## Versatile chromatic dispersion measurement of a single mode fiber using spectral white light interferometry

Optics Express, Vol. 14, Issue 24, pp. 11608-11615 (2006)

http://dx.doi.org/10.1364/OE.14.011608

Acrobat PDF (158 KB)

### Abstract

We present a versatile and accurate chromatic dispersion measurement method for single mode optical fibers over a wide spectral range (200 nm) using a spectral domain white light interferometer. This technique is based on spectral interferometry with a Mach-Zehnder interferometer setup and a broad band light source. It takes less than a second to obtain a spectral interferogram for a few tens of centimeter length fiber sample. We have demonstrated that the relative group velocity, the chromatic dispersion and the dispersion slope of a sample fiber can be obtained very accurately regardless of the zero-dispersion wavelength (ZDW) of a sample after frequency dependent optical phase was directly retrieved from a spectral interferogram. The measured results with our proposed method were compared with those obtained with a conventional time-domain dispersion measurement method. A good agreement between those results indicates that our proposed method can measure the chromatic dispersion of a short length optical fiber with very high accuracy.

© 2006 Optical Society of America

## 1. Introduction

1. S. Diddams and J. C. Diels, “Dispersion measurements with white light interferometry,” J. Opt. Soc. Am. B **13**, 1120–1129 (1996). [CrossRef]

3. L. G Cohen, “Comparison of single-mode fiber dispersion measurement techniques,” J. Lightwave Technol. **3**, 958–966 (1985). [CrossRef]

4. J. Brendel, H. Zbinden, and N. Gision, “Measurement of chromatic dispersion in optical fibers using pairs of correlated photons,” Opt. Commun. **151**, 35–39 (1998). [CrossRef]

5. K. Takada, T. Kitagawa, K. Hattori, M. Yamada, M. Horiguchi, and R. K. Hickernell, “Direct dispersion measurement of highly-erbium-doped optical amplifiers using a low coherence reflectometer coupled with dispersive Fourier spectroscopy,” Electron. Lett. **28**, 889–890 (1992). [CrossRef]

6. D. D Shellee and K. B. Rochford, “Low-coherence interferometric measurements of the dispersion of multiple fiber bragg gratings,” IEEE Photon. Technol. Lett. **13**, 230–232 (2001). [CrossRef]

9. J. Tignon, M. V Marquezini, T. Hasch, and D. S. Chemals, “Spectral interferometry of semiconductor nanostructures,” IEEE J. Quantum Electron. **35**, 510–522 (1999). [CrossRef]

13. A. B. Vakhtin, K. A. Peterson, W. R Wood, and D. J. Kane, “Differential spectal interferometery and imaging technique for biomedical applications,” Opt. Lett. **28**, 1332–1334 (2003). [CrossRef] [PubMed]

18. D. Hammer, A. Welch, G. Noojin, R. Thomas, D. Stolarski, and B. Rockwell, “Spectrally resolved white-light interferometry for measurement of ocular dispersion,” J. Opt. Soc. Am. A **16**, 2092–2102 (1999). [CrossRef]

19. V. N. Kumer and D. N. Rao, “Using interference in the frequency domain for precise determination of thickness and refractive indices of normal dispersive material,” J. Opt. Soc. Am. B **12**, 1559–1563 (1995). [CrossRef]

20. A. F. Fercher, C. K. Hitzenberger, G. Kamp, and S. Y. Elzaiat, “Measurement of Intraocular Distances by Backscattering Spectral Interferometry,” Opt. Commun.117, 43–48 (1995). [CrossRef]

## 2. Theory

*f*is optical frequency, 〈|

*E*(

*f*)|

^{2}〉 is the spectral intensity of a broadband source,

*a*

^{2}is relative optical power for the transmitted optical signal through a tested fiber,

*ϕ*(

*f*) is relative phase between a reference signal and a transmitted signal through a tested fiber, and < > denotes an ensemble average. The relative phase can be expressed as

