshold vertical-cavity laser diodes,” IEEE J. Quantum Electron. 29, 1963–1974 (1993).
[Crossref]

Elsässer, W.

J. L. Vey, P. Gallion, and W. Elsässer, “Amplitude squeezing with complex laser structures” in International Quantum Electronics Conference, Vol. 16 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), pp. 43–44.

J. L. Vey and W. Elsässer, “Amplitude noise squeezing with vertical cavity semiconductor lasers,” in Proceedings of the European Quantum Electronics Conference (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1996), p. 218.

Fiedler, U.

K. J. Ebeling, U. Fiedler, R. Michalzik, G. Reiner, and B. Weigel, “Efficient vertical cavity surface emitting laser diodes for high bit rate optical data transmission,” Int. J. Electron. Commun. 50, 316–326 (1996).

Florez, L. T.

C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. Von Lehmen, L. T. Florez, and N. G. Stoffel, “Dynamic, polarization and transverse mode characteristics of vertical cavity surface emitting lasers,” IEEE J. Quantum Electron. 27, 1402–1409 (1991).
[Crossref]

J. L. Jewell, J. P. Harbison, A. Scherer, Y. H. Lee, and L. T. Florez, “Vertical-cavity surface-emitting lasers: design, growth, fabrication, characterization,” IEEE J. Quantum Electron. 27, 1332–1346 (1991).
[Crossref]

Gallion, P.

J. L. Vey and P. Gallion, “Amplitude noise squeezing with gain suppression: existence of optimum conditions,” Opt. Lett. 20, 2018–2020 (1995).
[Crossref] [PubMed]

G. H. Duan, P. Gallion, and G. P. Agrawal, “Dynamic and noise properties of tunable multielectrode semiconductor lasers including spatial hole burning and non linear gain,” IEEE J. Quantum Electron. 29, 844 (1993).
[Crossref]

J. L. Vey, P. Gallion, and W. Elsässer, “Amplitude squeezing with complex laser structures” in International Quantum Electronics Conference, Vol. 16 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), pp. 43–44.

Gamelin, J.

D. M. Kutcha, J. Gamelin, J. D. Walker, J. Lin, K. Y. Lau, J. S. Smith, M. Hong, and J. P. Mannaerts, “Relative intensity noise of vertical cavity surface emitting lasers,” Appl. Phys. Lett. 62, 1194–1196 (1993).
[Crossref]

Geels, R. S.

J. W. Scott, R. S. Geels, S. W. Corzine, and L. A. Coldren, “Modeling temperature effects and spatial hole burning to optimize vertical-cavity surface-emitting laser performance,” IEEE J. Quantum Electron. 29, 1295–1308 (1993).
[Crossref]

Girardin, F.

F. Girardin, G.-H. Duan, A. Talneau, and A. Ougazzaden, “Experimental investigation of the relative importance of carrier heating and spectral-hole-burning on nonlinear gain in bulk and strained multiquantum-well 1.55-µm lasers,” Appl. Phys. Lett. 67, 771–773 (1995).
[Crossref]

Goobar, E.

E. Goobar, J. W. Scott, B. Thibeault, G. Robinson, Y. Akulova, and L. A. Coldren, “Calibrated intensity noise measurements in microcavity laser diodes,” Appl. Phys. Lett. 67, 3697–3699 (1995).
[Crossref]

Harbison, J. P.

J. L. Jewell, J. P. Harbison, A. Scherer, Y. H. Lee, and L. T. Florez, “Vertical-cavity surface-emitting lasers: design, growth, fabrication, characterization,” IEEE J. Quantum Electron. 27, 1332–1346 (1991).
[Crossref]

C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. Von Lehmen, L. T. Florez, and N. G. Stoffel, “Dynamic, polarization and transverse mode characteristics of vertical cavity surface emitting lasers,” IEEE J. Quantum Electron. 27, 1402–1409 (1991).
[Crossref]

Hasnain, G.

C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. Von Lehmen, L. T. Florez, and N. G. Stoffel, “Dynamic, polarization and transverse mode characteristics of vertical cavity surface emitting lasers,” IEEE J. Quantum Electron. 27, 1402–1409 (1991).
[Crossref]

Hong, M.

D. M. Kutcha, J. Gamelin, J. D. Walker, J. Lin, K. Y. Lau, J. S. Smith, M. Hong, and J. P. Mannaerts, “Relative intensity noise of vertical cavity surface emitting lasers,” Appl. Phys. Lett. 62, 1194–1196 (1993).
[Crossref]

Iga, K.

