Abstract

We study the method of Voigt profile fitting for ultra-narrow linewidth measurement. It filters out the effect of the spectrum broadening due to the 1/f frequency noise and extracts out the Lorentzian lineshape from the measured spectrum. The resolution is thus greatly promoted than the direct measurement from the self-heterodyne technique. We apply this method to an ultra-narrow-linewidth (~40 Hz by heterodyne beat technique) Brillouin/erbium fiber laser. The linewidth estimated from Voigt fitting method is indicated to be more accurate. In contrast, the linewidths estimated direct from the 3-dB and the 20-dB heterodyne-spectrum width are far over the true linewidth of the BEFL. The Voigt fitting method provides an efficient tool for ultra-narrow-linewidth measurement. And compared with heterodyne beat technique, it is applicable for all types of lasers.

© 2015 Optical Society of America

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References

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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  14. L. E. Richter, H. I. Mandelberg, S. Kruger, and P. A. Mcgrath, “Linewidth determination from self-heterodyne measurement with subcoherence delay times,” Quan. Electron. Lett. QE-22(11), 2070–2074 (1986).
    [Crossref]

2015 (1)

M. Chen, Z. Meng, Y. Zhang, J. Wang, and W. Chen, “Ultra-narrow-linewidth Brillouin/erbium fiber laser based on 45-cm erbium-doped fiber,” IEEE Photon. J. 7(1), 1500606 (2015).
[Crossref]

2014 (1)

2013 (2)

2010 (1)

2009 (1)

S. M. Abrarov, B. M. Quine, and R. K. Jagpal, “A simple interpolating algorithm for the rapid and accurate calculation of the Voigt function,” J. Quant. Spectrosc. Radiat. Transf. 110(6-7), 376–383 (2009).
[Crossref]

2006 (1)

2005 (2)

H. O. Di Rocco, “The exact expression of the Voigt profile function,” J. Quant. Spectrosc. Radiat. Transf. 92(2), 231–237 (2005).
[Crossref]

G. D. Roston and F. S. Obaid, “Exact analytical formula for Voigt spectral line profile,” J. Quant. Spectrosc. Radiat. Transf. 94(2), 255–263 (2005).
[Crossref]

2004 (1)

2000 (1)

S. D. Bruce, J. Higinbotham, I. Marshall, and P. H. Beswick, “An analytical derivation of a popular approximation of the Voigt function for quantification of NMR spectra,” J. Magn. Reson. 142(1), 57–63 (2000).
[Crossref] [PubMed]

1997 (1)

M. Kuntz, “A new implementation of the humlicek algorithm for the calculation of the Voigt profile function,” J. Quant. Spectrosc. Radiat. Transf. 57(6), 819–824 (1997).
[Crossref]

1991 (1)

L. B. Mercer, “1/f frequency noise effect on self-heterodyne linewidth measurements,” J. Lightwave Technol. 9(4), 485–493 (1991).
[Crossref]

1986 (1)

L. E. Richter, H. I. Mandelberg, S. Kruger, and P. A. Mcgrath, “Linewidth determination from self-heterodyne measurement with subcoherence delay times,” Quan. Electron. Lett. QE-22(11), 2070–2074 (1986).
[Crossref]

Abrarov, S. M.

S. M. Abrarov, B. M. Quine, and R. K. Jagpal, “A simple interpolating algorithm for the rapid and accurate calculation of the Voigt function,” J. Quant. Spectrosc. Radiat. Transf. 110(6-7), 376–383 (2009).
[Crossref]

Bacquet, D.

Beswick, P. H.

S. D. Bruce, J. Higinbotham, I. Marshall, and P. H. Beswick, “An analytical derivation of a popular approximation of the Voigt function for quantification of NMR spectra,” J. Magn. Reson. 142(1), 57–63 (2000).
[Crossref] [PubMed]

Bober, M.

Bruce, S. D.

S. D. Bruce, J. Higinbotham, I. Marshall, and P. H. Beswick, “An analytical derivation of a popular approximation of the Voigt function for quantification of NMR spectra,” J. Magn. Reson. 142(1), 57–63 (2000).
[Crossref] [PubMed]

Chen, M.

