Abstract

We present a fully quantum model to process the intensity noise reduction of a single-frequency intracavity-doubled laser with an electronic feedback loop connected directly to the pump current of a laser diode. Adding an electronic feedback term to the quantum Langevin equations for a free-running single-frequency-doubling laser yields an analytical expression for the intensity noise spectrum of this system. Our previous experimental results with a Nd:YVO4/KTP green laser are basically in agreement with the theoretical calculation.

© 2002 Optical Society of America

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References

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  1. T. J. Kane and R. L. Bayer, “Monolithic, unidirectional single-mode Nd:YAG ring laser,” Opt. Lett. 10, 65–67 (1985).
    [Crossref] [PubMed]
  2. I. Fretag, A. Tunnermann, and H. Welling, “Power scaling of diode-pumped monolithic Nd:YAG ring lasers to output powers of several watts,” Opt. Commun. 115, 511–515 (1995).
    [Crossref]
  3. K. I. Martin, W. A. Clarkson, and D. C. Hanna, “3 W of single-frequency output at 532 nm by intracavity frequency doubling of a diode-bar-pumped Nd:YAG ring laser,” Opt. Lett. 21, 875–877 (1996).
    [Crossref] [PubMed]
  4. P. J. Hardman, W. A. Clarkson, and D. C. Hanna, “High-power diode-bar-pumped intracavity-frequency-doubling Nd:YLF ring laser,” Opt. Commun. 156, 49–52 (1998).
    [Crossref]
  5. T. C. Ralph, C. C. Harb, and H.-A. Bachor, “Intensity noise of injection locked lasers: quantum theory using a linearized input/output method,” Phys. Rev. A 54, 4359–4369 (1996).
    [Crossref] [PubMed]
  6. T. J. Kane, “Intensity noise in a diode-pumped single frequency Nd:YAG laser and its control by electronic feedback,” IEEE Photon. Technol. Lett. 2, 244–245 (1990).
    [Crossref]
  7. C. C. Harb, M. B. Gray, H.-A. Bachor, R. Schilling, P. Rottengatter, I. Freitag, and H. Welling, “Suppression of the intensity noise in a diode-pumped neodymium:YAG nonplanar ring laser,” IEEE J. Quantum Electron. 30, 2907–2913 (1994).
    [Crossref]
  8. B. C. Buchler, E. H. Huntington, C. C. Harb, and H.-A. Bachor, “Feedback control of laser intensity noise” Phys. Rev. A 57, 1286–1294 (1998).
    [Crossref]
  9. V. Mizrahi, D. J. DiGiovanni, R. M. Atkins, S. G. Grubb, Y. Park, and J. P. Delavaux, “Stable single-mode erbium fiber-grating laser for digital communication,” Lightwave Technol. 11, 2021–2025 (1993).
    [Crossref]
  10. A. D. Farinas, E. K. Gustavson, and R. L. Bayer, “Frequency and intensity noise in an injection-locked lasers” J. Opt. Soc. Am. B 12, 328–334 (1995).
    [Crossref]
  11. C. C. Harb, T. C. Ralph, E. H. Huntington, I. Freitag, D. E. McClelland, and H.-A. Bachor, “Intensity-noise properties of injection-locked lasers,” Phys. Rev. A 54, 4370–4381 (1996).
    [Crossref] [PubMed]
  12. E. H. Huntington, B. C. Buchler, C. C. Harb, T. C. Ralph, D. E. McClelland, and H.-A. Bachor, “Feedback control of the intensity noise of injection locked laser,” Opt. Commun. 145, 359–366 (1998).
    [Crossref]
  13. C. Becher and K.-J. Boller, “Low-intensity-noise operation of Nd:YVO4 microchip lasers by pump-noise suppression,” J. Opt. Soc. Am. B 16, 286–295 (1999).
    [Crossref]
  14. A. Bramati, J.-P. Hermier, V. Jost, and E. Giacobino, “Feedback control and nonlinear intensity noise of Nd:YVO4 microchip lasers,” Phys. Rev. A 62, 043806 (2000).
    [Crossref]
  15. J. Zhang, Y. L. Cheng, T. C. Zhang, K. S. Zhang, C. D. Xie, and K. C. Peng, “Investigation of the characteristic of the intensity noise of singly resonant active second-harmonic generation,” J. Opt. Soc. Am. B 17, 1695–1703 (2000).
    [Crossref]
  16. J. Zhang, H. Chang, X. J. Jia, H. X. Lei, R. L. Wang, C. D. Xie, and K. C. Peng, “Suppression of the intensity noise of a laser-diode-pumped single-frenquency ring Nd:YVO4-KTP green laser by optoelectronic feedback,” Opt. Lett. 26, 695–697 (2001).
    [Crossref]
  17. H. A. Haus and Y. Yamamoto, “Theory of feedback-generated squeezed states,” Phys. Rev. A 34, 270–292 (1986).
    [Crossref] [PubMed]
  18. H. M. Wiseman and G. J. Milburn, “Squeezing via feedback,” Phys. Rev. A 49, 1350–1366 (1994).
    [Crossref] [PubMed]
  19. H. M. Wiseman, “Quantum theory of continuous feedback,” Phys. Rev. A 49, 2133–2150 (1994).
    [Crossref] [PubMed]

