## Origin of coupling to antisymmetric modes in arc-induced long-period fiber gratings

Optics Express, Vol. 15, Issue 21, pp. 13936-13941 (2007)

http://dx.doi.org/10.1364/OE.15.013936

Acrobat PDF (479 KB)

### Abstract

We study the origin of antisymmetric perturbation of the fiber in arc-induced long-period gratings that couple the core mode into the antisymmetric cladding modes. We demonstrate that this perturbation is caused by the temperature gradient in the fiber, which is induced, in turn, by the temperature gradient in the arc discharge. The reproducibility of the process of the grating inscription is higher when the fiber is placed in a region with larger temperature gradient.

© 2007 Optical Society of America

## 1. Introduction

4. G. Rego, O. Ivanov, and P. V. S. Marques, “Demonstration of coupling to symmetric and antisymmetric cladding modes in arc-induced long-period fiber gratings,” Opt. Express **14**, 9594–9599 (2006). [CrossRef] [PubMed]

1. G. Rego, R. Falate, J. L. Fabris, J. L. Santos, H. M. Salgado, S. L. Semjonov, and E. M. Dianov, “Arc-induced long-period gratings in aluminosilicate glass fibers,” Opt. Lett. **30**, 2065–2067 (2005). [CrossRef] [PubMed]

_{1i}cladding modes, the corresponding perturbation being antisymmetric. The origin of this asymmetry in the perturbation is unknown. In this paper, we investigate the process of grating inscription in more detail to find the asymmetric factor. In particular, we measure the temperature gradient in the arc and the resulting temperature gradient in the fiber. We discuss the contribution of the latter gradient to the formation of LPFGs in SMF-28 fiber. One of the consequences of the temperature gradient is the periodical microdeformation that consists in a shift of the fiber core under arc discharges. We analyze if such microdeformation can be responsible for the coupling to the antisymmetric cladding modes.

## 2. Temperature distribution in the arc discharge

5. L. Xiao, W. Jin, M. S. Demokan, H. L. Ho, Y. L. Hoo, and C. Zhao, “Fabrication of selective injection microstructured optical fibers with a conventional fusion splicer,” Opt. Express **13**, 9014–9022 (2005). [CrossRef] [PubMed]

6. M. Tachikura, “Fusion mass-splicing for optical fibers using electric discharges between two pairs of electrodes,” Appl. Opt. **23**, 492–498 (1984). [CrossRef] [PubMed]

7. F. Durr, G. Rego, P. V. S. Marques, S. L. Semjonov, E. Dianov, H. G. Limberger, and R. P. Salathé, “Stress profiling of arc-induced long period fiber gratings,” J. Lightwave Technol. **23**, 3947–3953 (2005). [CrossRef]

*y*axis).

*y*–

*z*plane). The decrease in the fiber diameter is a function of fluidity of the fiber in the arc and the duration of the arc or, rather, a function of the product of the fiber fluidity (which is assumed to be constant over the cross-section of the fiber) and the arc duration: Δ

*D*=

*K*(

*tF*). This function can be obtained by measuring the decrease in the fiber diameter for various values of the arc duration or, equivalently, by applying the same discharge (having duration

*t*

_{0}) several times (

*N*times) on the same fiber section:

*F*

_{0}is the fiber fluidity in the arc and is constant for all discharges. Knowing the function

*G*, we can calculate the fiber fluidity in a different arc from the decrease in diameter upon one discharge as

*F*=

*F*

_{0}

*G*

^{-1}(Δ

*D*), where

*G*

^{-1}is the inverse of the function

*G*.

*G*

^{-1}(Δ

*D*). Then we placed the fiber in the

*x*–

*y*plane and measured the dependence of the fiber diameter reduction on the

*y*coordinate. Using the expression for

*G*

^{-1}, we obtained the fiber fluidity normalized by

*F*

_{0}, which is shown in Fig. 3 by the dashed curve. Afterwards, the temperature was calculated by using the following equation (derived from the dependence of the silica viscosity on temperature in the range 1000–1400 °C; Eq. (2) from Ref. [8

8. R. H. Doremus, “Viscosity of silica,” J. Appl. Phys. **92**, 7619–7629 (2002). [CrossRef]

*F*is the silica fluidity (Pa

^{-1}s

^{-1}) and

*T*is the temperature (K). The temperature gradient is shown by the solid curve of Fig. 3. To find the absolute value of

*F*we used

*F*

_{0}, which was obtained by assuming that the temperature of the fiber in the center between the electrodes is 1350 °C [9

9. G. Rego, L. M. N. B. F. Santos, B. Schröder, P. V. S. Marques, J. L. Santos, and H. M. Salgado, “In situ temperature measurement of an optical fiber submitted to electric arc discharges,” IEEE Photon. Technol. Lett. **16**, 2111–2113 (2004). [CrossRef]

*z*axis. In Fig. 4, the corresponding fluidity and temperature gradients are shown. From Figs. 3 and 4, we obtained a constant temperature gradient of ~0.35 °C/μm along the

*y*axis and a temperature gradient having a maximum of ~0.7 °C/μm along the

*z*axis.