*ϕ*(

*f*)=

*β*(

*f*)·

*L*-

*β*

_{0}·

*L*

_{0}where

*β*(

*f*) is the propagation constant of transmitted light in a tested fiber,

*L*is the length of the tested fiber,

*β*

_{0}is the propagation constant in vacuum,

*L*

_{0}is the length of the reference arm in an interferometer. When

*c*is the speed of light in vacuum,

*n*(

*f*) is the refractive index of a test fiber, we have

*β*(

*f*)≡2

*π*/

*c*·

*n*(

*f*)·

*f*and

*β*

_{0}·

*L*

_{0}=2

*π*/

*λ*·

*L*

_{0}=2

*πτ*

_{0}·

*f*where have used a relation

*λf*=

*c*between optical frequency

*f*and optical wavelength λ. Delay time associated with the reference arm of an interferometer is defined as

*τ*

_{0}≡

*L*

_{0}/

*c*. This can be controlled arbitrarily by adjusting a translation stage in the reference arm of an interferometer. Then, the relative phase can be expressed as

*v*(

_{g}*f*) is the group velocity of light in a sample fiber, and

*τ*(

_{g}*f*) is the group delay after transmitting through a given sample fiber whose length is

*L*. The chromatic dispersion coefficient

*D*(

*λ*) of a fiber is the variation in the group delay with respect to wavelength per unit length of a fiber,

*D*(

*λ*)=(1/

*L*)·

*∂τ*(

_{g}*λ*)/

*∂λ*. In our experiment, we retrieve phase

*ϕ*(

*f*) directly from a spectral interferogram 〈

*I*(

*f*)〉 and calculate the group delay

*τ*(

_{g}*f*), dispersion coefficient

*D*(

*λ*), and second order dispersion coefficient

*dD*(

*λ*)/

*dλ*of a tested fiber from the relative phase function.

## 3. Experiments and results

*ϕ*(

*λ*) with respect to wavelength. Then, the calculated relative phase function was converted from the wavelength domain into the frequency domain to obtain

*ϕ*(

*f*) in Eq. (2). Note that the frequency axis in the converted function is not regular while wavelength difference between data points in

*ϕ*(

*λ*) is constant. We have used a cubic spline fitting processing to recalculate a regularly spaced phase function

*ϕ*(

*f*) in the frequency domain [17

17. C. D. Dorrer, N. Belabas, J. P. Likforman, and M. Joffre, “Spectral resolution and sampling in Fourier transform spectral interferometry,” J. Opt. Soc. Am. B **17**, 1795–1802 (2000). [CrossRef]

*τ*(

_{g}*f*) of a fiber is proportional to the first derivative of the calculated

*ϕ*(

*f*) and the dispersion

*D*(

*f*) of a fiber depends on the second derivative of

*ϕ*(

*f*). Blue empty squares In Fig. 3(a) are calculated from the first order derivative of the relative phase function, which is

*f*

_{0}is the frequency at which the group delay is minimum, and it can be calculated to be

*f*

_{0}=-

*ϕ*/

_{2}*ϕ*from Eq. (6). Therefore, we can calculate the zerodispersion frequency or the zero-dispersion wavelength of a sample fiber as long as we find ϕ

_{3}_{2}, ϕ

_{3}coefficients with high accuracy by doing a least square curve fitting process for measured phase spectrum data ϕ(

*f*). When we replace

*f*with

*c*/

*λ*in Eq. (6) and take the first order derivative with respect to

*λ*, we have an expression for the chromatic dispersion coefficient of a sample fiber

*D*(

*λ*) of a sample fiber obtained with our proposed method. It also shows the second order dispersion coefficient

*dD*(

*λ*)/

*dλ*which signifies the dispersion slop of the sample fiber. Red empty dots are measurement results by a conventional MPS method for a 1km length of same fiber. The measurement result has in good agreement with those of the conventional measurement method. We have also measured the chromatic dispersion and the second order dispersion of another optical fiber sample: DSF (Sumitomo Electric). The length of the sample fiber was only 550 mm. Figure 4(a) is the measured spectral interferogram obtained by an OSA. It was normalized by its maximum intensity. Figure 4(b) is the close-up view of Fig. 4(a) near 1550 nm wavelength. A 3rd polynomial curve fitting method was used to determine the wavelength of each peak in Fig. 4(b). Figure 5(a) shows the calculated phase spectra and relative group delay spectra for the DSF sample. Black empty squares are equally spaced phase function. A fitted function with third order polynomials is drawn with a red line. The relative group delay of the DSF sample is calculated from the first order derivative of the fitting curve for the relative phase function, and it is drawn with empty