2001 (1)

2000 (2)

1999 (1)

1998 (3)

P. J. Hardman, W. A. Clarkson, and D. C. Hanna, “High-power diode-bar-pumped intracavity-frequency-doubling Nd:YLF ring laser,” Opt. Commun. 156, 49–52 (1998).
[Crossref]

B. C. Buchler, E. H. Huntington, C. C. Harb, and H.-A. Bachor, “Feedback control of laser intensity noise” Phys. Rev. A 57, 1286–1294 (1998).
[Crossref]

E. H. Huntington, B. C. Buchler, C. C. Harb, T. C. Ralph, D. E. McClelland, and H.-A. Bachor, “Feedback control of the intensity noise of injection locked laser,” Opt. Commun. 145, 359–366 (1998).
[Crossref]

1996 (3)

C. C. Harb, T. C. Ralph, E. H. Huntington, I. Freitag, D. E. McClelland, and H.-A. Bachor, “Intensity-noise properties of injection-locked lasers,” Phys. Rev. A 54, 4370–4381 (1996).
[Crossref] [PubMed]

T. C. Ralph, C. C. Harb, and H.-A. Bachor, “Intensity noise of injection locked lasers: quantum theory using a linearized input/output method,” Phys. Rev. A 54, 4359–4369 (1996).
[Crossref] [PubMed]

K. I. Martin, W. A. Clarkson, and D. C. Hanna, “3 W of single-frequency output at 532 nm by intracavity frequency doubling of a diode-bar-pumped Nd:YAG ring laser,” Opt. Lett. 21, 875–877 (1996).
[Crossref] [PubMed]

1995 (2)

A. D. Farinas, E. K. Gustavson, and R. L. Bayer, “Frequency and intensity noise in an injection-locked lasers” J. Opt. Soc. Am. B 12, 328–334 (1995).
[Crossref]

I. Fretag, A. Tunnermann, and H. Welling, “Power scaling of diode-pumped monolithic Nd:YAG ring lasers to output powers of several watts,” Opt. Commun. 115, 511–515 (1995).
[Crossref]

1994 (3)

C. C. Harb, M. B. Gray, H.-A. Bachor, R. Schilling, P. Rottengatter, I. Freitag, and H. Welling, “Suppression of the intensity noise in a diode-pumped neodymium:YAG nonplanar ring laser,” IEEE J. Quantum Electron. 30, 2907–2913 (1994).
[Crossref]

H. M. Wiseman and G. J. Milburn, “Squeezing via feedback,” Phys. Rev. A 49, 1350–1366 (1994).
[Crossref] [PubMed]

H. M. Wiseman, “Quantum theory of continuous feedback,” Phys. Rev. A 49, 2133–2150 (1994).
[Crossref] [PubMed]

1993 (1)

V. Mizrahi, D. J. DiGiovanni, R. M. Atkins, S. G. Grubb, Y. Park, and J. P. Delavaux, “Stable single-mode erbium fiber-grating laser for digital communication,” Lightwave Technol. 11, 2021–2025 (1993).
[Crossref]

1990 (1)

T. J. Kane, “Intensity noise in a diode-pumped single frequency Nd:YAG laser and its control by electronic feedback,” IEEE Photon. Technol. Lett. 2, 244–245 (1990).
[Crossref]

1986 (1)

H. A. Haus and Y. Yamamoto, “Theory of feedback-generated squeezed states,” Phys. Rev. A 34, 270–292 (1986).
[Crossref] [PubMed]

1985 (1)

Atkins, R. M.

