Abstract

We report on a comprehensive theoretical and experimental analysis of the feed-forward method for external frequency stabilization of a continuous wave laser against a frequency comb. Application of the method to a distributed feedback diode laser at 1.55 μm allows line narrowing from 800 to 10 kHz, with frequency noise reduction by more than 2 decades up to a Fourier frequency of 100 kHz and a maximum control bandwidth of 0.8 MHz. The results are consistent with a relative phase fluctuation of 1.4 rad rms, as limited by uncompensated high-frequency noise of the slave laser.

© 2012 OSA

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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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2012

2011

S. Bartalini, S. Borri, I. Galli, G. Giusfredi, D. Mazzotti, T. Edamura, N. Akikusa, M. Yamanishi, and P. De Natale, “Measuring frequency noise and intrinsic linewidth of a room-temperature DFB quantum cascade laser,” Opt. Express19(19), 17996–18003 (2011).
[CrossRef] [PubMed]

A. Gambetta, D. Gatti, A. Castrillo, G. Galzerano, P. Laporta, L. Gianfrani, and M. Marangoni, “Mid-infrared quantitative spectroscopy by comb-referencing of a quantum-cascade-laser: Application to the CO2 spectrum at 4.3 μm,” Appl. Phys. Lett.99(25), 251107 (2011).
[CrossRef]

C. P. McRaven, M. J. Cich, G. V. Lopez, T. J. Sears, D. Hurtmans, and A. W. Mantz, “Frequency comb-referenced measurements of self- and nitrogen-broadening in the ν1 + ν3 band of acetylene,” J. Mol. Spectrosc.266(1), 43–51 (2011).
[CrossRef]

C. G. Parthey, A. Matveev, J. Alnis, B. Bernhardt, A. Beyer, R. Holzwarth, A. Maistrou, R. Pohl, K. Predehl, T. Udem, T. Wilken, N. Kolachevsky, M. Abgrall, D. Rovera, C. Salomon, P. Laurent, and T. W. Hänsch, “Improved Measurement of the Hydrogen 1S-2S Transition Frequency,” Phys. Rev. Lett.107(20), 203001 (2011).
[CrossRef] [PubMed]

2010

S. A. Diddams, “The evolving optical frequency comb,” J. Opt. Soc. Am. B27(11), B51–B62 (2010).
[CrossRef]

S. Koke, C. Grebing, H. Frei, A. Anderson, A. Assion, and G. Steinmeyer, “Direct frequency comb synthesis with arbitrary offset and shot-noise-limited phase noise,” Nat. Photonics4(7), 462–465 (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(25), 4801–4807 (2010).
[CrossRef] [PubMed]

2009

2006

2005

E. A. Donley, T. P. Heavner, F. Levi, M. O. Tataw, and S. R. Jefferts, “Double-pass acousto-optic modulator system,” Rev. Sci. Instrum.76(6), 063112 (2005).
[CrossRef]

2003

2002

1984

Abgrall, M.

C. G. Parthey, A. Matveev, J. Alnis, B. Bernhardt, A. Beyer, R. Holzwarth, A. Maistrou, R. Pohl, K. Predehl, T. Udem, T. Wilken, N. Kolachevsky, M. Abgrall, D. Rovera, C. Salomon, P. Laurent, and T. W. Hänsch, “Improved Measurement of the Hydrogen 1S-2S Transition Frequency,” Phys. Rev. Lett.107(20), 203001 (2011).
[CrossRef] [PubMed]

Ahtee, V.

Akikusa, N.

Alnis, J.

C. G. Parthey, A. Matveev, J. Alnis, B. Bernhardt, A. Beyer, R. Holzwarth, A. Maistrou, R. Pohl, K. Predehl, T. Udem, T. Wilken, N. Kolachevsky, M. Abgrall, D. Rovera, C. Salomon, P. Laurent, and T. W. Hänsch, “Improved Measurement of the Hydrogen 1S-2S Transition Frequency,” Phys. Rev. Lett.107(20), 203001 (2011).
[CrossRef] [PubMed]

Anderson, A.

S. Koke, C. Grebing, H. Frei, A. Anderson, A. Assion, and G. Steinmeyer, “Direct frequency comb synthesis with arbitrary offset and shot-noise-limited phase noise,” Nat. Photonics4(7), 462–465 (2010).
[CrossRef]

Apolonski, A.

Assion, A.

