Abstract

The measurement of the spectral broadening, or temporal coherence property of very narrow linewidth lasers is not an easy task, while such a measurement is essential in any interferometric applications of the lasers. The beat note between two assumingly identical lasers only provides the convolutional spectral profile of the two lasers, but not characterizes the single laser. The delayed self-heterodyne interferometer (DSHI) would not be effective for kHz linewidth range because the finite delay cannot realize complete de-correlation. Here, we demonstrate, for the first time to our knowledge, the complete characterization of the modulus of the degree of coherence (DOC) of kHz linewidth lasers, with a self-referenced fashion where any other reference beam is not used, accordingly, characterize the spectral profile. The method is based on speckle statistical analysis of the Rayleigh scattering in the coherent fiber reflectometry, and would be a novel strong tool to characterize very narrow linewidth lasers.

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References

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

2011 (1)

2007 (1)

1998 (1)

1997 (1)

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 (1)

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

1984 (1)

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

1981 (1)

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

1980 (2)

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]

E. Brinkmeyer, “Backscattering in single-mode fibres,” Electron. Lett.16(9), 329–330 (1980).
[CrossRef]

1971 (2)

F. M. Mottier and R. Dandliker, “A simple spectrum analyzer for laser light using speckles,” Opt. Commun.3(5), 366–368 (1971).
[CrossRef]

R. A. Dandliker and F. M. Mottier, “Determination of coherence length from speckle contrast on a rough surface,” Z. Angew. Math. Phys.22(3), 369–381 (1971) (ZAMP).
[CrossRef]

1970 (1)

J. C. Dainty, “Some statistical properties of random speckle patterns in coherent and partially coherent illumination,” Opt. Acta (Lond.)17(10), 761–772 (1970).
[CrossRef]

1966 (1)

1964 (1)

1963 (1)

B. M. Oliver, “Sparkling spots and random diffraction,” Proc. IEEE51(1), 220–221 (1963).
[CrossRef]

Brinkmeyer, E.

E. Brinkmeyer, “Backscattering in single-mode fibres,” Electron. Lett.16(9), 329–330 (1980).
[CrossRef]

Connes, J.

Connes, P.

Dainty, J. C.

J. C. Dainty, “Some statistical properties of random speckle patterns in coherent and partially coherent illumination,” Opt. Acta (Lond.)17(10), 761–772 (1970).
[CrossRef]

Dandliker, R.

F. M. Mottier and R. Dandliker, “A simple spectrum analyzer for laser light using speckles,” Opt. Commun.3(5), 366–368 (1971).
[CrossRef]

Dandliker, R. A.

R. A. Dandliker and F. M. Mottier, “Determination of coherence length from speckle contrast on a rough surface,” Z. Angew. Math. Phys.22(3), 369–381 (1971) (ZAMP).
[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.

Froggatt, M.

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]

Inoue, M.

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. S.

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

Mandelberg, H. I.

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

McGrath, P. A.

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

Moore, J.

Mottier, F. M.

F. M. Mottier and R. Dandliker, “A simple spectrum analyzer for laser light using speckles,” Opt. Commun.3(5), 366–368 (1971).
[CrossRef]

R. A. Dandliker and F. M. Mottier, “Determination of coherence length from speckle contrast on a rough surface,” Z. Angew. Math. Phys.22(3), 369–381 (1971) (ZAMP).
[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]

Oliver, B. M.

B. M. Oliver, “Sparkling spots and random diffraction,” Proc. IEEE51(1), 220–221 (1963).
[CrossRef]

Richards, P. L.

Richter, L. E.