V. Mizrahi, D. J. DiGiovanni, R. M. Atkins, S. G. Grubb, Y. Park, and J. P. Delavaux, “Stable single-mode erbium fiber-grating laser for digital communication,” Lightwave Technol. 11, 2021–2025 (1993).
[Crossref]

Bachor, H.-A.

B. C. Buchler, E. H. Huntington, C. C. Harb, and H.-A. Bachor, “Feedback control of laser intensity noise” Phys. Rev. A 57, 1286–1294 (1998).
[Crossref]

E. H. Huntington, B. C. Buchler, C. C. Harb, T. C. Ralph, D. E. McClelland, and H.-A. Bachor, “Feedback control of the intensity noise of injection locked laser,” Opt. Commun. 145, 359–366 (1998).
[Crossref]

C. C. Harb, T. C. Ralph, E. H. Huntington, I. Freitag, D. E. McClelland, and H.-A. Bachor, “Intensity-noise properties of injection-locked lasers,” Phys. Rev. A 54, 4370–4381 (1996).
[Crossref] [PubMed]

T. C. Ralph, C. C. Harb, and H.-A. Bachor, “Intensity noise of injection locked lasers: quantum theory using a linearized input/output method,” Phys. Rev. A 54, 4359–4369 (1996).
[Crossref] [PubMed]

C. C. Harb, M. B. Gray, H.-A. Bachor, R. Schilling, P. Rottengatter, I. Freitag, and H. Welling, “Suppression of the intensity noise in a diode-pumped neodymium:YAG nonplanar ring laser,” IEEE J. Quantum Electron. 30, 2907–2913 (1994).
[Crossref]

Bayer, R. L.

Becher, C.

Boller, K.-J.

Bramati, A.

A. Bramati, J.-P. Hermier, V. Jost, and E. Giacobino, “Feedback control and nonlinear intensity noise of Nd:YVO4 microchip lasers,” Phys. Rev. A 62, 043806 (2000).
[Crossref]

Buchler, B. C.

E. H. Huntington, B. C. Buchler, C. C. Harb, T. C. Ralph, D. E. McClelland, and H.-A. Bachor, “Feedback control of the intensity noise of injection locked laser,” Opt. Commun. 145, 359–366 (1998).
[Crossref]

B. C. Buchler, E. H. Huntington, C. C. Harb, and H.-A. Bachor, “Feedback control of laser intensity noise” Phys. Rev. A 57, 1286–1294 (1998).
[Crossref]

Chang, H.

Cheng, Y. L.

Clarkson, W. A.

P. J. Hardman, W. A. Clarkson, and D. C. Hanna, “High-power diode-bar-pumped intracavity-frequency-doubling Nd:YLF ring laser,” Opt. Commun. 156, 49–52 (1998).
[Crossref]

K. I. Martin, W. A. Clarkson, and D. C. Hanna, “3 W of single-frequency output at 532 nm by intracavity frequency doubling of a diode-bar-pumped Nd:YAG ring laser,” Opt. Lett. 21, 875–877 (1996).
[Crossref] [PubMed]

Delavaux, J. P.

V. Mizrahi, D. J. DiGiovanni, R. M. Atkins, S. G. Grubb, Y. Park, and J. P. Delavaux, “Stable single-mode erbium fiber-grating laser for digital communication,” Lightwave Technol. 11, 2021–2025 (1993).
[Crossref]

DiGiovanni, D. J.

V. Mizrahi, D. J. DiGiovanni, R. M. Atkins, S. G. Grubb, Y. Park, and J. P. Delavaux, “Stable single-mode erbium fiber-grating laser for digital communication,” Lightwave Technol. 11, 2021–2025 (1993).
[Crossref]

Farinas, A. D.

Freitag, I.

