## Very long range quasi-Fourier spectroscopy for narrowband lasers |

Optics Express, Vol. 20, Issue 26, pp. B566-B573 (2012)

http://dx.doi.org/10.1364/OE.20.00B566

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### 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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## 1. Introduction

3. J. Connes and P. Connes, “Near-infrared planetary spectra by Fourier spectroscopy. I. Instruments and results,” J. Opt. Soc. Am. **56**(7), 896–910 (1966). [CrossRef]

4. M. Inoue, Y. Koshikiya, X. Fan, and F. Ito, “Coherence characterization of narrow-linewidth beam by C-OFDR based Rayleigh speckle analysis,” Opt. Express **19**(21), 19790–19796 (2011). [CrossRef] [PubMed]

## 2. Theory of principle

13. M. Froggatt and J. Moore, “High-spatial-resolution distributed strain measurement in optical fiber with Rayleigh scatter,” Appl. Opt. **37**(10), 1735–1740 (1998). [CrossRef] [PubMed]

16. X. Fan, Y. Koshikiya, and F. Ito, “Phase-noise-compensated optical frequency domain reflectometry with measurement range beyond laser coherence length realized using concatenative reference method,” Opt. Lett. **32**(22), 3227–3229 (2007). [CrossRef] [PubMed]

*g*is the sweep rate (Hz/s),

*τ'*in the fiber is detected as the spectrum (Fourier transfer),

*τ*),

*τ*is the superposition of the spectrum,

*τ*[12

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

*s*”, with respect to “

*q*”. The sole difference is the fluctuation of the tested beam represented by

*T*is sufficiently long compared with the coherence time so that the time average equals the ensemble average, and the average product of the independent

*q*-th and

*s*-th processes equals the product of each average. Hence, we obtainand find that

## 3. Experimental set-up and laser under test

## 4. Experimental results

*τ*). Since the SMF we used was a non-polarization-hold type, the polarization diversity was incorporated in the coherent receiver. The intensity plot of the scattering is the square sum of the x- and y-polarizations. The blue plots show the results of the first (

_{c}*q*-th) measurement, and red dashed plots shows those of the second (

*s*-th) measurement that was performed successively with the same LUT. As shown in the figure, when

*τ*<

*τ*, these two results exhibit a strong correlation, whereas when

_{c}*τ*>

*τ*, the correlation diminishes. This tendency was observed for all the LUTs used in the experiment, and was well predicted by the theoretical analysis.

_{c}*T*, we collected data for several

*T*s, as shown in Fig. 5 . The observed tendency in LUT#1 in particular, which has the longest expected coherence time of the three, is that the obtained

*T*was short, while the perturbation disappeared when

*T*was long. As described in the theoretical consideration, we presumed that the observed perturbation is a result of the fact that there is insufficient sampling time to contain all possible random events. In such cases, the light sometimes appears coherent even with very large delays, while the interference may diminish at a specific delay, and the cases are dependent on each individual event.

## 5. Conclusion

18. 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]

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]

## References and links

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

2. | P. L. Richards, “High-resolution Fourier transform spectroscopy in the far-infrared,” J. Opt. Soc. Am. |

3. | J. Connes and P. Connes, “Near-infrared planetary spectra by Fourier spectroscopy. I. Instruments and results,” J. Opt. Soc. Am. |

4. | M. Inoue, Y. Koshikiya, X. Fan, and F. Ito, “Coherence characterization of narrow-linewidth beam by C-OFDR based Rayleigh speckle analysis,” Opt. Express |

5. | J. D. Rigden and E. I. Gorden, “The granularity of scattered optical maser light,” |

6. | B. M. Oliver, “Sparkling spots and random diffraction,” Proc. IEEE |

7. | J. W. Goodman, “Speckle phenomena in optics,” in |

8. | J. C. Dainty, “Some statistical properties of random speckle patterns in coherent and partially coherent illumination,” Opt. Acta (Lond.) |

9. | F. M. Mottier and R. Dandliker, “A simple spectrum analyzer for laser light using speckles,” Opt. Commun. |

