Abstract

I propose and demonstrate the use of the recirculating delayed self-heterodyne (DSH) method for measuring FM noise power spectral densities (PSDs), which are the most fundamental measure characterizing the spectral purity of laser sources. By analyzing the DSH beat signals with 1, 10, and 160km delays, the FM noise PSD of a narrow- linewidth fiber laser is evaluated for Fourier frequency range between 10Hz and 100kHz, which exhibits flicker noise as the dominant contribution.

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References

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  2. J. A. Barnes, A. R. Chi, L. S. Cutler, D. J. Healey, D. B. Leeson, T. E. McGunigal, J. A. Mullen, W. L. Smith, R. Sydnor, R. F. Vessot, and G. M. R. Winkler, IEEE Trans. Instrum. Meas. IM-20, 105 (1971).
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  3. C. Spiegelberg, J. Geng, Y. Hu, Y. Kaneda, S. Jiang, and N. Peyghambarian, J. Lightwave Technol. 22, 57 (2004).
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  4. S. B. Foster and A. E. Tikhomirov, IEEE J. Quantum Electron. 46, 734 (2010).
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  5. A. Laurain, M. Myara, G. Beaudoin, I. Sagnes, and A. Garnache, Opt. Express 18, 14627 (2010).
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  7. O. Ishida, J. Lightwave Technol. 9, 1528 (1991).
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  8. O. Ishida, IEEE Photon. Technol. Lett. 4, 1304 (1992).
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  9. T. Okoshi, K. Kikuchi, and A. Nakayama, Electron. Lett. 16, 630 (1980).
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  10. H. Tsuchida, Opt. Lett. 15, 640 (1990).
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  11. J. W. Dawson, N. Park, and K. J. Vahala, IEEE Photon. Technol. Lett. 4, 1063 (1992).
    [CrossRef]
  12. P. Kartaschoff, Frequency and Time (Academic, 1978).
  13. K. Kikuchi, IEEE J. Quantum Electron. 25, 684 (1989).
    [CrossRef]

2010 (2)

2004 (1)

1992 (2)

O. Ishida, IEEE Photon. Technol. Lett. 4, 1304 (1992).
[CrossRef]

J. W. Dawson, N. Park, and K. J. Vahala, IEEE Photon. Technol. Lett. 4, 1063 (1992).
[CrossRef]

1991 (1)

O. Ishida, J. Lightwave Technol. 9, 1528 (1991).
[CrossRef]

1990 (2)

H. Tsuchida, Opt. Lett. 15, 640 (1990).
[CrossRef] [PubMed]

O. Ishida, IEEE Photon. Technol. Lett. 2, 784 (1990).
[CrossRef]

1989 (1)

K. Kikuchi, IEEE J. Quantum Electron. 25, 684 (1989).
[CrossRef]

1980 (1)

T. Okoshi, K. Kikuchi, and A. Nakayama, Electron. Lett. 16, 630 (1980).
[CrossRef]

1971 (1)

J. A. Barnes, A. R. Chi, L. S. Cutler, D. J. Healey, D. B. Leeson, T. E. McGunigal, J. A. Mullen, W. L. Smith, R. Sydnor, R. F. Vessot, and G. M. R. Winkler, IEEE Trans. Instrum. Meas. IM-20, 105 (1971).
[CrossRef]

Barnes, J. A.

J. A. Barnes, A. R. Chi, L. S. Cutler, D. J. Healey, D. B. Leeson, T. E. McGunigal, J. A. Mullen, W. L. Smith, R. Sydnor, R. F. Vessot, and G. M. R. Winkler, IEEE Trans. Instrum. Meas. IM-20, 105 (1971).
[CrossRef]

Beaudoin, G.

Chi, A. R.

J. A. Barnes, A. R. Chi, L. S. Cutler, D. J. Healey, D. B. Leeson, T. E. McGunigal, J. A. Mullen, W. L. Smith, R. Sydnor, R. F. Vessot, and G. M. R. Winkler, IEEE Trans. Instrum. Meas. IM-20, 105 (1971).
[CrossRef]

Cutler, L. S.

J. A. Barnes, A. R. Chi, L. S. Cutler, D. J. Healey, D. B. Leeson, T. E. McGunigal, J. A. Mullen, W. L. Smith, R. Sydnor, R. F. Vessot, and G. M. R. Winkler, IEEE Trans. Instrum. Meas. IM-20, 105 (1971).
[CrossRef]

Dawson, J. W.

