Abstract

Laser frequency fluctuations can be characterized either comprehensively by the frequency noise spectrum or in a simple but incomplete manner by the laser linewidth. A formal relation exists to calculate the linewidth from the frequency noise spectrum, but it is laborious to apply in practice. We recently proposed a much simpler geometrical approximation applicable to any arbitrary frequency noise spectrum. Here we present an experimental validation of this approximation using laser sources of different spectral characteristics. For each of them, we measured both the frequency noise spectrum to calculate the approximate linewidth and the actual linewidth directly. We observe a very good agreement between the approximate and directly measured linewidths over a broad range of values (from kilohertz to megahertz) and for significantly different laser line shapes.

© 2012 Optical Society of America

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  1. S. Spiessberger, M. Schiemangk, A. Wicht, H. Wenzel, G. Erbert, and G. Tränkle, “DBR laser diodes emitting near 1064 nm with a narrow intrinsic linewidth of 2 kHz,” Appl. Phys. B 104, 813–818 (2011).
    [CrossRef]
  2. S. Bartalini, S. Borri, P. Cancio, A. Castrillo, I. Galli, G. Giusfredi, D. Mazzotti, L. Gianfrani, and P. De Natale, “Observing the intrinsic linewidth of a quantum-cascade laser: beyond the Schawlow-Townes limit,” Phys. Rev. Lett. 104, 083904 (2010).
    [CrossRef]
  3. L. Tombez, J. Di Francesco, S. Schilt, G. Di Domenico, J. Faist, P. Thomann, and D. Hofstetter, “Frequency noise of free-running 4.6 μm DFB quantum cascade lasers near room temperature,” Opt. Lett. 36, 3109–3111 (2011).
    [CrossRef]
  4. J.-P. Tourrenc, “Caractérisation et modélisation du bruit d’amplitude optique, du bruit de fréquence et de la largeur de raie de VCSELs monomode,” Ph.D. dissertation (Université de Montpellier II, 2005).
  5. S. Schilt, N. Bucalovic, L. Tombez, V. Dolgovskiy, C. Schori, G. Di Domenico, M. Zaffalon, and P. Thomann, “Frequency discriminators for the characterization of narrow-spectrum heterodyne beat signals: application to the measurement of a sub-hertz carrier-envelope-offset beat in an optical frequency comb,” Rev. Sci. Instrum. 82, 123116 (2011).
    [CrossRef]
  6. D. S. Elliott, R. Roy, and S. J. Smith, “Extracavity laser band shape and bandwidth modification,” Phys. Rev. A 26, 12–18 (1982).
    [CrossRef]
  7. P. B. Gallion and G. Debarge, “Quantum phase noise and field correlation in single frequency semiconductor laser systems,” IEEE J. Quantum Electron. 20, 343–349 (1984).
    [CrossRef]
  8. G. M. Stéphan, T. T. Tam, S. Blin, P. Besnard, and M. Têtu, “Laser line shape and spectral density of frequency noise,” Phys. Rev. A 71, 043809 (2005).
    [CrossRef]
  9. L. B. Mercer, “1/f frequency noise effects on self-heterodyne linewidth measurements,” J. Lightwave Technol. 9, 485–493 (1991).
    [CrossRef]
  10. G. Di Domenico, S. Schilt, and P. Thomann, “Simple approach to the relation between laser frequency noise and laser line shape,” Appl. Opt. 49, 4801–4807 (2010).
    [CrossRef]
  11. C. H. Henry, “Theory of the linewidth of semiconductor lasers,” IEEE J. Quantum Electron. 18, 259–264 (1982).
    [CrossRef]
  12. A. L. Schawlow and C. H. Townes, “Infrared and optical masers,” Phys. Rev. 112, 1940–1949 (1958).
    [CrossRef]
  13. H. R. Telle, G. Steinmeyer, A. E. Dunlop, J. Stenger, D. H. Sutter, and U. Keller, “Carrier-envelope offset phase control: a novel concept for absolute optical frequency measurement and ultrashort pulse generation,” Appl. Phys. B 69, 327–332 (1999).
    [CrossRef]
  14. T. W. Hänsch, “Nobel lecture: passion for precision,” Rev. Mod. Phys. 78, 1297–1309 (2006).
    [CrossRef]
  15. S. T. Cundiff and J. Ye, “Femtosecond optical frequency combs,” Rev. Mod. Phys. 75, 325–342 (2003).
    [CrossRef]
  16. E. Benkler, H. Telle, A. Zach, and F. Tauser, “Circumvention of noise contributions in fiber laser based frequency combs,” Opt. Express 13, 5662–5668 (2005).
    [CrossRef]
  17. M. C. Stumpf, S. Pekarek, A. E. H. Oehler, T. Südmeyer, J. M. Dudley, and U. Keller, “Self-referencable frequency comb from a 170 fs, 1.5 μm solid-state laser oscillator,” Appl. Phys. B 99, 401–408 (2010).
    [CrossRef]
  18. S. Schilt, N. Bucalovic, V. Dolgovskiy, C. Schori, M. C. Stumpf, G. Di Domenico, S. Pekarek, A. E. H. Oehler, T. Südmeyer, U. Keller, and P. Thomann, “Fully stabilized optical frequency comb with sub-radian CEO phase noise from a SESAM-modelocked 1.5 μm solid-state laser,” Opt. Express 19, 24171–24181 (2011).
    [CrossRef]
  19. V. Dolgovskiy, N. Bucalovic, P. Thomann, C. Schori, G. Di Domenico, and S. Schilt, “Cross-influence between the two servo-loops of a fully stabilized Er:fiber optical frequency comb,” submitted.
  20. V. Dolgovskiy, S. Schilt, G. Di Domenico, N. Bucalovic, C. Schori, and P. Thomann, “1.5 μm cavity-stabilized laser for ultra-stable microwave generation,” presented at IEEE International Frequency Control Symposium and European Frequency and Time Forum Joint Conference, San Francisco, California, USA, 2–5 May 2011.
  21. J. J. Olivero, and R. L. Longbothum, “Empirical fits to the Voigt line width: a brief review,” J. Quant. Spectrosc. Radiat. Transfer 17, 233–236 (1977).
    [CrossRef]