*D*(

*λ*) of the DSF is shown in Fig. 5 (b) with a black line. Red empty dots are few discrete measurement results obtained by a commercially available dispersion measurement system based on the MPS method. It shows that these two different measurement results are in good agreement with each other. In the commercially available measurement system, they have used a five-term Sellmeier equation to fit the group delay as a function of wavelength near the zero dispersion wavelength of the DSF sample [24

24. P. Merritt, R. P. Tatam, and D. A. Jacson, “Interferometric chromatic dispersion measurements on short lengths of monomode optical fiber,” J. Lightwave Technol. **7**, 703–716 (1989). [CrossRef]

25. M. Galli, F. Marabelli, and G. Guizzetti, “Direct measurement of refractive-index dispersion of transparent media by white-light inerferometry,” Appl. Opt. **42**, 3910–3914 (2003). [CrossRef] [PubMed]

*dD*(

*λ*)/

*dλ*obtained with our proposed method is drawn with a blue solid line in Fig. 5(b). The dispersion slope at 1550 nm wavelength with both methods was found to be the same: 0.066 ps/nm

^{2}/km. This confirms that our proposed method can determine the second order dispersion coefficient with a reliable accuracy.

26. R. Leitgeb, C. Hitzenberger, and A. Fercher, “Performance of Fourier domain vs. time domain optical coherence tomography,” Opt. Express **11**, 889–894 (2004). [CrossRef]

_{o}. Therefore, our proposed method can be used to measure a sample with wide range dispersion.

## 3. Conclusion

## Acknowledgments

## References and links

1. | S. Diddams and J. C. Diels, “Dispersion measurements with white light interferometry,” J. Opt. Soc. Am. B |

2. | C. Peucheret, F. Lin, and R. J. S. Pedersen, “Measurement of small dispersion values in optical components [WDM networks],” Electron. Lett. |

3. | L. G Cohen, “Comparison of single-mode fiber dispersion measurement techniques,” J. Lightwave Technol. |

4. | J. Brendel, H. Zbinden, and N. Gision, “Measurement of chromatic dispersion in optical fibers using pairs of correlated photons,” Opt. Commun. |

5. | K. Takada, T. Kitagawa, K. Hattori, M. Yamada, M. Horiguchi, and R. K. Hickernell, “Direct dispersion measurement of highly-erbium-doped optical amplifiers using a low coherence reflectometer coupled with dispersive Fourier spectroscopy,” Electron. Lett. |

6. | D. D Shellee and K. B. Rochford, “Low-coherence interferometric measurements of the dispersion of multiple fiber bragg gratings,” IEEE Photon. Technol. Lett. |

7. | J. Gehler and W. Spahn, “Dispersion measurement of arrayed-waveguide grating by Fourier transform spectroscopy,” Electron. Lett. |

8. | R. Cella and W. Wood, “Measurement of chromatic dispersion in erbium doped fiber using low coherence interferometry,” Proceedings of the Sixth Optical Fibre Measurement Conference, 207–210 (2001) |

9. | J. Tignon, M. V Marquezini, T. Hasch, and D. S. Chemals, “Spectral interferometry of semiconductor nanostructures,” IEEE J. Quantum Electron. |

10. | A. Wax, C. Yang, and J. A. Izatt, “Fourier-domain low-coherence interferometry for light-scattering spectroscopy,” Opt. Lett. |

11. | P. Hlubina, T. Martynkien, and W. Urbańczyk, “Dispersion of group and phase modal birefringence in elliptical-core fiber measured by white-light spectral interferometry,” Opt. Express |

12. | P. Hlubina, “White-light spectral interferometry to measure intermodal dispersion in two-mode elliptical-core optical fibers,” Opt. Commun. |

13. | A. B. Vakhtin, K. A. Peterson, W. R Wood, and D. J. Kane, “Differential spectal interferometery and imaging technique for biomedical applications,” Opt. Lett. |

14. | R. Leitgeb, W. Drexler, A. Unterhuber, B. Hermann, T. Bajraszewski, T. Le, A. Stingl, and A. Fercher, “Ultra high resolution Fourier domain optical coherence tomography,” Opt. Express |

15. | D. Huang, E. A Swang, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang. M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science |

16. | K. Takada, I. Yokohama, K. Chida, and J. Noda, “New measurement system for fault location in optical waveguide devices based on an interfermetric technique,” Appl. Opt. |