C. C. Harb, T. C. Ralph, E. H. Huntington, I. Freitag, D. E. McClelland, and H.-A. Bachor, “Intensity-noise properties of injection-locked lasers,” Phys. Rev. A 54, 4370–4381 (1996).
[Crossref] [PubMed]

C. C. Harb, M. B. Gray, H.-A. Bachor, R. Schilling, P. Rottengatter, I. Freitag, and H. Welling, “Suppression of the intensity noise in a diode-pumped neodymium:YAG nonplanar ring laser,” IEEE J. Quantum Electron. 30, 2907–2913 (1994).
[Crossref]

Fretag, I.

I. Fretag, A. Tunnermann, and H. Welling, “Power scaling of diode-pumped monolithic Nd:YAG ring lasers to output powers of several watts,” Opt. Commun. 115, 511–515 (1995).
[Crossref]

Giacobino, E.

A. Bramati, J.-P. Hermier, V. Jost, and E. Giacobino, “Feedback control and nonlinear intensity noise of Nd:YVO4 microchip lasers,” Phys. Rev. A 62, 043806 (2000).
[Crossref]

Gray, M. B.

C. C. Harb, M. B. Gray, H.-A. Bachor, R. Schilling, P. Rottengatter, I. Freitag, and H. Welling, “Suppression of the intensity noise in a diode-pumped neodymium:YAG nonplanar ring laser,” IEEE J. Quantum Electron. 30, 2907–2913 (1994).
[Crossref]

Grubb, S. G.

V. Mizrahi, D. J. DiGiovanni, R. M. Atkins, S. G. Grubb, Y. Park, and J. P. Delavaux, “Stable single-mode erbium fiber-grating laser for digital communication,” Lightwave Technol. 11, 2021–2025 (1993).
[Crossref]

Gustavson, E. K.

Hanna, D. C.

P. J. Hardman, W. A. Clarkson, and D. C. Hanna, “High-power diode-bar-pumped intracavity-frequency-doubling Nd:YLF ring laser,” Opt. Commun. 156, 49–52 (1998).
[Crossref]

K. I. Martin, W. A. Clarkson, and D. C. Hanna, “3 W of single-frequency output at 532 nm by intracavity frequency doubling of a diode-bar-pumped Nd:YAG ring laser,” Opt. Lett. 21, 875–877 (1996).
[Crossref] [PubMed]

Harb, C. C.

B. C. Buchler, E. H. Huntington, C. C. Harb, and H.-A. Bachor, “Feedback control of laser intensity noise” Phys. Rev. A 57, 1286–1294 (1998).
[Crossref]

E. H. Huntington, B. C. Buchler, C. C. Harb, T. C. Ralph, D. E. McClelland, and H.-A. Bachor, “Feedback control of the intensity noise of injection locked laser,” Opt. Commun. 145, 359–366 (1998).
[Crossref]

C. C. Harb, T. C. Ralph, E. H. Huntington, I. Freitag, D. E. McClelland, and H.-A. Bachor, “Intensity-noise properties of injection-locked lasers,” Phys. Rev. A 54, 4370–4381 (1996).
[Crossref] [PubMed]

T. C. Ralph, C. C. Harb, and H.-A. Bachor, “Intensity noise of injection locked lasers: quantum theory using a linearized input/output method,” Phys. Rev. A 54, 4359–4369 (1996).
[Crossref] [PubMed]

C. C. Harb, M. B. Gray, H.-A. Bachor, R. Schilling, P. Rottengatter, I. Freitag, and H. Welling, “Suppression of the intensity noise in a diode-pumped neodymium:YAG nonplanar ring laser,” IEEE J. Quantum Electron. 30, 2907–2913 (1994).
[Crossref]

Hardman, P. J.

P. J. Hardman, W. A. Clarkson, and D. C. Hanna, “High-power diode-bar-pumped intracavity-frequency-doubling Nd:YLF ring laser,” Opt. Commun. 156, 49–52 (1998).
[Crossref]

Haus, H. A.

H. A. Haus and Y. Yamamoto, “Theory of feedback-generated squeezed states,” Phys. Rev. A 34, 270–292 (1986).
[Crossref] [PubMed]

Hermier, J.-P.

A. Bramati, J.-P. Hermier, V. Jost, and E. Giacobino, “Feedback control and nonlinear intensity noise of Nd:YVO4 microchip lasers,” Phys. Rev. A 62, 043806 (2000).
[Crossref]

Huntington, E. H.

