Abstract

We revisit and improve the optical heterodyne technique for the measurement of the laser coherence, by digital acquisition of the beat-note and numerical analysis of the resulting signal. Our main result is that with the same experimental setup we reach the very “short-time linewidth” with the highest accuracy as well as the frequency noise spectrum.

© 2016 Optical Society of America

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References

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2016 (1)

B. Abbott, R. Abbott, T. Abbott, M. Abernathy, F. Acernese, K. Ackley, C. Adams, T. Adams, P. Addesso, and R. Adhikari, “Observation of gravitational waves from a binary black hole merger,” Phys. Rev. Lett. 116, 061102 (2016).
[Crossref] [PubMed]

2012 (2)

2011 (3)

2010 (3)

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] [PubMed]

A. Laurain, M. Myara, G. Beaudoin, I. Sagnes, and A. Garnache, “Multiwatt-power highly-coherent compact single-frequency tunable vertical external cavity surface emitting semiconductor laser,” Opt. Express 14, 14631 (2010).

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

2007 (1)

2005 (1)

J.-P. Tourrenc, P. Signoret, M. Myara, M. Bellon, J.-P. Perez, J.-M. Gosalbes, R. Alabedra, and B. Orsal, “Low-frequency fm-noise-induced lineshape : A theoretical and experimental approach,” IEEE J. Quantum Electron. 41, 549–553 (2005).
[Crossref]

2004 (3)

C. Spiegelberg, J. Geng, Y. Hu, Y. Kaneda, S. Jiang, and N. Peyghambarian, “Low-noise narrow-linewidth fiber laser at 1550 nm (june 2003),” J. Lightwave Technol. 22, 57–62 (2004).
[Crossref]

P. Signoret, M. Myara, J.-P. Tourrenc, B. Orsal, M.-H. Monier, J. Jacquet, P. Leboudec, and F. Marin, “Bragg section effects on linewidth and lineshape in 1.55 µ m dbr tunable laser diodes,” IEEE Photonics Technol. Lett. 25, 1429–1431 (2004).
[Crossref]

M. Myara, P. Signoret, J.-P. Tourrenc, J.-P. Perez, B. Orsal, and J. Jacquet, “Strongly sub-poissonian electrical noise in 1.55 µ m dbr tunable laser diodes,” IEEE J. Quantum Electron. 40, 852–857 (2004).
[Crossref]

2002 (2)

T. Laurila, T. Joutsenoja, R. Hernberg, and M. Kuittinen, “Tunable external cavity diode laser at 650 nm based on a transmission diffraction grating,” Appl. Opt. 41, 5632 (2002).
[Crossref] [PubMed]

S. Viciani, M. Gabrysch, F. Marin, F. M. di Sopra, M. Moser, and K. H. Gulden, “Lineshape of a vertical cavity surface emitting laser,” Opt. Commun. 206(1), 89–97 (2002).
[Crossref]

2001 (1)

P. Signoret, F. Marin, S. Viciani, G. Belleville, M. Myara, J.-P. Tourrenc, B. Orsal, A. Plais, F. Gaborit, and J. Jacquet, “3.6-mhz linewidth 1.55 µ m monomode vertical-cavity surface-emitting laser,” IEEE Photonics Technol. Lett. 13, 269–271 (2001).
[Crossref]

2000 (1)

D. M. Baney, P. Gallion, and R. S. Tucker, “Theory and measurement techniques for the noise figure of optical amplifiers,” Opt. Fiber Technol. 6, 122–154 (2000).
[Crossref]

1999 (1)

F. M. di Sopra, H. P. Zappe, M. Moser, R. Hövel, H.-P. Gauggel, and K. G. Gulden, “Near-infrared vertical-cavity surface emitting lasers with 3-mhz linewidth,” IEEE Photonics Technol. Lett. 11, 1533–1535 (1999).
[Crossref]

1998 (1)

1996 (1)

R. W. Tkach and A. R. Chraplyvy, “Phase noise and linewidth in an inaasp dfb laser,” J. Lightwave Technol. 4, 1711 (1996).
[Crossref]

1995 (1)

H. Ishii, F. Kano, Y. Tohmori, Y. Kondo, T. Tamamura, and Y. Yoshikuni, “Narrow spectral linewidth under wavelength tuning in thermaly tunable super-structure-grating (ssg) dbr lasers,” IEEE J. Sel. Top. Quantum Electron. 1, 401–407 (1995).
[Crossref]

1994 (1)

A. McLean, C. Mitchell, and D. Swanston, “Implementation of an efficient analytical approximation to the voigt function for photoemission lineshape analysis,” J. Electron Spectrosc. 69, 125–132 (1994).
[Crossref]

1993 (1)

S. M. Melle, A. T. Alavie, S. Karr, T. Coroy, K. Liu, and R. M. Measures, “A bragg grating-tuned fiber laser strain sensor system,” IEEE Photonics Technol. Lett. 5, 263–266 (1993).
[Crossref]

