Abstract

We investigated the frequency noise in the distributed Bragg reflector single-frequency fiber laser (DBR-SFFL) theoretically and experimentally. A complete theoretical analysis is demonstrated by considering the energy-transfer upconversion (ETU) process and establishing linkages between the frequency noise and the relative intensity noise (RIN) of the DBR-SFFL. The experimental results of the diverse DBR-SFFLs in different working conditions are in good agreement with the theoretical analyses. These investigations are beneficial to optimizing frequency noise property to promote the wide application of the DBR-SFFLs. The proposed results can be generally applicable to the short-linear-cavity SFFL with centimeters order of the cavity length.

© 2017 Optical Society of America

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2016 (1)

2015 (1)

2014 (2)

R. P. M. J. W. Notermans and W. Vassen, “High-Precision Spectroscopy of the Forbidden 2 3s1→2 1p1 Transition in Quantum Degenerate Metastable Helium,” Phys. Rev. Lett. 112(25), 253002 (2014).
[Crossref] [PubMed]

S. Mo, X. Huang, S. Xu, C. Li, C. Yang, Z. Feng, W. Zhang, D. Chen, and Z. Yang, “600-Hz linewidth short-linear-cavity fiber laser,” Opt. Lett. 39(20), 5818–5821 (2014).
[Crossref] [PubMed]

2013 (4)

T. Wu, X. Peng, W. Gong, Y. Zhan, Z. Lin, B. Luo, and H. Guo, “Observation and optimization of 4He atomic polarization spectroscopy,” Opt. Lett. 38(6), 986–988 (2013).
[Crossref] [PubMed]

S. Mo, Z. Feng, S. Xu, W. Zhang, D. Chen, T. Yang, W. Fan, C. Li, C. Yang, and Z. Yang, “Microwave signal generation from a dual-wavelength single-frequency highly co-doped phosphate fiber laser,” IEEE Photonics J. 5(6), 5502306 (2013).
[Crossref]

C. Li, S. Xu, C. Yang, X. Wei, and Z. Yang, “Frequency noise of high-gain phosphate fiber single-frequency laser,” Laser Phys. 23(4), 045107 (2013).
[Crossref]

W. Yue, Y. Wang, C.-D. Xiong, Z.-Y. Wang, and Q. Qiu, “Intensity noise of erbium-doped fiber laser based on full quantum theory,” J. Opt. Soc. Am. B 30(2), 275–281 (2013).
[Crossref]

2012 (2)

2011 (3)

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s−1 line- rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[Crossref]

Y. Y. Jiang, A. D. Ludlow, N. D. Lemke, R. W. Fox, J. A. Sherman, L.-S. Ma, and C. W. Oates, “Making optical atomic clocks more stable with 10−16-level laser stabilization,” Nat. Photonics 5(3), 158–161 (2011).
[Crossref]

S. Xu, Z. Yang, W. Zhang, X. Wei, Q. Qian, D. Chen, Q. Zhang, S. Shen, M. Peng, and J. Qiu, “400 mW ultrashort cavity low-noise single-frequency Yb3+-doped phosphate fiber laser,” Opt. Lett. 36(18), 3708–3710 (2011).
[Crossref] [PubMed]

2010 (2)

S. B. Foster and A. E. Tikhomirov, “Pump-noise contribution to frequency noise and linewidth of distributed-feedback fiber lasers,” IEEE J. Quantum Electron. 46(5), 734–741 (2010).
[Crossref]

S. H. Xu, Z. M. Yang, T. Liu, W. N. Zhang, Z. M. Feng, Q. Y. Zhang, and Z. H. Jiang, “An efficient compact 300 mW narrow-linewidth single frequency fiber laser at 1.5 µm,” Opt. Express 18(2), 1249–1254 (2010).
[Crossref] [PubMed]

2009 (2)

S. Foster, G. A. Cranch, and A. Tikhomirov, “Experimental evidence for the thermal origin of 1/f frequency noise in erbium-doped fiber lasers,” Phys. Rev. A 79(5), 053802 (2009).
[Crossref]

T. Liu, Z. M. Yang, and S. H. Xu, “3-Dimensional heat analysis in short-length Er3+/Yb3+ co-doped phosphate fiber laser with upconversion,” Opt. Express 17(1), 235–247 (2009).
[Crossref] [PubMed]

2006 (2)