F. Lücking, A. Assion, A. Apolonski, F. Krausz, and G. Steinmeyer, “Long-term carrier-envelope-phase-stable few-cycle pulses by use of the feed-forward method,” Opt. Lett.37(11), 2076–2078 (2012).
[CrossRef] [PubMed]

S. Koke, C. Grebing, H. Frei, A. Anderson, A. Assion, and G. Steinmeyer, “Direct frequency comb synthesis with arbitrary offset and shot-noise-limited phase noise,” Nat. Photonics4(7), 462–465 (2010).
[CrossRef]

Bartalini, S.

Bernhardt, B.

C. G. Parthey, A. Matveev, J. Alnis, B. Bernhardt, A. Beyer, R. Holzwarth, A. Maistrou, R. Pohl, K. Predehl, T. Udem, T. Wilken, N. Kolachevsky, M. Abgrall, D. Rovera, C. Salomon, P. Laurent, and T. W. Hänsch, “Improved Measurement of the Hydrogen 1S-2S Transition Frequency,” Phys. Rev. Lett.107(20), 203001 (2011).
[CrossRef] [PubMed]

Beyer, A.

C. G. Parthey, A. Matveev, J. Alnis, B. Bernhardt, A. Beyer, R. Holzwarth, A. Maistrou, R. Pohl, K. Predehl, T. Udem, T. Wilken, N. Kolachevsky, M. Abgrall, D. Rovera, C. Salomon, P. Laurent, and T. W. Hänsch, “Improved Measurement of the Hydrogen 1S-2S Transition Frequency,” Phys. Rev. Lett.107(20), 203001 (2011).
[CrossRef] [PubMed]

Borri, S.

Castrillo, A.

A. Gambetta, D. Gatti, A. Castrillo, G. Galzerano, P. Laporta, L. Gianfrani, and M. Marangoni, “Mid-infrared quantitative spectroscopy by comb-referencing of a quantum-cascade-laser: Application to the CO2 spectrum at 4.3 μm,” Appl. Phys. Lett.99(25), 251107 (2011).
[CrossRef]

Chen, J.

Cich, M. J.

C. P. McRaven, M. J. Cich, G. V. Lopez, T. J. Sears, D. Hurtmans, and A. W. Mantz, “Frequency comb-referenced measurements of self- and nitrogen-broadening in the ν1 + ν3 band of acetylene,” J. Mol. Spectrosc.266(1), 43–51 (2011).
[CrossRef]

Coluccelli, N.

De Natale, P.

Di Domenico, G.

Diddams, S. A.

Donley, E. A.

E. A. Donley, T. P. Heavner, F. Levi, M. O. Tataw, and S. R. Jefferts, “Double-pass acousto-optic modulator system,” Rev. Sci. Instrum.76(6), 063112 (2005).
[CrossRef]

Edamura, T.

Fermann, M.

Frei, H.

S. Koke, C. Grebing, H. Frei, A. Anderson, A. Assion, and G. Steinmeyer, “Direct frequency comb synthesis with arbitrary offset and shot-noise-limited phase noise,” Nat. Photonics4(7), 462–465 (2010).
[CrossRef]

Galli, I.

Galzerano, G.

T. Sala, D. Gatti, A. Gambetta, N. Coluccelli, G. Galzerano, P. Laporta, and M. Marangoni, “Wide-bandwidth phase lock between a CW laser and a frequency comb based on a feed-forward configuration,” Opt. Lett.37(13), 2592–2594 (2012).
[CrossRef] [PubMed]

A. Gambetta, D. Gatti, A. Castrillo, G. Galzerano, P. Laporta, L. Gianfrani, and M. Marangoni, “Mid-infrared quantitative spectroscopy by comb-referencing of a quantum-cascade-laser: Application to the CO2 spectrum at 4.3 μm,” Appl. Phys. Lett.99(25), 251107 (2011).
[CrossRef]

Gambetta, A.

T. Sala, D. Gatti, A. Gambetta, N. Coluccelli, G. Galzerano, P. Laporta, and M. Marangoni, “Wide-bandwidth phase lock between a CW laser and a frequency comb based on a feed-forward configuration,” Opt. Lett.37(13), 2592–2594 (2012).
[CrossRef] [PubMed]

A. Gambetta, D. Gatti, A. Castrillo, G. Galzerano, P. Laporta, L. Gianfrani, and M. Marangoni, “Mid-infrared quantitative spectroscopy by comb-referencing of a quantum-cascade-laser: Application to the CO2 spectrum at 4.3 μm,” Appl. Phys. Lett.99(25), 251107 (2011).
[CrossRef]

Gatti, D.