K. Iga, F. Koyama, and S. Kinoshita, “Surface emitting semiconductor lasers,” IEEE J. Quantum Electron. 24, 1845–1855 (1988).
[Crossref]

Itaya, Y.

S. Machida, Y. Yamamoto, and Y. Itaya, “Observation of amplitude squeezing in a constant-current-driven semiconductor laser,” Phys. Rev. Lett. 58, 1000–1003 (1987).
[Crossref] [PubMed]

Jahnke, F.

F. Jahnke and S. W. Koch, “Many-body theory for semiconductor microcavity lasers,” Phys. Rev. A 52, 1712–1727 (1995).
[Crossref] [PubMed]

Jewell, J. L.

J. L. Jewell and G. R. Olbright, “Surface-emitting lasers emerge from the laboratory,” Laser Focus World 28(5), 217–223 (1992).

J. L. Jewell, J. P. Harbison, A. Scherer, Y. H. Lee, and L. T. Florez, “Vertical-cavity surface-emitting lasers: design, growth, fabrication, characterization,” IEEE J. Quantum Electron. 27, 1332–1346 (1991).
[Crossref]

Karlsson, A.

O. Nilsson, A. Karlsson, and E. Berglind, “Modulation and noise spectra of complicated laser structures” in Coherence, Amplification and Quantum Effects in Semiconductor Lasers, Y. Yamamoto, ed. (Wiley, New York, 1991), pp. 76–95.

Kinoshita, S.

K. Iga, F. Koyama, and S. Kinoshita, “Surface emitting semiconductor lasers,” IEEE J. Quantum Electron. 24, 1845–1855 (1988).
[Crossref]

Koch, S. W.

F. Jahnke and S. W. Koch, “Many-body theory for semiconductor microcavity lasers,” Phys. Rev. A 52, 1712–1727 (1995).
[Crossref] [PubMed]

Koyama, F.

K. Iga, F. Koyama, and S. Kinoshita, “Surface emitting semiconductor lasers,” IEEE J. Quantum Electron. 24, 1845–1855 (1988).
[Crossref]

Kuksnkov, D. V.

D. V. Kuksnkov, H. Temkin, and S. Swirhun, “Polarization instability and relative intensity noise in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 67, 2141–2143 (1995).
[Crossref]

Kutcha, D. M.

D. M. Kutcha, J. Gamelin, J. D. Walker, J. Lin, K. Y. Lau, J. S. Smith, M. Hong, and J. P. Mannaerts, “Relative intensity noise of vertical cavity surface emitting lasers,” Appl. Phys. Lett. 62, 1194–1196 (1993).
[Crossref]

Lassen, H.-E.

B. Tromborg, H.-E. Lassen, and H. Olesen, “Traveling wave analysis of semiconductor lasers: modulation responses, mode stability and quantum mechanical treatment of noise spectra,” IEEE J. Quantum Electron. 30, 939–956 (1994).
[Crossref]

Lau, K. Y.

D. M. Kutcha, J. Gamelin, J. D. Walker, J. Lin, K. Y. Lau, J. S. Smith, M. Hong, and J. P. Mannaerts, “Relative intensity noise of vertical cavity surface emitting lasers,” Appl. Phys. Lett. 62, 1194–1196 (1993).
[Crossref]

Lee, Y. H.

J. L. Jewell, J. P. Harbison, A. Scherer, Y. H. Lee, and L. T. Florez, “Vertical-cavity surface-emitting lasers: design, growth, fabrication, characterization,” IEEE J. Quantum Electron. 27, 1332–1346 (1991).
[Crossref]

Lin, J.

D. M. Kutcha, J. Gamelin, J. D. Walker, J. Lin, K. Y. Lau, J. S. Smith, M. Hong, and J. P. Mannaerts, “Relative intensity noise of vertical cavity surface emitting lasers,” Appl. Phys. Lett. 62, 1194–1196 (1993).
[Crossref]

Machida, S.

Y. Yamamoto, S. Machida, and G. Björk, “Micro-cavity semiconductor lasers with controlled spontaneous emission,” Opt. Quantum Electron. 24, 215–243 (1992).
[Crossref]

S. Machida, Y. Yamamoto, and Y. Itaya, “Observation of amplitude squeezing in a constant-current-driven semiconductor laser,” Phys. Rev. Lett. 58, 1000–1003 (1987).
[Crossref] [PubMed]

Y. Yamamoto, S. Machida, and O. Nilsson, “Amplitude squeezing in a pump-noise-suppressed laser oscillator,” Phys. Rev. A 14, 4025–4042 (1986).
[Crossref]

Mannaerts, J. P.