J. W. Dawson, N. Park, and K. J. Vahala, IEEE Photon. Technol. Lett. 4, 1063 (1992).
[CrossRef]

Foster, S. B.

S. B. Foster and A. E. Tikhomirov, IEEE J. Quantum Electron. 46, 734 (2010).
[CrossRef]

Garnache, A.

Geng, J.

Healey, D. J.

J. A. Barnes, A. R. Chi, L. S. Cutler, D. J. Healey, D. B. Leeson, T. E. McGunigal, J. A. Mullen, W. L. Smith, R. Sydnor, R. F. Vessot, and G. M. R. Winkler, IEEE Trans. Instrum. Meas. IM-20, 105 (1971).
[CrossRef]

Hu, Y.

Ishida, O.

O. Ishida, IEEE Photon. Technol. Lett. 4, 1304 (1992).
[CrossRef]

O. Ishida, J. Lightwave Technol. 9, 1528 (1991).
[CrossRef]

O. Ishida, IEEE Photon. Technol. Lett. 2, 784 (1990).
[CrossRef]

Jiang, S.

Kaneda, Y.

Kartaschoff, P.

P. Kartaschoff, Frequency and Time (Academic, 1978).

Kikuchi, K.

K. Kikuchi, IEEE J. Quantum Electron. 25, 684 (1989).
[CrossRef]

T. Okoshi, K. Kikuchi, and A. Nakayama, Electron. Lett. 16, 630 (1980).
[CrossRef]

Laurain, A.

Leeson, D. B.

J. A. Barnes, A. R. Chi, L. S. Cutler, D. J. Healey, D. B. Leeson, T. E. McGunigal, J. A. Mullen, W. L. Smith, R. Sydnor, R. F. Vessot, and G. M. R. Winkler, IEEE Trans. Instrum. Meas. IM-20, 105 (1971).
[CrossRef]

McGunigal, T. E.

J. A. Barnes, A. R. Chi, L. S. Cutler, D. J. Healey, D. B. Leeson, T. E. McGunigal, J. A. Mullen, W. L. Smith, R. Sydnor, R. F. Vessot, and G. M. R. Winkler, IEEE Trans. Instrum. Meas. IM-20, 105 (1971).
[CrossRef]

Mullen, J. A.

J. A. Barnes, A. R. Chi, L. S. Cutler, D. J. Healey, D. B. Leeson, T. E. McGunigal, J. A. Mullen, W. L. Smith, R. Sydnor, R. F. Vessot, and G. M. R. Winkler, IEEE Trans. Instrum. Meas. IM-20, 105 (1971).
[CrossRef]

Myara, M.

Nakayama, A.

T. Okoshi, K. Kikuchi, and A. Nakayama, Electron. Lett. 16, 630 (1980).
[CrossRef]

Okoshi, T.

T. Okoshi, K. Kikuchi, and A. Nakayama, Electron. Lett. 16, 630 (1980).
[CrossRef]

Park, N.

J. W. Dawson, N. Park, and K. J. Vahala, IEEE Photon. Technol. Lett. 4, 1063 (1992).
[CrossRef]

Peyghambarian, N.

Sagnes, I.

Seimetz, M.

M. Seimetz, High-Order Modulation for Optical Fiber Transmission (Springer, 2009).
[CrossRef]

Smith, W. L.

J. A. Barnes, A. R. Chi, L. S. Cutler, D. J. Healey, D. B. Leeson, T. E. McGunigal, J. A. Mullen, W. L. Smith, R. Sydnor, R. F. Vessot, and G. M. R. Winkler, IEEE Trans. Instrum. Meas. IM-20, 105 (1971).
[CrossRef]

Spiegelberg, C.

Sydnor, R.

J. A. Barnes, A. R. Chi, L. S. Cutler, D. J. Healey, D. B. Leeson, T. E. McGunigal, J. A. Mullen, W. L. Smith, R. Sydnor, R. F. Vessot, and G. M. R. Winkler, IEEE Trans. Instrum. Meas. IM-20, 105 (1971).
[CrossRef]

Tikhomirov, A. E.

S. B. Foster and A. E. Tikhomirov, IEEE J. Quantum Electron. 46, 734 (2010).
[CrossRef]

Tsuchida, H.

Vahala, K. J.

