Abstract

The noise properties of mode-locked fiber lasers differ in various respects from those of bulk lasers. The reasons for this are both quantitative and qualitative differences concerning the pulse formation. The underlying theoretical aspects are discussed in detail. It is found that the achievable noise level and the limiting effects depend strongly on the type of fiber laser. Depending on the pulse formation mechanism, noise levels may be much higher than predicted by simplified models.

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References

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  1. L. F. Mollenauer and R. H. Stolen, “The soliton laser,” Opt. Lett. 9(1), 13–15 (1984).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  3. F. Ö. Ilday, J. R. Buckley, H. Lim, F. W. Wise, and W. G. Clark, “Generation of 50-fs, 5-nJ pulses at 1.03 μm from a wave-breaking-free fiber laser,” Opt. Lett. 28(15), 1365–1367 (2003).
    [CrossRef] [PubMed]
  4. F. Ö. Ilday, J. R. Buckley, W. G. Clark, and F. W. Wise, “Self-similar evolution of parabolic pulses in a laser,” Phys. Rev. Lett. 92(21), 213902–213905 (2004).
    [CrossRef] [PubMed]
  5. A. Chong, W. H. Renninger, and F. W. Wise, “Properties of normal-dispersion femtosecond fiber lasers,” J. Opt. Soc. Am. B 25(2), 140–148 (2008).
    [CrossRef]
  6. T. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416(6877), 233–237 (2002).
    [CrossRef] [PubMed]
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    [CrossRef]
  8. M. E. Grein, L. A. Jiang, H. A. Haus, E. P. Ippen, C. McNeilage, J. H. Searls, and R. S. Windeler, “Observation of quantum-limited timing jitter in an active, harmonically mode-locked fiber laser,” Opt. Lett. 27(11), 957–959 (2002).
    [CrossRef]
  9. O. Prochnow, R. Paschotta, E. Benkler, U. Morgner, J. Neumann, D. Wandt, and D. Kracht, “Quantum-limited noise performance of a femtosecond all-fiber ytterbium laser,” Opt. Express 17(18), 15525–15533 (2009), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-17-18-15525 .
    [CrossRef] [PubMed]
  10. H. A. Haus and A. Mecozzi, “Noise of mode-locked lasers,” IEEE J. Quantum Electron. 29(3), 983–996 (1993).
    [CrossRef]
  11. R. Paschotta, “Noise of mode-locked lasers. Part II: Timing jitter and other fluctuations,” Appl. Phys. B 79(2), 163–173 (2004).
    [CrossRef]
  12. R. Paschotta, A. Schlatter, S. C. Zeller, H. R. Telle, and U. Keller, “Optical phase noise and carrier–envelope offset noise of mode-locked lasers,” Appl. Phys. B 82(2), 265–273 (2006).
    [CrossRef]
  13. A. L. Schawlow and C. H. Townes, “Infrared and optical masers,” Phys. Rev. 112(6), 1940–1949 (1958).
    [CrossRef]
  14. R. Paschotta, H. R. Telle, and U. Keller, Noise of Solid State Lasers (CRC Press, Boca Raton, 2007), Chap. 12.
  15. P.-T. Ho, “Phase and amplitude fluctuations in a mode-locked laser,” IEEE J. Quantum Electron. QE 21(11), 1806–1813 (1985).
    [CrossRef]
  16. H. R. Telle, B. Lipphardt, and J. Stenger, “Kerr-lens mode-locked lasers as transfer oscillators for optical frequency measurements,” Appl. Phys. B 74(1), 1–6 (2002).
    [CrossRef]
  17. L. Krainer, R. Paschotta, G. J. Spühler, I. Klimov, C. Y. Teisset, K. J. Weingarten, and U. Keller, “Tunable picosecond pulse-generating laser with a repetition rate exceeding 10 GHz,” Electron. Lett. 38(5), 225–227 (2002).
    [CrossRef]
  18. U. Morgner, F. X. Kärtner, S. H. Cho, Y. Chen, H. A. Haus, J. G. Fujimoto, E. P. Ippen, V. Scheuer, G. Angelow, and T. Tschudi, “Sub-two-cycle pulses from a Kerr-lens mode-locked Ti:sapphire laser,” Opt. Lett. 24(6), 411–413 (1999).
    [CrossRef]
  19. D. H. Sutter, G. Steinmeyer, L. Gallmann, N. Matuschek, F. Morier-Genoud, U. Keller, V. Scheuer, G. Angelow, and T. Tschudi, “Semiconductor saturable-absorber mirror assisted Kerr-lens mode-locked Ti:sapphire laser producing pulses in the two-cycle regime,” Opt. Lett. 24(9), 631–633 (1999).
    [CrossRef]
  20. R. Paschotta, “Noise of mode-locked lasers. Part I: Numerical model,” Appl. Phys. B 79(2), 153–162 (2004).
    [CrossRef]
  21. T. R. Schibli, I. Hartl, D. C. Yost, M. J. Martin, A. Marcinkevičius, M. E. Fermann, and J. Ye, “Optical frequency comb with submillihertz linewidth and more than 10 W average power,” Nat. Photonics 2(6), 355–359 (2008).
    [CrossRef]