D. M. Kutcha, J. Gamelin, J. D. Walker, J. Lin, K. Y. Lau, J. S. Smith, M. Hong, and J. P. Mannaerts, “Relative intensity noise of vertical cavity surface emitting lasers,” Appl. Phys. Lett. 62, 1194–1196 (1993).
[Crossref]

Marcenac, D. D.

D. D. Marcenac and J. E. Carroll, “Modeling of intensity noise including squeezing in DFB and Fabry–Perot semiconductor laser diodes,” IEEE J. Quantum Electron. 30, 2064–2072 (1994).
[Crossref]

D. D. Marcenac and J. E. Carroll, “Quantum-mechanical model for realistic Fabry–Perot lasers,” Proc. Inst. Electr. Eng. 140, 157–171 (1993).

Michalzik, R.

K. J. Ebeling, U. Fiedler, R. Michalzik, G. Reiner, and B. Weigel, “Efficient vertical cavity surface emitting laser diodes for high bit rate optical data transmission,” Int. J. Electron. Commun. 50, 316–326 (1996).

R. Michalzik and K. J. Ebeling, “Modeling and design of proton-implanted ultralow-threshold vertical-cavity laser diodes,” IEEE J. Quantum Electron. 29, 1963–1974 (1993).
[Crossref]

Nilsson, O.

Y. Yamamoto, S. Machida, and O. Nilsson, “Amplitude squeezing in a pump-noise-suppressed laser oscillator,” Phys. Rev. A 14, 4025–4042 (1986).
[Crossref]

O. Nilsson, A. Karlsson, and E. Berglind, “Modulation and noise spectra of complicated laser structures” in Coherence, Amplification and Quantum Effects in Semiconductor Lasers, Y. Yamamoto, ed. (Wiley, New York, 1991), pp. 76–95.

Olbright, G. R.

J. L. Jewell and G. R. Olbright, “Surface-emitting lasers emerge from the laboratory,” Laser Focus World 28(5), 217–223 (1992).

Olesen, H.

B. Tromborg, H.-E. Lassen, and H. Olesen, “Traveling wave analysis of semiconductor lasers: modulation responses, mode stability and quantum mechanical treatment of noise spectra,” IEEE J. Quantum Electron. 30, 939–956 (1994).
[Crossref]

Ougazzaden, A.

F. Girardin, G.-H. Duan, A. Talneau, and A. Ougazzaden, “Experimental investigation of the relative importance of carrier heating and spectral-hole-burning on nonlinear gain in bulk and strained multiquantum-well 1.55-µm lasers,” Appl. Phys. Lett. 67, 771–773 (1995).
[Crossref]

Reiner, G.

K. J. Ebeling, U. Fiedler, R. Michalzik, G. Reiner, and B. Weigel, “Efficient vertical cavity surface emitting laser diodes for high bit rate optical data transmission,” Int. J. Electron. Commun. 50, 316–326 (1996).

Robinson, G.

E. Goobar, J. W. Scott, B. Thibeault, G. Robinson, Y. Akulova, and L. A. Coldren, “Calibrated intensity noise measurements in microcavity laser diodes,” Appl. Phys. Lett. 67, 3697–3699 (1995).
[Crossref]

Scherer, A.

J. L. Jewell, J. P. Harbison, A. Scherer, Y. H. Lee, and L. T. Florez, “Vertical-cavity surface-emitting lasers: design, growth, fabrication, characterization,” IEEE J. Quantum Electron. 27, 1332–1346 (1991).
[Crossref]

Scott, J. W.

E. Goobar, J. W. Scott, B. Thibeault, G. Robinson, Y. Akulova, and L. A. Coldren, “Calibrated intensity noise measurements in microcavity laser diodes,” Appl. Phys. Lett. 67, 3697–3699 (1995).
[Crossref]

J. W. Scott, R. S. Geels, S. W. Corzine, and L. A. Coldren, “Modeling temperature effects and spatial hole burning to optimize vertical-cavity surface-emitting laser performance,” IEEE J. Quantum Electron. 29, 1295–1308 (1993).
[Crossref]

Smith, J. S.

D. M. Kutcha, J. Gamelin, J. D. Walker, J. Lin, K. Y. Lau, J. S. Smith, M. Hong, and J. P. Mannaerts, “Relative intensity noise of vertical cavity surface emitting lasers,” Appl. Phys. Lett. 62, 1194–1196 (1993).
[Crossref]

Stoffel, N. G.