2011 (4)

S. Spiessberger, M. Schiemangk, A. Wicht, H. Wenzel, G. Erbert, and G. Tränkle, “DBR laser diodes emitting near 1064 nm with a narrow intrinsic linewidth of 2 kHz,” Appl. Phys. B 104, 813–818 (2011).
[CrossRef]

L. Tombez, J. Di Francesco, S. Schilt, G. Di Domenico, J. Faist, P. Thomann, and D. Hofstetter, “Frequency noise of free-running 4.6 μm DFB quantum cascade lasers near room temperature,” Opt. Lett. 36, 3109–3111 (2011).
[CrossRef]

S. Schilt, N. Bucalovic, L. Tombez, V. Dolgovskiy, C. Schori, G. Di Domenico, M. Zaffalon, and P. Thomann, “Frequency discriminators for the characterization of narrow-spectrum heterodyne beat signals: application to the measurement of a sub-hertz carrier-envelope-offset beat in an optical frequency comb,” Rev. Sci. Instrum. 82, 123116 (2011).
[CrossRef]

S. Schilt, N. Bucalovic, V. Dolgovskiy, C. Schori, M. C. Stumpf, G. Di Domenico, S. Pekarek, A. E. H. Oehler, T. Südmeyer, U. Keller, and P. Thomann, “Fully stabilized optical frequency comb with sub-radian CEO phase noise from a SESAM-modelocked 1.5 μm solid-state laser,” Opt. Express 19, 24171–24181 (2011).
[CrossRef]

2010 (3)

M. C. Stumpf, S. Pekarek, A. E. H. Oehler, T. Südmeyer, J. M. Dudley, and U. Keller, “Self-referencable frequency comb from a 170 fs, 1.5 μm solid-state laser oscillator,” Appl. Phys. B 99, 401–408 (2010).
[CrossRef]

S. Bartalini, S. Borri, P. Cancio, A. Castrillo, I. Galli, G. Giusfredi, D. Mazzotti, L. Gianfrani, and P. De Natale, “Observing the intrinsic linewidth of a quantum-cascade laser: beyond the Schawlow-Townes limit,” Phys. Rev. Lett. 104, 083904 (2010).
[CrossRef]

G. Di Domenico, S. Schilt, and P. Thomann, “Simple approach to the relation between laser frequency noise and laser line shape,” Appl. Opt. 49, 4801–4807 (2010).
[CrossRef]

2006 (1)

T. W. Hänsch, “Nobel lecture: passion for precision,” Rev. Mod. Phys. 78, 1297–1309 (2006).
[CrossRef]

2005 (2)

E. Benkler, H. Telle, A. Zach, and F. Tauser, “Circumvention of noise contributions in fiber laser based frequency combs,” Opt. Express 13, 5662–5668 (2005).
[CrossRef]

G. M. Stéphan, T. T. Tam, S. Blin, P. Besnard, and M. Têtu, “Laser line shape and spectral density of frequency noise,” Phys. Rev. A 71, 043809 (2005).
[CrossRef]

2003 (1)

S. T. Cundiff and J. Ye, “Femtosecond optical frequency combs,” Rev. Mod. Phys. 75, 325–342 (2003).
[CrossRef]

1999 (1)

H. R. Telle, G. Steinmeyer, A. E. Dunlop, J. Stenger, D. H. Sutter, and U. Keller, “Carrier-envelope offset phase control: a novel concept for absolute optical frequency measurement and ultrashort pulse generation,” Appl. Phys. B 69, 327–332 (1999).
[CrossRef]

1991 (1)

L. B. Mercer, “1/f frequency noise effects on self-heterodyne linewidth measurements,” J. Lightwave Technol. 9, 485–493 (1991).
[CrossRef]

1984 (1)

P. B. Gallion and G. Debarge, “Quantum phase noise and field correlation in single frequency semiconductor laser systems,” IEEE J. Quantum Electron. 20, 343–349 (1984).
[CrossRef]

1982 (2)

C. H. Henry, “Theory of the linewidth of semiconductor lasers,” IEEE J. Quantum Electron. 18, 259–264 (1982).
[CrossRef]

D. S. Elliott, R. Roy, and S. J. Smith, “Extracavity laser band shape and bandwidth modification,” Phys. Rev. A 26, 12–18 (1982).
[CrossRef]

1977 (1)

J. J. Olivero, and R. L. Longbothum, “Empirical fits to the Voigt line width: a brief review,” J. Quant. Spectrosc. Radiat. Transfer 17, 233–236 (1977).
[CrossRef]

1958 (1)

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

Bartalini, S.