2009 (1)

2008 (2)

A. Chong, W. H. Renninger, and F. W. Wise, “Properties of normal-dispersion femtosecond fiber lasers,” J. Opt. Soc. Am. B 25(2), 140–148 (2008).
[CrossRef]

T. R. Schibli, I. Hartl, D. C. Yost, M. J. Martin, A. Marcinkevičius, M. E. Fermann, and J. Ye, “Optical frequency comb with submillihertz linewidth and more than 10 W average power,” Nat. Photonics 2(6), 355–359 (2008).
[CrossRef]

2006 (1)

R. Paschotta, A. Schlatter, S. C. Zeller, H. R. Telle, and U. Keller, “Optical phase noise and carrier–envelope offset noise of mode-locked lasers,” Appl. Phys. B 82(2), 265–273 (2006).
[CrossRef]

2004 (3)

F. Ö. Ilday, J. R. Buckley, W. G. Clark, and F. W. Wise, “Self-similar evolution of parabolic pulses in a laser,” Phys. Rev. Lett. 92(21), 213902–213905 (2004).
[CrossRef] [PubMed]

R. Paschotta, “Noise of mode-locked lasers. Part II: Timing jitter and other fluctuations,” Appl. Phys. B 79(2), 163–173 (2004).
[CrossRef]

R. Paschotta, “Noise of mode-locked lasers. Part I: Numerical model,” Appl. Phys. B 79(2), 153–162 (2004).
[CrossRef]

2003 (1)

2002 (4)

M. E. Grein, L. A. Jiang, H. A. Haus, E. P. Ippen, C. McNeilage, J. H. Searls, and R. S. Windeler, “Observation of quantum-limited timing jitter in an active, harmonically mode-locked fiber laser,” Opt. Lett. 27(11), 957–959 (2002).
[CrossRef]

H. R. Telle, B. Lipphardt, and J. Stenger, “Kerr-lens mode-locked lasers as transfer oscillators for optical frequency measurements,” Appl. Phys. B 74(1), 1–6 (2002).
[CrossRef]

L. Krainer, R. Paschotta, G. J. Spühler, I. Klimov, C. Y. Teisset, K. J. Weingarten, and U. Keller, “Tunable picosecond pulse-generating laser with a repetition rate exceeding 10 GHz,” Electron. Lett. 38(5), 225–227 (2002).
[CrossRef]

T. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416(6877), 233–237 (2002).
[CrossRef] [PubMed]

1999 (2)

1996 (1)

1993 (2)

1985 (1)

P.-T. Ho, “Phase and amplitude fluctuations in a mode-locked laser,” IEEE J. Quantum Electron. QE 21(11), 1806–1813 (1985).
[CrossRef]

1984 (1)

1958 (1)

A. L. Schawlow and C. H. Townes, “Infrared and optical masers,” Phys. Rev. 112(6), 1940–1949 (1958).
[CrossRef]

Angelow, G.

Benkler, E.

Buckley, J. R.