17. | C. D. Dorrer, N. Belabas, J. P. Likforman, and M. Joffre, “Spectral resolution and sampling in Fourier transform spectral interferometry,” J. Opt. Soc. Am. B |

18. | D. Hammer, A. Welch, G. Noojin, R. Thomas, D. Stolarski, and B. Rockwell, “Spectrally resolved white-light interferometry for measurement of ocular dispersion,” J. Opt. Soc. Am. A |

19. | V. N. Kumer and D. N. Rao, “Using interference in the frequency domain for precise determination of thickness and refractive indices of normal dispersive material,” J. Opt. Soc. Am. B |

20. | A. F. Fercher, C. K. Hitzenberger, G. Kamp, and S. Y. Elzaiat, “Measurement of Intraocular Distances by Backscattering Spectral Interferometry,” Opt. Commun.117, 43–48 (1995). [CrossRef] |

21. | G. Häusler and M. W. Lindner, ““Coherence Radar” and “Spectral Radar”—New tools for dermatological diagnosis,” J. Biomed. Opt. |

22. | M. Wojtkowski, R. Leitgeb, A. Kowalczyk, T. Bajraszewski, and A. F. Fercher, “In vivo human retinal imaging by Fourier domain optical coherence tomography,” J. Biomed. Opt. |

23. | M. Wojtkowski, A. Kowalczyk, R. Leitgeb, and A. F. Fercher, “Full range complex spectral optical coherence tomography technique in eye imaging,” Opt. Lett. |

24. | P. Merritt, R. P. Tatam, and D. A. Jacson, “Interferometric chromatic dispersion measurements on short lengths of monomode optical fiber,” J. Lightwave Technol. |

25. | M. Galli, F. Marabelli, and G. Guizzetti, “Direct measurement of refractive-index dispersion of transparent media by white-light inerferometry,” Appl. Opt. |

26. | R. Leitgeb, C. Hitzenberger, and A. Fercher, “Performance of Fourier domain vs. time domain optical coherence tomography,” Opt. Express |

**OCIS Codes**

(060.2300) Fiber optics and optical communications : Fiber measurements

(120.3180) Instrumentation, measurement, and metrology : Interferometry

(120.5050) Instrumentation, measurement, and metrology : Phase measurement

(260.2030) Physical optics : Dispersion

**ToC Category:**

Instrumentation, Measurement, and Metrology

**History**

Original Manuscript: August 30, 2006

Revised Manuscript: November 15, 2006

Manuscript Accepted: November 16, 2006

Published: November 27, 2006

**Citation**

Ji Yong Lee and Dug Young Kim, "Versatile chromatic dispersion measurement of a single mode fiber using
spectral white light interferometry," Opt. Express **14**, 11608-11615 (2006)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-24-11608