S. Bartalini, S. Borri, P. Cancio, A. Castrillo, I. Galli, G. Giusfredi, D. Mazzotti, L. Gianfrani, and P. De Natale, “Observing the intrinsic linewidth of a quantum-cascade laser: beyond the Schawlow-Townes limit,” Phys. Rev. Lett. 104, 083904 (2010).
[CrossRef]

Benkler, E.

Besnard, P.

G. M. Stéphan, T. T. Tam, S. Blin, P. Besnard, and M. Têtu, “Laser line shape and spectral density of frequency noise,” Phys. Rev. A 71, 043809 (2005).
[CrossRef]

Blin, S.

G. M. Stéphan, T. T. Tam, S. Blin, P. Besnard, and M. Têtu, “Laser line shape and spectral density of frequency noise,” Phys. Rev. A 71, 043809 (2005).
[CrossRef]

Borri, S.

S. Bartalini, S. Borri, P. Cancio, A. Castrillo, I. Galli, G. Giusfredi, D. Mazzotti, L. Gianfrani, and P. De Natale, “Observing the intrinsic linewidth of a quantum-cascade laser: beyond the Schawlow-Townes limit,” Phys. Rev. Lett. 104, 083904 (2010).
[CrossRef]

Bucalovic, N.

S. Schilt, N. Bucalovic, L. Tombez, V. Dolgovskiy, C. Schori, G. Di Domenico, M. Zaffalon, and P. Thomann, “Frequency discriminators for the characterization of narrow-spectrum heterodyne beat signals: application to the measurement of a sub-hertz carrier-envelope-offset beat in an optical frequency comb,” Rev. Sci. Instrum. 82, 123116 (2011).
[CrossRef]

S. Schilt, N. Bucalovic, V. Dolgovskiy, C. Schori, M. C. Stumpf, G. Di Domenico, S. Pekarek, A. E. H. Oehler, T. Südmeyer, U. Keller, and P. Thomann, “Fully stabilized optical frequency comb with sub-radian CEO phase noise from a SESAM-modelocked 1.5 μm solid-state laser,” Opt. Express 19, 24171–24181 (2011).
[CrossRef]

V. Dolgovskiy, N. Bucalovic, P. Thomann, C. Schori, G. Di Domenico, and S. Schilt, “Cross-influence between the two servo-loops of a fully stabilized Er:fiber optical frequency comb,” submitted.

V. Dolgovskiy, S. Schilt, G. Di Domenico, N. Bucalovic, C. Schori, and P. Thomann, “1.5 μm cavity-stabilized laser for ultra-stable microwave generation,” presented at IEEE International Frequency Control Symposium and European Frequency and Time Forum Joint Conference, San Francisco, California, USA, 2–5 May 2011.

Cancio, P.

S. Bartalini, S. Borri, P. Cancio, A. Castrillo, I. Galli, G. Giusfredi, D. Mazzotti, L. Gianfrani, and P. De Natale, “Observing the intrinsic linewidth of a quantum-cascade laser: beyond the Schawlow-Townes limit,” Phys. Rev. Lett. 104, 083904 (2010).
[CrossRef]

Castrillo, A.

S. Bartalini, S. Borri, P. Cancio, A. Castrillo, I. Galli, G. Giusfredi, D. Mazzotti, L. Gianfrani, and P. De Natale, “Observing the intrinsic linewidth of a quantum-cascade laser: beyond the Schawlow-Townes limit,” Phys. Rev. Lett. 104, 083904 (2010).
[CrossRef]

Cundiff, S. T.

S. T. Cundiff and J. Ye, “Femtosecond optical frequency combs,” Rev. Mod. Phys. 75, 325–342 (2003).
[CrossRef]

De Natale, P.

S. Bartalini, S. Borri, P. Cancio, A. Castrillo, I. Galli, G. Giusfredi, D. Mazzotti, L. Gianfrani, and P. De Natale, “Observing the intrinsic linewidth of a quantum-cascade laser: beyond the Schawlow-Townes limit,” Phys. Rev. Lett. 104, 083904 (2010).
[CrossRef]

Debarge, G.

P. B. Gallion and G. Debarge, “Quantum phase noise and field correlation in single frequency semiconductor laser systems,” IEEE J. Quantum Electron. 20, 343–349 (1984).
[CrossRef]

Di Domenico, G.