1992 (3)

J.-M. Verdiell, U. Koren, and T. L. Koch, “Linewidth and alpha-factor of detuned-loaded dbr lasers,” IEEE Photonics Technol. Lett. 4, 302–305 (1992).
[Crossref]

W. A. Hamel, M. P. van Exter, and J. P. Woerdman, “Coherence properties of a semiconductor laser with feedback from a distant reflector: Eperiment and theory,” IEEE J. Quantum Electron. 28, 1459–1469 (1992).
[Crossref]

B. Boashash, “Estimating and interpreting the instantaneous frequency of a signal. i. fundamentals,” Proc. IEEE 80, 520–538 (1992).
[Crossref]

1991 (3)

L. B. Mercer, “1/f frequency noise effects on self-heterodyne linewidth measurements,” J. Lightwave Technol. 9, 485–492 (1991).
[Crossref]

G. H. Duan and P. Gallion, “Drive curent noise induced linewidth in tunable multielectrode lasers,” IEEE Photonics Technol. Lett. 3, 302–304 (1991).
[Crossref]

S. P. Smith, F. Zarinetchi, and S. Ezekiel, “Narrow-linewidth stimulated brillouin fiber laser and applications,” Opt. Lett. 16, 393–395 (1991).
[Crossref] [PubMed]

1990 (3)

M. Okai, T. Tsuchiya, K. Uomi, N. Chimone, and T. Harada, “Corrugation-pitch-modulated mqw-dfb laser with narrow spectral linewidth (170 khz),” IEEE Photonics Technol. Lett. 2, 529–534 (1990).
[Crossref]

H. Yamazaki, M. Yamaguchi, and Kitamura, “Spectral linewidth rebroadening in mqw-dfb lds caused by spontaneous emission noise in sch/barrier layers,” IEEE Photonics Technol. Lett. 2, 529–534 (1990).

M. Ohtsu, M. Murata, and M. Kourogi, “FM noise reduction and subkilohertz linewidth of an algaas laser by negative electrical feedback,” IEEE J. Quantum Electron. 26, 231–241 (1990).
[Crossref]

1989 (1)

J. L. Gimlett and N. K. Cheung, “Effects of phase to intensity noise conversion by multiple reflections on gigabit-per-second dfb laser transmission systems,” J. Lightwave Technol. 7, 888–895 (1989).
[Crossref]

1988 (1)

R. J. Fronen and L. K. J. Vandamme, “Low-frequency intensity noise semiconductor lasers,” IEEE J. Quantum Electron. 24, 724–736 (1988).
[Crossref]

1984 (1)

P. 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]

1983 (1)

C. H. Henry, “Theory of the phase noise and power spectum of a single mode injection laser,” IEEE J. Quantum Electron. 19, 1391–1397 (1983).
[Crossref]

1982 (1)

C. H. Henry, “Theory of the linewidth of semiconductor lasers,” IEEE J. Quantum Electron. 18, 256–263 (1982).
[Crossref]

1981 (1)

F. Hooge, T. G. M. Kleinpenning, and L. K. J. Vandamme, “Experimental studies on 1/f noise,” Rep. Prog. Phys. 44, 479 (1981).
[Crossref]

1977 (1)

J. Olivero and R. Longbothum, “Empirical fits to the voigt line width: A brief review,” J. Quant. Spectrosc. Rad. 17, 233–236 (1977).
[Crossref]

1958 (1)

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

Abbott, B.

B. Abbott, R. Abbott, T. Abbott, M. Abernathy, F. Acernese, K. Ackley, C. Adams, T. Adams, P. Addesso, and R. Adhikari, “Observation of gravitational waves from a binary black hole merger,” Phys. Rev. Lett. 116, 061102 (2016).
[Crossref] [PubMed]

Abbott, R.

B. Abbott, R. Abbott, T. Abbott, M. Abernathy, F. Acernese, K. Ackley, C. Adams, T. Adams, P. Addesso, and R. Adhikari, “Observation of gravitational waves from a binary black hole merger,” Phys. Rev. Lett. 116, 061102 (2016).
[Crossref] [PubMed]

Abbott, T.

B. Abbott, R. Abbott, T. Abbott, M. Abernathy, F. Acernese, K. Ackley, C. Adams, T. Adams, P. Addesso, and R. Adhikari, “Observation of gravitational waves from a binary black hole merger,” Phys. Rev. Lett. 116, 061102 (2016).
[Crossref] [PubMed]

Abernathy, M.

B. Abbott, R. Abbott, T. Abbott, M. Abernathy, F. Acernese, K. Ackley, C. Adams, T. Adams, P. Addesso, and R. Adhikari, “Observation of gravitational waves from a binary black hole merger,” Phys. Rev. Lett. 116, 061102 (2016).
[Crossref] [PubMed]

Acernese, F.