Gianfrani, L.

A. A. Mills, D. Gatti, J. Jiang, C. Mohr, W. Mefford, L. Gianfrani, M. Fermann, I. Hartl, and M. Marangoni, “Coherent phase lock of a 9 μm quantum cascade laser to a 2 μm thulium optical frequency comb,” Opt. Lett.37(19), 4083–4085 (2012).
[CrossRef] [PubMed]

A. Gambetta, D. Gatti, A. Castrillo, G. Galzerano, P. Laporta, L. Gianfrani, and M. Marangoni, “Mid-infrared quantitative spectroscopy by comb-referencing of a quantum-cascade-laser: Application to the CO2 spectrum at 4.3 μm,” Appl. Phys. Lett.99(25), 251107 (2011).
[CrossRef]

Giusfredi, G.

Grebing, C.

S. Koke, C. Grebing, H. Frei, A. Anderson, A. Assion, and G. Steinmeyer, “Direct frequency comb synthesis with arbitrary offset and shot-noise-limited phase noise,” Nat. Photonics4(7), 462–465 (2010).
[CrossRef]

Guo, R.

Hall, J. L.

Hänsch, T. W.

C. G. Parthey, A. Matveev, J. Alnis, B. Bernhardt, A. Beyer, R. Holzwarth, A. Maistrou, R. Pohl, K. Predehl, T. Udem, T. Wilken, N. Kolachevsky, M. Abgrall, D. Rovera, C. Salomon, P. Laurent, and T. W. Hänsch, “Improved Measurement of the Hydrogen 1S-2S Transition Frequency,” Phys. Rev. Lett.107(20), 203001 (2011).
[CrossRef] [PubMed]

J. L. Hall and T. W. Hänsch, “External dye-laser frequency stabilizer,” Opt. Lett.9(11), 502–504 (1984).
[CrossRef] [PubMed]

Hartl, I.

Heavner, T. P.

E. A. Donley, T. P. Heavner, F. Levi, M. O. Tataw, and S. R. Jefferts, “Double-pass acousto-optic modulator system,” Rev. Sci. Instrum.76(6), 063112 (2005).
[CrossRef]

Holzwarth, R.

C. G. Parthey, A. Matveev, J. Alnis, B. Bernhardt, A. Beyer, R. Holzwarth, A. Maistrou, R. Pohl, K. Predehl, T. Udem, T. Wilken, N. Kolachevsky, M. Abgrall, D. Rovera, C. Salomon, P. Laurent, and T. W. Hänsch, “Improved Measurement of the Hydrogen 1S-2S Transition Frequency,” Phys. Rev. Lett.107(20), 203001 (2011).
[CrossRef] [PubMed]

Hong, F. L.

Hurtmans, D.

C. P. McRaven, M. J. Cich, G. V. Lopez, T. J. Sears, D. Hurtmans, and A. W. Mantz, “Frequency comb-referenced measurements of self- and nitrogen-broadening in the ν1 + ν3 band of acetylene,” J. Mol. Spectrosc.266(1), 43–51 (2011).
[CrossRef]

Inaba, H.

Jefferts, S. R.

E. A. Donley, T. P. Heavner, F. Levi, M. O. Tataw, and S. R. Jefferts, “Double-pass acousto-optic modulator system,” Rev. Sci. Instrum.76(6), 063112 (2005).
[CrossRef]

Jiang, J.

Jost, J. D.

Kärtner, F. X.

Koke, S.

S. Koke, C. Grebing, H. Frei, A. Anderson, A. Assion, and G. Steinmeyer, “Direct frequency comb synthesis with arbitrary offset and shot-noise-limited phase noise,” Nat. Photonics4(7), 462–465 (2010).
[CrossRef]

Kolachevsky, N.

C. G. Parthey, A. Matveev, J. Alnis, B. Bernhardt, A. Beyer, R. Holzwarth, A. Maistrou, R. Pohl, K. Predehl, T. Udem, T. Wilken, N. Kolachevsky, M. Abgrall, D. Rovera, C. Salomon, P. Laurent, and T. W. Hänsch, “Improved Measurement of the Hydrogen 1S-2S Transition Frequency,” Phys. Rev. Lett.107(20), 203001 (2011).
[CrossRef] [PubMed]

Krausz, F.

Laporta, P.