## 3. Asymmetry of perturbation in the fiber

*y*axis by the distance equal to its diameter (125 μm), the fiber fluidity changes by a factor of 4–5; the change may be even higher when the fiber is shifted along the

*z*axis. This is demonstrated in Fig. 5, which shows the fluidity ratio between the two sides of the fiber in the arc, neglecting the thermal conductivity of the silica. The value of this ratio was calculated from the temperature difference between two points separated by 125 μm. If the fiber is in the center between the electrodes, only the temperature gradient in the

*y*direction is present. However, an error, for example, of 20 μm in the

*z*coordinate of the fiber produces such a temperature gradient that the fiber fluidity differs by a factor of 2 in two points separated by 125 μm. We should expect that the temperature gradient in the arc can create some temperature gradient inside the fiber itself, the latter gradient being weaker due to thermal conductivity of the fiber. Therefore, we attempted to reveal the existence of a temperature gradient inside the fiber, which may be the asymmetric perturbation that forms the LPFG.

_{1j}modes. To determine the influence of the value of the core shift on the coupling strength we use the coupled mode theory. The coupling coefficient is defined through the overlap integral between the core and cladding mode fields and the perturbation Δ

*n*induced by the core shift and can be expressed as

*C*

*π*Δ

*n*

*I*/

*λ*

_{r}, where

*I*is the overlap integral,

*λ*

_{r}is the resonance wavelength, and

*C*is the constant equal to the first coefficient in the Fourier transform of the grating pitch shape [11

11. S. A. Vasiliev and O. I. Medvedkov, “Long-period refractive index fiber gratings: properties, applications, and fabrication techniques,” Proc. SPIE **4083**, 212–223 (2000). [CrossRef]

*n*= 0.0052, D

_{co}=8.2 μm). Δ

*n*is equal to

*n*

_{co}-

*n*

_{cl}at around

*r*

_{co}and

*n*

_{cl}-1 at around

*r*

_{cl}. The change at the cladding-air interface can be neglected in the calculation of the coupling coefficient because the core mode amplitude is vanishingly small at this interface. Using the perturbation that is shown in Fig. 9, we calculated the coupling constant as a function of the core shift for the first four cladding modes (Fig. 10). As seen from Fig. 10, the coupling coefficient increases with an increase in the core shift achieving 100% coupling (

*kL*= π/2) for values in the range 0.3–0.35 μm. The value of the core shift measured from Fig. 6 is of about 0.35 μm, being, therefore, sufficient to obtain gratings with large coupling strength. Assuming the value of the core shift to be 0.35 μm, we fitted the experimental spectrum of an arc induced LPFG with a length of 21.6 mm by using the simulation program Apollo v2.2 (Fig. 11). It is seen that the simulation agrees well with the experiment.

*z*axis should be zero in this case. However, a small uncontrolled displacement of about 20 μm in the

*z*coordinate may change this gradient from zero to a large magnitude. We suppose this is why the reproducibility of the inscription is usually low. To improve the situation, it is possible to shift the fiber from the center position to one or another side. This would make the gradient in the

*z*direction nonzero and its value would not depend so strongly on the fiber position. To examine our hypothesis we investigated the reproducibility of the technique in two different positions of the fiber. We followed the growth of gratings (SMF28, 13 g, 9 mA, 1s, 540 μm), discharge by discharge (the transmission loss of LP

_{14}was monitored), for two different positions along the z axis: 0 and 50 μm. We also shifted the fiber by 100 μm closer to the colder electrode, where the arc is wider. Two gratings were written in each position. It was observed that, for the fiber displaced by 50 μm from the line between the electrodes, the growth of the resonance is smooth and linear and the two curves corresponding to the same writing parameters almost coincide (Fig. 12). Whereas, for the fiber without displacement, the growth is not so linear and the two curves diverge significantly. This demonstrates higher reproducibility in the case when the fiber is displaced. For the same number of discharges, the gratings strength is larger for 0 μm then for 50 μm due to lower average temperature in the displaced position, in spite of the fact that the temperature gradient is higher.

## 4. Conclusion

_{1i}cladding modes is the temperature gradient in the arc discharge. We have shown that this gradient causes a temperature gradient in the fiber, which results in a gradient of viscosity and a corresponding asymmetry of fiber deformation. The effect of microdeformation consisting in periodical core shift is strong enough to produce gratings with coupling strengths as large as measured in experiments. By shifting the fiber to a region with stronger temperature gradient it is possible to increase the reproducibility of the process of the grating inscription for the case of coupling to the antisymmetric cladding modes.