B. Abbott, R. Abbott, T. Abbott, M. Abernathy, F. Acernese, K. Ackley, C. Adams, T. Adams, P. Addesso, and R. Adhikari, “Observation of gravitational waves from a binary black hole merger,” Phys. Rev. Lett. 116, 061102 (2016).
[Crossref] [PubMed]

Ackley, K.

B. Abbott, R. Abbott, T. Abbott, M. Abernathy, F. Acernese, K. Ackley, C. Adams, T. Adams, P. Addesso, and R. Adhikari, “Observation of gravitational waves from a binary black hole merger,” Phys. Rev. Lett. 116, 061102 (2016).
[Crossref] [PubMed]

Adams, C.

B. Abbott, R. Abbott, T. Abbott, M. Abernathy, F. Acernese, K. Ackley, C. Adams, T. Adams, P. Addesso, and R. Adhikari, “Observation of gravitational waves from a binary black hole merger,” Phys. Rev. Lett. 116, 061102 (2016).
[Crossref] [PubMed]

Adams, T.

B. Abbott, R. Abbott, T. Abbott, M. Abernathy, F. Acernese, K. Ackley, C. Adams, T. Adams, P. Addesso, and R. Adhikari, “Observation of gravitational waves from a binary black hole merger,” Phys. Rev. Lett. 116, 061102 (2016).
[Crossref] [PubMed]

Addesso, P.

B. Abbott, R. Abbott, T. Abbott, M. Abernathy, F. Acernese, K. Ackley, C. Adams, T. Adams, P. Addesso, and R. Adhikari, “Observation of gravitational waves from a binary black hole merger,” Phys. Rev. Lett. 116, 061102 (2016).
[Crossref] [PubMed]

Adhikari, R.

B. Abbott, R. Abbott, T. Abbott, M. Abernathy, F. Acernese, K. Ackley, C. Adams, T. Adams, P. Addesso, and R. Adhikari, “Observation of gravitational waves from a binary black hole merger,” Phys. Rev. Lett. 116, 061102 (2016).
[Crossref] [PubMed]

Alabedra, R.

J.-P. Tourrenc, P. Signoret, M. Myara, M. Bellon, J.-P. Perez, J.-M. Gosalbes, R. Alabedra, and B. Orsal, “Low-frequency fm-noise-induced lineshape : A theoretical and experimental approach,” IEEE J. Quantum Electron. 41, 549–553 (2005).
[Crossref]

Alavie, A. T.

S. M. Melle, A. T. Alavie, S. Karr, T. Coroy, K. Liu, and R. M. Measures, “A bragg grating-tuned fiber laser strain sensor system,” IEEE Photonics Technol. Lett. 5, 263–266 (1993).
[Crossref]

Amann, M.-C.

C. Lauer and M.-C. Amann, “Calculation of the linewidth broadening in vertical-cavity surface-emitting lasers due to temperature fluctuations,” Appl. Phys. Lett.86 (2005).
[Crossref]

Azeredo-Leme, C.

C. Azeredo-Leme, Clock jitter effects on sampling: a tutorial, IEEE Circuits Syst Mag. 11, 26–37 (2011).
[Crossref]

Baney, D. M.

D. M. Baney, P. Gallion, and R. S. Tucker, “Theory and measurement techniques for the noise figure of optical amplifiers,” Opt. Fiber Technol. 6, 122–154 (2000).
[Crossref]

Beaudoin, G.

A. Laurain, M. Myara, G. Beaudoin, I. Sagnes, and A. Garnache, “Multiwatt-power highly-coherent compact single-frequency tunable vertical external cavity surface emitting semiconductor laser,” Opt. Express 14, 14631 (2010).

Belleville, G.

P. Signoret, F. Marin, S. Viciani, G. Belleville, M. Myara, J.-P. Tourrenc, B. Orsal, A. Plais, F. Gaborit, and J. Jacquet, “3.6-mhz linewidth 1.55 µ m monomode vertical-cavity surface-emitting laser,” IEEE Photonics Technol. Lett. 13, 269–271 (2001).
[Crossref]

Bellon, M.

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S. Viciani, M. Gabrysch, F. Marin, F. M. di Sopra, M. Moser, and K. H. Gulden, “Lineshape of a vertical cavity surface emitting laser,” Opt. Commun. 206(1), 89–97 (2002).
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A. Laurain, M. Myara, G. Beaudoin, I. Sagnes, and A. Garnache, “Multiwatt-power highly-coherent compact single-frequency tunable vertical external cavity surface emitting semiconductor laser,” Opt. Express 14, 14631 (2010).