E. H. Huntington, B. C. Buchler, C. C. Harb, T. C. Ralph, D. E. McClelland, and H.-A. Bachor, “Feedback control of the intensity noise of injection locked laser,” Opt. Commun. 145, 359–366 (1998).
[Crossref]

B. C. Buchler, E. H. Huntington, C. C. Harb, and H.-A. Bachor, “Feedback control of laser intensity noise” Phys. Rev. A 57, 1286–1294 (1998).
[Crossref]

C. C. Harb, T. C. Ralph, E. H. Huntington, I. Freitag, D. E. McClelland, and H.-A. Bachor, “Intensity-noise properties of injection-locked lasers,” Phys. Rev. A 54, 4370–4381 (1996).
[Crossref] [PubMed]

Jia, X. J.

Jost, V.

A. Bramati, J.-P. Hermier, V. Jost, and E. Giacobino, “Feedback control and nonlinear intensity noise of Nd:YVO4 microchip lasers,” Phys. Rev. A 62, 043806 (2000).
[Crossref]

Kane, T. J.

T. J. Kane, “Intensity noise in a diode-pumped single frequency Nd:YAG laser and its control by electronic feedback,” IEEE Photon. Technol. Lett. 2, 244–245 (1990).
[Crossref]

T. J. Kane and R. L. Bayer, “Monolithic, unidirectional single-mode Nd:YAG ring laser,” Opt. Lett. 10, 65–67 (1985).
[Crossref] [PubMed]

Lei, H. X.

Martin, K. I.

McClelland, D. E.

E. H. Huntington, B. C. Buchler, C. C. Harb, T. C. Ralph, D. E. McClelland, and H.-A. Bachor, “Feedback control of the intensity noise of injection locked laser,” Opt. Commun. 145, 359–366 (1998).
[Crossref]

C. C. Harb, T. C. Ralph, E. H. Huntington, I. Freitag, D. E. McClelland, and H.-A. Bachor, “Intensity-noise properties of injection-locked lasers,” Phys. Rev. A 54, 4370–4381 (1996).
[Crossref] [PubMed]

Milburn, G. J.

H. M. Wiseman and G. J. Milburn, “Squeezing via feedback,” Phys. Rev. A 49, 1350–1366 (1994).
[Crossref] [PubMed]

Mizrahi, V.

V. Mizrahi, D. J. DiGiovanni, R. M. Atkins, S. G. Grubb, Y. Park, and J. P. Delavaux, “Stable single-mode erbium fiber-grating laser for digital communication,” Lightwave Technol. 11, 2021–2025 (1993).
[Crossref]

Park, Y.

V. Mizrahi, D. J. DiGiovanni, R. M. Atkins, S. G. Grubb, Y. Park, and J. P. Delavaux, “Stable single-mode erbium fiber-grating laser for digital communication,” Lightwave Technol. 11, 2021–2025 (1993).
[Crossref]

Peng, K. C.

Ralph, T. C.

E. H. Huntington, B. C. Buchler, C. C. Harb, T. C. Ralph, D. E. McClelland, and H.-A. Bachor, “Feedback control of the intensity noise of injection locked laser,” Opt. Commun. 145, 359–366 (1998).
[Crossref]

C. C. Harb, T. C. Ralph, E. H. Huntington, I. Freitag, D. E. McClelland, and H.-A. Bachor, “Intensity-noise properties of injection-locked lasers,” Phys. Rev. A 54, 4370–4381 (1996).
[Crossref] [PubMed]

T. C. Ralph, C. C. Harb, and H.-A. Bachor, “Intensity noise of injection locked lasers: quantum theory using a linearized input/output method,” Phys. Rev. A 54, 4359–4369 (1996).
[Crossref] [PubMed]

Rottengatter, P.

C. C. Harb, M. B. Gray, H.-A. Bachor, R. Schilling, P. Rottengatter, I. Freitag, and H. Welling, “Suppression of the intensity noise in a diode-pumped neodymium:YAG nonplanar ring laser,” IEEE J. Quantum Electron. 30, 2907–2913 (1994).
[Crossref]

Schilling, R.

C. C. Harb, M. B. Gray, H.-A. Bachor, R. Schilling, P. Rottengatter, I. Freitag, and H. Welling, “Suppression of the intensity noise in a diode-pumped neodymium:YAG nonplanar ring laser,” IEEE J. Quantum Electron. 30, 2907–2913 (1994).
[Crossref]

Tunnermann, A.