## References and links

1. | G. Rego, R. Falate, J. L. Fabris, J. L. Santos, H. M. Salgado, S. L. Semjonov, and E. M. Dianov, “Arc-induced long-period gratings in aluminosilicate glass fibers,” Opt. Lett. |

2. | G. Rego, A. Fernandez Fernandez, A. Gusarov, B. Brichard, F. Berghmans, J. L. Santos, and H. M. Salgado, “Effect of ionizing radiation on the properties of long-period fiber gratings,” Appl. Opt. |

3. | G. Rego, R. Falate, O. Ivanov, and J. L. Santos, “Simultaneous temperature and strain measurements performed by a step-changed arc-induced long-period fiber grating,” Appl. Opt. |

4. | G. Rego, O. Ivanov, and P. V. S. Marques, “Demonstration of coupling to symmetric and antisymmetric cladding modes in arc-induced long-period fiber gratings,” Opt. Express |

5. | L. Xiao, W. Jin, M. S. Demokan, H. L. Ho, Y. L. Hoo, and C. Zhao, “Fabrication of selective injection microstructured optical fibers with a conventional fusion splicer,” Opt. Express |

6. | M. Tachikura, “Fusion mass-splicing for optical fibers using electric discharges between two pairs of electrodes,” Appl. Opt. |

7. | F. Durr, G. Rego, P. V. S. Marques, S. L. Semjonov, E. Dianov, H. G. Limberger, and R. P. Salathé, “Stress profiling of arc-induced long period fiber gratings,” J. Lightwave Technol. |

8. | R. H. Doremus, “Viscosity of silica,” J. Appl. Phys. |

9. | G. Rego, L. M. N. B. F. Santos, B. Schröder, P. V. S. Marques, J. L. Santos, and H. M. Salgado, “In situ temperature measurement of an optical fiber submitted to electric arc discharges,” IEEE Photon. Technol. Lett. |

10. | G. Rego, O. Ivanov, P. V. S. Marques, and J. L. Santos, “Investigation of formation mechanisms of arc-induced long-period fiber gratings,” in Proc. of OFS-18, paper TuE84 (2006). |

11. | S. A. Vasiliev and O. I. Medvedkov, “Long-period refractive index fiber gratings: properties, applications, and fabrication techniques,” Proc. SPIE |

**OCIS Codes**

(050.2770) Diffraction and gratings : Gratings

(060.2340) Fiber optics and optical communications : Fiber optics components

**ToC Category:**

Fiber Optics and Optical Communications

**History**

Original Manuscript: June 7, 2007

Revised Manuscript: August 13, 2007

Manuscript Accepted: August 13, 2007

Published: October 8, 2007

**Citation**

O. V. Ivanov and G. Rego, "Origin of coupling to antisymmetric modes in arc-induced long-period fiber gratings," Opt. Express **15**, 13936-13941 (2007)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-21-13936

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### References

- G. Rego, R. Falate, J. L. Fabris, J. L. Santos, H. M. Salgado, S. L. Semjonov, and E. M. Dianov, "Arc-induced long-period gratings in aluminosilicate glass fibers," Opt. Lett. 30, 2065-2067 (2005). [CrossRef] [PubMed]
- G. Rego, A. Fernandez Fernandez, A. Gusarov, B. Brichard, F. Berghmans, J. L. Santos, and H. M. Salgado, "Effect of ionizing radiation on the properties of long-period fiber gratings," Appl. Opt. 44, 6258-6263 (2005). [CrossRef] [PubMed]
- G. Rego, R. Falate, O. Ivanov, and J. L. Santos, "Simultaneous temperature and strain measurements performed by a step-changed arc-induced long-period fiber grating," Appl. Opt. 46, 1392-1396 (2007). [CrossRef] [PubMed]
- G. Rego, O. Ivanov, and P. V. S. Marques, "Demonstration of coupling to symmetric and antisymmetric cladding modes in arc-induced long-period fiber gratings," Opt. Express 14, 9594-9599 (2006). [CrossRef] [PubMed]
- L. Xiao, W. Jin, M. S. Demokan, H. L. Ho, Y. L. Hoo, and C. Zhao, "Fabrication of selective injection microstructured optical fibers with a conventional fusion splicer," Opt. Express 13, 9014-9022 (2005). [CrossRef] [PubMed]
- M. Tachikura, "Fusion mass-splicing for optical fibers using electric discharges between two pairs of electrodes," Appl. Opt. 23, 492-498 (1984). [CrossRef] [PubMed]
- F. Durr, G. Rego, P. V. S. Marques, S. L. Semjonov, E. Dianov, H. G. Limberger, and R. P. Salathé, "Stress profiling of arc-induced long period fiber gratings," J. Lightwave Technol. 23, 3947-3953 (2005). [CrossRef]
- R. H. Doremus, "Viscosity of silica," J. Appl. Phys. 92, 7619-7629 (2002). [CrossRef]
- G. Rego, L. M. N. B. F. Santos, B. Schröder, P. V. S. Marques, J. L. Santos, and H. M. Salgado, "In situ temperature measurement of an optical fiber submitted to electric arc discharges," IEEE Photon. Technol. Lett. 16, 2111-2113 (2004). [CrossRef]
- G. Rego, O. Ivanov, P. V. S. Marques, and J. L. Santos, "Investigation of formation mechanisms of arc-induced long-period fiber gratings," in Proc. of OFS-18, paper TuE84 (2006).
- S. A. Vasiliev and O. I. Medvedkov, "Long-period refractive index fiber gratings: properties, applications, and fabrication techniques," Proc. SPIE 4083,212-223 (2000). [CrossRef]

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