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[Crossref]

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[Crossref]

M. Myara, P. Signoret, J.-P. Tourrenc, J.-P. Perez, B. Orsal, and J. Jacquet, “Strongly sub-poissonian electrical noise in 1.55 µ m dbr tunable laser diodes,” IEEE J. Quantum Electron. 40, 852–857 (2004).
[Crossref]

P. Signoret, F. Marin, S. Viciani, G. Belleville, M. Myara, J.-P. Tourrenc, B. Orsal, A. Plais, F. Gaborit, and J. Jacquet, “3.6-mhz linewidth 1.55 µ m monomode vertical-cavity surface-emitting laser,” IEEE Photonics Technol. Lett. 13, 269–271 (2001).
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M. Myara, M. Sellahi, A. Laurain, A. Garnache, A. Michon, and I. Sagnes, “Noise properties of nir and mir vecsels (invited paper),” in IEEE Proceedings of International Conference on Noise and Fluctuations (IEEE), (2013).

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M. Myara, P. Signoret, J.-P. Tourrenc, J.-P. Perez, B. Orsal, and J. Jacquet, “Strongly sub-poissonian electrical noise in 1.55 µ m dbr tunable laser diodes,” IEEE J. Quantum Electron. 40, 852–857 (2004).
[Crossref]

P. Signoret, F. Marin, S. Viciani, G. Belleville, M. Myara, J.-P. Tourrenc, B. Orsal, A. Plais, F. Gaborit, and J. Jacquet, “3.6-mhz linewidth 1.55 µ m monomode vertical-cavity surface-emitting laser,” IEEE Photonics Technol. Lett. 13, 269–271 (2001).
[Crossref]

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N. Von Bandel, M. Garcia, M. Lecomte, A. Larrue, Y. Robert, O. Driss, O. Parrilaud, M. Krakowski, F. Gruet, and R. Matthey, “Dfb-ridge laser diodes at 894 nm for cesium atomic clocks,” in SPIE OPTO, (ISOP, 2016), pp. 97552K.

Perez, J.-P.

J.-P. Tourrenc, P. Signoret, M. Myara, M. Bellon, J.-P. Perez, J.-M. Gosalbes, R. Alabedra, and B. Orsal, “Low-frequency fm-noise-induced lineshape : A theoretical and experimental approach,” IEEE J. Quantum Electron. 41, 549–553 (2005).
[Crossref]

M. Myara, P. Signoret, J.-P. Tourrenc, J.-P. Perez, B. Orsal, and J. Jacquet, “Strongly sub-poissonian electrical noise in 1.55 µ m dbr tunable laser diodes,” IEEE J. Quantum Electron. 40, 852–857 (2004).
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K. Petermann, Laser Diode Modulation and Noise (Kluwer Academic Publishers, 1988).
[Crossref]

J. Wang and K. Petermann, “Noise analysis of semiconductor lasers with coherence collapse regime,” IEEE J. Quantum Electron.27 (1991).
[Crossref]

Peyghambarian, N.

Plais, A.

P. Signoret, F. Marin, S. Viciani, G. Belleville, M. Myara, J.-P. Tourrenc, B. Orsal, A. Plais, F. Gaborit, and J. Jacquet, “3.6-mhz linewidth 1.55 µ m monomode vertical-cavity surface-emitting laser,” IEEE Photonics Technol. Lett. 13, 269–271 (2001).
[Crossref]

Press, W. H.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C - The Art of Scientific Computing - Second Edition, 3rd ed. (Cambridge University Press, 2007).

Robert, Y.

N. Von Bandel, M. Garcia, M. Lecomte, A. Larrue, Y. Robert, O. Driss, O. Parrilaud, M. Krakowski, F. Gruet, and R. Matthey, “Dfb-ridge laser diodes at 894 nm for cesium atomic clocks,” in SPIE OPTO, (ISOP, 2016), pp. 97552K.

Romanini, D.

J. Morville, D. Romanini, M. Chenevrier, and A. Kachanov, “Effects of laser phase noise on the injection of a high-finesse cavity,” Appl. Opt.41 (2002).
[Crossref] [PubMed]

Rubiola, E.

R. Boudot and E. Rubiola, “Phase noise in rf and microwave amplifiers,” IEEE Trans. Ultrason Ferr. 59, 2613–2624 (2012).
[Crossref]

Rüdiger, A.

G. Heinzel, A. Rüdiger, and R. Schilling, “Spectrum and spectral density estimation by the discrete fourier transform (dft-fft), including a comprehensive list of window functions and some new flat-top windows.” Tech. rep., Albert Einstein Institut (2002).

Sagnes, I.

A. Laurain, M. Myara, G. Beaudoin, I. Sagnes, and A. Garnache, “Multiwatt-power highly-coherent compact single-frequency tunable vertical external cavity surface emitting semiconductor laser,” Opt. Express 14, 14631 (2010).

M. Myara, M. Sellahi, A. Laurain, A. Garnache, A. Michon, and I. Sagnes, “Noise properties of nir and mir vecsels (invited paper),” in IEEE Proceedings of International Conference on Noise and Fluctuations (IEEE), (2013).

Saleh, B.

B. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley Interscience, 1991).
[Crossref]

Saleh, K.

Schawlow, A.

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

Schilling, R.