P. Horak, N. Y. Voo, M. Ibsen, and W. H. Loh, “Pump-noise-induced linewidth contributions in distributed feedback fiber lasers,” IEEE Photonics Technol. Lett. 18(9), 998–1000 (2006).
[Crossref]

K. Somiya, Y. Chen, S. Kawamura, and N. Mio, “Frequency noise and intensity noise of next-generation gravitational-wave detectors with RF/DC readout schemes,” Phys. Rev. D Part. Fields Gravit. Cosmol. 73(12), 122005 (2006).
[Crossref]

2005 (1)

C. Jacinto, T. Catunda, D. Jaque, and J. G. Solé, “Fluorescence quantum efficiency and Auger upconversion losses of the stoichiometric laser crystal NdAl3 (BO3)4,” Phys. Rev. B 72(23), 235111 (2005).
[Crossref]

2004 (2)

2001 (1)

E. Rønnekleiv, “Frequency and intensity noise of single frequency fiber Bragg grating lasers,” Opt. Fiber Technol. 7(3), 206–235 (2001).
[Crossref]

2000 (2)

B.-C. Hwang, S. Jiang, T. Luo, J. Watson, G. Sorbello, and N. Peyghambarian, “Cooperative upconversion and energy transfer of new high Er3+-and Yb3+-Er3+-doped phosphate glasses,” J. Opt. Soc. Am. B 17(5), 833–839 (2000).
[Crossref]

D. L. Veasey, D. S. Funk, P. M. Peters, N. A. Sanford, G. E. Obarski, N. Fontaine, M. Young, A. P. Peskin, W.-C. Liu, S. N. Houde-Walter, and J. S. Hayden, “Yb/Er-codoped and Yb-doped waveguide lasers in phosphate glass,” J. Non-Cryst. Solids 263, 369–381 (2000).
[Crossref]

1999 (1)

1998 (1)

S. Taccheo, P. Laporta, O. Svelto, and G. De Geronimo, “Theoretical and experimental analysis of intensity noise in a codoped erbium–ytterbium glass laser,” Appl. Phys. B 66(1), 19–26 (1998).
[Crossref]

Agger, S.

Becker, J.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s−1 line- rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[Crossref]

Ben Ezra, S.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s−1 line- rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[Crossref]

Bjurshagen, S.

Bonk, R.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s−1 line- rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[Crossref]

Catunda, T.

C. Jacinto, T. Catunda, D. Jaque, and J. G. Solé, “Fluorescence quantum efficiency and Auger upconversion losses of the stoichiometric laser crystal NdAl3 (BO3)4,” Phys. Rev. B 72(23), 235111 (2005).
[Crossref]

Chen, D.

Chen, Y.

K. Somiya, Y. Chen, S. Kawamura, and N. Mio, “Frequency noise and intensity noise of next-generation gravitational-wave detectors with RF/DC readout schemes,” Phys. Rev. D Part. Fields Gravit. Cosmol. 73(12), 122005 (2006).
[Crossref]

Cranch, G. A.

S. Foster, G. A. Cranch, and A. Tikhomirov, “Experimental evidence for the thermal origin of 1/f frequency noise in erbium-doped fiber lasers,” Phys. Rev. A 79(5), 053802 (2009).
[Crossref]

De Geronimo, G.

S. Taccheo, P. Laporta, O. Svelto, and G. De Geronimo, “Theoretical and experimental analysis of intensity noise in a codoped erbium–ytterbium glass laser,” Appl. Phys. B 66(1), 19–26 (1998).
[Crossref]

Deng, H.

Dreschmann, M.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s−1 line- rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[Crossref]

Ellermeyer, T.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s−1 line- rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[Crossref]

Fan, W.

S. Mo, Z. Feng, S. Xu, W. Zhang, D. Chen, T. Yang, W. Fan, C. Li, C. Yang, and Z. Yang, “Microwave signal generation from a dual-wavelength single-frequency highly co-doped phosphate fiber laser,” IEEE Photonics J. 5(6), 5502306 (2013).
[Crossref]

Feng, Z.

Feng, Z. M.

Fontaine, N.

D. L. Veasey, D. S. Funk, P. M. Peters, N. A. Sanford, G. E. Obarski, N. Fontaine, M. Young, A. P. Peskin, W.-C. Liu, S. N. Houde-Walter, and J. S. Hayden, “Yb/Er-codoped and Yb-doped waveguide lasers in phosphate glass,” J. Non-Cryst. Solids 263, 369–381 (2000).
[Crossref]

Foster, S.

