## Measurement of anomalous dispersion in microstructured fibers using spectral modulation

Optics Express, Vol. 12, Issue 5, pp. 929-934 (2004)

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### Abstract

We report on a simple technique to measure the anomalous dispersion of small-core microstructured fibers using short optical pulses. The method relies on the spectral modulation resulting from the evolution of the input pulse into a propagating soliton wave. The technique allows for a direct measurement of the dispersion at the desired wavelength from a single pulse. The measurement error is estimated to be less than 10%.

© 2004 Optical Society of America

## 1. Introduction

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

4. B. Costa, D. Mazzoni, M. Puelo, and E. Vezzoni, “Phase-shift technique for the measurement of chromatic dispersion in optical fibers using LED’s,” IEEE J. Quantum Electron. **18**, 1509–1515 (1982). [CrossRef]

8. M. J. Gander, R. McBride, J. D. C. Jones, D. Mogilevtsev, T. A. Birks, J. C. Knight, and P. S. Russell, “Experimental measurement of group velocity dispersion in photonic crystal fibre,” Electron. Lett. **35**, 63–64 (1999). [CrossRef]

## 2. Theory

9. M. W. Chbat, P. R. Prucnal, M. N. Islam, C. E. Soccolich, and J. P. Gordon, “Long-Range Interference Effects of Soliton Reshaping in Optical Fibers,” J. Opt. Soc. Am. B **10**, 1386–1395 (1993). [CrossRef]

10. N. J. Smith, K. J. Blow, and I. Andonovic, “Sideband generation through perturbations to the average soliton model,” J. Lightwave Technol. **10**, 1329–1333 (1992). [CrossRef]

11. D. U. Noske, N. Pandit, and J. R. Taylor, “Source of spectral and temporal instability in soliton fiber lasers,” Opt. Lett. **17**, 1515–1517 (1992). [CrossRef] [PubMed]

*N*is the soliton number defined by

*N*

^{2}=

*γP*

_{P}

*β*

_{2}| with

*T*

_{0}being the temporal width of the input pulse,

*P*

_{p}its peak power, and

*β*

_{2}and

*γ*representing the group-velocity dispersion and the nonlinear coefficient of the fiber, respectively. When the effects of dispersion and nonlinearity are in balance, i.e., when

*N*=1, the pulse propagates as a fundamental soliton which maintains its shape along propagation [12]. For input pulse parameters such that

*N*=1±

*ε*with

*ε*∈[-1/2,1/2], the pulse evolves asymptotically into a fundamental soliton, and during the reshaping process, a dispersive wave is stripped off from the pulse [13

13. J. Satsuma and N. Yajima, “Initial value problems of one-dimensional selfmodulation of nonlinear waves in dispersive media,” Suppl. Prog. Theo. Phys. **55**, 284–306 (1974). [CrossRef]

9. M. W. Chbat, P. R. Prucnal, M. N. Islam, C. E. Soccolich, and J. P. Gordon, “Long-Range Interference Effects of Soliton Reshaping in Optical Fibers,” J. Opt. Soc. Am. B **10**, 1386–1395 (1993). [CrossRef]

*L*and the wavelength

*λ*

_{0}of the input pulse as [9

9. M. W. Chbat, P. R. Prucnal, M. N. Islam, C. E. Soccolich, and J. P. Gordon, “Long-Range Interference Effects of Soliton Reshaping in Optical Fibers,” J. Opt. Soc. Am. B **10**, 1386–1395 (1993). [CrossRef]

*c*is the speed of light in vacuum. By making use of the fact that the phase difference between two consecutive maxima at wavelengths

*λ*

_{1}and

*λ*

_{2}in the optical spectrum is equal to 2

*π*,

*Δφ*(

*λ*

_{2})-

*Δφ*(

*λ*

_{1})=

*2π*, the dispersion parameter at the pulse wavelength

*λ*

_{0}can be approximated as

*L*and

*c*are expressed in m and m·s

^{-1}, respectively. In the derivation of Eq. (3), the contributions of the

*tan*

^{-1}terms to

*Δϕ*are assumed to cancel each other. This is a good approximation for

*ε*≠-0.5 and fiber lengths

*L*which exceeds two soliton periods, i.e.,

*L*>

*β*

_{2}|. Furthermore, in order to be able to apply Eq. (3), at least two oscillations need to be present on either side of the spectrum. This implies that the period of the oscillations should be much shorter than the width of the hyperbolic-secant shaped spectral envelope. This condition is again fulfilled for

*L*>

*β*

_{2}|. In practice, for the laser pulse widths in the range of hundreds of fs, the length of the fiber must typically be longer than tens of centimeters. The accuracy of the method is limited by the fact that the

*tan*

^{-1}terms of Eq. (2) are neglected in the calculation of the dispersion. Numerical calculations show that the accuracy is within 10% and improves as the ratio of

*L*to the soliton period increases.