G. Heinzel, A. Rüdiger, and R. Schilling, “Spectrum and spectral density estimation by the discrete fourier transform (dft-fft), including a comprehensive list of window functions and some new flat-top windows.” Tech. rep., Albert Einstein Institut (2002).

Schilt, S.

Schori, C.

Sellahi, M.

M. Myara, M. Sellahi, A. Laurain, A. Garnache, A. Michon, and I. Sagnes, “Noise properties of nir and mir vecsels (invited paper),” in IEEE Proceedings of International Conference on Noise and Fluctuations (IEEE), (2013).

Serna, J.

A. E. Siegman, G. Nemes, and J. Serna, “How to (maybe) measure laser beam quality,” in Diode Pumped Solid State Lasers: Applications and Issues (DLAI), M. Dowley, ed. (Optical Society of America, 1998), pp. MQ1.
[Crossref]

Siegman, A. E.

A. E. Siegman, G. Nemes, and J. Serna, “How to (maybe) measure laser beam quality,” in Diode Pumped Solid State Lasers: Applications and Issues (DLAI), M. Dowley, ed. (Optical Society of America, 1998), pp. MQ1.
[Crossref]

Signoret, P.

J.-P. Tourrenc, P. Signoret, M. Myara, M. Bellon, J.-P. Perez, J.-M. Gosalbes, R. Alabedra, and B. Orsal, “Low-frequency fm-noise-induced lineshape : A theoretical and experimental approach,” IEEE J. Quantum Electron. 41, 549–553 (2005).
[Crossref]

P. Signoret, M. Myara, J.-P. Tourrenc, B. Orsal, M.-H. Monier, J. Jacquet, P. Leboudec, and F. Marin, “Bragg section effects on linewidth and lineshape in 1.55 µ m dbr tunable laser diodes,” IEEE Photonics Technol. Lett. 25, 1429–1431 (2004).
[Crossref]

M. Myara, P. Signoret, J.-P. Tourrenc, J.-P. Perez, B. Orsal, and J. Jacquet, “Strongly sub-poissonian electrical noise in 1.55 µ m dbr tunable laser diodes,” IEEE J. Quantum Electron. 40, 852–857 (2004).
[Crossref]

P. Signoret, F. Marin, S. Viciani, G. Belleville, M. Myara, J.-P. Tourrenc, B. Orsal, A. Plais, F. Gaborit, and J. Jacquet, “3.6-mhz linewidth 1.55 µ m monomode vertical-cavity surface-emitting laser,” IEEE Photonics Technol. Lett. 13, 269–271 (2001).
[Crossref]

Smith, S. P.

Spiegelberg, C.

Swanston, D.

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Taczak, T. M.

Tamamura, T.

H. Ishii, F. Kano, Y. Tohmori, Y. Kondo, T. Tamamura, and Y. Yoshikuni, “Narrow spectral linewidth under wavelength tuning in thermaly tunable super-structure-grating (ssg) dbr lasers,” IEEE J. Sel. Top. Quantum Electron. 1, 401–407 (1995).
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Thomann, P.

Tikhomirov, A.

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

A. Tikhomirov and S. Foster, “DFB FL sensor cross-coupling reduction,” J. Lightwave Technol. 25, 533–538 (2007).
[Crossref]

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R. W. Tkach and A. R. Chraplyvy, “Phase noise and linewidth in an inaasp dfb laser,” J. Lightwave Technol. 4, 1711 (1996).
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Tohmori, Y.

H. Ishii, F. Kano, Y. Tohmori, Y. Kondo, T. Tamamura, and Y. Yoshikuni, “Narrow spectral linewidth under wavelength tuning in thermaly tunable super-structure-grating (ssg) dbr lasers,” IEEE J. Sel. Top. Quantum Electron. 1, 401–407 (1995).
[Crossref]

Tourrenc, J.-P.

J.-P. Tourrenc, P. Signoret, M. Myara, M. Bellon, J.-P. Perez, J.-M. Gosalbes, R. Alabedra, and B. Orsal, “Low-frequency fm-noise-induced lineshape : A theoretical and experimental approach,” IEEE J. Quantum Electron. 41, 549–553 (2005).
[Crossref]

P. Signoret, M. Myara, J.-P. Tourrenc, B. Orsal, M.-H. Monier, J. Jacquet, P. Leboudec, and F. Marin, “Bragg section effects on linewidth and lineshape in 1.55 µ m dbr tunable laser diodes,” IEEE Photonics Technol. Lett. 25, 1429–1431 (2004).
[Crossref]

M. Myara, P. Signoret, J.-P. Tourrenc, J.-P. Perez, B. Orsal, and J. Jacquet, “Strongly sub-poissonian electrical noise in 1.55 µ m dbr tunable laser diodes,” IEEE J. Quantum Electron. 40, 852–857 (2004).
[Crossref]

P. Signoret, F. Marin, S. Viciani, G. Belleville, M. Myara, J.-P. Tourrenc, B. Orsal, A. Plais, F. Gaborit, and J. Jacquet, “3.6-mhz linewidth 1.55 µ m monomode vertical-cavity surface-emitting laser,” IEEE Photonics Technol. Lett. 13, 269–271 (2001).
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A. Schawlow and C. Townes, “Infrared and optical masers,” Phys. Rev. 112, 1940–1949 (1958).
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M. Okai, T. Tsuchiya, K. Uomi, N. Chimone, and T. Harada, “Corrugation-pitch-modulated mqw-dfb laser with narrow spectral linewidth (170 khz),” IEEE Photonics Technol. Lett. 2, 529–534 (1990).
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Uomi, K.