S. Foster, “Low-frequency thermal noise in optical fiber cavities,” Phys. Rev. A 86(4), 043801 (2012).
[Crossref]

S. Foster, G. A. Cranch, and A. Tikhomirov, “Experimental evidence for the thermal origin of 1/f frequency noise in erbium-doped fiber lasers,” Phys. Rev. A 79(5), 053802 (2009).
[Crossref]

Foster, S. B.

S. B. Foster and A. E. Tikhomirov, “Pump-noise contribution to frequency noise and linewidth of distributed-feedback fiber lasers,” IEEE J. Quantum Electron. 46(5), 734–741 (2010).
[Crossref]

Fox, R. W.

Y. Y. Jiang, A. D. Ludlow, N. D. Lemke, R. W. Fox, J. A. Sherman, L.-S. Ma, and C. W. Oates, “Making optical atomic clocks more stable with 10−16-level laser stabilization,” Nat. Photonics 5(3), 158–161 (2011).
[Crossref]

Freude, W.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s−1 line- rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[Crossref]

Frey, F.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s−1 line- rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[Crossref]

Funk, D. S.

D. L. Veasey, D. S. Funk, P. M. Peters, N. A. Sanford, G. E. Obarski, N. Fontaine, M. Young, A. P. Peskin, W.-C. Liu, S. N. Houde-Walter, and J. S. Hayden, “Yb/Er-codoped and Yb-doped waveguide lasers in phosphate glass,” J. Non-Cryst. Solids 263, 369–381 (2000).
[Crossref]

Gan, J.

Gong, W.

Guo, H.

Hardy, A.

Hayden, J. S.

D. L. Veasey, D. S. Funk, P. M. Peters, N. A. Sanford, G. E. Obarski, N. Fontaine, M. Young, A. P. Peskin, W.-C. Liu, S. N. Houde-Walter, and J. S. Hayden, “Yb/Er-codoped and Yb-doped waveguide lasers in phosphate glass,” J. Non-Cryst. Solids 263, 369–381 (2000).
[Crossref]

Hillerkuss, D.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s−1 line- rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[Crossref]

Hoh, M.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s−1 line- rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[Crossref]

Horak, P.

P. Horak, N. Y. Voo, M. Ibsen, and W. H. Loh, “Pump-noise-induced linewidth contributions in distributed feedback fiber lasers,” IEEE Photonics Technol. Lett. 18(9), 998–1000 (2006).
[Crossref]

Houde-Walter, S. N.

D. L. Veasey, D. S. Funk, P. M. Peters, N. A. Sanford, G. E. Obarski, N. Fontaine, M. Young, A. P. Peskin, W.-C. Liu, S. N. Houde-Walter, and J. S. Hayden, “Yb/Er-codoped and Yb-doped waveguide lasers in phosphate glass,” J. Non-Cryst. Solids 263, 369–381 (2000).
[Crossref]

Huang, X.

Huber, G.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s−1 line- rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[Crossref]

Huebner, M.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s−1 line- rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[Crossref]

Hwang, B.-C.

Ibsen, M.

P. Horak, N. Y. Voo, M. Ibsen, and W. H. Loh, “Pump-noise-induced linewidth contributions in distributed feedback fiber lasers,” IEEE Photonics Technol. Lett. 18(9), 998–1000 (2006).
[Crossref]

Jacinto, C.

C. Jacinto, T. Catunda, D. Jaque, and J. G. Solé, “Fluorescence quantum efficiency and Auger upconversion losses of the stoichiometric laser crystal NdAl3 (BO3)4,” Phys. Rev. B 72(23), 235111 (2005).
[Crossref]

Jaque, D.

C. Jacinto, T. Catunda, D. Jaque, and J. G. Solé, “Fluorescence quantum efficiency and Auger upconversion losses of the stoichiometric laser crystal NdAl3 (BO3)4,” Phys. Rev. B 72(23), 235111 (2005).
[Crossref]

Jiang, S.

Jiang, Y. Y.

Y. Y. Jiang, A. D. Ludlow, N. D. Lemke, R. W. Fox, J. A. Sherman, L.-S. Ma, and C. W. Oates, “Making optical atomic clocks more stable with 10−16-level laser stabilization,” Nat. Photonics 5(3), 158–161 (2011).
[Crossref]

Jiang, Z. H.

Jordan, M.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s−1 line- rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[Crossref]

Kawamura, S.

