Abstract

The delayed self-heterodyne interferometric technique, first proposed in the context of semiconductor lasers, has been commonly used for over 20 years in the determination of the optical linewidth of lasers. We examine this technique in the light of recent work on fiber lasers, and point out further constraints in the applicability of these measurements. An approximate but simple and intuitive expression is provided for assessing the self-heterodyne technique when applied to fiber lasers.

© 2006 Optical Society of America

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References

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  1. T. Okoshi, K. Kikuchi, and A. Nakayama, “Novel method for high resolution measurement of laser output spectrum,” Electron. Lett. 16, 630–631 (1980).
    [Crossref]
  2. W. H. Loh, B. N. Samson, L. Dong, G. J. Cowle, and K. Hsu, “High performance single frequency fiber grating-based Erbium:Ytterbium-codoped fiber lasers,” J. Lightwave Technol.,  16, 114–118 (1998).
    [Crossref]
  3. M. Sejka, P. Varming, J. Hubner, and M. Kristensen, “Distributed feedback Er3+-doped fibre laser,” Electron. Lett. 31, 1445–1446 (1995).
    [Crossref]
  4. J. J. Pan and Y. Shi, “166-mW single-frequency output power interactive fiber lasers with low noise,” IEEE Photon. Technol. Lett. 11, 36–38 (1999).
    [Crossref]
  5. C. Spiegelberg, J. Geng, Y. Hu, Y. Kaneda, S. Jiang, and N. Peyghambarian, “Low-noise narrow-linewidth fiber laser at 1550nm,” J. Lightwave Technol. 22, 57–62 (2004).
    [Crossref]
  6. L. E. Richter, H. I. Mandelburg, M. S. Kruger, and P. A. McGrath, “Linewidth determination from self-heterodyne measurements with subcoherence delay times,” IEEE J. Quantum. Electron. QE-22, 2070–2074 (1986).
    [Crossref]
  7. C. H. Henry, “Theory of the linewidth of semiconductor lasers,” IEEE J. Quantum. Electron. QE-18, 259–264 (1982).
    [Crossref]
  8. G. A. Ball, C. G. Hull-Allen, and J. Livas, “Frequency noise of a Bragg grating fibre laser,” Electron. Lett. 30, 1229–1230 (1994).
    [Crossref]
  9. K. Kikuchi, “Effect of 1/f-type FM noise on semiconductor laser linewidth residual in high-power limit,” IEEE J. Quantum. Electron. QE-25, 684–688 (1989).
    [Crossref]
  10. L. B. Mercer, “1/f frequency noise effects on self-heterodyne linewidth measurements,” J. Lightwave Technol. 9, 485–493 (1991).
    [Crossref]
  11. P. Horak, N. Y. Voo, M. Ibsen, and W. H. Loh, “Pump-noise induced linewidth contributions in distributed feedback fiber lasers,” IEEE Photon. Technol. Lett. (to be published).
  12. J. W. Dawson, N. Park, and K. J. Vahala, “An improved delayed self-heterodyne interferometer for linewidth measurements,” IEEE Photon. Technol. Lett. 4, 1063–1066 (1992).
    [Crossref]
  13. N. Park, J. W. Dawson, and K. J. Vahala, “Linewidth and frequency jitter measurement of an erbium-doped fiber ring laser by using loss-compensated, delayed self-heterodyne interferometer,” Opt. Lett. 17, 1274–1276 (1992).
    [Crossref] [PubMed]

2004 (1)

1999 (1)

J. J. Pan and Y. Shi, “166-mW single-frequency output power interactive fiber lasers with low noise,” IEEE Photon. Technol. Lett. 11, 36–38 (1999).
[Crossref]

1998 (1)

1995 (1)

M. Sejka, P. Varming, J. Hubner, and M. Kristensen, “Distributed feedback Er3+-doped fibre laser,” Electron. Lett. 31, 1445–1446 (1995).
[Crossref]

1994 (1)

G. A. Ball, C. G. Hull-Allen, and J. Livas, “Frequency noise of a Bragg grating fibre laser,” Electron. Lett. 30, 1229–1230 (1994).
[Crossref]

1992 (2)