M. Okai, T. Tsuchiya, K. Uomi, N. Chimone, and T. Harada, “Corrugation-pitch-modulated mqw-dfb laser with narrow spectral linewidth (170 khz),” IEEE Photonics Technol. Lett. 2, 529–534 (1990).
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W. A. Hamel, M. P. van Exter, and J. P. Woerdman, “Coherence properties of a semiconductor laser with feedback from a distant reflector: Eperiment and theory,” IEEE J. Quantum Electron. 28, 1459–1469 (1992).
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S. Viciani, M. Gabrysch, F. Marin, F. M. di Sopra, M. Moser, and K. H. Gulden, “Lineshape of a vertical cavity surface emitting laser,” Opt. Commun. 206(1), 89–97 (2002).
[Crossref]

P. Signoret, F. Marin, S. Viciani, G. Belleville, M. Myara, J.-P. Tourrenc, B. Orsal, A. Plais, F. Gaborit, and J. Jacquet, “3.6-mhz linewidth 1.55 µ m monomode vertical-cavity surface-emitting laser,” IEEE Photonics Technol. Lett. 13, 269–271 (2001).
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N. Von Bandel, M. Garcia, M. Lecomte, A. Larrue, Y. Robert, O. Driss, O. Parrilaud, M. Krakowski, F. Gruet, and R. Matthey, “Dfb-ridge laser diodes at 894 nm for cesium atomic clocks,” in SPIE OPTO, (ISOP, 2016), pp. 97552K.

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C. K. Boggs, A. D. Doak, and F. Walls, “Measurement of voltage noise in chemical batteries,” in 49th Proceedings of the 1995 IEEE International Frequency Control Symposium (IEEE, 1995), pp. 367–373.

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[Crossref]

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W. A. Hamel, M. P. van Exter, and J. P. Woerdman, “Coherence properties of a semiconductor laser with feedback from a distant reflector: Eperiment and theory,” IEEE J. Quantum Electron. 28, 1459–1469 (1992).
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H. Yamazaki, M. Yamaguchi, and Kitamura, “Spectral linewidth rebroadening in mqw-dfb lds caused by spontaneous emission noise in sch/barrier layers,” IEEE Photonics Technol. Lett. 2, 529–534 (1990).

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H. Ishii, F. Kano, Y. Tohmori, Y. Kondo, T. Tamamura, and Y. Yoshikuni, “Narrow spectral linewidth under wavelength tuning in thermaly tunable super-structure-grating (ssg) dbr lasers,” IEEE J. Sel. Top. Quantum Electron. 1, 401–407 (1995).
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F. M. di Sopra, H. P. Zappe, M. Moser, R. Hövel, H.-P. Gauggel, and K. G. Gulden, “Near-infrared vertical-cavity surface emitting lasers with 3-mhz linewidth,” IEEE Photonics Technol. Lett. 11, 1533–1535 (1999).
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IEEE J. Sel. Top. Quantum Electron. (1)

H. Ishii, F. Kano, Y. Tohmori, Y. Kondo, T. Tamamura, and Y. Yoshikuni, “Narrow spectral linewidth under wavelength tuning in thermaly tunable super-structure-grating (ssg) dbr lasers,” IEEE J. Sel. Top. Quantum Electron. 1, 401–407 (1995).
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J.-M. Verdiell, U. Koren, and T. L. Koch, “Linewidth and alpha-factor of detuned-loaded dbr lasers,” IEEE Photonics Technol. Lett. 4, 302–305 (1992).
[Crossref]

M. Okai, T. Tsuchiya, K. Uomi, N. Chimone, and T. Harada, “Corrugation-pitch-modulated mqw-dfb laser with narrow spectral linewidth (170 khz),” IEEE Photonics Technol. Lett. 2, 529–534 (1990).
[Crossref]

H. Yamazaki, M. Yamaguchi, and Kitamura, “Spectral linewidth rebroadening in mqw-dfb lds caused by spontaneous emission noise in sch/barrier layers,” IEEE Photonics Technol. Lett. 2, 529–534 (1990).