K. Somiya, Y. Chen, S. Kawamura, and N. Mio, “Frequency noise and intensity noise of next-generation gravitational-wave detectors with RF/DC readout schemes,” Phys. Rev. D Part. Fields Gravit. Cosmol. 73(12), 122005 (2006).
[Crossref]

Kelson, I.

Kleinow, P.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s−1 line- rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[Crossref]

Koch, R.

Koenig, S.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s−1 line- rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[Crossref]

Koos, C.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s−1 line- rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[Crossref]

Laporta, P.

S. Taccheo, P. Laporta, O. Svelto, and G. De Geronimo, “Theoretical and experimental analysis of intensity noise in a codoped erbium–ytterbium glass laser,” Appl. Phys. B 66(1), 19–26 (1998).
[Crossref]

Lemke, N. D.

Y. Y. Jiang, A. D. Ludlow, N. D. Lemke, R. W. Fox, J. A. Sherman, L.-S. Ma, and C. W. Oates, “Making optical atomic clocks more stable with 10−16-level laser stabilization,” Nat. Photonics 5(3), 158–161 (2011).
[Crossref]

Leuthold, J.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s−1 line- rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[Crossref]

Li, C.

Li, J.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s−1 line- rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[Crossref]

Lin, W.

Lin, Z.

Liu, T.

Liu, W.-C.

D. L. Veasey, D. S. Funk, P. M. Peters, N. A. Sanford, G. E. Obarski, N. Fontaine, M. Young, A. P. Peskin, W.-C. Liu, S. N. Houde-Walter, and J. S. Hayden, “Yb/Er-codoped and Yb-doped waveguide lasers in phosphate glass,” J. Non-Cryst. Solids 263, 369–381 (2000).
[Crossref]

Loh, W. H.

P. Horak, N. Y. Voo, M. Ibsen, and W. H. Loh, “Pump-noise-induced linewidth contributions in distributed feedback fiber lasers,” IEEE Photonics Technol. Lett. 18(9), 998–1000 (2006).
[Crossref]

Ludlow, A. D.

Y. Y. Jiang, A. D. Ludlow, N. D. Lemke, R. W. Fox, J. A. Sherman, L.-S. Ma, and C. W. Oates, “Making optical atomic clocks more stable with 10−16-level laser stabilization,” Nat. Photonics 5(3), 158–161 (2011).
[Crossref]

Ludwig, A.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s−1 line- rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[Crossref]

Luo, B.

Luo, T.

Lutz, J.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s−1 line- rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[Crossref]

Ma, L.-S.

Y. Y. Jiang, A. D. Ludlow, N. D. Lemke, R. W. Fox, J. A. Sherman, L.-S. Ma, and C. W. Oates, “Making optical atomic clocks more stable with 10−16-level laser stabilization,” Nat. Photonics 5(3), 158–161 (2011).
[Crossref]

Ma, Y.

Marculescu, A.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s−1 line- rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[Crossref]

Meyer, J.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s−1 line- rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[Crossref]

Mio, N.

K. Somiya, Y. Chen, S. Kawamura, and N. Mio, “Frequency noise and intensity noise of next-generation gravitational-wave detectors with RF/DC readout schemes,” Phys. Rev. D Part. Fields Gravit. Cosmol. 73(12), 122005 (2006).
[Crossref]

Mo, S.

S. Mo, X. Huang, S. Xu, C. Li, C. Yang, Z. Feng, W. Zhang, D. Chen, and Z. Yang, “600-Hz linewidth short-linear-cavity fiber laser,” Opt. Lett. 39(20), 5818–5821 (2014).
[Crossref] [PubMed]

S. Mo, Z. Feng, S. Xu, W. Zhang, D. Chen, T. Yang, W. Fan, C. Li, C. Yang, and Z. Yang, “Microwave signal generation from a dual-wavelength single-frequency highly co-doped phosphate fiber laser,” IEEE Photonics J. 5(6), 5502306 (2013).
[Crossref]

Moeller, M.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s−1 line- rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[Crossref]

Narkiss, N.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s−1 line- rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[Crossref]

Nebendahl, B.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s−1 line- rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[Crossref]

Notermans, R. P. M. J. W.

R. P. M. J. W. Notermans and W. Vassen, “High-Precision Spectroscopy of the Forbidden 2 3s1→2 1p1 Transition in Quantum Degenerate Metastable Helium,” Phys. Rev. Lett. 112(25), 253002 (2014).
[Crossref] [PubMed]

Oates, C. W.