C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. Von Lehmen, L. T. Florez, and N. G. Stoffel, “Dynamic, polarization and transverse mode characteristics of vertical cavity surface emitting lasers,” IEEE J. Quantum Electron. 27, 1402–1409 (1991).
[Crossref]

Swirhun, S.

D. V. Kuksnkov, H. Temkin, and S. Swirhun, “Polarization instability and relative intensity noise in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 67, 2141–2143 (1995).
[Crossref]

Talneau, A.

F. Girardin, G.-H. Duan, A. Talneau, and A. Ougazzaden, “Experimental investigation of the relative importance of carrier heating and spectral-hole-burning on nonlinear gain in bulk and strained multiquantum-well 1.55-µm lasers,” Appl. Phys. Lett. 67, 771–773 (1995).
[Crossref]

Temkin, H.

D. V. Kuksnkov, H. Temkin, and S. Swirhun, “Polarization instability and relative intensity noise in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 67, 2141–2143 (1995).
[Crossref]

Thibeault, B.

E. Goobar, J. W. Scott, B. Thibeault, G. Robinson, Y. Akulova, and L. A. Coldren, “Calibrated intensity noise measurements in microcavity laser diodes,” Appl. Phys. Lett. 67, 3697–3699 (1995).
[Crossref]

Tromborg, B.

B. Tromborg, H.-E. Lassen, and H. Olesen, “Traveling wave analysis of semiconductor lasers: modulation responses, mode stability and quantum mechanical treatment of noise spectra,” IEEE J. Quantum Electron. 30, 939–956 (1994).
[Crossref]

Vey, J. L.

J. L. Vey and P. Gallion, “Amplitude noise squeezing with gain suppression: existence of optimum conditions,” Opt. Lett. 20, 2018–2020 (1995).
[Crossref] [PubMed]

J. L. Vey, P. Gallion, and W. Elsässer, “Amplitude squeezing with complex laser structures” in International Quantum Electronics Conference, Vol. 16 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), pp. 43–44.

J. L. Vey and W. Elsässer, “Amplitude noise squeezing with vertical cavity semiconductor lasers,” in Proceedings of the European Quantum Electronics Conference (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1996), p. 218.

Von Lehmen, A. C.

C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. Von Lehmen, L. T. Florez, and N. G. Stoffel, “Dynamic, polarization and transverse mode characteristics of vertical cavity surface emitting lasers,” IEEE J. Quantum Electron. 27, 1402–1409 (1991).
[Crossref]

Walker, J. D.

D. M. Kutcha, J. Gamelin, J. D. Walker, J. Lin, K. Y. Lau, J. S. Smith, M. Hong, and J. P. Mannaerts, “Relative intensity noise of vertical cavity surface emitting lasers,” Appl. Phys. Lett. 62, 1194–1196 (1993).
[Crossref]

Weigel, B.

K. J. Ebeling, U. Fiedler, R. Michalzik, G. Reiner, and B. Weigel, “Efficient vertical cavity surface emitting laser diodes for high bit rate optical data transmission,” Int. J. Electron. Commun. 50, 316–326 (1996).

Yamamoto, Y.

Y. Yamamoto, S. Machida, and G. Björk, “Micro-cavity semiconductor lasers with controlled spontaneous emission,” Opt. Quantum Electron. 24, 215–243 (1992).
[Crossref]

G. Björk and Y. Yamamoto, “Analysis of semiconductor microcavity lasers using rate equations,” IEEE J. Quantum Electron. 27, 2386–2396 (1991).
[Crossref]

S. Machida, Y. Yamamoto, and Y. Itaya, “Observation of amplitude squeezing in a constant-current-driven semiconductor laser,” Phys. Rev. Lett. 58, 1000–1003 (1987).
[Crossref] [PubMed]

Y. Yamamoto, S. Machida, and O. Nilsson, “Amplitude squeezing in a pump-noise-suppressed laser oscillator,” Phys. Rev. A 14, 4025–4042 (1986).
[Crossref]

Appl. Phys. Lett. (4)

D. V. Kuksnkov, H. Temkin, and S. Swirhun, “Polarization instability and relative intensity noise in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 67, 2141–2143 (1995).
[Crossref]