F. Ö. Ilday, J. R. Buckley, W. G. Clark, and F. W. Wise, “Self-similar evolution of parabolic pulses in a laser,” Phys. Rev. Lett. 92(21), 213902–213905 (2004).
[CrossRef] [PubMed]

F. Ö. Ilday, J. R. Buckley, H. Lim, F. W. Wise, and W. G. Clark, “Generation of 50-fs, 5-nJ pulses at 1.03 μm from a wave-breaking-free fiber laser,” Opt. Lett. 28(15), 1365–1367 (2003).
[CrossRef] [PubMed]

Chen, Y.

Cho, S. H.

Chong, A.

Clark, W. G.

F. Ö. Ilday, J. R. Buckley, W. G. Clark, and F. W. Wise, “Self-similar evolution of parabolic pulses in a laser,” Phys. Rev. Lett. 92(21), 213902–213905 (2004).
[CrossRef] [PubMed]

F. Ö. Ilday, J. R. Buckley, H. Lim, F. W. Wise, and W. G. Clark, “Generation of 50-fs, 5-nJ pulses at 1.03 μm from a wave-breaking-free fiber laser,” Opt. Lett. 28(15), 1365–1367 (2003).
[CrossRef] [PubMed]

Fermann, M. E.

T. R. Schibli, I. Hartl, D. C. Yost, M. J. Martin, A. Marcinkevičius, M. E. Fermann, and J. Ye, “Optical frequency comb with submillihertz linewidth and more than 10 W average power,” Nat. Photonics 2(6), 355–359 (2008).
[CrossRef]

Fujimoto, J. G.

Gallmann, L.

Grein, M. E.

Hänsch, T. W.

T. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416(6877), 233–237 (2002).
[CrossRef] [PubMed]

Hartl, I.

T. R. Schibli, I. Hartl, D. C. Yost, M. J. Martin, A. Marcinkevičius, M. E. Fermann, and J. Ye, “Optical frequency comb with submillihertz linewidth and more than 10 W average power,” Nat. Photonics 2(6), 355–359 (2008).
[CrossRef]

Haus, H. A.

Ho, P.-T.

P.-T. Ho, “Phase and amplitude fluctuations in a mode-locked laser,” IEEE J. Quantum Electron. QE 21(11), 1806–1813 (1985).
[CrossRef]

Holzwarth, R.

T. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416(6877), 233–237 (2002).
[CrossRef] [PubMed]

Ilday, F. Ö.

F. Ö. Ilday, J. R. Buckley, W. G. Clark, and F. W. Wise, “Self-similar evolution of parabolic pulses in a laser,” Phys. Rev. Lett. 92(21), 213902–213905 (2004).
[CrossRef] [PubMed]

F. Ö. Ilday, J. R. Buckley, H. Lim, F. W. Wise, and W. G. Clark, “Generation of 50-fs, 5-nJ pulses at 1.03 μm from a wave-breaking-free fiber laser,” Opt. Lett. 28(15), 1365–1367 (2003).
[CrossRef] [PubMed]

Ippen, E. P.

Jiang, L. A.

Kärtner, F. X.

Keller, U.

R. Paschotta, A. Schlatter, S. C. Zeller, H. R. Telle, and U. Keller, “Optical phase noise and carrier–envelope offset noise of mode-locked lasers,” Appl. Phys. B 82(2), 265–273 (2006).
[CrossRef]

L. Krainer, R. Paschotta, G. J. Spühler, I. Klimov, C. Y. Teisset, K. J. Weingarten, and U. Keller, “Tunable picosecond pulse-generating laser with a repetition rate exceeding 10 GHz,” Electron. Lett. 38(5), 225–227 (2002).
[CrossRef]

D. H. Sutter, G. Steinmeyer, L. Gallmann, N. Matuschek, F. Morier-Genoud, U. Keller, V. Scheuer, G. Angelow, and T. Tschudi, “Semiconductor saturable-absorber mirror assisted Kerr-lens mode-locked Ti:sapphire laser producing pulses in the two-cycle regime,” Opt. Lett. 24(9), 631–633 (1999).
[CrossRef]

Klimov, I.