## 3. Experiments

*T*

_{0}of approximately 60 fs. The spectrum of the pulses after propagation through the MF was recorded using an optical spectrum analyzer (Ando/AQ6315). The input power was gradually increased until oscillations were observed in the spectrum at the output of the MF. The first fiber under test was a 4.5-m long highly-birefringent MF (Crystal Fibre A/S/NL·PM·700) with an elliptical core of dimensions 1.5×2.4 µm

^{2}. By inserting a half-wave plate in the beam path, we could rotate the linear polarization of the input pulses and measure the dispersion along both principal axes. A typical experimental spectrum obtained at the output of the MF as well as the dispersion deduced from the data for both axes are presented in Fig. 1. For comparison, the dispersion was also measured with a low-coherence white-light interferometer using an unpolarized source. In that case, the dispersion values were obtained from the phase of the Fourier transform of the interferogram [2

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

*ε*=-0.2, -0.1, 0, 0.1 and 0.2. Figure 4 illustrates the results. In the simulations, the envelope of the input pulse is assumed to be of the form (1+

*ε*)sech(

*t*/

*T*

_{0}), and the dispersion, the nonlinear coefficient and

*T*

_{0}are chosen to be 100 ps/nm·km, 100 W

^{-1}·km

^{-1}, and 60 fs, respectively. The spectra exhibit similar characteristics to those presented in Fig. 2. For an increasing input power, the envelope of the spectrum broadens, which corresponds to the narrowing of the pulse in the time domain. Indeed, the asymptotic soliton takes the form (1+2

*ε*)sech[(1+2

*ε*)

*t*/

*T*

_{0}] [12]. Moreover, the amplitude of the oscillations on the wings of the spectra is seen to decrease as |

*ε*| decreases. For

*ε*=0 the pulse launched into the fiber is of the fundamental soliton form, and, consequently, no oscillations are observed.

*ε*)exp(-

*t*

^{2}/2

*ε*and

*T*

_{0}. The simulations were repeated for two different dispersion values (40 and 100 ps/nm·km, respectively). The dispersion was then estimated from the simulated output spectrum using Eq. (3). The accuracy of the method was evaluated by comparing the dispersion values fed to the simulation to the values retrieved using Eq. (3). The discrepancy was found to be of the order of 10% for fiber lengths exceeding four soliton periods. For the Gaussian pulse this distance is longer than for the sech-shaped pulse. Further increase of the fiber length results in a better accuracy. The analysis shows that the method is rather insensitive to the form of the input pulse. We also investigated what effect various optical components inserted in between the laser and the fiber have on the measured result. For this purpose, we imposed a frequency chirp on the input pulse and evaluated the measurement error. The effect was found to stay within 5% for a chirp corresponding to a doubling of the input pulse width. Increasing the fiber length again results in a better accuracy.

## 4. Conclusion

## Acknowledgments

## References and links

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

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

3. | L. Cohen and C. Lin, “A universal fiber-optic (UFO) measurement system based on a near-IR fiber Raman laser,” IEEE J. Quantum Electron. |

4. | B. Costa, D. Mazzoni, M. Puelo, and E. Vezzoni, “Phase-shift technique for the measurement of chromatic dispersion in optical fibers using LED’s,” IEEE J. Quantum Electron. |

5. | M. Wegmuller, F. Scholder, A. Fougeres, N. Gisin, T. Niemi, G. Genty, H. Ludvigsen, and O. Deparis, “Evaluation of measurement techniques for characterization of photonic crystal fibers,” in |

6. | Q. H. Ye, C. Xu, X. Liu, W. H. Knox, M. F. Yan, R. S. Windeler, and B. Eggleton, “Dispersion measurement of tapered air-silica microstructure fiber by white-light interferometry,” Appl. Optics |

7. | D. Ouzounov, D. Homoelle, W. Zipfel, W. W. Webb, A. L. Gaeta, J. A. West, J. C. Fajardo, and K. W. Koch, “Dispersion measurements of microstructured fibers using femtosecond laser pulses,” Opt. Commun. |

8. | M. J. Gander, R. McBride, J. D. C. Jones, D. Mogilevtsev, T. A. Birks, J. C. Knight, and P. S. Russell, “Experimental measurement of group velocity dispersion in photonic crystal fibre,” Electron. Lett. |

9. | M. W. Chbat, P. R. Prucnal, M. N. Islam, C. E. Soccolich, and J. P. Gordon, “Long-Range Interference Effects of Soliton Reshaping in Optical Fibers,” J. Opt. Soc. Am. B |

10. | N. J. Smith, K. J. Blow, and I. Andonovic, “Sideband generation through perturbations to the average soliton model,” J. Lightwave Technol. |

11. | D. U. Noske, N. Pandit, and J. R. Taylor, “Source of spectral and temporal instability in soliton fiber lasers,” Opt. Lett. |

12. | G. P. Agrawal, |

13. | J. Satsuma and N. Yajima, “Initial value problems of one-dimensional selfmodulation of nonlinear waves in dispersive media,” Suppl. Prog. Theo. Phys. |

**OCIS Codes**

(060.2270) Fiber optics and optical communications : Fiber characterization

(190.5530) Nonlinear optics : Pulse propagation and temporal solitons

(230.3990) Optical devices : Micro-optical devices

(260.2030) Physical optics : Dispersion

**ToC Category:**

Research Papers

**History**

Original Manuscript: January 20, 2004

Revised Manuscript: March 1, 2004

Published: March 8, 2004

**Citation**

, "Measurement of anomalous dispersion in microstructured fibers using spectral modulation," Opt. Express **12**, 929-934 (2004)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-12-5-929

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