S. Schilt, N. Bucalovic, L. Tombez, V. Dolgovskiy, C. Schori, G. Di Domenico, M. Zaffalon, and P. Thomann, “Frequency discriminators for the characterization of narrow-spectrum heterodyne beat signals: application to the measurement of a sub-hertz carrier-envelope-offset beat in an optical frequency comb,” Rev. Sci. Instrum. 82, 123116 (2011).
[CrossRef]

L. Tombez, J. Di Francesco, S. Schilt, G. Di Domenico, J. Faist, P. Thomann, and D. Hofstetter, “Frequency noise of free-running 4.6 μm DFB quantum cascade lasers near room temperature,” Opt. Lett. 36, 3109–3111 (2011).
[CrossRef]

S. Schilt, N. Bucalovic, V. Dolgovskiy, C. Schori, M. C. Stumpf, G. Di Domenico, S. Pekarek, A. E. H. Oehler, T. Südmeyer, U. Keller, and P. Thomann, “Fully stabilized optical frequency comb with sub-radian CEO phase noise from a SESAM-modelocked 1.5 μm solid-state laser,” Opt. Express 19, 24171–24181 (2011).
[CrossRef]

G. Di Domenico, S. Schilt, and P. Thomann, “Simple approach to the relation between laser frequency noise and laser line shape,” Appl. Opt. 49, 4801–4807 (2010).
[CrossRef]

V. Dolgovskiy, S. Schilt, G. Di Domenico, N. Bucalovic, C. Schori, and P. Thomann, “1.5 μm cavity-stabilized laser for ultra-stable microwave generation,” presented at IEEE International Frequency Control Symposium and European Frequency and Time Forum Joint Conference, San Francisco, California, USA, 2–5 May 2011.

V. Dolgovskiy, N. Bucalovic, P. Thomann, C. Schori, G. Di Domenico, and S. Schilt, “Cross-influence between the two servo-loops of a fully stabilized Er:fiber optical frequency comb,” submitted.

Di Francesco, J.

Dolgovskiy, V.

S. Schilt, N. Bucalovic, L. Tombez, V. Dolgovskiy, C. Schori, G. Di Domenico, M. Zaffalon, and P. Thomann, “Frequency discriminators for the characterization of narrow-spectrum heterodyne beat signals: application to the measurement of a sub-hertz carrier-envelope-offset beat in an optical frequency comb,” Rev. Sci. Instrum. 82, 123116 (2011).
[CrossRef]

S. Schilt, N. Bucalovic, V. Dolgovskiy, C. Schori, M. C. Stumpf, G. Di Domenico, S. Pekarek, A. E. H. Oehler, T. Südmeyer, U. Keller, and P. Thomann, “Fully stabilized optical frequency comb with sub-radian CEO phase noise from a SESAM-modelocked 1.5 μm solid-state laser,” Opt. Express 19, 24171–24181 (2011).
[CrossRef]

V. Dolgovskiy, N. Bucalovic, P. Thomann, C. Schori, G. Di Domenico, and S. Schilt, “Cross-influence between the two servo-loops of a fully stabilized Er:fiber optical frequency comb,” submitted.

V. Dolgovskiy, S. Schilt, G. Di Domenico, N. Bucalovic, C. Schori, and P. Thomann, “1.5 μm cavity-stabilized laser for ultra-stable microwave generation,” presented at IEEE International Frequency Control Symposium and European Frequency and Time Forum Joint Conference, San Francisco, California, USA, 2–5 May 2011.

Dudley, J. M.

M. C. Stumpf, S. Pekarek, A. E. H. Oehler, T. Südmeyer, J. M. Dudley, and U. Keller, “Self-referencable frequency comb from a 170 fs, 1.5 μm solid-state laser oscillator,” Appl. Phys. B 99, 401–408 (2010).
[CrossRef]

Dunlop, A. E.

H. R. Telle, G. Steinmeyer, A. E. Dunlop, J. Stenger, D. H. Sutter, and U. Keller, “Carrier-envelope offset phase control: a novel concept for absolute optical frequency measurement and ultrashort pulse generation,” Appl. Phys. B 69, 327–332 (1999).
[CrossRef]

Elliott, D. S.

D. S. Elliott, R. Roy, and S. J. Smith, “Extracavity laser band shape and bandwidth modification,” Phys. Rev. A 26, 12–18 (1982).
[CrossRef]

Erbert, G.

S. Spiessberger, M. Schiemangk, A. Wicht, H. Wenzel, G. Erbert, and G. Tränkle, “DBR laser diodes emitting near 1064 nm with a narrow intrinsic linewidth of 2 kHz,” Appl. Phys. B 104, 813–818 (2011).
[CrossRef]

Faist, J.

Galli, I.

S. Bartalini, S. Borri, P. Cancio, A. Castrillo, I. Galli, G. Giusfredi, D. Mazzotti, L. Gianfrani, and P. De Natale, “Observing the intrinsic linewidth of a quantum-cascade laser: beyond the Schawlow-Townes limit,” Phys. Rev. Lett. 104, 083904 (2010).
[CrossRef]

Gallion, P. B.