L. Krainer, R. Paschotta, G. J. Spühler, I. Klimov, C. Y. Teisset, K. J. Weingarten, and U. Keller, “Tunable picosecond pulse-generating laser with a repetition rate exceeding 10 GHz,” Electron. Lett. 38(5), 225–227 (2002).
[CrossRef]

Kracht, D.

Krainer, L.

L. Krainer, R. Paschotta, G. J. Spühler, I. Klimov, C. Y. Teisset, K. J. Weingarten, and U. Keller, “Tunable picosecond pulse-generating laser with a repetition rate exceeding 10 GHz,” Electron. Lett. 38(5), 225–227 (2002).
[CrossRef]

Lim, H.

Lipphardt, B.

H. R. Telle, B. Lipphardt, and J. Stenger, “Kerr-lens mode-locked lasers as transfer oscillators for optical frequency measurements,” Appl. Phys. B 74(1), 1–6 (2002).
[CrossRef]

Marcinkevicius, A.

T. R. Schibli, I. Hartl, D. C. Yost, M. J. Martin, A. Marcinkevičius, M. E. Fermann, and J. Ye, “Optical frequency comb with submillihertz linewidth and more than 10 W average power,” Nat. Photonics 2(6), 355–359 (2008).
[CrossRef]

Martin, M. J.

T. R. Schibli, I. Hartl, D. C. Yost, M. J. Martin, A. Marcinkevičius, M. E. Fermann, and J. Ye, “Optical frequency comb with submillihertz linewidth and more than 10 W average power,” Nat. Photonics 2(6), 355–359 (2008).
[CrossRef]

Matuschek, N.

McNeilage, C.

Mecozzi, A.

H. A. Haus and A. Mecozzi, “Noise of mode-locked lasers,” IEEE J. Quantum Electron. 29(3), 983–996 (1993).
[CrossRef]

Mollenauer, L. F.

Morgner, U.

Morier-Genoud, F.

Namiki, S.

Nelson, L. E.

Neumann, J.

Paschotta, R.

O. Prochnow, R. Paschotta, E. Benkler, U. Morgner, J. Neumann, D. Wandt, and D. Kracht, “Quantum-limited noise performance of a femtosecond all-fiber ytterbium laser,” Opt. Express 17(18), 15525–15533 (2009), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-17-18-15525 .
[CrossRef] [PubMed]

R. Paschotta, A. Schlatter, S. C. Zeller, H. R. Telle, and U. Keller, “Optical phase noise and carrier–envelope offset noise of mode-locked lasers,” Appl. Phys. B 82(2), 265–273 (2006).
[CrossRef]

R. Paschotta, “Noise of mode-locked lasers. Part I: Numerical model,” Appl. Phys. B 79(2), 153–162 (2004).
[CrossRef]

R. Paschotta, “Noise of mode-locked lasers. Part II: Timing jitter and other fluctuations,” Appl. Phys. B 79(2), 163–173 (2004).
[CrossRef]

L. Krainer, R. Paschotta, G. J. Spühler, I. Klimov, C. Y. Teisset, K. J. Weingarten, and U. Keller, “Tunable picosecond pulse-generating laser with a repetition rate exceeding 10 GHz,” Electron. Lett. 38(5), 225–227 (2002).
[CrossRef]

Prochnow, O.

Renninger, W. H.

Schawlow, A. L.

A. L. Schawlow and C. H. Townes, “Infrared and optical masers,” Phys. Rev. 112(6), 1940–1949 (1958).
[CrossRef]

Scheuer, V.

Schibli, T. R.

T. R. Schibli, I. Hartl, D. C. Yost, M. J. Martin, A. Marcinkevičius, M. E. Fermann, and J. Ye, “Optical frequency comb with submillihertz linewidth and more than 10 W average power,” Nat. Photonics 2(6), 355–359 (2008).
[CrossRef]

Schlatter, A.

R. Paschotta, A. Schlatter, S. C. Zeller, H. R. Telle, and U. Keller, “Optical phase noise and carrier–envelope offset noise of mode-locked lasers,” Appl. Phys. B 82(2), 265–273 (2006).
[CrossRef]

Searls, J. H.

Spühler, G. J.

