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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  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.

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]

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]

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.

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]

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]

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)

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]

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]

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. (3)

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]

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).

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. Lightwave Technol. (3)

Opt. Lett. (1)

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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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