Y. Y. Jiang, A. D. Ludlow, N. D. Lemke, R. W. Fox, J. A. Sherman, L.-S. Ma, and C. W. Oates, “Making optical atomic clocks more stable with 10−16-level laser stabilization,” Nat. Photonics 5(3), 158–161 (2011).
[Crossref]

Obarski, G. E.

D. L. Veasey, D. S. Funk, P. M. Peters, N. A. Sanford, G. E. Obarski, N. Fontaine, M. Young, A. P. Peskin, W.-C. Liu, S. N. Houde-Walter, and J. S. Hayden, “Yb/Er-codoped and Yb-doped waveguide lasers in phosphate glass,” J. Non-Cryst. Solids 263, 369–381 (2000).
[Crossref]

Oehler, A.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s−1 line- rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[Crossref]

Parmigiani, F.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s−1 line- rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[Crossref]

Peng, M.

Peng, X.

Peskin, A. P.

D. L. Veasey, D. S. Funk, P. M. Peters, N. A. Sanford, G. E. Obarski, N. Fontaine, M. Young, A. P. Peskin, W.-C. Liu, S. N. Houde-Walter, and J. S. Hayden, “Yb/Er-codoped and Yb-doped waveguide lasers in phosphate glass,” J. Non-Cryst. Solids 263, 369–381 (2000).
[Crossref]

Peters, P. M.

D. L. Veasey, D. S. Funk, P. M. Peters, N. A. Sanford, G. E. Obarski, N. Fontaine, M. Young, A. P. Peskin, W.-C. Liu, S. N. Houde-Walter, and J. S. Hayden, “Yb/Er-codoped and Yb-doped waveguide lasers in phosphate glass,” J. Non-Cryst. Solids 263, 369–381 (2000).
[Crossref]

Petropoulos, P.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s−1 line- rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[Crossref]

Peyghambarian, N.

Povlsen, J. H.

Qian, Q.

Qiu, J.

Qiu, Q.

Resan, B.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s−1 line- rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[Crossref]

Roeger, M.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s−1 line- rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[Crossref]

Rønnekleiv, E.

E. Rønnekleiv, “Frequency and intensity noise of single frequency fiber Bragg grating lasers,” Opt. Fiber Technol. 7(3), 206–235 (2001).
[Crossref]

Sanford, N. A.

D. L. Veasey, D. S. Funk, P. M. Peters, N. A. Sanford, G. E. Obarski, N. Fontaine, M. Young, A. P. Peskin, W.-C. Liu, S. N. Houde-Walter, and J. S. Hayden, “Yb/Er-codoped and Yb-doped waveguide lasers in phosphate glass,” J. Non-Cryst. Solids 263, 369–381 (2000).
[Crossref]

Schellinger, T.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s−1 line- rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[Crossref]

Schmogrow, R.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s−1 line- rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[Crossref]

Shen, S.

Sherman, J. A.

Y. Y. Jiang, A. D. Ludlow, N. D. Lemke, R. W. Fox, J. A. Sherman, L.-S. Ma, and C. W. Oates, “Making optical atomic clocks more stable with 10−16-level laser stabilization,” Nat. Photonics 5(3), 158–161 (2011).
[Crossref]

Solé, J. G.

C. Jacinto, T. Catunda, D. Jaque, and J. G. Solé, “Fluorescence quantum efficiency and Auger upconversion losses of the stoichiometric laser crystal NdAl3 (BO3)4,” Phys. Rev. B 72(23), 235111 (2005).
[Crossref]

Somiya, K.

K. Somiya, Y. Chen, S. Kawamura, and N. Mio, “Frequency noise and intensity noise of next-generation gravitational-wave detectors with RF/DC readout schemes,” Phys. Rev. D Part. Fields Gravit. Cosmol. 73(12), 122005 (2006).
[Crossref]

Sorbello, G.

Su, R.

Svelto, O.

S. Taccheo, P. Laporta, O. Svelto, and G. De Geronimo, “Theoretical and experimental analysis of intensity noise in a codoped erbium–ytterbium glass laser,” Appl. Phys. B 66(1), 19–26 (1998).
[Crossref]

Taccheo, S.

S. Taccheo, P. Laporta, O. Svelto, and G. De Geronimo, “Theoretical and experimental analysis of intensity noise in a codoped erbium–ytterbium glass laser,” Appl. Phys. B 66(1), 19–26 (1998).
[Crossref]

Tikhomirov, A.