J. W. Dawson, N. Park, and K. J. Vahala, “An improved delayed self-heterodyne interferometer for linewidth measurements,” IEEE Photon. Technol. Lett. 4, 1063–1066 (1992).
[Crossref]

N. Park, J. W. Dawson, and K. J. Vahala, “Linewidth and frequency jitter measurement of an erbium-doped fiber ring laser by using loss-compensated, delayed self-heterodyne interferometer,” Opt. Lett. 17, 1274–1276 (1992).
[Crossref] [PubMed]

1991 (1)

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

1989 (1)

K. Kikuchi, “Effect of 1/f-type FM noise on semiconductor laser linewidth residual in high-power limit,” IEEE J. Quantum. Electron. QE-25, 684–688 (1989).
[Crossref]

1986 (1)

L. E. Richter, H. I. Mandelburg, M. S. Kruger, and P. A. McGrath, “Linewidth determination from self-heterodyne measurements with subcoherence delay times,” IEEE J. Quantum. Electron. QE-22, 2070–2074 (1986).
[Crossref]

1982 (1)

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

1980 (1)

T. Okoshi, K. Kikuchi, and A. Nakayama, “Novel method for high resolution measurement of laser output spectrum,” Electron. Lett. 16, 630–631 (1980).
[Crossref]

Ball, G. A.

G. A. Ball, C. G. Hull-Allen, and J. Livas, “Frequency noise of a Bragg grating fibre laser,” Electron. Lett. 30, 1229–1230 (1994).
[Crossref]

Cowle, G. J.

Dawson, J. W.

J. W. Dawson, N. Park, and K. J. Vahala, “An improved delayed self-heterodyne interferometer for linewidth measurements,” IEEE Photon. Technol. Lett. 4, 1063–1066 (1992).
[Crossref]

N. Park, J. W. Dawson, and K. J. Vahala, “Linewidth and frequency jitter measurement of an erbium-doped fiber ring laser by using loss-compensated, delayed self-heterodyne interferometer,” Opt. Lett. 17, 1274–1276 (1992).
[Crossref] [PubMed]

Dong, L.

Geng, J.

Henry, C. H.

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

Horak, P.

P. Horak, N. Y. Voo, M. Ibsen, and W. H. Loh, “Pump-noise induced linewidth contributions in distributed feedback fiber lasers,” IEEE Photon. Technol. Lett. (to be published).

Hsu, K.

Hu, Y.

Hubner, J.

M. Sejka, P. Varming, J. Hubner, and M. Kristensen, “Distributed feedback Er3+-doped fibre laser,” Electron. Lett. 31, 1445–1446 (1995).
[Crossref]

Hull-Allen, C. G.

G. A. Ball, C. G. Hull-Allen, and J. Livas, “Frequency noise of a Bragg grating fibre laser,” Electron. Lett. 30, 1229–1230 (1994).
[Crossref]

Ibsen, M.

P. Horak, N. Y. Voo, M. Ibsen, and W. H. Loh, “Pump-noise induced linewidth contributions in distributed feedback fiber lasers,” IEEE Photon. Technol. Lett. (to be published).

Jiang, S.

Kaneda, Y.

Kikuchi, K.

K. Kikuchi, “Effect of 1/f-type FM noise on semiconductor laser linewidth residual in high-power limit,” IEEE J. Quantum. Electron. QE-25, 684–688 (1989).
[Crossref]

T. Okoshi, K. Kikuchi, and A. Nakayama, “Novel method for high resolution measurement of laser output spectrum,” Electron. Lett. 16, 630–631 (1980).
[Crossref]

Kristensen, M.

M. Sejka, P. Varming, J. Hubner, and M. Kristensen, “Distributed feedback Er3+-doped fibre laser,” Electron. Lett. 31, 1445–1446 (1995).
[Crossref]

Kruger, M. S.

L. E. Richter, H. I. Mandelburg, M. S. Kruger, and P. A. McGrath, “Linewidth determination from self-heterodyne measurements with subcoherence delay times,” IEEE J. Quantum. Electron. QE-22, 2070–2074 (1986).
[Crossref]

Livas, J.

G. A. Ball, C. G. Hull-Allen, and J. Livas, “Frequency noise of a Bragg grating fibre laser,” Electron. Lett. 30, 1229–1230 (1994).
[Crossref]

Loh, W. H.