L. Krainer, R. Paschotta, G. J. Spühler, I. Klimov, C. Y. Teisset, K. J. Weingarten, and U. Keller, “Tunable picosecond pulse-generating laser with a repetition rate exceeding 10 GHz,” Electron. Lett. 38(5), 225–227 (2002).
[CrossRef]

Steinmeyer, G.

Stenger, J.

H. R. Telle, B. Lipphardt, and J. Stenger, “Kerr-lens mode-locked lasers as transfer oscillators for optical frequency measurements,” Appl. Phys. B 74(1), 1–6 (2002).
[CrossRef]

Stolen, R. H.

Sutter, D. H.

Tamura, K.

Teisset, C. Y.

L. Krainer, R. Paschotta, G. J. Spühler, I. Klimov, C. Y. Teisset, K. J. Weingarten, and U. Keller, “Tunable picosecond pulse-generating laser with a repetition rate exceeding 10 GHz,” Electron. Lett. 38(5), 225–227 (2002).
[CrossRef]

Telle, H. R.

R. Paschotta, A. Schlatter, S. C. Zeller, H. R. Telle, and U. Keller, “Optical phase noise and carrier–envelope offset noise of mode-locked lasers,” Appl. Phys. B 82(2), 265–273 (2006).
[CrossRef]

H. R. Telle, B. Lipphardt, and J. Stenger, “Kerr-lens mode-locked lasers as transfer oscillators for optical frequency measurements,” Appl. Phys. B 74(1), 1–6 (2002).
[CrossRef]

Townes, C. H.

A. L. Schawlow and C. H. Townes, “Infrared and optical masers,” Phys. Rev. 112(6), 1940–1949 (1958).
[CrossRef]

Tschudi, T.

Udem, T.

T. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416(6877), 233–237 (2002).
[CrossRef] [PubMed]

Wandt, D.

Weingarten, K. J.

L. Krainer, R. Paschotta, G. J. Spühler, I. Klimov, C. Y. Teisset, K. J. Weingarten, and U. Keller, “Tunable picosecond pulse-generating laser with a repetition rate exceeding 10 GHz,” Electron. Lett. 38(5), 225–227 (2002).
[CrossRef]

Windeler, R. S.

Wise, F. W.

Ye, J.

T. R. Schibli, I. Hartl, D. C. Yost, M. J. Martin, A. Marcinkevičius, M. E. Fermann, and J. Ye, “Optical frequency comb with submillihertz linewidth and more than 10 W average power,” Nat. Photonics 2(6), 355–359 (2008).
[CrossRef]

Yost, D. C.

T. R. Schibli, I. Hartl, D. C. Yost, M. J. Martin, A. Marcinkevičius, M. E. Fermann, and J. Ye, “Optical frequency comb with submillihertz linewidth and more than 10 W average power,” Nat. Photonics 2(6), 355–359 (2008).
[CrossRef]

Yu, C. X.

Zeller, S. C.

R. Paschotta, A. Schlatter, S. C. Zeller, H. R. Telle, and U. Keller, “Optical phase noise and carrier–envelope offset noise of mode-locked lasers,” Appl. Phys. B 82(2), 265–273 (2006).
[CrossRef]

Appl. Phys. B (4)

R. Paschotta, “Noise of mode-locked lasers. Part II: Timing jitter and other fluctuations,” Appl. Phys. B 79(2), 163–173 (2004).
[CrossRef]

R. Paschotta, A. Schlatter, S. C. Zeller, H. R. Telle, and U. Keller, “Optical phase noise and carrier–envelope offset noise of mode-locked lasers,” Appl. Phys. B 82(2), 265–273 (2006).
[CrossRef]

H. R. Telle, B. Lipphardt, and J. Stenger, “Kerr-lens mode-locked lasers as transfer oscillators for optical frequency measurements,” Appl. Phys. B 74(1), 1–6 (2002).
[CrossRef]

R. Paschotta, “Noise of mode-locked lasers. Part I: Numerical model,” Appl. Phys. B 79(2), 153–162 (2004).
[CrossRef]

Electron. Lett. (1)