D. M. Kutcha, J. Gamelin, J. D. Walker, J. Lin, K. Y. Lau, J. S. Smith, M. Hong, and J. P. Mannaerts, “Relative intensity noise of vertical cavity surface emitting lasers,” Appl. Phys. Lett. 62, 1194–1196 (1993).
[Crossref]

E. Goobar, J. W. Scott, B. Thibeault, G. Robinson, Y. Akulova, and L. A. Coldren, “Calibrated intensity noise measurements in microcavity laser diodes,” Appl. Phys. Lett. 67, 3697–3699 (1995).
[Crossref]

F. Girardin, G.-H. Duan, A. Talneau, and A. Ougazzaden, “Experimental investigation of the relative importance of carrier heating and spectral-hole-burning on nonlinear gain in bulk and strained multiquantum-well 1.55-µm lasers,” Appl. Phys. Lett. 67, 771–773 (1995).
[Crossref]

IEEE J. Quantum Electron. (9)

B. Tromborg, H.-E. Lassen, and H. Olesen, “Traveling wave analysis of semiconductor lasers: modulation responses, mode stability and quantum mechanical treatment of noise spectra,” IEEE J. Quantum Electron. 30, 939–956 (1994).
[Crossref]

D. D. Marcenac and J. E. Carroll, “Modeling of intensity noise including squeezing in DFB and Fabry–Perot semiconductor laser diodes,” IEEE J. Quantum Electron. 30, 2064–2072 (1994).
[Crossref]

K. Iga, F. Koyama, and S. Kinoshita, “Surface emitting semiconductor lasers,” IEEE J. Quantum Electron. 24, 1845–1855 (1988).
[Crossref]

J. W. Scott, R. S. Geels, S. W. Corzine, and L. A. Coldren, “Modeling temperature effects and spatial hole burning to optimize vertical-cavity surface-emitting laser performance,” IEEE J. Quantum Electron. 29, 1295–1308 (1993).
[Crossref]

R. Michalzik and K. J. Ebeling, “Modeling and design of proton-implanted ultralow-threshold vertical-cavity laser diodes,” IEEE J. Quantum Electron. 29, 1963–1974 (1993).
[Crossref]

C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. Von Lehmen, L. T. Florez, and N. G. Stoffel, “Dynamic, polarization and transverse mode characteristics of vertical cavity surface emitting lasers,” IEEE J. Quantum Electron. 27, 1402–1409 (1991).
[Crossref]

J. L. Jewell, J. P. Harbison, A. Scherer, Y. H. Lee, and L. T. Florez, “Vertical-cavity surface-emitting lasers: design, growth, fabrication, characterization,” IEEE J. Quantum Electron. 27, 1332–1346 (1991).
[Crossref]

G. H. Duan, P. Gallion, and G. P. Agrawal, “Dynamic and noise properties of tunable multielectrode semiconductor lasers including spatial hole burning and non linear gain,” IEEE J. Quantum Electron. 29, 844 (1993).
[Crossref]

G. Björk and Y. Yamamoto, “Analysis of semiconductor microcavity lasers using rate equations,” IEEE J. Quantum Electron. 27, 2386–2396 (1991).
[Crossref]

Int. J. Electron. Commun. (1)

K. J. Ebeling, U. Fiedler, R. Michalzik, G. Reiner, and B. Weigel, “Efficient vertical cavity surface emitting laser diodes for high bit rate optical data transmission,” Int. J. Electron. Commun. 50, 316–326 (1996).

Laser Focus World (1)

J. L. Jewell and G. R. Olbright, “Surface-emitting lasers emerge from the laboratory,” Laser Focus World 28(5), 217–223 (1992).

Opt. Lett. (1)

Opt. Quantum Electron. (2)

Y. Yamamoto, S. Machida, and G. Björk, “Micro-cavity semiconductor lasers with controlled spontaneous emission,” Opt. Quantum Electron. 24, 215–243 (1992).
[Crossref]

J. Arnaud, “Classical theory of laser noise,” Opt. Quantum Electron. 27, 63–89 (1995).
[Crossref]

Phys. Rev. A (2)

Y. Yamamoto, S. Machida, and O. Nilsson, “Amplitude squeezing in a pump-noise-suppressed laser oscillator,” Phys. Rev. A 14, 4025–4042 (1986).
[Crossref]

F. Jahnke and S. W. Koch, “Many-body theory for semiconductor microcavity lasers,” Phys. Rev. A 52, 1712–1727 (1995).
[Crossref] [PubMed]

Phys. Rev. A. (1)

J. Arnaud, “Corpuscular theory of intensity noise with gain compression,” Phys. Rev. A. 45, 1775–1786 (1992).
[Crossref] [PubMed]

Phys. Rev. Lett. (1)

S. Machida, Y. Yamamoto, and Y. Itaya, “Observation of amplitude squeezing in a constant-current-driven semiconductor laser,” Phys. Rev. Lett. 58, 1000–1003 (1987).
[Crossref] [PubMed]

Proc. Inst. Electr. Eng. (1)

D. D. Marcenac and J. E. Carroll, “Quantum-mechanical model for realistic Fabry–Perot lasers,” Proc. Inst. Electr. Eng. 140, 157–171 (1993).