J. W. Dawson, N. Park, and K. J. Vahala, IEEE Photon. Technol. Lett. 4, 1063 (1992).
[CrossRef]

Vessot, R. F.

J. A. Barnes, A. R. Chi, L. S. Cutler, D. J. Healey, D. B. Leeson, T. E. McGunigal, J. A. Mullen, W. L. Smith, R. Sydnor, R. F. Vessot, and G. M. R. Winkler, IEEE Trans. Instrum. Meas. IM-20, 105 (1971).
[CrossRef]

Winkler, G. M. R.

J. A. Barnes, A. R. Chi, L. S. Cutler, D. J. Healey, D. B. Leeson, T. E. McGunigal, J. A. Mullen, W. L. Smith, R. Sydnor, R. F. Vessot, and G. M. R. Winkler, IEEE Trans. Instrum. Meas. IM-20, 105 (1971).
[CrossRef]

Electron. Lett. (1)

T. Okoshi, K. Kikuchi, and A. Nakayama, Electron. Lett. 16, 630 (1980).
[CrossRef]

IEEE J. Quantum Electron. (2)

K. Kikuchi, IEEE J. Quantum Electron. 25, 684 (1989).
[CrossRef]

S. B. Foster and A. E. Tikhomirov, IEEE J. Quantum Electron. 46, 734 (2010).
[CrossRef]

IEEE Photon. Technol. Lett. (3)

O. Ishida, IEEE Photon. Technol. Lett. 2, 784 (1990).
[CrossRef]

O. Ishida, IEEE Photon. Technol. Lett. 4, 1304 (1992).
[CrossRef]

J. W. Dawson, N. Park, and K. J. Vahala, IEEE Photon. Technol. Lett. 4, 1063 (1992).
[CrossRef]

IEEE Trans. Instrum. Meas. (1)

J. A. Barnes, A. R. Chi, L. S. Cutler, D. J. Healey, D. B. Leeson, T. E. McGunigal, J. A. Mullen, W. L. Smith, R. Sydnor, R. F. Vessot, and G. M. R. Winkler, IEEE Trans. Instrum. Meas. IM-20, 105 (1971).
[CrossRef]

J. Lightwave Technol. (2)

Opt. Express (1)

Opt. Lett. (1)

Other (2)

P. Kartaschoff, Frequency and Time (Academic, 1978).

M. Seimetz, High-Order Modulation for Optical Fiber Transmission (Springer, 2009).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

(a) Schematic of FM noise measurement. (b) DSH beat signal spectra for 60 km delay. Curve A represents the measured result with the center frequency, resolution bandwidth, and number of averaging are 600 MHz , 100 Hz , and 64, respectively. Curve B corresponds to the numerically calculated spectrum based on the flicker noise model.

Fig. 2
Fig. 2

A: PSD S μ ( f ) of the DSH beat signal obtained with the 160 km delay (4 circulations with 40 km fiber), where the resolution bandwidth and number of averaging are 3 Hz and 64, respectively. B: PSD S ν ( f ) of the laser FM noise calculated using (4).

Fig. 3
Fig. 3

FM noise PSDs S ν ( f ) measured for various delays. The number of averaging is 64 and the resolution bandwidths are 3, 10, 30, 100, and 300 Hz for 160, 40, 10, 3, and 1 km delays, respectively.

Fig. 4
Fig. 4

(a) FM noise PSD S ν ( f ) . The straight line corresponds to the flicker noise model. (b) Allan deviation σ ν ( τ ) calculated from the PSD S ν ( f ) using (5).

Equations (5)

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V N ( t ) = ξ cos [ 2 π N f S t + 2 π N ν 0 τ d + ψ ( t ) ψ ( t N τ d ) ] ,
μ N ( t ) = [ ψ ˙ ( t ) ψ ˙ ( t N τ d ) ] / 2 π = ν ( t ) ν ( t N τ d ) .
R μ ( τ ) = lim T 1 2 T T T μ N ( t ) μ N ( t + τ ) d t = 2 R ν ( τ ) R ν ( τ N τ d ) R ν ( τ + N τ d ) ,
S μ ( f ) = R μ ( τ ) exp ( i 2 π f τ ) d τ = 2 [ 1 cos ( 2 π f N τ d ) ] S ν ( f ) ,
σ ν ( τ ) = [ 2 S ν ( f ) sin 4 ( π f τ ) ( π f τ ) 2 d f ] 1 / 2 .

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