10. | R. A. Dandliker and F. M. Mottier, “Determination of coherence length from speckle contrast on a rough surface,” Z. Angew. Math. Phys. |

11. | E. Brinkmeyer, “Backscattering in single-mode fibres,” Electron. Lett. |

12. | P. Healey, “Fading in heterodyne OTDR,” Electron. Lett. |

13. | M. Froggatt and J. Moore, “High-spatial-resolution distributed strain measurement in optical fiber with Rayleigh scatter,” Appl. Opt. |

14. | W. Eickhoff and R. Ulrich, “Optical frequency domain reflectometry in single-mode fiber,” Appl. Phys. Lett. |

15. | K. Tsuji, K. Shimizu, T. Horiguchi, and Y. Koyamada, “Coherent optical frequency domain reflectometry using phase-decorrelated reflected and reference lightwaves,” J. Lightwave Technol. |

16. | X. Fan, Y. Koshikiya, and F. Ito, “Phase-noise-compensated optical frequency domain reflectometry with measurement range beyond laser coherence length realized using concatenative reference method,” Opt. Lett. |

17. | M. Born and E. Wolf, |

18. | T. Okoshi, K. Kikuchi, and A. Nakayama, “Novel method for high resolution measurement of laser output spectrum,” Electron. Lett. |

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. |

**OCIS Codes**

(030.0030) Coherence and statistical optics : Coherence and statistical optics

(120.3180) Instrumentation, measurement, and metrology : Interferometry

**ToC Category:**

Fibers, Fiber Devices, and Amplifiers

**History**

Original Manuscript: September 28, 2012

Revised Manuscript: November 27, 2012

Manuscript Accepted: November 27, 2012

Published: December 6, 2012

**Virtual Issues**

European Conference on Optical Communication 2012 (2012) *Optics Express*

**Citation**

Masaaki Inoue, Fumihiko Ito, Xinyu Fan, and Yusuke Koshikiya, "Very long range quasi-Fourier spectroscopy for narrowband lasers," Opt. Express **20**, B566-B573 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-26-B566

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### References

- P. Fellgett, “Thesis,” in University of Cambridge, (1951).
- P. L. Richards, “High-resolution Fourier transform spectroscopy in the far-infrared,” J. Opt. Soc. Am.54(12), 1474–1484 (1964). [CrossRef]
- J. Connes and P. Connes, “Near-infrared planetary spectra by Fourier spectroscopy. I. Instruments and results,” J. Opt. Soc. Am.56(7), 896–910 (1966). [CrossRef]
- M. Inoue, Y. Koshikiya, X. Fan, and F. Ito, “Coherence characterization of narrow-linewidth beam by C-OFDR based Rayleigh speckle analysis,” Opt. Express19(21), 19790–19796 (2011). [CrossRef] [PubMed]
- J. D. Rigden and E. I. Gorden, “The granularity of scattered optical maser light,” Proc. IRE50, 2367–2368 (1962).
- B. M. Oliver, “Sparkling spots and random diffraction,” Proc. IEEE51(1), 220–221 (1963). [CrossRef]
- J. W. Goodman, “Speckle phenomena in optics,” in Roberts and Company, (Englewood, 2007).
- 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]
- 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]
- 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]
- M. Froggatt and J. Moore, “High-spatial-resolution distributed strain measurement in optical fiber with Rayleigh scatter,” Appl. Opt.37(10), 1735–1740 (1998). [CrossRef] [PubMed]
- W. Eickhoff and R. Ulrich, “Optical frequency domain reflectometry in single-mode fiber,” Appl. Phys. Lett.39(9), 693–695 (1981). [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]
- X. Fan, Y. Koshikiya, and F. Ito, “Phase-noise-compensated optical frequency domain reflectometry with measurement range beyond laser coherence length realized using concatenative reference method,” Opt. Lett.32(22), 3227–3229 (2007). [CrossRef] [PubMed]
- M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University Press, 1999).
- 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]
- 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]

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