T. Sala, D. Gatti, A. Gambetta, N. Coluccelli, G. Galzerano, P. Laporta, and M. Marangoni, “Wide-bandwidth phase lock between a CW laser and a frequency comb based on a feed-forward configuration,” Opt. Lett.37(13), 2592–2594 (2012).
[CrossRef] [PubMed]

A. Gambetta, D. Gatti, A. Castrillo, G. Galzerano, P. Laporta, L. Gianfrani, and M. Marangoni, “Mid-infrared quantitative spectroscopy by comb-referencing of a quantum-cascade-laser: Application to the CO2 spectrum at 4.3 μm,” Appl. Phys. Lett.99(25), 251107 (2011).
[CrossRef]

Laurent, P.

C. G. Parthey, A. Matveev, J. Alnis, B. Bernhardt, A. Beyer, R. Holzwarth, A. Maistrou, R. Pohl, K. Predehl, T. Udem, T. Wilken, N. Kolachevsky, M. Abgrall, D. Rovera, C. Salomon, P. Laurent, and T. W. Hänsch, “Improved Measurement of the Hydrogen 1S-2S Transition Frequency,” Phys. Rev. Lett.107(20), 203001 (2011).
[CrossRef] [PubMed]

Levi, F.

E. A. Donley, T. P. Heavner, F. Levi, M. O. Tataw, and S. R. Jefferts, “Double-pass acousto-optic modulator system,” Rev. Sci. Instrum.76(6), 063112 (2005).
[CrossRef]

Lopez, G. V.

C. P. McRaven, M. J. Cich, G. V. Lopez, T. J. Sears, D. Hurtmans, and A. W. Mantz, “Frequency comb-referenced measurements of self- and nitrogen-broadening in the ν1 + ν3 band of acetylene,” J. Mol. Spectrosc.266(1), 43–51 (2011).
[CrossRef]

Lücking, F.

Maistrou, A.

C. G. Parthey, A. Matveev, J. Alnis, B. Bernhardt, A. Beyer, R. Holzwarth, A. Maistrou, R. Pohl, K. Predehl, T. Udem, T. Wilken, N. Kolachevsky, M. Abgrall, D. Rovera, C. Salomon, P. Laurent, and T. W. Hänsch, “Improved Measurement of the Hydrogen 1S-2S Transition Frequency,” Phys. Rev. Lett.107(20), 203001 (2011).
[CrossRef] [PubMed]

Mantz, A. W.

C. P. McRaven, M. J. Cich, G. V. Lopez, T. J. Sears, D. Hurtmans, and A. W. Mantz, “Frequency comb-referenced measurements of self- and nitrogen-broadening in the ν1 + ν3 band of acetylene,” J. Mol. Spectrosc.266(1), 43–51 (2011).
[CrossRef]

Marangoni, M.

Matos, L.

Matsumoto, H.

Matveev, A.

C. G. Parthey, A. Matveev, J. Alnis, B. Bernhardt, A. Beyer, R. Holzwarth, A. Maistrou, R. Pohl, K. Predehl, T. Udem, T. Wilken, N. Kolachevsky, M. Abgrall, D. Rovera, C. Salomon, P. Laurent, and T. W. Hänsch, “Improved Measurement of the Hydrogen 1S-2S Transition Frequency,” Phys. Rev. Lett.107(20), 203001 (2011).
[CrossRef] [PubMed]

Mazzotti, D.

McRaven, C. P.

C. P. McRaven, M. J. Cich, G. V. Lopez, T. J. Sears, D. Hurtmans, and A. W. Mantz, “Frequency comb-referenced measurements of self- and nitrogen-broadening in the ν1 + ν3 band of acetylene,” J. Mol. Spectrosc.266(1), 43–51 (2011).
[CrossRef]

Mefford, W.

Merimaa, M.

Mills, A. A.

Minoshima, K.

Mohr, C.

Mücke, O. D.

Nakagawa, K.

Nyholm, K.

Onae, A.

Parthey, C. G.

C. G. Parthey, A. Matveev, J. Alnis, B. Bernhardt, A. Beyer, R. Holzwarth, A. Maistrou, R. Pohl, K. Predehl, T. Udem, T. Wilken, N. Kolachevsky, M. Abgrall, D. Rovera, C. Salomon, P. Laurent, and T. W. Hänsch, “Improved Measurement of the Hydrogen 1S-2S Transition Frequency,” Phys. Rev. Lett.107(20), 203001 (2011).
[CrossRef] [PubMed]

Pohl, R.