L. E. Richter, H. I. Mandelberg, M. S. Kruger, and P. A. 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. Opt. (1)

Appl. Phys. Lett. (1)

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

Electron. Lett. (3)

E. Brinkmeyer, “Backscattering in single-mode fibres,” Electron. Lett.16(9), 329–330 (1980).
[CrossRef]

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

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]

IEEE J. Quantum Electron. (1)

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

J. Lightwave Technol. (1)

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]

J. Opt. Soc. Am. (2)

Opt. Acta (Lond.) (1)

J. C. Dainty, “Some statistical properties of random speckle patterns in coherent and partially coherent illumination,” Opt. Acta (Lond.)17(10), 761–772 (1970).
[CrossRef]

Opt. Commun. (1)

F. M. Mottier and R. Dandliker, “A simple spectrum analyzer for laser light using speckles,” Opt. Commun.3(5), 366–368 (1971).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Proc. IEEE (1)

B. M. Oliver, “Sparkling spots and random diffraction,” Proc. IEEE51(1), 220–221 (1963).
[CrossRef]

Z. Angew. Math. Phys. (1)

R. A. Dandliker and F. M. Mottier, “Determination of coherence length from speckle contrast on a rough surface,” Z. Angew. Math. Phys.22(3), 369–381 (1971) (ZAMP).
[CrossRef]

Other (4)

J. W. Goodman, “Speckle phenomena in optics,” in Roberts and Company, (Englewood, 2007).

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

P. Fellgett, “Thesis,” in University of Cambridge, (1951).

J. D. Rigden and E. I. Gorden, “The granularity of scattered optical maser light,” Proc. IRE50, 2367–2368 (1962).

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Figures (7)

Fig. 1
Fig. 1

Coherent-optical frequency domain reflectometry (C-OFDR) based setup for Rayleigh speckle measurement. The optical frequency of the laser under test (LUT) at 1.55 μm is swept linearly by the single side band (SSB) modulator by using the generated + 1st order sideband. A/D, Analog-to-digital converter ; FFT, fast Fourier transform.

Fig. 2
Fig. 2

OFDR traces of eq(τ) (blue) and es(τ) (red) in τ < τ c (left side) and τ > τ c (right side) for LUT #1. The top row shows the total intensities of x- and y-polarizations. The bottom row shows the phases of the x-polarization.

Fig. 3
Fig. 3

(a) The real and imaginary parts of the correlation of e q (τ) e s * (τ) ¯ observed for the three LUTs. N = 1000 samples of amplitude values in the vicinity of the specific delay were used to obtain a single correlation value. (b) The squared modulus of DOCs obtained from the real and imaginary parts.

Fig. 4
Fig. 4

Measured spectral profiles of LUTs. The power spectral densities are obtained with Wiener-Khinchin's theorem by using the DOCs shown in Fig. 3.

Fig. 5
Fig. 5

The observed squared modulus of DOCs in the setting of different sweep times.

Fig. 6
Fig. 6

Common reference experiment design based on a Mach-Zehnder interferometer with a few fixed delays. (a) We used an acousto-optic frequency shifter to enable us to employ ac-coupled photo detectors, and this frequency bias was removed by signal processing. The delay fiber was placed in the same soundproof box as in Fig. 1. AOF: acousto-optical frequency shifter. (b) By obtaining the autocorrelation of the phase noise at delays of 0, ~25, ~50, ~100 and ~200 ms in LUT#1, we analysed the DOC with | γ( τ ) | 2 =exp( σ( τ ) 2 ) ; that is, | γ( τ ) | 2 = 1.0, 0.85, 0.7, 0.4 and 0.08, respectively. The squared modulus DOCs of LUT#1 and #2 are indicated within the bar as in Fig. 3(b). The integration time T was 64 ms.

Fig. 7
Fig. 7

Experimental set-up for measuring the effect of the mechanical vibration of SMF. (a) SMFs with identical 40 km lengths (~200 μs delay) were inserted in both paths of the interferometer. The two SMFs were placed apart from each other in different soundproof boxes. (b) Observed constellation diagram. The corresponding | γ( τ ) | 2 was 0.95. (c) Sound pressure densities in the soundproof box.

Equations (5)

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e q (τ) e s * (τ) ¯ = e j2π( ν q ν s )τ 0 T a (τ) q a q * (tτ) a s * (τ) a s (tτ)dt.
e q (τ) e s * (τ) ¯ = e j2π( ν q ν s )τ | γ(τ) | 2 ,
γ(τ)= 0 T a q,s (t) a q,s * (tτ)dt
e q (τ) e s * (τ) ¯ = e q (x) (τ) e s (x)* (τ)+ e q (y) (τ) e s (y)* (τ) ¯ .
| γ( τ ) | 2 =exp( σ ( τ ) 2 ).

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