Abstract

A novel method for characterizing the amplitude of a coherence function with respect to a delay between two optical waves is proposed and demonstrated by using a distributional Rayleigh speckle analysis based on C-OFDR. This technique allows us to estimate both the coherence time of the laser and that of the spectral profiles from the measured amplitude of the coherence function, if the symmetry of the spectrum can be assumed. The spectral width obtained in the experiment agrees roughly with that obtained using a delayed self-heterodyne method.

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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(16), 630–631 (1980).
    [CrossRef]
  2. L. Richter, H. Mandelberg, M. Kruger, and P. McGrath, “Linewidth determination from self-heterodyne measurements with subcoherence delay times,” IEEE J. Quantum Electron. 22(11), 2070–2074 (1986).
    [CrossRef]
  3. S. A. Havestad, Y. Xie, A. B. Sahin, Z. Pan, A. E. Willner, and B. Fischer, “Delayed self-heterodyne interferometer measurements of narrow linewidth fiber lasers” in Proceedings of lasers and Electro-Optics,2000(CLEO 2000), pp. 310–311.
  4. P. Healey, “Fading in heterodyne OTDR,” Electron. Lett. 20(1), 30–32 (1984).
    [CrossRef]
  5. W. Eickhoff and R. Ulrich, “Optical frequency domain reflectometry in single-mode fiber,” Appl. Phys. Lett. 39(9), 693–695 (1981).
    [CrossRef]
  6. K. Tsuji, K. Shimizu, T. Horiguchi, and Y. Koyamada, “Coherent optical frequency domain reflectometry using phase-decorrelated reflected and reference lightwaves,” J. Lightwave Technol. 15(7), 1102–1109 (1997).
    [CrossRef]
  7. J. W. Goodman, “Statistical Optics,” in Wiley-Interscience, (NJ & Oxford, 2000)
  8. Y. Koshikiya, X. Fan, and F. Ito, “Long range and cm-level spatial resolution measurement using coherent optical frequency domain reflectometry with SSB-SC modulator and narrow linewidth fiber laser,” J. Lightwave Technol. 26(18), 3287–3294 (2008).
    [CrossRef]
  9. M. Born and E. Wolf, Principles of Optics 7th ed. (Cambridge University Press, 1999).

2008

1997

K. Tsuji, K. Shimizu, T. Horiguchi, and Y. Koyamada, “Coherent optical frequency domain reflectometry using phase-decorrelated reflected and reference lightwaves,” J. Lightwave Technol. 15(7), 1102–1109 (1997).
[CrossRef]

1986

L. Richter, H. Mandelberg, M. Kruger, and P. McGrath, “Linewidth determination from self-heterodyne measurements with subcoherence delay times,” IEEE J. Quantum Electron. 22(11), 2070–2074 (1986).
[CrossRef]

1984

P. Healey, “Fading in heterodyne OTDR,” Electron. Lett. 20(1), 30–32 (1984).
[CrossRef]

1981

W. Eickhoff and R. Ulrich, “Optical frequency domain reflectometry in single-mode fiber,” Appl. Phys. Lett. 39(9), 693–695 (1981).
[CrossRef]

1980

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

Eickhoff, W.

W. Eickhoff and R. Ulrich, “Optical frequency domain reflectometry in single-mode fiber,” Appl. Phys. Lett. 39(9), 693–695 (1981).
[CrossRef]

Fan, X.

Healey, P.

P. Healey, “Fading in heterodyne OTDR,” Electron. Lett. 20(1), 30–32 (1984).
[CrossRef]

Horiguchi, T.

K. Tsuji, K. Shimizu, T. Horiguchi, and Y. Koyamada, “Coherent optical frequency domain reflectometry using phase-decorrelated reflected and reference lightwaves,” J. Lightwave Technol. 15(7), 1102–1109 (1997).
[CrossRef]

Ito, F.

Kikuchi, K.

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

Koshikiya, Y.

Koyamada, Y.

K. Tsuji, K. Shimizu, T. Horiguchi, and Y. Koyamada, “Coherent optical frequency domain reflectometry using phase-decorrelated reflected and reference lightwaves,” J. Lightwave Technol. 15(7), 1102–1109 (1997).
[CrossRef]

Kruger, M.

L. Richter, H. Mandelberg, M. Kruger, and P. McGrath, “Linewidth determination from self-heterodyne measurements with subcoherence delay times,” IEEE J. Quantum Electron. 22(11), 2070–2074 (1986).
[CrossRef]

Mandelberg, H.

L. Richter, H. Mandelberg, M. Kruger, and P. McGrath, “Linewidth determination from self-heterodyne measurements with subcoherence delay times,” IEEE J. Quantum Electron. 22(11), 2070–2074 (1986).
[CrossRef]

McGrath, P.

L. Richter, H. Mandelberg, M. Kruger, and P. McGrath, “Linewidth determination from self-heterodyne measurements with subcoherence delay times,” IEEE J. Quantum Electron. 22(11), 2070–2074 (1986).
[CrossRef]

Nakayama, A.

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

Richter, L.