C. G. Parthey, A. Matveev, J. Alnis, B. Bernhardt, A. Beyer, R. Holzwarth, A. Maistrou, R. Pohl, K. Predehl, T. Udem, T. Wilken, N. Kolachevsky, M. Abgrall, D. Rovera, C. Salomon, P. Laurent, and T. W. Hänsch, “Improved Measurement of the Hydrogen 1S-2S Transition Frequency,” Phys. Rev. Lett.107(20), 203001 (2011).
[CrossRef] [PubMed]

Predehl, K.

C. G. Parthey, A. Matveev, J. Alnis, B. Bernhardt, A. Beyer, R. Holzwarth, A. Maistrou, R. Pohl, K. Predehl, T. Udem, T. Wilken, N. Kolachevsky, M. Abgrall, D. Rovera, C. Salomon, P. Laurent, and T. W. Hänsch, “Improved Measurement of the Hydrogen 1S-2S Transition Frequency,” Phys. Rev. Lett.107(20), 203001 (2011).
[CrossRef] [PubMed]

Rovera, D.

C. G. Parthey, A. Matveev, J. Alnis, B. Bernhardt, A. Beyer, R. Holzwarth, A. Maistrou, R. Pohl, K. Predehl, T. Udem, T. Wilken, N. Kolachevsky, M. Abgrall, D. Rovera, C. Salomon, P. Laurent, and T. W. Hänsch, “Improved Measurement of the Hydrogen 1S-2S Transition Frequency,” Phys. Rev. Lett.107(20), 203001 (2011).
[CrossRef] [PubMed]

Sala, T.

Salomon, C.

C. G. Parthey, A. Matveev, J. Alnis, B. Bernhardt, A. Beyer, R. Holzwarth, A. Maistrou, R. Pohl, K. Predehl, T. Udem, T. Wilken, N. Kolachevsky, M. Abgrall, D. Rovera, C. Salomon, P. Laurent, and T. W. Hänsch, “Improved Measurement of the Hydrogen 1S-2S Transition Frequency,” Phys. Rev. Lett.107(20), 203001 (2011).
[CrossRef] [PubMed]

Schibli, T. R.

Schilt, S.

Sears, T. J.

C. P. McRaven, M. J. Cich, G. V. Lopez, T. J. Sears, D. Hurtmans, and A. W. Mantz, “Frequency comb-referenced measurements of self- and nitrogen-broadening in the ν1 + ν3 band of acetylene,” J. Mol. Spectrosc.266(1), 43–51 (2011).
[CrossRef]

Steinmeyer, G.

F. Lücking, A. Assion, A. Apolonski, F. Krausz, and G. Steinmeyer, “Long-term carrier-envelope-phase-stable few-cycle pulses by use of the feed-forward method,” Opt. Lett.37(11), 2076–2078 (2012).
[CrossRef] [PubMed]

S. Koke, C. Grebing, H. Frei, A. Anderson, A. Assion, and G. Steinmeyer, “Direct frequency comb synthesis with arbitrary offset and shot-noise-limited phase noise,” Nat. Photonics4(7), 462–465 (2010).
[CrossRef]

Tataw, M. O.

E. A. Donley, T. P. Heavner, F. Levi, M. O. Tataw, and S. R. Jefferts, “Double-pass acousto-optic modulator system,” Rev. Sci. Instrum.76(6), 063112 (2005).
[CrossRef]

Thomann, P.

Udem, T.

C. G. Parthey, A. Matveev, J. Alnis, B. Bernhardt, A. Beyer, R. Holzwarth, A. Maistrou, R. Pohl, K. Predehl, T. Udem, T. Wilken, N. Kolachevsky, M. Abgrall, D. Rovera, C. Salomon, P. Laurent, and T. W. Hänsch, “Improved Measurement of the Hydrogen 1S-2S Transition Frequency,” Phys. Rev. Lett.107(20), 203001 (2011).
[CrossRef] [PubMed]

Wilken, T.

C. G. Parthey, A. Matveev, J. Alnis, B. Bernhardt, A. Beyer, R. Holzwarth, A. Maistrou, R. Pohl, K. Predehl, T. Udem, T. Wilken, N. Kolachevsky, M. Abgrall, D. Rovera, C. Salomon, P. Laurent, and T. W. Hänsch, “Improved Measurement of the Hydrogen 1S-2S Transition Frequency,” Phys. Rev. Lett.107(20), 203001 (2011).
[CrossRef] [PubMed]

Yamanishi, M.