P. B. Gallion and G. Debarge, “Quantum phase noise and field correlation in single frequency semiconductor laser systems,” IEEE J. Quantum Electron. 20, 343–349 (1984).
[CrossRef]

Gianfrani, L.

S. Bartalini, S. Borri, P. Cancio, A. Castrillo, I. Galli, G. Giusfredi, D. Mazzotti, L. Gianfrani, and P. De Natale, “Observing the intrinsic linewidth of a quantum-cascade laser: beyond the Schawlow-Townes limit,” Phys. Rev. Lett. 104, 083904 (2010).
[CrossRef]

Giusfredi, G.

S. Bartalini, S. Borri, P. Cancio, A. Castrillo, I. Galli, G. Giusfredi, D. Mazzotti, L. Gianfrani, and P. De Natale, “Observing the intrinsic linewidth of a quantum-cascade laser: beyond the Schawlow-Townes limit,” Phys. Rev. Lett. 104, 083904 (2010).
[CrossRef]

Hänsch, T. W.

T. W. Hänsch, “Nobel lecture: passion for precision,” Rev. Mod. Phys. 78, 1297–1309 (2006).
[CrossRef]

Henry, C. H.

C. H. Henry, “Theory of the linewidth of semiconductor lasers,” IEEE J. Quantum Electron. 18, 259–264 (1982).
[CrossRef]

Hofstetter, D.

Keller, U.

S. Schilt, N. Bucalovic, V. Dolgovskiy, C. Schori, M. C. Stumpf, G. Di Domenico, S. Pekarek, A. E. H. Oehler, T. Südmeyer, U. Keller, and P. Thomann, “Fully stabilized optical frequency comb with sub-radian CEO phase noise from a SESAM-modelocked 1.5 μm solid-state laser,” Opt. Express 19, 24171–24181 (2011).
[CrossRef]

M. C. Stumpf, S. Pekarek, A. E. H. Oehler, T. Südmeyer, J. M. Dudley, and U. Keller, “Self-referencable frequency comb from a 170 fs, 1.5 μm solid-state laser oscillator,” Appl. Phys. B 99, 401–408 (2010).
[CrossRef]

H. R. Telle, G. Steinmeyer, A. E. Dunlop, J. Stenger, D. H. Sutter, and U. Keller, “Carrier-envelope offset phase control: a novel concept for absolute optical frequency measurement and ultrashort pulse generation,” Appl. Phys. B 69, 327–332 (1999).
[CrossRef]

Longbothum, R. L.

J. J. Olivero, and R. L. Longbothum, “Empirical fits to the Voigt line width: a brief review,” J. Quant. Spectrosc. Radiat. Transfer 17, 233–236 (1977).
[CrossRef]

Mazzotti, D.

S. Bartalini, S. Borri, P. Cancio, A. Castrillo, I. Galli, G. Giusfredi, D. Mazzotti, L. Gianfrani, and P. De Natale, “Observing the intrinsic linewidth of a quantum-cascade laser: beyond the Schawlow-Townes limit,” Phys. Rev. Lett. 104, 083904 (2010).
[CrossRef]

Mercer, L. B.

L. B. Mercer, “1/f frequency noise effects on self-heterodyne linewidth measurements,” J. Lightwave Technol. 9, 485–493 (1991).
[CrossRef]

Oehler, A. E. H.

Olivero, J. J.

J. J. Olivero, and R. L. Longbothum, “Empirical fits to the Voigt line width: a brief review,” J. Quant. Spectrosc. Radiat. Transfer 17, 233–236 (1977).
[CrossRef]

Pekarek, S.

Roy, R.

D. S. Elliott, R. Roy, and S. J. Smith, “Extracavity laser band shape and bandwidth modification,” Phys. Rev. A 26, 12–18 (1982).
[CrossRef]

Schawlow, A. L.

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

Schiemangk, M.

S. Spiessberger, M. Schiemangk, A. Wicht, H. Wenzel, G. Erbert, and G. Tränkle, “DBR laser diodes emitting near 1064 nm with a narrow intrinsic linewidth of 2 kHz,” Appl. Phys. B 104, 813–818 (2011).
[CrossRef]

Schilt, S.

L. Tombez, J. Di Francesco, S. Schilt, G. Di Domenico, J. Faist, P. Thomann, and D. Hofstetter, “Frequency noise of free-running 4.6 μm DFB quantum cascade lasers near room temperature,” Opt. Lett. 36, 3109–3111 (2011).
[CrossRef]

S. Schilt, N. Bucalovic, L. Tombez, V. Dolgovskiy, C. Schori, G. Di Domenico, M. Zaffalon, and P. Thomann, “Frequency discriminators for the characterization of narrow-spectrum heterodyne beat signals: application to the measurement of a sub-hertz carrier-envelope-offset beat in an optical frequency comb,” Rev. Sci. Instrum. 82, 123116 (2011).
[CrossRef]