W. H. Loh, B. N. Samson, L. Dong, G. J. Cowle, and K. Hsu, “High performance single frequency fiber grating-based Erbium:Ytterbium-codoped fiber lasers,” J. Lightwave Technol.,  16, 114–118 (1998).
[Crossref]

P. Horak, N. Y. Voo, M. Ibsen, and W. H. Loh, “Pump-noise induced linewidth contributions in distributed feedback fiber lasers,” IEEE Photon. Technol. Lett. (to be published).

Mandelburg, H. I.

L. E. Richter, H. I. Mandelburg, M. S. Kruger, and P. A. McGrath, “Linewidth determination from self-heterodyne measurements with subcoherence delay times,” IEEE J. Quantum. Electron. QE-22, 2070–2074 (1986).
[Crossref]

McGrath, P. A.

L. E. Richter, H. I. Mandelburg, M. S. Kruger, and P. A. McGrath, “Linewidth determination from self-heterodyne measurements with subcoherence delay times,” IEEE J. Quantum. Electron. QE-22, 2070–2074 (1986).
[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]

Nakayama, A.

T. Okoshi, K. Kikuchi, and A. Nakayama, “Novel method for high resolution measurement of laser output spectrum,” Electron. Lett. 16, 630–631 (1980).
[Crossref]

Okoshi, T.

T. Okoshi, K. Kikuchi, and A. Nakayama, “Novel method for high resolution measurement of laser output spectrum,” Electron. Lett. 16, 630–631 (1980).
[Crossref]

Pan, J. J.

J. J. Pan and Y. Shi, “166-mW single-frequency output power interactive fiber lasers with low noise,” IEEE Photon. Technol. Lett. 11, 36–38 (1999).
[Crossref]

Park, N.

J. W. Dawson, N. Park, and K. J. Vahala, “An improved delayed self-heterodyne interferometer for linewidth measurements,” IEEE Photon. Technol. Lett. 4, 1063–1066 (1992).
[Crossref]

N. Park, J. W. Dawson, and K. J. Vahala, “Linewidth and frequency jitter measurement of an erbium-doped fiber ring laser by using loss-compensated, delayed self-heterodyne interferometer,” Opt. Lett. 17, 1274–1276 (1992).
[Crossref] [PubMed]

Peyghambarian, N.

Richter, L. E.

L. E. Richter, H. I. Mandelburg, M. S. Kruger, and P. A. McGrath, “Linewidth determination from self-heterodyne measurements with subcoherence delay times,” IEEE J. Quantum. Electron. QE-22, 2070–2074 (1986).
[Crossref]

Samson, B. N.

Sejka, M.

M. Sejka, P. Varming, J. Hubner, and M. Kristensen, “Distributed feedback Er3+-doped fibre laser,” Electron. Lett. 31, 1445–1446 (1995).
[Crossref]

Shi, Y.

J. J. Pan and Y. Shi, “166-mW single-frequency output power interactive fiber lasers with low noise,” IEEE Photon. Technol. Lett. 11, 36–38 (1999).
[Crossref]

Spiegelberg, C.

Vahala, K. J.

J. W. Dawson, N. Park, and K. J. Vahala, “An improved delayed self-heterodyne interferometer for linewidth measurements,” IEEE Photon. Technol. Lett. 4, 1063–1066 (1992).
[Crossref]

N. Park, J. W. Dawson, and K. J. Vahala, “Linewidth and frequency jitter measurement of an erbium-doped fiber ring laser by using loss-compensated, delayed self-heterodyne interferometer,” Opt. Lett. 17, 1274–1276 (1992).
[Crossref] [PubMed]

Varming, P.

M. Sejka, P. Varming, J. Hubner, and M. Kristensen, “Distributed feedback Er3+-doped fibre laser,” Electron. Lett. 31, 1445–1446 (1995).
[Crossref]

Voo, N. Y.

P. Horak, N. Y. Voo, M. Ibsen, and W. H. Loh, “Pump-noise induced linewidth contributions in distributed feedback fiber lasers,” IEEE Photon. Technol. Lett. (to be published).