I. Fretag, A. Tunnermann, and H. Welling, “Power scaling of diode-pumped monolithic Nd:YAG ring lasers to output powers of several watts,” Opt. Commun. 115, 511–515 (1995).
[Crossref]

Wang, R. L.

Welling, H.

I. Fretag, A. Tunnermann, and H. Welling, “Power scaling of diode-pumped monolithic Nd:YAG ring lasers to output powers of several watts,” Opt. Commun. 115, 511–515 (1995).
[Crossref]

C. C. Harb, M. B. Gray, H.-A. Bachor, R. Schilling, P. Rottengatter, I. Freitag, and H. Welling, “Suppression of the intensity noise in a diode-pumped neodymium:YAG nonplanar ring laser,” IEEE J. Quantum Electron. 30, 2907–2913 (1994).
[Crossref]

Wiseman, H. M.

H. M. Wiseman, “Quantum theory of continuous feedback,” Phys. Rev. A 49, 2133–2150 (1994).
[Crossref] [PubMed]

H. M. Wiseman and G. J. Milburn, “Squeezing via feedback,” Phys. Rev. A 49, 1350–1366 (1994).
[Crossref] [PubMed]

Xie, C. D.

Yamamoto, Y.

H. A. Haus and Y. Yamamoto, “Theory of feedback-generated squeezed states,” Phys. Rev. A 34, 270–292 (1986).
[Crossref] [PubMed]

Zhang, J.

Zhang, K. S.

Zhang, T. C.

IEEE J. Quantum Electron. (1)

C. C. Harb, M. B. Gray, H.-A. Bachor, R. Schilling, P. Rottengatter, I. Freitag, and H. Welling, “Suppression of the intensity noise in a diode-pumped neodymium:YAG nonplanar ring laser,” IEEE J. Quantum Electron. 30, 2907–2913 (1994).
[Crossref]

IEEE Photon. Technol. Lett. (1)

T. J. Kane, “Intensity noise in a diode-pumped single frequency Nd:YAG laser and its control by electronic feedback,” IEEE Photon. Technol. Lett. 2, 244–245 (1990).
[Crossref]

J. Opt. Soc. Am. B (3)

Lightwave Technol. (1)

V. Mizrahi, D. J. DiGiovanni, R. M. Atkins, S. G. Grubb, Y. Park, and J. P. Delavaux, “Stable single-mode erbium fiber-grating laser for digital communication,” Lightwave Technol. 11, 2021–2025 (1993).
[Crossref]

Opt. Commun. (3)

E. H. Huntington, B. C. Buchler, C. C. Harb, T. C. Ralph, D. E. McClelland, and H.-A. Bachor, “Feedback control of the intensity noise of injection locked laser,” Opt. Commun. 145, 359–366 (1998).
[Crossref]

I. Fretag, A. Tunnermann, and H. Welling, “Power scaling of diode-pumped monolithic Nd:YAG ring lasers to output powers of several watts,” Opt. Commun. 115, 511–515 (1995).
[Crossref]

P. J. Hardman, W. A. Clarkson, and D. C. Hanna, “High-power diode-bar-pumped intracavity-frequency-doubling Nd:YLF ring laser,” Opt. Commun. 156, 49–52 (1998).
[Crossref]

Opt. Lett. (3)

Phys. Rev. A (7)

H. A. Haus and Y. Yamamoto, “Theory of feedback-generated squeezed states,” Phys. Rev. A 34, 270–292 (1986).
[Crossref] [PubMed]

H. M. Wiseman and G. J. Milburn, “Squeezing via feedback,” Phys. Rev. A 49, 1350–1366 (1994).
[Crossref] [PubMed]

H. M. Wiseman, “Quantum theory of continuous feedback,” Phys. Rev. A 49, 2133–2150 (1994).
[Crossref] [PubMed]

C. C. Harb, T. C. Ralph, E. H. Huntington, I. Freitag, D. E. McClelland, and H.-A. Bachor, “Intensity-noise properties of injection-locked lasers,” Phys. Rev. A 54, 4370–4381 (1996).
[Crossref] [PubMed]