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### References

- S. Diddams and J. C. Diels, "Dispersion measurements with white light interferometry," J. Opt. Soc. Am. B 13, 1120-1129 (1996). [CrossRef]
- C. Peucheret, F. Lin, and R. J. S. Pedersen, "Measurement of small dispersion values in optical components [WDM networks]," Electron. Lett. 35, 409-410 (1999). [CrossRef]
- L. G Cohen, "Comparison of single-mode fiber dispersion measurement techniques," J. Lightwave Technol. 3, 958 -966 (1985). [CrossRef]
- J. Brendel, H. Zbinden, and N. Gision, "Measurement of chromatic dispersion in optical fibers using pairs of correlated photons," Opt. Commun. 151, 35-39 (1998). [CrossRef]
- K. Takada, T. Kitagawa, K. Hattori, M. Yamada, M. Horiguchi, and R. K. Hickernell, "Direct dispersion measurement of highly-erbium-doped optical amplifiers using a low coherence reflectometer coupled with dispersive Fourier spectroscopy," Electron. Lett. 28, 889-890 (1992). [CrossRef]
- D. D Shellee and K. B. Rochford, "Low-coherence interferometric measurements of the dispersion of multiple fiber bragg gratings," IEEE Photon. Technol. Lett. 13, 230-232 (2001). [CrossRef]
- J. Gehler and W. Spahn, "Dispersion measurement of arrayed-waveguide grating by Fourier transform spectroscopy," Electron. Lett. 36,338-340 (2000). [CrossRef]
- R. Cella and W. Wood, "Measurement of chromatic dispersion in erbium doped fiber using low coherence interferometry," Proceedings of the Sixth Optical Fibre Measurement Conference, 207-210 (2001)
- J. Tignon, M. V Marquezini, T. Hasch, and D. S. Chemals, "Spectral interferometry of semiconductor nanostructures," IEEE J. Quantum Electron. 35,510-522 (1999). [CrossRef]
- A. Wax, C. Yang, and J. A. Izatt, "Fourier-domain low-coherence interferometry for light-scattering spectroscopy," Opt. Lett. 28,1230-1232 (2003). [CrossRef] [PubMed]
- P. Hlubina, T. Martynkien, and W. Urbañczyk, "Dispersion of group and phase modal birefringence in elliptical-core fiber measured by white-light spectral interferometry," Opt. Express 11, 2793-2798 (2003). [PubMed]
- P. Hlubina, "White-light spectral interferometry to measure intermodal dispersion in two-mode elliptical-core optical fibers," Opt. Commun. 218, 283-289 (2003). [CrossRef]
- A. B. Vakhtin, K. A. Peterson, W. R Wood, and D. J. Kane, "Differential spectal interferometery and imaging technique for biomedical applications," Opt. Lett. 28, 1332-1334 (2003). [CrossRef] [PubMed]
- R. Leitgeb, W. Drexler, A. Unterhuber, B. Hermann, T. Bajraszewski, T. Le, A. Stingl, and A. Fercher, "Ultra high resolution Fourier domain optical coherence tomography," Opt. Express 12, 2156-2165 (2004). [CrossRef] [PubMed]
- D. Huang, E. A Swang, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang. M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, "Optical coherence tomography," Science 254, 1178-1181 (1991). [CrossRef] [PubMed]
- K. Takada, I. Yokohama, K. Chida, and J. Noda, "New measurement system for fault location in optical waveguide devices based on an interfermetric technique," Appl. Opt. 26, 1603-1605 (1987). [CrossRef] [PubMed]
- C. D. Dorrer, N. Belabas, J. P. Likforman, and M. Joffre, "Spectral resolution and sampling in Fourier transform spectral interferometry," J. Opt. Soc. Am. B 17, 1795-1802 (2000). [CrossRef]
- D. Hammer, A. Welch, G. Noojin, R. Thomas, D. Stolarski, and B. Rockwell, "Spectrally resolved white-light interferometry for measurement of ocular dispersion," J. Opt. Soc. Am. A 16, 2092-2102 (1999). [CrossRef]
- V. N. Kumer and D. N. Rao, "Using interference in the frequency domain for precise determination of thickness and refractive indices of normal dispersive material," J. Opt. Soc. Am. B 12, 1559-1563 (1995). [CrossRef]
- A. F. Fercher, C. K. Hitzenberger, G. Kamp, and S. Y. Elzaiat, "Measurement of Intraocular Distances by Backscattering Spectral Interferometry," Opt. Commun. 117, 43-48 (1995). [CrossRef]
- G. Häusler and M. W. Lindner, ""Coherence Radar" and "Spectral Radar"—New tools for dermatological diagnosis," J. Biomed. Opt. 3, 21-31 (1998). [CrossRef]
- M. Wojtkowski, R. Leitgeb, A. Kowalczyk, T. Bajraszewski, and A. F. Fercher, "In vivo human retinal imaging by Fourier domain optical coherence tomography," J. Biomed. Opt. 7, 457-463 (2002). [CrossRef] [PubMed]
- M. Wojtkowski, A. Kowalczyk, R. Leitgeb, and A. F. Fercher, "Full range complex spectral optical coherence tomography technique in eye imaging," Opt. Lett. 27, 1415-1417 (2002). [CrossRef]
- P. Merritt, R. P. Tatam, and D. A. Jacson, "Interferometric chromatic dispersion measurements on short lengths of monomode optical fiber," J. Lightwave Technol. 7, 703-716 (1989). [CrossRef]
- M. Galli, F. Marabelli, and G. Guizzetti, "Direct measurement of refractive-index dispersion of transparent media by white-light inerferometry," Appl. Opt. 42. 3910-3914 (2003). [CrossRef] [PubMed]
- R. Leitgeb, C. Hitzenberger, and A. Fercher, "Performance of Fourier domain vs. time domain optical coherence tomography," Opt. Express 11, 889-894 (2004). [CrossRef]

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