S. Schilt, N. Bucalovic, V. Dolgovskiy, C. Schori, M. C. Stumpf, G. Di Domenico, S. Pekarek, A. E. H. Oehler, T. Südmeyer, U. Keller, and P. Thomann, “Fully stabilized optical frequency comb with sub-radian CEO phase noise from a SESAM-modelocked 1.5 μm solid-state laser,” Opt. Express 19, 24171–24181 (2011).
[CrossRef]

G. Di Domenico, S. Schilt, and P. Thomann, “Simple approach to the relation between laser frequency noise and laser line shape,” Appl. Opt. 49, 4801–4807 (2010).
[CrossRef]

V. Dolgovskiy, N. Bucalovic, P. Thomann, C. Schori, G. Di Domenico, and S. Schilt, “Cross-influence between the two servo-loops of a fully stabilized Er:fiber optical frequency comb,” submitted.

V. Dolgovskiy, S. Schilt, G. Di Domenico, N. Bucalovic, C. Schori, and P. Thomann, “1.5 μm cavity-stabilized laser for ultra-stable microwave generation,” presented at IEEE International Frequency Control Symposium and European Frequency and Time Forum Joint Conference, San Francisco, California, USA, 2–5 May 2011.

Schori, C.

S. Schilt, N. Bucalovic, V. Dolgovskiy, C. Schori, M. C. Stumpf, G. Di Domenico, S. Pekarek, A. E. H. Oehler, T. Südmeyer, U. Keller, and P. Thomann, “Fully stabilized optical frequency comb with sub-radian CEO phase noise from a SESAM-modelocked 1.5 μm solid-state laser,” Opt. Express 19, 24171–24181 (2011).
[CrossRef]

S. Schilt, N. Bucalovic, L. Tombez, V. Dolgovskiy, C. Schori, G. Di Domenico, M. Zaffalon, and P. Thomann, “Frequency discriminators for the characterization of narrow-spectrum heterodyne beat signals: application to the measurement of a sub-hertz carrier-envelope-offset beat in an optical frequency comb,” Rev. Sci. Instrum. 82, 123116 (2011).
[CrossRef]

V. Dolgovskiy, N. Bucalovic, P. Thomann, C. Schori, G. Di Domenico, and S. Schilt, “Cross-influence between the two servo-loops of a fully stabilized Er:fiber optical frequency comb,” submitted.

V. Dolgovskiy, S. Schilt, G. Di Domenico, N. Bucalovic, C. Schori, and P. Thomann, “1.5 μm cavity-stabilized laser for ultra-stable microwave generation,” presented at IEEE International Frequency Control Symposium and European Frequency and Time Forum Joint Conference, San Francisco, California, USA, 2–5 May 2011.

Smith, S. J.

D. S. Elliott, R. Roy, and S. J. Smith, “Extracavity laser band shape and bandwidth modification,” Phys. Rev. A 26, 12–18 (1982).
[CrossRef]

Spiessberger, S.

S. Spiessberger, M. Schiemangk, A. Wicht, H. Wenzel, G. Erbert, and G. Tränkle, “DBR laser diodes emitting near 1064 nm with a narrow intrinsic linewidth of 2 kHz,” Appl. Phys. B 104, 813–818 (2011).
[CrossRef]

Steinmeyer, G.

H. R. Telle, G. Steinmeyer, A. E. Dunlop, J. Stenger, D. H. Sutter, and U. Keller, “Carrier-envelope offset phase control: a novel concept for absolute optical frequency measurement and ultrashort pulse generation,” Appl. Phys. B 69, 327–332 (1999).
[CrossRef]

Stenger, J.

H. R. Telle, G. Steinmeyer, A. E. Dunlop, J. Stenger, D. H. Sutter, and U. Keller, “Carrier-envelope offset phase control: a novel concept for absolute optical frequency measurement and ultrashort pulse generation,” Appl. Phys. B 69, 327–332 (1999).
[CrossRef]

Stéphan, G. M.

G. M. Stéphan, T. T. Tam, S. Blin, P. Besnard, and M. Têtu, “Laser line shape and spectral density of frequency noise,” Phys. Rev. A 71, 043809 (2005).
[CrossRef]

Stumpf, M. C.

Südmeyer, T.

Sutter, D. H.

H. R. Telle, G. Steinmeyer, A. E. Dunlop, J. Stenger, D. H. Sutter, and U. Keller, “Carrier-envelope offset phase control: a novel concept for absolute optical frequency measurement and ultrashort pulse generation,” Appl. Phys. B 69, 327–332 (1999).
[CrossRef]

Tam, T. T.

G. M. Stéphan, T. T. Tam, S. Blin, P. Besnard, and M. Têtu, “Laser line shape and spectral density of frequency noise,” Phys. Rev. A 71, 043809 (2005).
[CrossRef]

Tauser, F.

Telle, H.

Telle, H. R.

H. R. Telle, G. Steinmeyer, A. E. Dunlop, J. Stenger, D. H. Sutter, and U. Keller, “Carrier-envelope offset phase control: a novel concept for absolute optical frequency measurement and ultrashort pulse generation,” Appl. Phys. B 69, 327–332 (1999).
[CrossRef]

Têtu, M.