L. Krainer, R. Paschotta, G. J. Spühler, I. Klimov, C. Y. Teisset, K. J. Weingarten, and U. Keller, “Tunable picosecond pulse-generating laser with a repetition rate exceeding 10 GHz,” Electron. Lett. 38(5), 225–227 (2002).
[CrossRef]

IEEE J. Quantum Electron. (1)

H. A. Haus and A. Mecozzi, “Noise of mode-locked lasers,” IEEE J. Quantum Electron. 29(3), 983–996 (1993).
[CrossRef]

IEEE J. Quantum Electron. QE (1)

P.-T. Ho, “Phase and amplitude fluctuations in a mode-locked laser,” IEEE J. Quantum Electron. QE 21(11), 1806–1813 (1985).
[CrossRef]

J. Opt. Soc. Am. B (2)

Nat. Photonics (1)

T. R. Schibli, I. Hartl, D. C. Yost, M. J. Martin, A. Marcinkevičius, M. E. Fermann, and J. Ye, “Optical frequency comb with submillihertz linewidth and more than 10 W average power,” Nat. Photonics 2(6), 355–359 (2008).
[CrossRef]

Nature (1)

T. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416(6877), 233–237 (2002).
[CrossRef] [PubMed]

Opt. Express (1)

Opt. Lett. (6)

Phys. Rev. (1)

A. L. Schawlow and C. H. Townes, “Infrared and optical masers,” Phys. Rev. 112(6), 1940–1949 (1958).
[CrossRef]

Phys. Rev. Lett. (1)

F. Ö. Ilday, J. R. Buckley, W. G. Clark, and F. W. Wise, “Self-similar evolution of parabolic pulses in a laser,” Phys. Rev. Lett. 92(21), 213902–213905 (2004).
[CrossRef] [PubMed]

Other (1)

R. Paschotta, H. R. Telle, and U. Keller, Noise of Solid State Lasers (CRC Press, Boca Raton, 2007), Chap. 12.

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Figures (4)

Fig. 1
Fig. 1

Schematic setup of a stretched-pulse laser as assumed for the numerical model.

Fig. 2
Fig. 2

Simulated timing phase noise for a stretched-pulse fiber laser (dots), compared with analytical estimates (lines) based on the minimum and maximum pulse duration occurring within the laser resonator. The simulated data have been averaged over 8 simulation runs.

Fig. 3
Fig. 3

Simulated timing phase noise of a wavebreaking-free fiber laser. For noise frequencies below 5 MHz, the timing jitter is substantially stronger than according to estimates based on a simplified analytical model. The solid and dashed lines show the jitter with and without the effect of center frequency fluctuations, respectively, according to the analytical model.

Fig. 4
Fig. 4

Numerically simulated noise of the optical center frequency (normalized to the mean frequency) of a wavebreaking-free fiber laser. For noise frequencies below 5 MHz, this noise is much stronger than expected from a simple analytical model (solid curve). This largely explains why the timing jitter is also stronger.

Equations (14)

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

S Δ t ,direct ( f ) 0.53 θ h ν E p l tot T rt τ p 2 1 ( 2 π f ) 2
S Δ t ,indirect ( f ) = ( D 2 f T rt ) 2 S ν c ( f )
S ν c ( f ) 0.53 1 ( 2 π f ) 2 + τ ν c 2 θ h ν E p l tot T rt Δ ν p 2
τ ν c 0.47 T rt g ( Δ ν g Δ ν p ) 2 .
τ ν c = T rt ( Δ ν f Δ ν p ) 2 .
Δ ν ST = θ h ν l tot 4 π T rt 2 P int .
Δ ν ST = 1 4 π θ h ν E p l tot T rt
S φ opt,ST ( f ) = 1 8 π 2 θ h ν E p l tot T rt 1 f 2 .
T rt φ t = φ nl δ E p E p .
S φ ,nl ( f ) = ( φ nl 2 π f T rt ) 2 S I ( f )
S I ( f ) = θ h ν E p / T rt
S φ ,nl ( f ) = ( φ nl 2 π f ) 2 θ h ν E p 1 T rt .
S φ ,nl ( f ) S φ opt,ST ( f ) = 2 φ nl 2 l tot .
0 g d x E p,fin e x = 1 e g E p,fin = e g 1 E p,fout

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