B. C. Buchler, E. H. Huntington, C. C. Harb, and H.-A. Bachor, “Feedback control of laser intensity noise” Phys. Rev. A 57, 1286–1294 (1998).
[Crossref]

T. C. Ralph, C. C. Harb, and H.-A. Bachor, “Intensity noise of injection locked lasers: quantum theory using a linearized input/output method,” Phys. Rev. A 54, 4359–4369 (1996).
[Crossref] [PubMed]

A. Bramati, J.-P. Hermier, V. Jost, and E. Giacobino, “Feedback control and nonlinear intensity noise of Nd:YVO4 microchip lasers,” Phys. Rev. A 62, 043806 (2000).
[Crossref]

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Figures (6)

Fig. 1
Fig. 1

Schematic of a quantum model description of the diode-pumped single-frequency doubling laser. γt and γs are spontaneous-emission rates; Γ is the pump rate; G is the stimulated-emission coefficient; Vcout is the output harmonic noise; Vcin is second-harmonic input noise; Vpump is the noise entering the laser from its pump source; Vab is quantum (or vacuum) noise that is due to imperfect absorption in the pump field; Vspont32 and Vspont21 are noises from spontaneous emission; Vdipole is the noise from dipole fluctuations; and Vlosses is the noise from intracavity losses. DM is a dichroic mirror (reflectivity, R1 for the fundamental and R0 for the harmonic); NLC, nonlinear crystal.

Fig. 2
Fig. 2

Amplitude (1) and phase (2) of the pump noise transfer function for the single-frequency intracavity frequency-doubling laser.

Fig. 3
Fig. 3

Circuit of a phase advance filter. GND, the ground of the circuit.

Fig. 4
Fig. 4

Effect of feedback on intensity noise in a typical Nd:YVO4/KTP single-frequency-doubling laser. a, Free-running laser spectrum; b, spectrum with feedback and without a phase advance filter; c, spectrum with feedback and with an optimized phase advance filter. Parameters used in the calculation were Vpump=106, =0.05, and η1=0.9. The phase advance is 45°.

Fig. 5
Fig. 5

Experimental arrangement for noise control and monitoring of the laser. A and B are the test points.

Fig. 6
Fig. 6

Comparison of theoretical calculation and experimental result. QNL, quantum-noise limit.

Tables (1)

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Table 1 Properties of the Nd:YVO4/KTP Single-Frequency Doubling Ring Laser

Equations (46)