Ye, J.

Appl. Opt.

Appl. Phys. Lett.

A. Gambetta, D. Gatti, A. Castrillo, G. Galzerano, P. Laporta, L. Gianfrani, and M. Marangoni, “Mid-infrared quantitative spectroscopy by comb-referencing of a quantum-cascade-laser: Application to the CO2 spectrum at 4.3 μm,” Appl. Phys. Lett.99(25), 251107 (2011).
[CrossRef]

J. Mol. Spectrosc.

C. P. McRaven, M. J. Cich, G. V. Lopez, T. J. Sears, D. Hurtmans, and A. W. Mantz, “Frequency comb-referenced measurements of self- and nitrogen-broadening in the ν1 + ν3 band of acetylene,” J. Mol. Spectrosc.266(1), 43–51 (2011).
[CrossRef]

J. Opt. Soc. Am. B

Nat. Photonics

S. Koke, C. Grebing, H. Frei, A. Anderson, A. Assion, and G. Steinmeyer, “Direct frequency comb synthesis with arbitrary offset and shot-noise-limited phase noise,” Nat. Photonics4(7), 462–465 (2010).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. Lett.

C. G. Parthey, A. Matveev, J. Alnis, B. Bernhardt, A. Beyer, R. Holzwarth, A. Maistrou, R. Pohl, K. Predehl, T. Udem, T. Wilken, N. Kolachevsky, M. Abgrall, D. Rovera, C. Salomon, P. Laurent, and T. W. Hänsch, “Improved Measurement of the Hydrogen 1S-2S Transition Frequency,” Phys. Rev. Lett.107(20), 203001 (2011).
[CrossRef] [PubMed]

Rev. Sci. Instrum.

E. A. Donley, T. P. Heavner, F. Levi, M. O. Tataw, and S. R. Jefferts, “Double-pass acousto-optic modulator system,” Rev. Sci. Instrum.76(6), 063112 (2005).
[CrossRef]

Other

J. L. Hall and M. Zhu, “An Introduction to Phase Stable Optical Sources,” in Laser Manipulation of Atoms and Ions, E. Arimondo, W. D. Phillips, and F. Strumia, eds. (North Holland, 1992), 671.

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Figures (4)

Fig. 1
Fig. 1

Experimental setup. AOFS, acousto-optical frequency shifter; BS, beam splitter; SM, spherical mirror; DM, dichroic mirror; G, grating; PD, photodetector; HVA, RF power amplifier; PBS, polarizer beam splitter; FD, frequency divider; ESA, electrical spectrum analyser.

Fig. 2
Fig. 2

(a) Time response of the AOFS for different displacements of the beam from the piezo-actuator. (b) Frequency noise spectral density of the DFB slave laser in free running (FR) and in feed-forward (FF) regime for time delays corresponding to those of Fig. 2(a).

Fig. 3
Fig. 3

Self-heterodyne spectra in different regimes with logarithmic (a) and linear (b) scale. The inset refers to feed-forward at the fastest control bandwidth.

Fig. 4
Fig. 4

Beating signal between comb and DFB laser in the feed-forward regime at decreasing RBW from 300 to 10 Hz. Inset: normalized beating signal at 10 Hz RBW.

Tables (1)

Tables Icon

Table 1 Calculated and measured full-width-at-half-maximum (FWHM) linewidths in different regimes.

Equations (5)

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ν 1st ( t )= ν cw ( t )+ f beat ( tΔ )=[ ν cw ( t ) ν 1st ( tΔ ) ]+ ν n ( tΔ )
R 1st ( τ )= ν 1st ( t ) ν 1st ( t+τ ) = ν cw ( t ) ν cw ( t+τ ) + ν cw ( tΔ ) ν cw ( tΔ+τ ) + + ν n ( tΔ ) ν n ( tΔ+τ ) ν cw ( t ) ν cw ( tΔ+τ ) ν cw ( tΔ ) ν cw ( t+τ ) = =2 R cw ( τ )+ R n ( τ ) R cw ( τΔ ) R cw ( τ+Δ )
S 1st ν ( f )={ R 1st ( τ ) }=2 S cw ν ( f )+ S n ν ( f ) S cw ν ( f ) e i2πfΔ S cw ν ( f ) e i2πfΔ
S 1st ν ( f )= S n ν ( f )+2 S cw ν ( f )( 1cos2πfΔ )
B= 1 6Δ

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