L. Richter, H. Mandelberg, M. Kruger, and P. McGrath, “Linewidth determination from self-heterodyne measurements with subcoherence delay times,” IEEE J. Quantum Electron. 22(11), 2070–2074 (1986).
[CrossRef]

Shimizu, K.

K. Tsuji, K. Shimizu, T. Horiguchi, and Y. Koyamada, “Coherent optical frequency domain reflectometry using phase-decorrelated reflected and reference lightwaves,” J. Lightwave Technol. 15(7), 1102–1109 (1997).
[CrossRef]

Tsuji, K.

K. Tsuji, K. Shimizu, T. Horiguchi, and Y. Koyamada, “Coherent optical frequency domain reflectometry using phase-decorrelated reflected and reference lightwaves,” J. Lightwave Technol. 15(7), 1102–1109 (1997).
[CrossRef]

Ulrich, R.

W. Eickhoff and R. Ulrich, “Optical frequency domain reflectometry in single-mode fiber,” Appl. Phys. Lett. 39(9), 693–695 (1981).
[CrossRef]

Appl. Phys. Lett.

W. Eickhoff and R. Ulrich, “Optical frequency domain reflectometry in single-mode fiber,” Appl. Phys. Lett. 39(9), 693–695 (1981).
[CrossRef]

Electron. Lett.

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

P. Healey, “Fading in heterodyne OTDR,” Electron. Lett. 20(1), 30–32 (1984).
[CrossRef]

IEEE J. Quantum Electron.

L. Richter, H. Mandelberg, M. Kruger, and P. McGrath, “Linewidth determination from self-heterodyne measurements with subcoherence delay times,” IEEE J. Quantum Electron. 22(11), 2070–2074 (1986).
[CrossRef]

J. Lightwave Technol.

Y. Koshikiya, X. Fan, and F. Ito, “Long range and cm-level spatial resolution measurement using coherent optical frequency domain reflectometry with SSB-SC modulator and narrow linewidth fiber laser,” J. Lightwave Technol. 26(18), 3287–3294 (2008).
[CrossRef]

K. Tsuji, K. Shimizu, T. Horiguchi, and Y. Koyamada, “Coherent optical frequency domain reflectometry using phase-decorrelated reflected and reference lightwaves,” J. Lightwave Technol. 15(7), 1102–1109 (1997).
[CrossRef]

Other

J. W. Goodman, “Statistical Optics,” in Wiley-Interscience, (NJ & Oxford, 2000)

M. Born and E. Wolf, Principles of Optics 7th ed. (Cambridge University Press, 1999).

S. A. Havestad, Y. Xie, A. B. Sahin, Z. Pan, A. E. Willner, and B. Fischer, “Delayed self-heterodyne interferometer measurements of narrow linewidth fiber lasers” in Proceedings of lasers and Electro-Optics,2000(CLEO 2000), pp. 310–311.

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Figures (5)

Fig. 1
Fig. 1

Schematic configuration of coherence function measurement.

Fig. 2
Fig. 2

Experimental setup. LUT is Laser Under Test; HWP is Half Wavelength Plate; QWP is Quarter Wavelength Plate; SSB is Single Side Band; SMF is Single Mode Fiber; PBS is Polarization Beam Splitter; BPD is Balanced Photo Detector; A/D is Analog-Digital Converter; BPF is Band Pass Filter; OSC is Oscillator; Es is Polarization S; Ep is Polarization P.

Fig. 3
Fig. 3

OFDR traces of Pq(τ) and Ps(τ) in (a) τ < τc and (b) τ > τc of the Rio LD.

Fig. 4
Fig. 4

The measured coherence functions of LUT (I) and (II) are plotted in (a) and (b), respectively.

Fig. 5
Fig. 5

Fourier transform spectra of coherence functions.

Tables (1)

Tables Icon

Table 1 List of LUTs

Equations (11)

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f q ( τ i )= E q (t) E q * (tτ) e 2πg τ i t dt.
γ(τ) E q (t) E q * (tτ) ¯ ,
P q (τ)= | 1 N i N f q ( τ i )r( τ i ) | 2 ,
f q ( τ i )=γ(τ)+ n q ( τ i ).
P q (τ)= 1 N 2 i N j N f q ( τ i )r( τ i ) f q * ( τ j ) r * ( τ j ) = 1 N 2 i N j N (γ+ n q,i )( γ * + n q,j * ) r i r j * .
n a,i n b,i * ¯ δ ab n 2 ¯ ,
r a r b * ¯ = δ ab r 2 ¯ ,
P q (τ) P s (τ) ¯ = 1 N 2 i j k l (γ+ n q,i )( γ * + n q,j * )(γ+ n s,k )( γ * + n s,l * ) r i r j * r k r l * =( 2γγ γ * γ * +2γ γ * n n * ¯ + ( n n * ¯ ) 2 ) r 2 ¯ r 2 ¯ =( γ 4 +1 ) r 2 ¯ r 2 ¯ .
P q (τ) P s (τ) ¯ P q (τ) ¯ P s (τ) ¯ = | γ(τ) | 4 +1.
S(ν)= γ(τ) e j2πντ dτ .
S(ν)= | γ(τ) | e j2πντ dτ .

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