## Analysis and suppression of nonlinear frequency modulation in an optical frequency-domain reflectometer

Optics Express, Vol. 17, Issue 7, pp. 5845-5851 (2009)

http://dx.doi.org/10.1364/OE.17.005845

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### Abstract

A new method for monitoring the nonlinearities perturbing the optical frequency sweep in high speed tunable laser sources is presented. The swept-frequency monitoring system comprises a Mach-Zehnder interferometer and simple signal processing steps. It has been implemented in a coherent optical frequency domain reflectometer which allowed to drastically reduce the effects of nonlinear sweep, resulting to a spatial resolution enhancement of 30 times.

© 2009 Optical Society of America

## 1. Introduction

1. J. Martins-Filho, C. Bastos-Filho, M. Carvalho, M. Sundheimer, and A. Gomes, “Dual-Wavelength (1050nm + 1550 nm) Pumped Thulium-Doped Fiber Amplifier Characterization by Optical Frequency-Domain Reflectometer,” IEEE Photon. Technol. Lett. **15**, 24–26 (2003). [CrossRef]

3. C. Ndiaye, T. Hara, and H. Ito, “Profilometry using a frequency-shifted feedback laser,” in *Proceedings Conference on Lasers and Electro-Optics (CLEO)*, pp. 1757–1759 (CThM2) (Baltimore, Maryland, 2005). [CrossRef]

4. H. Lim, J. de Boer, B. Park, E. Lee, R. Yelin, and S. Yun, “Optical frequency domain imaging with a rapidly swept laser in the 815–870 nm range,” Opt. Express **14**, 5937–5944 (2006). [CrossRef] [PubMed]

5. J. Zheng, “Analysis of optical frequency-modulated continuous-wave interference,” Appl. Opt. **43**, 4189–4197 (2004). [CrossRef] [PubMed]

6. U. Glombitza and E. Brinkmeyer, “Coherent Frequency-Domain Reflectometry for Characterization of Single-Mode Integrated-Optical Waveguides,” J. Lightwave Technol. **11**, 1377–1384 (1993). [CrossRef]

6. U. Glombitza and E. Brinkmeyer, “Coherent Frequency-Domain Reflectometry for Characterization of Single-Mode Integrated-Optical Waveguides,” J. Lightwave Technol. **11**, 1377–1384 (1993). [CrossRef]

7. J. B. Soller, D. Gifford, M. Wolfe, and M. Froggatt, “High resolution optical frequency domain reflectometry for characterization of components and assemblies,” Opt. Express **13**, 666–674 (2005). [CrossRef] [PubMed]

8. T.-J. Ahn, J. Lee, and D. Kim, “Suppression of nonlinear frequency sweep in an optical frequency-domain re-flectometer by use of Hilbert transformation,” Appl. Opt. **44**, 7630–7634 (2005). [CrossRef] [PubMed]

9. K. Tsuji, K. Shimizu, T. Horiguchi, and Y. Koyamada, “Spatial-resolution improvement in long-range coherent optical frequency domain reflectometry by frequency-sweep linearisation,” Electron. Lett. **33**, 408–410 (1997). [CrossRef]

8. T.-J. Ahn, J. Lee, and D. Kim, “Suppression of nonlinear frequency sweep in an optical frequency-domain re-flectometer by use of Hilbert transformation,” Appl. Opt. **44**, 7630–7634 (2005). [CrossRef] [PubMed]

10. T.-J. Ahn and D. Kim, “Analysis of nonlinear frequency sweep in high-speed tunable laser sources using self-homodyne measurement and Hilbert transformation,” Appl. Opt. **46**, 2394–2400 (2007). [CrossRef] [PubMed]

## 2. Principles of optical frequency measurement

*E*

_{0}is the amplitude of the electric field and

*ϕ*(

*t*) is the phase component. The phase component can be written as

*ϕ*

_{0}is the initial phase (

*t*= 0) of the light source and

*v*(

*t*) is the instantaneous optical frequency of the laser. The probe light is divided into two waves at the first coupler which propagate along both arms of the interferometer having different lengths and then are recombined at the second coupler. The group delay difference between the two arms of the interferometer is known and denoted by

*τ*.