G. M. Stéphan, T. T. Tam, S. Blin, P. Besnard, and M. Têtu, “Laser line shape and spectral density of frequency noise,” Phys. Rev. A 71, 043809 (2005).
[CrossRef]

Thomann, P.

S. Schilt, N. Bucalovic, L. Tombez, V. Dolgovskiy, C. Schori, G. Di Domenico, M. Zaffalon, and P. Thomann, “Frequency discriminators for the characterization of narrow-spectrum heterodyne beat signals: application to the measurement of a sub-hertz carrier-envelope-offset beat in an optical frequency comb,” Rev. Sci. Instrum. 82, 123116 (2011).
[CrossRef]

L. Tombez, J. Di Francesco, S. Schilt, G. Di Domenico, J. Faist, P. Thomann, and D. Hofstetter, “Frequency noise of free-running 4.6 μm DFB quantum cascade lasers near room temperature,” Opt. Lett. 36, 3109–3111 (2011).
[CrossRef]

S. Schilt, N. Bucalovic, V. Dolgovskiy, C. Schori, M. C. Stumpf, G. Di Domenico, S. Pekarek, A. E. H. Oehler, T. Südmeyer, U. Keller, and P. Thomann, “Fully stabilized optical frequency comb with sub-radian CEO phase noise from a SESAM-modelocked 1.5 μm solid-state laser,” Opt. Express 19, 24171–24181 (2011).
[CrossRef]

G. Di Domenico, S. Schilt, and P. Thomann, “Simple approach to the relation between laser frequency noise and laser line shape,” Appl. Opt. 49, 4801–4807 (2010).
[CrossRef]

V. Dolgovskiy, N. Bucalovic, P. Thomann, C. Schori, G. Di Domenico, and S. Schilt, “Cross-influence between the two servo-loops of a fully stabilized Er:fiber optical frequency comb,” submitted.

V. Dolgovskiy, S. Schilt, G. Di Domenico, N. Bucalovic, C. Schori, and P. Thomann, “1.5 μm cavity-stabilized laser for ultra-stable microwave generation,” presented at IEEE International Frequency Control Symposium and European Frequency and Time Forum Joint Conference, San Francisco, California, USA, 2–5 May 2011.

Tombez, L.

L. Tombez, J. Di Francesco, S. Schilt, G. Di Domenico, J. Faist, P. Thomann, and D. Hofstetter, “Frequency noise of free-running 4.6 μm DFB quantum cascade lasers near room temperature,” Opt. Lett. 36, 3109–3111 (2011).
[CrossRef]

S. Schilt, N. Bucalovic, L. Tombez, V. Dolgovskiy, C. Schori, G. Di Domenico, M. Zaffalon, and P. Thomann, “Frequency discriminators for the characterization of narrow-spectrum heterodyne beat signals: application to the measurement of a sub-hertz carrier-envelope-offset beat in an optical frequency comb,” Rev. Sci. Instrum. 82, 123116 (2011).
[CrossRef]

Tourrenc, J.-P.

J.-P. Tourrenc, “Caractérisation et modélisation du bruit d’amplitude optique, du bruit de fréquence et de la largeur de raie de VCSELs monomode,” Ph.D. dissertation (Université de Montpellier II, 2005).

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

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S. Spiessberger, M. Schiemangk, A. Wicht, H. Wenzel, G. Erbert, and G. Tränkle, “DBR laser diodes emitting near 1064 nm with a narrow intrinsic linewidth of 2 kHz,” Appl. Phys. B 104, 813–818 (2011).
[CrossRef]

Wenzel, H.

S. Spiessberger, M. Schiemangk, A. Wicht, H. Wenzel, G. Erbert, and G. Tränkle, “DBR laser diodes emitting near 1064 nm with a narrow intrinsic linewidth of 2 kHz,” Appl. Phys. B 104, 813–818 (2011).
[CrossRef]

Wicht, A.

S. Spiessberger, M. Schiemangk, A. Wicht, H. Wenzel, G. Erbert, and G. Tränkle, “DBR laser diodes emitting near 1064 nm with a narrow intrinsic linewidth of 2 kHz,” Appl. Phys. B 104, 813–818 (2011).
[CrossRef]

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S. T. Cundiff and J. Ye, “Femtosecond optical frequency combs,” Rev. Mod. Phys. 75, 325–342 (2003).
[CrossRef]

Zach, A.

Zaffalon, M.