Chen, W.

M. Chen, Z. Meng, Y. Zhang, J. Wang, and W. Chen, “Ultra-narrow-linewidth Brillouin/erbium fiber laser based on 45-cm erbium-doped fiber,” IEEE Photon. J. 7(1), 1500606 (2015).
[Crossref]

Ciurylo, R.

Cygan, A.

Di Rocco, H. O.

H. O. Di Rocco, “The exact expression of the Voigt profile function,” J. Quant. Spectrosc. Radiat. Transf. 92(2), 231–237 (2005).
[Crossref]

Geng, J.

Higinbotham, J.

S. D. Bruce, J. Higinbotham, I. Marshall, and P. H. Beswick, “An analytical derivation of a popular approximation of the Voigt function for quantification of NMR spectra,” J. Magn. Reson. 142(1), 57–63 (2000).
[Crossref] [PubMed]

Hu, Y.

Jagpal, R. K.

S. M. Abrarov, B. M. Quine, and R. K. Jagpal, “A simple interpolating algorithm for the rapid and accurate calculation of the Voigt function,” J. Quant. Spectrosc. Radiat. Transf. 110(6-7), 376–383 (2009).
[Crossref]

Jiang, S.

Kaneda, Y.

Kruger, S.

L. E. Richter, H. I. Mandelberg, S. Kruger, and P. A. Mcgrath, “Linewidth determination from self-heterodyne measurement with subcoherence delay times,” Quan. Electron. Lett. QE-22(11), 2070–2074 (1986).
[Crossref]

Kuntz, M.

M. Kuntz, “A new implementation of the humlicek algorithm for the calculation of the Voigt profile function,” J. Quant. Spectrosc. Radiat. Transf. 57(6), 819–824 (1997).
[Crossref]

Lisak, D.

Mandelberg, H. I.

L. E. Richter, H. I. Mandelberg, S. Kruger, and P. A. Mcgrath, “Linewidth determination from self-heterodyne measurement with subcoherence delay times,” Quan. Electron. Lett. QE-22(11), 2070–2074 (1986).
[Crossref]

Marshall, I.

S. D. Bruce, J. Higinbotham, I. Marshall, and P. H. Beswick, “An analytical derivation of a popular approximation of the Voigt function for quantification of NMR spectra,” J. Magn. Reson. 142(1), 57–63 (2000).
[Crossref] [PubMed]

Mcgrath, P. A.

L. E. Richter, H. I. Mandelberg, S. Kruger, and P. A. Mcgrath, “Linewidth determination from self-heterodyne measurement with subcoherence delay times,” Quan. Electron. Lett. QE-22(11), 2070–2074 (1986).
[Crossref]

Meng, Z.

Mercer, L. B.

L. B. Mercer, “1/f frequency noise effect on self-heterodyne linewidth measurements,” J. Lightwave Technol. 9(4), 485–493 (1991).
[Crossref]

Mihélic, F.

Morzynski, P.

Obaid, F. S.

G. D. Roston and F. S. Obaid, “Exact analytical formula for Voigt spectral line profile,” J. Quant. Spectrosc. Radiat. Transf. 94(2), 255–263 (2005).
[Crossref]

Pazderski, E.

Peyghambarian, N.

Quine, B. M.

S. M. Abrarov, B. M. Quine, and R. K. Jagpal, “A simple interpolating algorithm for the rapid and accurate calculation of the Voigt function,” J. Quant. Spectrosc. Radiat. Transf. 110(6-7), 376–383 (2009).
[Crossref]

Richter, L. E.

L. E. Richter, H. I. Mandelberg, S. Kruger, and P. A. Mcgrath, “Linewidth determination from self-heterodyne measurement with subcoherence delay times,” Quan. Electron. Lett. QE-22(11), 2070–2074 (1986).
[Crossref]

Roston, G. D.

G. D. Roston and F. S. Obaid, “Exact analytical formula for Voigt spectral line profile,” J. Quant. Spectrosc. Radiat. Transf. 94(2), 255–263 (2005).
[Crossref]

Spiegelberg, C.