P. Signoret, F. Marin, S. Viciani, G. Belleville, M. Myara, J.-P. Tourrenc, B. Orsal, A. Plais, F. Gaborit, and J. Jacquet, “3.6-mhz linewidth 1.55 µ m monomode vertical-cavity surface-emitting laser,” IEEE Photonics Technol. Lett. 13, 269–271 (2001).
[Crossref]

P. Signoret, M. Myara, J.-P. Tourrenc, B. Orsal, M.-H. Monier, J. Jacquet, P. Leboudec, and F. Marin, “Bragg section effects on linewidth and lineshape in 1.55 µ m dbr tunable laser diodes,” IEEE Photonics Technol. Lett. 25, 1429–1431 (2004).
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S. M. Melle, A. T. Alavie, S. Karr, T. Coroy, K. Liu, and R. M. Measures, “A bragg grating-tuned fiber laser strain sensor system,” IEEE Photonics Technol. Lett. 5, 263–266 (1993).
[Crossref]

F. M. di Sopra, H. P. Zappe, M. Moser, R. Hövel, H.-P. Gauggel, and K. G. Gulden, “Near-infrared vertical-cavity surface emitting lasers with 3-mhz linewidth,” IEEE Photonics Technol. Lett. 11, 1533–1535 (1999).
[Crossref]

IEEE Trans. Ultrason Ferr. (1)

R. Boudot and E. Rubiola, “Phase noise in rf and microwave amplifiers,” IEEE Trans. Ultrason Ferr. 59, 2613–2624 (2012).
[Crossref]

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A. McLean, C. Mitchell, and D. Swanston, “Implementation of an efficient analytical approximation to the voigt function for photoemission lineshape analysis,” J. Electron Spectrosc. 69, 125–132 (1994).
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L. B. Mercer, “1/f frequency noise effects on self-heterodyne linewidth measurements,” J. Lightwave Technol. 9, 485–492 (1991).
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A. Tikhomirov and S. Foster, “DFB FL sensor cross-coupling reduction,” J. Lightwave Technol. 25, 533–538 (2007).
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Opt. Commun. (1)

S. Viciani, M. Gabrysch, F. Marin, F. M. di Sopra, M. Moser, and K. H. Gulden, “Lineshape of a vertical cavity surface emitting laser,” Opt. Commun. 206(1), 89–97 (2002).
[Crossref]

Opt. Express (1)

A. Laurain, M. Myara, G. Beaudoin, I. Sagnes, and A. Garnache, “Multiwatt-power highly-coherent compact single-frequency tunable vertical external cavity surface emitting semiconductor laser,” Opt. Express 14, 14631 (2010).

Opt. Fiber Technol. (1)

D. M. Baney, P. Gallion, and R. S. Tucker, “Theory and measurement techniques for the noise figure of optical amplifiers,” Opt. Fiber Technol. 6, 122–154 (2000).
[Crossref]

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A. Schawlow and C. Townes, “Infrared and optical masers,” Phys. Rev. 112, 1940–1949 (1958).
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J. Morville, D. Romanini, M. Chenevrier, and A. Kachanov, “Effects of laser phase noise on the injection of a high-finesse cavity,” Appl. Opt.41 (2002).
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J. Wang and K. Petermann, “Noise analysis of semiconductor lasers with coherence collapse regime,” IEEE J. Quantum Electron.27 (1991).
[Crossref]

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C - The Art of Scientific Computing - Second Edition, 3rd ed. (Cambridge University Press, 2007).

G. Heinzel, A. Rüdiger, and R. Schilling, “Spectrum and spectral density estimation by the discrete fourier transform (dft-fft), including a comprehensive list of window functions and some new flat-top windows.” Tech. rep., Albert Einstein Institut (2002).

A. E. Siegman, G. Nemes, and J. Serna, “How to (maybe) measure laser beam quality,” in Diode Pumped Solid State Lasers: Applications and Issues (DLAI), M. Dowley, ed. (Optical Society of America, 1998), pp. MQ1.
[Crossref]

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, 1995).
[Crossref]

B. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley Interscience, 1991).
[Crossref]

C. K. Boggs, A. D. Doak, and F. Walls, “Measurement of voltage noise in chemical batteries,” in 49th Proceedings of the 1995 IEEE International Frequency Control Symposium (IEEE, 1995), pp. 367–373.

C. Ye, Tunable External Cavity Diode Lasers (World Scientific, 2004).
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F. W. King, Hilbert transforms, vol. 2 (Cambridge University PressCambridge, 2009).

M. Myara, N. Von Bandel, and M. Sellahi, “LaserCoherenceAnalyser - DOI:10.5281/zenodo.162952,” https://doi.org/10.5281/zenodo.162952 (2016).

N. Von Bandel, M. Garcia, M. Lecomte, A. Larrue, Y. Robert, O. Driss, O. Parrilaud, M. Krakowski, F. Gruet, and R. Matthey, “Dfb-ridge laser diodes at 894 nm for cesium atomic clocks,” in SPIE OPTO, (ISOP, 2016), pp. 97552K.