Other (3)

O. Nilsson, A. Karlsson, and E. Berglind, “Modulation and noise spectra of complicated laser structures” in Coherence, Amplification and Quantum Effects in Semiconductor Lasers, Y. Yamamoto, ed. (Wiley, New York, 1991), pp. 76–95.

J. L. Vey, P. Gallion, and W. Elsässer, “Amplitude squeezing with complex laser structures” in International Quantum Electronics Conference, Vol. 16 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), pp. 43–44.

J. L. Vey and W. Elsässer, “Amplitude noise squeezing with vertical cavity semiconductor lasers,” in Proceedings of the European Quantum Electronics Conference (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1996), p. 218.

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Figures (7)

Fig. 1
Fig. 1

Schematic depiction of a vertical cavity surface-emitting laser including noise forces.

Fig. 2
Fig. 2

Shot-noise normalized external amplitude noise at low frequency for a VCSEL without internal loss when it is normally and quietly pumped as a function of the upper power reflection coefficient R2.

Fig. 3
Fig. 3

Shot-noise normalized external amplitude noise for an edge-emitting laser and a VCSEL with R1=1 and R2=0.95 as a function of the power emitted by the laser.

Fig. 4
Fig. 4

Pumping level R50 needed for 50% amplitude noise squeezing for a VCSEL with R2=0.97 as a function of internal loss.

Fig. 5
Fig. 5

Shot-noise normalized external amplitude noise at low frequency as a function of the pumping level R of a VCSEL with R2=0.97 and no internal loss for various gain suppression coefficients : 1, 0; 2, 10-19; 3, 10-18; 4, 5.0×10-18, and 5, 10-17 cm3.

Fig. 6
Fig. 6

Field envelope distribution inside the VCSEL cavity for various coupling coefficients κL of the Bragg reflector R1=0.97: 1, 0.5; 2, 0.75; 3, 1; and 4, 2.

Fig. 7
Fig. 7

Comparative value of the Petermann factor for a simple VCSEL and with the distributed Bragg reflector taken into account as a function of the coupling coefficient of the Bragg reflector κL, R1=0.97.

Tables (1)

Tables Icon

Table 1 Laser Parameters Used for the Simulation

Equations (15)

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dPdt=2 0L Im(WN)ΔN(z)dzP(t)+Re(GNL)×(N, S)P(t)+FP(t),
dϕdt=ω0-ω¯-0L Re(WN)ΔN(z)dz+1/2 Im(GNL)×(N, S)+Fϕ(t),
dN(z, t)dt=J(z, t)-R[N(z, t)]-νgg(z, t)×S(z, t)+FN(z, t),
τ/V[1-R1fvac(t)δ(z)+1-R2fvac(t)δ(z-L)],
fvac(t)fvac(t)*=½δ(t-t).
floss(t)floss(t)*=νgαint2Vδ(t-t),
2DPP=2 P¯V{Rsp+[νgαint+τ(1-R1)|Z1(0)|2+τ(1-R2)|Z1(L)|2]}2DΦΦ=2DPPP¯2,
Z1(0)=k0nZ0(0)W/ω,Z1(L)=k0nZ0(L)W/ω,
2DPP=2KnspνggP¯+2P¯1τPloss+1-R1τ1+R12R12+1+R22R221-R2τ.
2DNN=2(nsp-1)νggP¯+(N¯/τe),
Eext(t)=1-R2V/τβ0(t)-R2fvac(t),
SAext(0)S.N.=21+R22R221-R2ln(R2)2+R2+(1+R2)(1-R2)ln(R2)-4(K-1)(1-R2)ln(R2),
SAext(0)S.N.=2 1-R2ln(R2)1+R22R221-R2ln(R2)+12+R2+(1+R2)(1-R2)ln(R2)-4(K-1)(1-R2)ln(R2),
K=1-R222R2 ln(R2)2
g=gd(N-N0)(1-P),

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