*η*is a constant that depends on the insertion loss of the two couplers. Equation 3 assumes the best case where the two incident fields have the same polarization. In general, a polarization controller is inserted in one arm of the interferometer to maximize the interference signal. It should be also noted that the optical path difference between the interferometer arms is much smaller than the coherence length of the laser source. The AC part of the interference signal detected at the photodiode is given by

*U*

_{0}= 2

*η*

*σ*|

*E*

_{0}|

^{2}and

*σ*a constant that depends on the photodetector sensitivity. Next, by Taylor expanding the phase

*ϕ*(

*t*-

*τ*) about

*t*we obtain

*u*(

*t*) in Eq. 6, the optical frequency quantification can be obtained by applying the data processing steps schematically represented in Fig. 2.

*u*(

_{N}*t*) is obtained by dividing the

*u*(

*t*) by its peak amplitude

*U*

_{0}. The time-varying optical frequency is then converted to amplitude variations by taking the differential of the normalized signal,

*u*(

_{N}*t*)

*A*(

*t*) which in turn yields the time-varying tuning rate (

*γ*(

*t*)) of the optical frequency as follows

8. T.-J. Ahn, J. Lee, and D. Kim, “Suppression of nonlinear frequency sweep in an optical frequency-domain re-flectometer by use of Hilbert transformation,” Appl. Opt. **44**, 7630–7634 (2005). [CrossRef] [PubMed]

10. T.-J. Ahn and D. Kim, “Analysis of nonlinear frequency sweep in high-speed tunable laser sources using self-homodyne measurement and Hilbert transformation,” Appl. Opt. **46**, 2394–2400 (2007). [CrossRef] [PubMed]

11. E. Moore and R. McLeod, “Correction of sampling errors due to laser tuning rate fluctuations in swept-wavelength interferometry,” Opt. Express **16**, 13,139–13,149 (2008). [CrossRef]

## 3. Experimental set-up and results

*τ*= 12.8 ns.

*γ*= 1.25 THz/s (about 1 nm sweep span over 100 ms sweep time) which means that the inequality

_{v}12. 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**, 1102–1109 (1997). [CrossRef]

*γ*),

*c*is the speed of light in vacuum,

*n*is the refractive group index of the DUT, and ∆

_{g}*f*is the frequency-resolution bandwidth of the system. In the ideal case of linear frequency modulation, the best spatial resolution in our system was about 0.2 cm considering the sampling rate of 0.4 MSample/s with 16384 sampling points at DAQ and constant tuning rate of 1.25 THz/s applied to the TLS.

**44**, 7630–7634 (2005). [CrossRef] [PubMed]

## 4. Conclusion

## Acknowledgments

## References and links

1. | J. Martins-Filho, C. Bastos-Filho, M. Carvalho, M. Sundheimer, and A. Gomes, “Dual-Wavelength (1050nm + 1550 nm) Pumped Thulium-Doped Fiber Amplifier Characterization by Optical Frequency-Domain Reflectometer,” IEEE Photon. Technol. Lett. |

2. | B. Soller, S. Kreger, D. Gifford, M. Wolfe, and M. Froggatt, “Optical Frequency Domain Reflectometry for Single- and Multi-Mode Avionics Fiber-Optics Applications,” in |

3. | C. Ndiaye, T. Hara, and H. Ito, “Profilometry using a frequency-shifted feedback laser,” in |

4. | H. Lim, J. de Boer, B. Park, E. Lee, R. Yelin, and S. Yun, “Optical frequency domain imaging with a rapidly swept laser in the 815–870 nm range,” Opt. Express |

5. | J. Zheng, “Analysis of optical frequency-modulated continuous-wave interference,” Appl. Opt. |

6. | U. Glombitza and E. Brinkmeyer, “Coherent Frequency-Domain Reflectometry for Characterization of Single-Mode Integrated-Optical Waveguides,” J. Lightwave Technol. |

7. | J. B. Soller, D. Gifford, M. Wolfe, and M. Froggatt, “High resolution optical frequency domain reflectometry for characterization of components and assemblies,” Opt. Express |

8. | T.-J. Ahn, J. Lee, and D. Kim, “Suppression of nonlinear frequency sweep in an optical frequency-domain re-flectometer by use of Hilbert transformation,” Appl. Opt. |

9. | K. Tsuji, K. Shimizu, T. Horiguchi, and Y. Koyamada, “Spatial-resolution improvement in long-range coherent optical frequency domain reflectometry by frequency-sweep linearisation,” Electron. Lett. |