Supplementary Material (1)

NameDescription
» Code 1       Laser Coherence Analyser

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Figures (15)

Fig. 1
Fig. 1 Basic Heterodyne Set-up.
Fig. 2
Fig. 2 Sweeping (superheterodyne) RF spectrum analyzer at work: the resolution filter sweeps in time across all the frequencies to obtain the whole spectrum. The spectrum does not reflect a specific timeframe.
Fig. 3
Fig. 3 Frequency variations induced by typical mechanical noise. In this case, the RMS value is not stable as a function of the starting time Ti of the experiment.
Fig. 4
Fig. 4 Heterodyne Set-up proposed in this work: use of a sampler and numerical signal analysis.
Fig. 5
Fig. 5 Summary of the relevant signals and the mathematical relationships between them. No arrow is for no possible path. Dashed arrow is for no conceptual impossibility but not reported in literature. Wavy arrow is for possible path with approximations.
Fig. 6
Fig. 6 Beat-note sampling and short-time linewidth estimation. Thanks to the change of the length of the sub-sample, a time-dependent linewidth study is possible.
Fig. 7
Fig. 7 Michelson-Based Frequency Noise set-up.
Fig. 8
Fig. 8 Frequency noise spectrum obtained from Michelson experiments and beating experiments for the DFB-SC (each close to 40mW). The 1/fα noise part usually comes from electrical transport phenomena [43], whereas the white noise part comes from the spontaneous emission (Shawlow-Townes-Henry).
Fig. 9
Fig. 9 Frequency Noise spectra obtained from DFB-SC, ECDL and DFB-FL beating.
Fig. 10
Fig. 10 Relevance (a) and irrelevance (b) of the FWHM depending on the spectral shape. a) case of a semiconductor DFB: the width and the associated RMS value do not change too much over one decade of magnitude. b) case of an ECDL: the width and associated RMS value changes dramatically in the same conditions.
Fig. 11
Fig. 11 Estimated Δνc for the ECDL/DFB-FL experiments as a function of the beat-note time sample length. The main curve is the average value and the error bars are the standard deviation over 128 samples up to 1 ms. Above this duration, the beat-note sample size imposes the amount of averages to decrease, down to a single full-size sample for the last point at 60 ms. In the insets, various spectra have been displayed to show the instability of the central frequency and of the linewidth due to mechanical fluctuations; the vertical scale of the insets is the RF power in arbitrary unit.
Fig. 12
Fig. 12 a) Spectral width of the DFB-SC beating and comparison of the Δνc criterion with the Voigt profile fitting. b) Δνc for configurations 1, 2 and 3.
Fig. 13
Fig. 13 a) β-separation line illustration, the slow modulation area (filled) is represented for ΔT = 1 ms. b) Time-dependent linewidth computed thanks to the numerical methods proposed here, compared to the β-separation line approach.
Fig. 14
Fig. 14 a) Frequency noise limit measured b) Linewidth limit measured.
Fig. 15
Fig. 15 a) Intrinsic linewidth computed from time-domain frequency noise signal using “virtual” carrier. b) Frequency noise spectrum computed from the time domain frequency noise signal.

Tables (1)

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Table 1 Relations between standard FWHM and Δνc

Equations (16)

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1 Δ T T i T i + Δ T sin 2 ( 2 π f M t ) d t
b ( t ) = a ( t ) × cos ( φ ( t ) )
b a ( t ) = b ( t ) + j [ b ( t ) ]
ν ( t ) = 1 2 π × d φ ( t ) d t
= ν ¯ + ν ˜ ( t )
P S D ν ( f ) = ( lim T 1 2 T T + T ν ˜ * ( t ) ν ˜ ( t + τ ) d t )
P S D ν ( f ) ( ν ˜ ( t ) ) × * ( ν ˜ ( t ) )
( f ) = ( lim T 1 2 T T + T b * ( t ) b ( t + τ ) d t )
T i , Δ T ( f ) = ( lim T 1 2 T T + T b T i , Δ T * ( t ) b T i , Δ T ( t + τ ) d t )
T i , Δ T ( f ) = ( b T i , Δ T * ( t ) ) × ( b T i , Δ T ( t ) )
Δ ν T i , Δ T = ( 0 + T i , Δ T ( f ) d f ) 2 0 + T i , Δ T 2 ( f ) d f
Δ ν c ¯ = 1 M i = 1 M Δ ν T i , Δ T
Δ ν c = Δ ν c ¯ ± 1 2 1 M i = 1 M ( Δ ν T i , Δ T Δ ν c ¯ ) 2
b ( t ) = A cos ( 2 π f b t + β sin ( 2 π f M t ) ) = A n = + J n ( β ) cos ( 2 π ( f P + n f M ) t ) .
ϵ ( f ) = j 2 π f ( b ( t ) ) * Δ T ( f )
P S D f = 4 π f 2 P S D ϵ V 0 2

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