## Straightforward method for measuring optical fiber’s nonlinear coefficient based on phase mismatching FWM |

Optics Express, Vol. 21, Issue 17, pp. 20463-20469 (2013)

http://dx.doi.org/10.1364/OE.21.020463

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### Abstract

A novel method for measuring optical fiber’s nonlinear coefficient, based on phase mismatching four-wave mixing is proposed. Measurements for both high nonlinearity dispersion shifted fiber and low nonlinearity standard single mode fiber are demonstrated with simple setup. Chromatic dispersion is also measured with high precision simultaneously, and therefore its effect to the nonlinear coefficient measurement can be removed.

© 2013 OSA

## 1. Introduction

1. M. Hirano, T. Nakanishi, T. Okuno, and M. Onishi, “Silica-based highly nonlinear fibers and their application,” IEEE J. Sel. Top. Quant. **15**(1), 103–113 (2009). [CrossRef]

_{2}/(λ·A

_{eff}), where n

_{2}, λ, and A

_{eff}are nonlinear refractive index, wavelength, and effective area, respectively. Therefore, accurate measurement of the γ is one of the important issues for designing transmission systems and HNLF-based devices.

2. R. H. Stolen and L. Chinlon, “Self-phase-modulation in silica optical fibers,” Phys. Rev. A **17**(4), 1448–1453 (1978). [CrossRef]

3. M. Monerie and Y. Durteste, “Direct interferometric measurement of nonlinear refractive index of optical fiber by cross-phase modulation,” Electron. Lett. **23**(18), 961–963 (1987). [CrossRef]

5. C. Vinegoni, M. Wegmuller, and N. Gisin, “Measurement of the nonlinear coefficient of standard SMF, DSF, and DCF fiber using a self-aligned interferometer and a Faraday Mirror,” IEEE Photon. Technol. Lett. **13**(12), 1337–1339 (2001). [CrossRef]

6. A. Boskovic, S. V. Chernikov, J. R. Taylor, L. Gruner-Nielsen, and O. A. Levring, “Direct continuous-wave measurement of n_{2} in various types of telecommunication fiber at 155 µm,” Opt. Lett. **21**(24), 1966–1968 (1996). [CrossRef] [PubMed]

7. L. Prigent and J.-P. Hamaide, “Measurement of fiber nonlinear Kerr coefficient by Four-Wave Mixing,” IEEE Photon. Technol. Lett. **5**(9), 1062–1065 (1993). [CrossRef]

## 2. Principle of PM-FWM method

_{pump}and ω

_{probe}, respectively, propagate together through a fiber, idler light is newly generated at a frequency of 2ω

_{pump}-ω

_{probe}through the FWM process. For linearly co-polarized lights propagating in a fiber, the output power of the idler light, P

_{idler}, can be described as below in the case of that the fiber loss is negligibly low [10],where L, P

_{pump}and P

_{probe}are the fiber length, launched pump and probe powers, respectively. Δβ is the phase mismatching parameter defined aswhere β

_{2}represents the second-order dispersion at ω

_{pump}, and Δω = ω

_{probe}– ω

_{pump}is a angular frequency difference between the pump and the probe.

_{2}of the tested fiber. For a low β

_{2}fiber, whose zero-dispersion wavelength is within or close to the measuring wavelengths, ω

_{pump}is scanned while keeping the Δω constant. On the other hand, for a high β

_{2}fiber, ω

_{pump}and therefore β

_{2}are kept constant while ω

_{probe}is scanned to change Δω.

### I. Low β_{2} fiber

_{idler}is a periodic function of ω

_{pump}as shown in Fig. 1(a) because β

_{2}monotonically increase or decrease with ω

_{pump}. From Eq. (1), P

_{idler}becomes maximum at ΔβL/2 = 0, and has minimal values at which Δβ satisfiesFor the limit of P

_{pump}to be zero, at a pump frequency of ω

_{Z}

^{(N)}providing the minimal P

_{idler}, β

_{2z}

^{(N)}can be expressed as [9]In the case where P

_{pump}> 0, the pump frequency indicating the minimal P

_{idler}will shift to ω

_{P}

^{(N)}as shown by solid curve in Fig. 1(a). Here, β

_{2}at ω

_{P}

^{(N)}, β

_{2P}

^{(N)}can be approximated using the third order dispersion at ω

_{Z}

^{(N)}, β

_{3Z}

^{(N)}asPSubstituting Eqs. (2) and (5) into Eq. (3), ω

_{P}

^{(N)}can be described asAs a corollary, ω

_{P}

^{(N)}becomes a linear function of P

_{pump}, and the nonlinear coefficient γ can be calculated asTherefore, γ at ω

_{P}

^{(N)}can be determined from the slope of the ω

_{P}

^{(N)}versus P

_{pump}graph. Here, β

_{3Z}

^{(N)}in Eq. (7) can be also obtained using Eq. (3). Although the condition of P

_{pump}= 0 in Eq. (3) would be impossible for actual measurement, ω

_{Z}

^{(N)}can be estimated by calculating the y-intercept on the ω

_{p}

^{(N)}versus P

_{pump}graph in Eq. (6). β

_{2}spectrum can be also determined with β

_{2z}

^{(N)}for several N from Eq. (4), and β

_{3Z}

^{(N)}can be then calculated by a biquadratic approximation of the β

_{2}spectrum. The definitions of β are summarized in Table 1.