Stewart, G.

Sun, Q.

Sun, S.

Szriftgiser, P.

Tu, X.

Wang, J.

M. Chen, Z. Meng, Y. Zhang, J. Wang, and W. Chen, “Ultra-narrow-linewidth Brillouin/erbium fiber laser based on 45-cm erbium-doped fiber,” IEEE Photon. J. 7(1), 1500606 (2015).
[Crossref]

Whitenett, G.

Zawada, M.

Zemmouri, J.

Zhang, Y.

M. Chen, Z. Meng, Y. Zhang, J. Wang, and W. Chen, “Ultra-narrow-linewidth Brillouin/erbium fiber laser based on 45-cm erbium-doped fiber,” IEEE Photon. J. 7(1), 1500606 (2015).
[Crossref]

Zhou, H.

IEEE Photon. J. (1)

M. Chen, Z. Meng, Y. Zhang, J. Wang, and W. Chen, “Ultra-narrow-linewidth Brillouin/erbium fiber laser based on 45-cm erbium-doped fiber,” IEEE Photon. J. 7(1), 1500606 (2015).
[Crossref]

J. Lightwave Technol. (3)

J. Magn. Reson. (1)

S. D. Bruce, J. Higinbotham, I. Marshall, and P. H. Beswick, “An analytical derivation of a popular approximation of the Voigt function for quantification of NMR spectra,” J. Magn. Reson. 142(1), 57–63 (2000).
[Crossref] [PubMed]

J. Quant. Spectrosc. Radiat. Transf. (4)

G. D. Roston and F. S. Obaid, “Exact analytical formula for Voigt spectral line profile,” J. Quant. Spectrosc. Radiat. Transf. 94(2), 255–263 (2005).
[Crossref]

S. M. Abrarov, B. M. Quine, and R. K. Jagpal, “A simple interpolating algorithm for the rapid and accurate calculation of the Voigt function,” J. Quant. Spectrosc. Radiat. Transf. 110(6-7), 376–383 (2009).
[Crossref]

H. O. Di Rocco, “The exact expression of the Voigt profile function,” J. Quant. Spectrosc. Radiat. Transf. 92(2), 231–237 (2005).
[Crossref]

M. Kuntz, “A new implementation of the humlicek algorithm for the calculation of the Voigt profile function,” J. Quant. Spectrosc. Radiat. Transf. 57(6), 819–824 (1997).
[Crossref]

Opt. Express (2)

Opt. Lett. (2)

Quan. Electron. Lett. (1)

L. E. Richter, H. I. Mandelberg, S. Kruger, and P. A. Mcgrath, “Linewidth determination from self-heterodyne measurement with subcoherence delay times,” Quan. Electron. Lett. QE-22(11), 2070–2074 (1986).
[Crossref]

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Figures (4)

Fig. 1
Fig. 1 Experimental setup: BP, Brillouin pump; EDF, erbium-doped fiber; BOF, bandpass optical filter; AOM, acousto-optic modulator; EDFA, erbium-doped fiber amplifier; ESA, electrical spectrum analyzer.
Fig. 2
Fig. 2 Self-heterodyne spectrum of the BEFL measured with 25 km delay fiber and the fitting curves.
Fig. 3
Fig. 3 Self-heterodyne spectra of the BEFL measured with 25 km, 50 km, and 100 km delay fiber.
Fig. 4
Fig. 4 Self-heterodyne spectrum of the BEFL measured with 100 km delay fiber and its Guassion fitting curve.

Tables (1)

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Table 1 Estimated linewidths of the Voigt fitting and the direct measurement methods

Equations (4)

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V(ν)= + G( ν ' )L(ν ν ' )d ν '
G(ν)= 2 ln2 π Δ ν G exp[4ln2 (ν ν 0 ) 2 /Δ ν G 2 ]
L(ν)= Δ ν L 2π 1 (ν ν 0 ) 2 +Δ ν L 2 /4
Δ ν V = 1 2 (1.0692Δ ν L + 0.866639Δ ν L 2 +4Δ ν G 2 )

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