S. Schilt, N. Bucalovic, L. Tombez, V. Dolgovskiy, C. Schori, G. Di Domenico, M. Zaffalon, and P. Thomann, “Frequency discriminators for the characterization of narrow-spectrum heterodyne beat signals: application to the measurement of a sub-hertz carrier-envelope-offset beat in an optical frequency comb,” Rev. Sci. Instrum. 82, 123116 (2011).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. B (3)

H. R. Telle, G. Steinmeyer, A. E. Dunlop, J. Stenger, D. H. Sutter, and U. Keller, “Carrier-envelope offset phase control: a novel concept for absolute optical frequency measurement and ultrashort pulse generation,” Appl. Phys. B 69, 327–332 (1999).
[CrossRef]

M. C. Stumpf, S. Pekarek, A. E. H. Oehler, T. Südmeyer, J. M. Dudley, and U. Keller, “Self-referencable frequency comb from a 170 fs, 1.5 μm solid-state laser oscillator,” Appl. Phys. B 99, 401–408 (2010).
[CrossRef]

S. Spiessberger, M. Schiemangk, A. Wicht, H. Wenzel, G. Erbert, and G. Tränkle, “DBR laser diodes emitting near 1064 nm with a narrow intrinsic linewidth of 2 kHz,” Appl. Phys. B 104, 813–818 (2011).
[CrossRef]

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[CrossRef]

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[CrossRef]

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[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Phys. Rev. (1)

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

Phys. Rev. A (2)

G. M. Stéphan, T. T. Tam, S. Blin, P. Besnard, and M. Têtu, “Laser line shape and spectral density of frequency noise,” Phys. Rev. A 71, 043809 (2005).
[CrossRef]

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[CrossRef]

Phys. Rev. Lett. (1)

S. Bartalini, S. Borri, P. Cancio, A. Castrillo, I. Galli, G. Giusfredi, D. Mazzotti, L. Gianfrani, and P. De Natale, “Observing the intrinsic linewidth of a quantum-cascade laser: beyond the Schawlow-Townes limit,” Phys. Rev. Lett. 104, 083904 (2010).
[CrossRef]

Rev. Mod. Phys. (2)

T. W. Hänsch, “Nobel lecture: passion for precision,” Rev. Mod. Phys. 78, 1297–1309 (2006).
[CrossRef]

S. T. Cundiff and J. Ye, “Femtosecond optical frequency combs,” Rev. Mod. Phys. 75, 325–342 (2003).
[CrossRef]

Rev. Sci. Instrum. (1)

S. Schilt, N. Bucalovic, L. Tombez, V. Dolgovskiy, C. Schori, G. Di Domenico, M. Zaffalon, and P. Thomann, “Frequency discriminators for the characterization of narrow-spectrum heterodyne beat signals: application to the measurement of a sub-hertz carrier-envelope-offset beat in an optical frequency comb,” Rev. Sci. Instrum. 82, 123116 (2011).
[CrossRef]

Other (3)

J.-P. Tourrenc, “Caractérisation et modélisation du bruit d’amplitude optique, du bruit de fréquence et de la largeur de raie de VCSELs monomode,” Ph.D. dissertation (Université de Montpellier II, 2005).

V. Dolgovskiy, N. Bucalovic, P. Thomann, C. Schori, G. Di Domenico, and S. Schilt, “Cross-influence between the two servo-loops of a fully stabilized Er:fiber optical frequency comb,” submitted.

V. Dolgovskiy, S. Schilt, G. Di Domenico, N. Bucalovic, C. Schori, and P. Thomann, “1.5 μm cavity-stabilized laser for ultra-stable microwave generation,” presented at IEEE International Frequency Control Symposium and European Frequency and Time Forum Joint Conference, San Francisco, California, USA, 2–5 May 2011.

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Figures (3)

Fig. 1.
Fig. 1.

Graphical representation of the simple approximation proposed to determine the linewidth of a laser from its frequency noise PSD Sδν(f), calculated from the surface A of the slow modulation area [10]. The shadowed areas on this schematized frequency noise spectrum represent the surface A that encloses all spectral components for which Sδν(f) exceeds the β-separation line Sδν(f)=8ln2π2f (dashed line).

Fig. 2.
Fig. 2.

Representative examples of frequency noise PSD (upper row) and corresponding line shapes (lower row) for three different laser systems: CEO beat in the ERGO comb (left), heterodyne beat between one line of the Er:fiber comb and a cavity-stabilized laser (middle), and CEO beat in the Er:fiber comb (right). The linewidth FWHMPSD is calculated from the shadowed area for which the frequency noise PSD exceeds the β-separation line (dashed line). The line shapes were recorded using an ESA (grey circles) and were fitted by a Voigt profile (line) to extract the actual linewidth FWHMVoigt. Fit residuals shown on top of the lower row represent the difference between the values of the fit function and the measured data. The uncertainty on the FWHM is given in parentheses following the FWHM value.

Fig. 3.
Fig. 3.

Comparison between the approximate linewidth FWHMPSD, calculated from the measured frequency noise PSD (y axis), and the actual linewidth FWHMVoigt (x axis) determined from the Voigt fit of the ESA trace, obtained over a broad range with three different laser systems. The uncertainty on each point is indicated by the error bars.

Equations (3)

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SE(ν)=2ei2πντ[E02ei2πν0τexp(20Sδν(f)sin2(πfτ)f2df)]dτ.
FWHM=(8ln2)A.
A=1/T0H(Sδν(f)8ln2π2f)Sδν(f)df.

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