10. | T.-J. Ahn and D. Kim, “Analysis of nonlinear frequency sweep in high-speed tunable laser sources using self-homodyne measurement and Hilbert transformation,” Appl. Opt. |

11. | E. Moore and R. McLeod, “Correction of sampling errors due to laser tuning rate fluctuations in swept-wavelength interferometry,” Opt. Express |

12. | K. Tsuji, K. Shimizu, T. Horiguchi, and Y. Koyamada, “Coherent Optical Frequency Domain Reflectometry Using Phase-Decorrelated Reflected and Reference Lightwaves,” J. Lightwave Technol. |

**OCIS Codes**

(060.2300) Fiber optics and optical communications : Fiber measurements

(120.2920) Instrumentation, measurement, and metrology : Homodyning

(120.3180) Instrumentation, measurement, and metrology : Interferometry

(120.3940) Instrumentation, measurement, and metrology : Metrology

**ToC Category:**

Instrumentation, Measurement, and Metrology

**History**

Original Manuscript: February 5, 2009

Revised Manuscript: March 24, 2009

Manuscript Accepted: March 25, 2009

Published: March 26, 2009

**Citation**

Kivilcim Yuksel, Marc Wuilpart, and Patrice Mégret, "Analysis and suppression of nonlinear frequency modulation in an optical frequency-domain reflectometer," Opt. Express **17**, 5845-5851 (2009)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-7-5845

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### References

- J. Martins-Filho, C. Bastos-Filho, M. Carvalho, M. Sundheimer, and A. Gomes, "Dual-Wavelength (1050nm + 1550 nm) Pumped Thulium-Doped Fiber Amplifier Characterization by Optical Frequency-Domain Reflectometer," IEEE Photon. Technol. Lett. 15, 24-26 (2003). [CrossRef]
- B. Soller, S. Kreger, D. Gifford, M. Wolfe, and M. Froggatt, "Optical Frequency Domain Reflectometry for Single- and Multi-Mode Avionics Fiber-Optics Applications," in Avionics Fiber-Optics and Photonics, 2006, pp. 38-39 (2006).
- C. Ndiaye, T. Hara, and H. Ito, "Profilometry using a frequency-shifted feedback laser," in Proceedings Conference on Lasers and Electro-Optics (CLEO), pp. 1757-1759 (CThM2) (Baltimore, Maryland, 2005). [CrossRef]
- H. Lim, J. de Boer, B. Park, E. Lee, R. Yelin, and S. Yun, "Optical frequency domain imaging with a rapidly swept laser in the 815-870 nm range," Opt. Express 14, 5937-5944 (2006). [CrossRef] [PubMed]
- J. Zheng, "Analysis of optical frequency-modulated continuous-wave interference," Appl. Opt. 43, 4189-4197 (2004). [CrossRef] [PubMed]
- U. Glombitza and E. Brinkmeyer, "Coherent Frequency-Domain Reflectometry for Characterization of Single-Mode Integrated-Optical Waveguides," J. Lightwave Technol. 11, 1377-1384 (1993). [CrossRef]
- J. B. Soller, D. Gifford, M. Wolfe, and M. Froggatt, "High resolution optical frequency domain reflectometry for characterization of components and assemblies," Opt. Express 13, 666-674 (2005). [CrossRef] [PubMed]
- T.-J. Ahn, J. Lee, and D. Kim, "Suppression of nonlinear frequency sweep in an optical frequency-domain reflectometer by use of Hilbert transformation," Appl. Opt. 44, 7630-7634 (2005). [CrossRef] [PubMed]
- K. Tsuji, K. Shimizu, T. Horiguchi, and Y. Koyamada, "Spatial-resolution improvement in long-range coherent optical frequency domain reflectometry by frequency-sweep linearisation," Electron. Lett. 33, 408-410 (1997). [CrossRef]
- T.-J. Ahn and D. Kim, "Analysis of nonlinear frequency sweep in high-speed tunable laser sources using selfhomodyne measurement and Hilbert transformation," Appl. Opt. 46, 2394-2400 (2007). [CrossRef] [PubMed]
- E. Moore and R. McLeod, "Correction of sampling errors due to laser tuning rate fluctuations in sweptwavelength interferometry," Opt. Express 16, 13,139-13,149 (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, 1102-1109 (1997). [CrossRef]

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