### 2.1 High β_{2} fiber

_{2}fibers such as SSMF at wavelengths around 1550 nm, it is difficult to exactly know N in Eq. (4) because the measured frequencies are far away from the frequency at which ΔβL/2 = 0 and N becomes a large value. Therefore, β

_{3Z}

^{(N)}in Eq. (7) cannot be obtained. Here, keeping ω

_{pump}constant, only Δω and P

_{pump}become the variable in Eq. (2). In this case, P

_{idler}also be a periodic function of squared frequency difference (Δω)

^{2}as shown in Fig. 1(b). From Eqs. (2) and (3), the conditions for P

_{idler}to be minimum with N and N-1 are given by where Δω

_{P}

^{(N)}is the N-th frequency difference providing the minimal P

_{idler}for P

_{pump}>0. From two adjacent frequency differences of Δω

_{P}

^{(N)}and Δω

_{P}

^{(N-1)}in Eqs. (8) and (9), β

_{2}at ω

_{pump}can be determined independently of N asSimilar to Eq. (4), a frequency difference Δω

_{z}

^{(N)}providing the minimal P

_{idler}for the limit of P

_{pump}to be zero is given byFrom Eqs. (8) and (11), the following equation is obtainedThis eauation shows that, [Δω

_{P}

^{(N)}]

^{2}also becomes a linear function of P

_{pump}, and γ can be evaluated by the slope of the [Δω

_{P}

^{(N)}]

^{2}versus P

_{pump}graph, aswhere β

_{2}can be obtained from Eq. (10).

## 3. Experimental setup and results

_{2}. Respective frequencies of the pump and probe lights were scanned together with a constant difference of Δω = 7.8 × 10

^{12}rad/s. Examples of the generated idler power P

_{idler}against the pump frequency are shown in Fig. 3(a). The periodical minima are observed, and we confirmed that the ω

_{P}

^{(N)}were shifted with increase of the pump power from 1.6 to 26mW, as theoretically predicted in Fig. 1(a). Measured ω

_{P}

^{(N)}as a function of P

_{pump}are shown in Figs. 3(b) and 3(c), satisfying the condition of Eq. (3) with (b) N = 1 and (c) N = 2, which correspond to the wavelength of about 1535 nm and 1539 nm, respectively. In accordance with Eq. (6), ω

_{P}

^{(N)}are linearly decreasing with the increasing of P

_{pump}.

_{P}

^{(N)}for N = −1 at wavelength of around 1558 nm is shown in Fig. 3(d), where Δω was fixed to 15.3 × 10

^{12}rad/s. From Fig. 3(d), the measured γ was 19 /W/km, which is closely accorded with the one in the 1km-long HNLDSF.

_{2}(about-22 ps

^{2}/km or chromatic dispersion of about + 17 ps/nm/km) fiber, γ of a 1km-long SSMF was measured using Eqs. (10) and (13). The probe frequency was scanned while pump frequency is kept to be 1.2 × 10

^{15}rad/s (wavelength of 1550 nm). Figure 4(a) shows the periodic change of the generated idler power P

_{idler}against the squared frequency difference (Δω)

^{2}for P

_{pump}of 208 mW. β

_{2}at ω

_{pump}was determined from Eq. (10) to be −21.4 ps

^{2}/km. Measured Δω

_{P}

^{(N)}against P

_{pump}is also shown in Fig. 4(b) for N = −1. We successfully determined the nonlinear coefficient γ and n

_{2}as 1.3 W/km and 2.7 × 10

^{−20}m

^{2}/W, respectively. In addition, the chromatic dispersion was also measured as 16.5 ps/nm/km at the wavelength of 1550 nm.

_{2}measured with the PM-FWM method to the ones with CW-SPM method [6

6. A. Boskovic, S. V. Chernikov, J. R. Taylor, L. Gruner-Nielsen, and O. A. Levring, “Direct continuous-wave measurement of n_{2} in various types of telecommunication fiber at 155 µm,” Opt. Lett. **21**(24), 1966–1968 (1996). [CrossRef] [PubMed]

_{2}measured with PM-FWM method are 5%-larger than that with CW-SPM method for HNLDSFs and 2%-smaller for SSMF. The chromatic dispersion and dipersion slope measured with PM-FWM method are also shown in Table 2, which agree well with ones with commercially available modulation phase shft (MPS) method [11

11. T. Dennis and P. A. Williams, “Achieving high absolute accuracy for group-delay measurements using the modulation phase-shift technique,” J. Lightwave Technol. **23**(11), 3748–3754 (2005). [CrossRef]

^{2}/km in disersion slope.