Electron. Lett. (3)

T. Okoshi, K. Kikuchi, and A. Nakayama, “Novel method for high resolution measurement of laser output spectrum,” Electron. Lett. 16, 630–631 (1980).
[Crossref]

M. Sejka, P. Varming, J. Hubner, and M. Kristensen, “Distributed feedback Er3+-doped fibre laser,” Electron. Lett. 31, 1445–1446 (1995).
[Crossref]

G. A. Ball, C. G. Hull-Allen, and J. Livas, “Frequency noise of a Bragg grating fibre laser,” Electron. Lett. 30, 1229–1230 (1994).
[Crossref]

IEEE J. Quantum. Electron. (3)

K. Kikuchi, “Effect of 1/f-type FM noise on semiconductor laser linewidth residual in high-power limit,” IEEE J. Quantum. Electron. QE-25, 684–688 (1989).
[Crossref]

L. E. Richter, H. I. Mandelburg, M. S. Kruger, and P. A. McGrath, “Linewidth determination from self-heterodyne measurements with subcoherence delay times,” IEEE J. Quantum. Electron. QE-22, 2070–2074 (1986).
[Crossref]

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

IEEE Photon. Technol. Lett. (2)

J. W. Dawson, N. Park, and K. J. Vahala, “An improved delayed self-heterodyne interferometer for linewidth measurements,” IEEE Photon. Technol. Lett. 4, 1063–1066 (1992).
[Crossref]

J. J. Pan and Y. Shi, “166-mW single-frequency output power interactive fiber lasers with low noise,” IEEE Photon. Technol. Lett. 11, 36–38 (1999).
[Crossref]

J. Lightwave Technol. (3)

Opt. Lett. (1)

Other (1)

P. Horak, N. Y. Voo, M. Ibsen, and W. H. Loh, “Pump-noise induced linewidth contributions in distributed feedback fiber lasers,” IEEE Photon. Technol. Lett. (to be published).

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Figures (3)

Fig. 1.
Fig. 1.

Normalized integral I(τ) for a simple low-pass noise function SF(f).

Fig. 2.
Fig. 2.

Sampling of the frequency noise for two different delay lengths. The integral in Eq. (15) is given by the area under the dashed (dotted) curve. It is clear that with the fiber delay time τd insufficiently long, the laser frequency noise will be significantly under-estimated, and the resulting linewidth correspondingly under-reported.

Fig. 3.
Fig. 3.

Dependence of measured linewidth on fiber delay, and comparison to previously reported experimental data. Solid line: Eq. (16). Data points are from Ref. [12].

Equations (17)

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τ coherence << τ d
Δ υ res c n L d = 1 τ d
S ( f ) = [ exp { 8 I ( τ ) } ]
I ( τ ) = 0 S F ( ν ) sin 2 πντ ν 2 sin 2 ( πν τ d )
S ( f ) 2 S F 0 ( S F 0 ) 2 + 2 π ( f f 0 ) 2 × ( 1 e S F 0 τ d ( cos [ 2 π τ d ( f f 0 ) ] + S F 0 2 π ( f f 0 ) sin [ 2 π τ d ( f f 0 ) ] ) )
I ( τ ) = τ 2 0 f c S F ( ν ) π 2 sin 2 ( πν τ d ) τ 4 0 f c S F ( ν ) π 4 3 ν 2 sin 2 ( πν τ d ) + O ( τ 6 )
1 τ g 2 = 0 f c S F ( ν ) π 2 sin 2 ( πν τ d )
1 ( τ ) = τ 2 τ g 2 + O ( τ 4 )
f c S ¯ F << 1
S ¯ F = 1 f c 0 f c S F ( ν ) sin 2 ( πν τ d )
I ( ) = 1 2 0 f c S F ( ν ) sin 2 ( πν τ d ) 1 ν 2 > 1 2 π 2 f c 2 τ g 2 >> 1
S F ( f ) = S F 0 for f < f c
= 0 for f > f c
exp { 8 I ( τ ) } exp { 8 τ 2 τ g 2 }
S ( f ) [ exp { 8 τ 2 τ g 2 } ]
Δ υ 1 / 2 4 { 2 log ( 2 ) 0 f c S F ( f ) sin 2 ( πf τ d ) df } 1 2
Δ υ 1 / 2 = 4 log ( 2 ) f c S F 0 ( 1 sin x x )

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