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α˙0=G2(J3-J2)α0-κlα0-μ˜α0*α02,
J˙1=-ΓJ1+γsJ2,
J˙2=G(J3-J2)α0α0*+γtJ3-γsJ2,
J˙3=-G(J3-J2)α0α0*-γtJ3+ΓJ1,
J1+J2+J3=1,
cout=μ˜α02,
G=εsρc,
δXˆ˙a=G(δσˆ3-δσˆ2)α0-μ˜α0*α0δXˆa-μ˜α02δXˆa+2κlδXˆAl+2μ˜α0*δXˆc-[G(J3+J2)]1/2δXˆCp,
δσˆ˙1=-Γ1-ηδσˆ1+γsδσˆ2-ΓJ1ηδXˆB+γsJ2δXˆCs+[Γ(1-η)J1]1/2δXˆq,
δσˆ˙2=G(δσˆ3-δσˆ2)α02+G(J3-J2)α0δXˆa+γtδσˆ3-γsδσˆ2+γsJ2δXˆCs-γtJ3δXˆCt-[G(J3+J2)]1/2α0δXˆCp,
δσˆ˙3=-G(δσˆ3-δσˆ2)α02-G(J3-J2)α0δXˆa-γtδσˆ3+Γ1-ηδσˆ1+ΓJ1ηδXˆB+γsJ2δXˆCs-[Γ(1-η)J1]1/2δXˆq+γtJ3δXˆCt+[G(J3+J2)]1/2α0δXˆCp,
δXˆcout=2μ˜α0δXˆa-δXˆc.
δXfree_cout=W0(ω)δXB+W1(ω)δXc+W2(ω)δXq+W3(ω)δXCs+W4(ω)δXCt+W5(ω)δXp+W6(ω)δXAl,
W0(ω)=2μ˜α0ηΓJ1Gα0(iω+γs-γt)(iω+2μ˜α02)ζ(ω)+G2α02(J3-J2)(2iω+γs+2Γ˜),
W1(ω)=4μ˜α02ζ(ω)(iω+2μ˜α02)ζ(ω)+G2α02(J3-J2)(2iω+γs+2Γ˜)-1,
W2(ω)=1-ηη1/2W0(ω),
W3(ω)=2μ˜α0Gα0γsJ2(iω+2Γ˜+γt)(iω+2μ˜α02)ζ(ω)+G2α02(J3-J2)(2iω+γs+2Γ˜),
W4(ω)=2μ˜α0γtJ3Ga0(iω+2Γ˜+γs)(iω+2μ˜α02)ζ(ω)+G2α02(J3-J2)(2iω+γs+2Γ˜),
W5(ω)=2μ˜α0[G(J3+J2)]1/2[Gα02(iω+2Γ˜+γs)-ζ(ω)](iω+2μ˜α02)ζ(ω)+G2α02(J3-J2)(2iω+γs+2Γ˜),
W6(ω)=2μ˜α02klζ(ω)(iω+2μ˜α02)ζ(ω)+G2α02(J3-J2)(2iω+γs+2Γ˜),
ζ(ω)=(iω+Γ˜)(iω+γs+2Gα02+γt)+γs(Gα02+γt),
Vfree_cout(ω)=|δXfree_cout|2=|W0(ω)|2Vpump+|W1(ω)|2Vcin+|W2(ω)|2Vab+|W3(ω)|2Vspont21|W4(ω)|2Vspont32+|W5(ω)|2Vdipole+|W6(ω)|2Vlosses.
Pˆ=Bˆ+δEˆ,
Pˆ=B¯+δBˆ+δEˆδPˆ=δBˆ+δEˆδXˆP=δX˙B+δXˆE.
δEˆ=-β - k(v)δiˆ1(t-v)dv-1-βδvˆβ,
 iˆ1={ηDcˆout+[ηD(1-)]1/2δvˆs+1-ηDδvˆD}×{ηDcˆout+[ηD(1-)]1/2δvˆs+1-ηDδvˆD},
δiˆ1=ηDμ˜α02{ηDδXˆcout+[ηD(1-)]1/2δXˆvs+1-ηDδXˆvD},
δXˆi1=ηDδXˆcout+[ηD(1-)]1/2δXˆvs+1-ηDδXˆvD,
δXˆE=-ηDμ˜a02 -+ k(v)δXˆi1(t-v)dv-1-ηDδXˆvβ,
δXfd_cout=W0(ω)δXB-1-βη1/2δXβ-W0(ω)H(ω)×1-1/2δXvs+1-ηDηD1/2δXvD+W1(ω)δXc+W2(ω)δXq+W3(ω)δXCs+W4(ω)δXCt+W5(ω)δXCp+W6(ω)δXAl[1+W0(ω)H(ω)],
H(ω)=2βηDμ˜α02K(ω).
δXc1=δXfd_cout+1-δXvs,
δXc2=1-δXfd_cout-δXvs.
Vc1=[Vfree_cout+|W0(ω)|2(1-β/η)]+|W0(ω)H(ω)|2(1-ηD/ηD)+(1-)Vvs|1+W0(ω)H(ω)|2,
Vc2=(1-)[Vfree_cout+|W0(ω)|2(1-β/η)+|W0(ω)H(ω)|2)(1-ηD/ηD)]+(Vvs/)|+W0(ω)H(ω)||1+W0(ω)H(ω)|2,
limH(ω)(Vc2)=(1-)(1-ηD)ηD+Vvs.
limH(ω)(Vc1)=1-ηDηD.
W0(ω)=2(μ˜α02ΓηJ1)1/2Gα0iωγL+(ωr2-ω2),
ωr=[2μ˜α02(Gα02+Γ˜+γt)+2Gα02(μ˜α02+κl)]1/2,
γL=2μ˜α02+Gα02+Γ˜+γt.
Had(ω)=F R2(1+iωCR1)R2(1+iωCR1)+R1,
tan ϕm=R12[R2(R2+R1)]1/2,
ωm=[(R2+R1)/C2R12R2]1/2.
|W0(ωm)Had(ωm|=1,
ωm=[(R2+R1)/C2R12R2]1/2.
H(ω)=ρK(ω)exp(-iωτ),

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