## 4. Conclusion

## References and links

1. | M. Hirano, T. Nakanishi, T. Okuno, and M. Onishi, “Silica-based highly nonlinear fibers and their application,” IEEE J. Sel. Top. Quant. |

2. | R. H. Stolen and L. Chinlon, “Self-phase-modulation in silica optical fibers,” Phys. Rev. A |

3. | M. Monerie and Y. Durteste, “Direct interferometric measurement of nonlinear refractive index of optical fiber by cross-phase modulation,” Electron. Lett. |

4. | F. Wittl, “Interferometric determination of the nonlinear refractive index n2 of optical fibers,” Proc. Symposium on Optical Fiber Measurements’96, 71–74 (1996). |

5. | C. Vinegoni, M. Wegmuller, and N. Gisin, “Measurement of the nonlinear coefficient of standard SMF, DSF, and DCF fiber using a self-aligned interferometer and a Faraday Mirror,” IEEE Photon. Technol. Lett. |

6. | A. Boskovic, S. V. Chernikov, J. R. Taylor, L. Gruner-Nielsen, and O. A. Levring, “Direct continuous-wave measurement of n |

7. | L. Prigent and J.-P. Hamaide, “Measurement of fiber nonlinear Kerr coefficient by Four-Wave Mixing,” IEEE Photon. Technol. Lett. |

8. | O. Aso, M. Tadakuma, and S. Namiki, “Four-Wave Mixing in Optical Fibers and Its Applications,” Furukawa Review, No. |

9. | M. Hirano and T. Sasaki, “Straightforward chromatic dispersion measurement based on phase mismatching FWM,” Proc. ECOC’2009, Vienna, Austria, Paper 4.1.6. |

10. | G. P. Agrawal, |

11. | T. Dennis and P. A. Williams, “Achieving high absolute accuracy for group-delay measurements using the modulation phase-shift technique,” J. Lightwave Technol. |

**OCIS Codes**

(060.0060) Fiber optics and optical communications : Fiber optics and optical communications

(060.4370) Fiber optics and optical communications : Nonlinear optics, fibers

**ToC Category:**

Fiber Optics and Optical Communications

**History**

Original Manuscript: May 30, 2013

Revised Manuscript: August 13, 2013

Manuscript Accepted: August 14, 2013

Published: August 23, 2013

**Citation**

Guoxiu Huang, Yoshinori Yamamoto, Masaaki Hirano, Akihiro Maruta, Takashi Sasaki, and Kenichi Kitayama, "Straightforward method for measuring optical fiber’s nonlinear coefficient based on phase mismatching FWM," Opt. Express **21**, 20463-20469 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-17-20463

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### References

- M. Hirano, T. Nakanishi, T. Okuno, and M. Onishi, “Silica-based highly nonlinear fibers and their application,” IEEE J. Sel. Top. Quant.15(1), 103–113 (2009). [CrossRef]
- R. H. Stolen and L. Chinlon, “Self-phase-modulation in silica optical fibers,” Phys. Rev. A17(4), 1448–1453 (1978). [CrossRef]
- M. Monerie and Y. Durteste, “Direct interferometric measurement of nonlinear refractive index of optical fiber by cross-phase modulation,” Electron. Lett.23(18), 961–963 (1987). [CrossRef]
- F. Wittl, “Interferometric determination of the nonlinear refractive index n2 of optical fibers,” Proc. Symposium on Optical Fiber Measurements’96, 71–74 (1996).
- C. Vinegoni, M. Wegmuller, and N. Gisin, “Measurement of the nonlinear coefficient of standard SMF, DSF, and DCF fiber using a self-aligned interferometer and a Faraday Mirror,” IEEE Photon. Technol. Lett.13(12), 1337–1339 (2001). [CrossRef]
- A. Boskovic, S. V. Chernikov, J. R. Taylor, L. Gruner-Nielsen, and O. A. Levring, “Direct continuous-wave measurement of n2 in various types of telecommunication fiber at 155 µm,” Opt. Lett.21(24), 1966–1968 (1996). [CrossRef] [PubMed]
- L. Prigent and J.-P. Hamaide, “Measurement of fiber nonlinear Kerr coefficient by Four-Wave Mixing,” IEEE Photon. Technol. Lett.5(9), 1062–1065 (1993). [CrossRef]
- O. Aso, M. Tadakuma, and S. Namiki, “Four-Wave Mixing in Optical Fibers and Its Applications,” Furukawa Review, No.19, 63–68 (2000).
- M. Hirano and T. Sasaki, “Straightforward chromatic dispersion measurement based on phase mismatching FWM,” Proc. ECOC’2009, Vienna, Austria, .
- G. P. Agrawal, Nonlinear Fiber Optics, 4th Edition, Academic Press, (2007).
- T. Dennis and P. A. Williams, “Achieving high absolute accuracy for group-delay measurements using the modulation phase-shift technique,” J. Lightwave Technol.23(11), 3748–3754 (2005). [CrossRef]

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