S. Foster, G. A. Cranch, and A. Tikhomirov, “Experimental evidence for the thermal origin of 1/f frequency noise in erbium-doped fiber lasers,” Phys. Rev. A 79(5), 053802 (2009).
[Crossref]

Tikhomirov, A. E.

S. B. Foster and A. E. Tikhomirov, “Pump-noise contribution to frequency noise and linewidth of distributed-feedback fiber lasers,” IEEE J. Quantum Electron. 46(5), 734–741 (2010).
[Crossref]

Vallaitis, T.

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Appl. Opt. (1)

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[Crossref]

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D. L. Veasey, D. S. Funk, P. M. Peters, N. A. Sanford, G. E. Obarski, N. Fontaine, M. Young, A. P. Peskin, W.-C. Liu, S. N. Houde-Walter, and J. S. Hayden, “Yb/Er-codoped and Yb-doped waveguide lasers in phosphate glass,” J. Non-Cryst. Solids 263, 369–381 (2000).
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[Crossref] [PubMed]

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Figures (6)

Fig. 1
Fig. 1

The simulated frequency noise spectra of the DBR-SFFL with a 1.7 cm long active fiber versus different pump powers Pp with ETU (a) and without ETU (b). The inset in (a) is the total heat transformation Ω versus the pump power Pp.

Fig. 2
Fig. 2

The simulated frequency noise spectra of the DBR-SFFLs pumping by 200 mW versus different lengths of the active fiber l with ETU (a) and without ETU (b). The inset in (a) is the fractional thermal loading η at different lengths of the active fiber l.

Fig. 3
Fig. 3

The simulated frequency noise spectra of the DBR-SFFL pumping by 200 mW with a 1.7 cm long active fiber with different RINFL with ETU.

Fig. 4
Fig. 4

Experimental scheme of the DBR-SFFL and the measurement equipment of the frequency noise.

Fig. 5
Fig. 5

The calculated and tested frequency noise spectra of the DBR-SFFL with 1.7 cm long active fiber with the pump power Pp of 169 mW (a), 225 mW (b), 279 mW (c) and the comprehensively tested frequency noise spectrum (d). The inset is the measured RINFL spectrum versus the pump power Pp.

Fig. 6
Fig. 6

The calculated and tested frequency noise spectra of the DBR-SFFL pumping by 225 mW with different lengths of the active fiber of 1.4 cm (a), 1.7 cm (b), 2.0 cm (c), 2.3 cm (d), 2.6 cm (e) and the comprehensively tested frequency noise spectrum (f). The inset is the measured RINFL spectrum.

Tables (1)

Tables Icon

Table 1 The related parameters used in this article

Equations (15)

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Q(z,r,t)= α ap ηP(t)h(z) | e(r) | 2 .
0 2π 0 ω p r | e(r) | 2 drdθ =1.
| e(r) | 2 = 2 π ω p 2 exp( 2 r 2 ω p 2 ).
T(f,z)=Θ(f)P(f)N(z)= P(f)N(z) 4 π 2 k t 0 exp( ω p 2 k 2 /4)k k 2 +2i k 1 2 dk.
Θ(f)= exp(i ω p 2 c v f/4 k t ) 8 π 2 k t E 1 [i ω p 2 c v f/4 k t ].
Δν(f)=νq 0 l ΔT(f,z)dz =νq 0 l Δ[Θ(f)P(f)N(z)]dz .
S v (f)= v 2 q 2 [Θ(f)] 2 S p (f) [ 0 l N(z)dz ] 2 = v 2 q 2 [Θ(f)] 2 P p 2 RI N p (f) [ 0 l N(z)dz ] 2 .
Ω= P p 0 l N(z) dz= P p 0 l α ap ηh(z) dz.
h(z) dz =γh(z).
h(z)=h(0)exp(γz).
η= F ETU +[1 F ETU ](1 λ p / λ s ).
F ETU =1 2 1+ [ 1+ 4W τ 2 R r p +4W τ 2 cσ n N a 0 Φ ϕ 0 ( 1+ cστ n f c Φ ϕ 0 ) 2 ] 1/2 .
Ω= α ap η P p 1 γ (1exp(γl)).
S v (f)= v 2 q 2 [Θ(f)] 2 [ α ap η P p 1 γ (1exp(γl))] 2 RI N p (f).
S v (f)= v 2 q 2 [Θ(f)] 2 [ α ap η P p 1 γ (1exp(γl))] 2 RI N FL (f).

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