## Spectral characterization of polarization dependent loss of locally pressed fiber Bragg grating |

Optics Express, Vol. 19, Issue 25, pp. 25535-25544 (2011)

http://dx.doi.org/10.1364/OE.19.025535

Acrobat PDF (1180 KB)

### Abstract

In this paper, the spectral characterization of polarization dependent loss (PDL) of locally pressed fiber Bragg grating (FBG) is analyzed. The evolution of the PDL response of a FBG as functions of the load magnitude the loaded length of the grating and the position of the load are studied. The physical model is presented and a numerical simulation based on the modified transfer matrix method is also used to calculate the PDL response of the FBG. The theoretical analysis and numerical simulation suggest that the PDL response of the FBG has potential applications for distributed diametric load sensor. Good agreements between experimental results and numerical simulations have been obtained.

© 2011 OSA

## 1. Introduction

1. A. D. Kersey, M. A. Davis, H. J. Patrick, M. LeBlanc, K. P. Koo, C. G. Askins, M. A. Putnam, and E. J. Friebele, “Fiber Grating Sensors,” J. Lightwave Technol. **15**(8), 1442–1463 (1997). [CrossRef]

2. Y. Wang, N. Chen, B. Yun, and Y. Cui, “Use of Fiber Bragg Grating Sensors for Determination of a Simply Supported Rectangular Plane Plate Deformation,” IEEE Photon. Technol. Lett. **19**(16), 1242–1244 (2007). [CrossRef]

3. Y. Wang, M. Wang, and X. Huang, “High-sensitivity fiber Bragg grating transverse force sensor based on centroid measurement of polarization-dependent loss,” Meas. Sci. Technol. **21**(6), 065304 (2010). [CrossRef]

5. C. Caucheteur, S. Bette, R. Garcia-Olcina, M. Wuilpart, S. Sales, J. Capmany, and P. Mégret, “Transverse strain measurements using the birefringence effect in fiber Bragg gratings,” IEEE Photon. Technol. Lett. **19**(13), 966–968 (2007). [CrossRef]

6. S. Bette, C. Caucheteur, M. Wuilpart, and P. Mégret, “Theoretical and experimental study of differential group delay and polarization dependent loss of Bragg gratings written in birefringent fiber,” Opt. Commun. **269**(2), 331–337 (2007). [CrossRef]

8. S. Bette, C. Caucheteur, M. Wuilpart, P. Mégret, R. Garcia-Olcina, S. Sales, and J. Capmany, “Spectral characterization of differential group delay in uniform fiber Bragg gratings,” Opt. Express **13**(25), 9954–9960 (2005). [CrossRef] [PubMed]

9. Y. Wang, B. Yun, N. Chen, and Y. Cui, “Characterization of a high birefringence fiber Bragg grating sensor subjected to non-homogeneous transverse strain fields,” Meas. Sci. Technol. **17**, 939–942 (2006). [CrossRef]

## 2.Theoretical model

10. J. F. Botero-Cadavid, J. D. Causado-Buelvas, and P. Torres, “Spectral Properties of Locally Pressed Fiber Bragg Gratings Written in Polarization Maintaining Fibers,” J. Lightwave Technol. **28**(9), 1291–1297 (2010). [CrossRef]

*y*(fast axis), another direction perpendicular to

*y*-axis is

*x*direction (slow axis),

*z*is along the fiber axial direction, as shown in Fig. 1 . Purely compression load on a glass cylinder could be modeled as a line force since both optical fiber and compression platform are hard media. Since the length of a FBG is much longer than the diameter of the fiber, it is reasonable to assume the loading situations to be contained in a single plane. In our experimental condition, the test FBG is fixed at both ends and thus the FBG is under a loading state of plane strain (

*ε*=0). The stress state of the loaded section of grating can be found from the plane strain elasticity solution for stress along the central axis in a disk given by [11

_{z}11. R. B. Wagreich, W. A. Atia, H. Singh, and J. S. Sirkis, “Effects of diametric load on fiber Bragg gratings fabricated in low birefringent fiber,” Electron. Lett. **32**(13), 1223–1224 (1996). [CrossRef]

12. R. Gafsi and M. A. E. Sherif, “Analysis of induced-Birefringence Effects on Fiber Bragg Gratings,” Opt. Fiber Technol. **6**(3), 299–323 (2000). [CrossRef]

*F*is the diametric load,

*l*is the length of optical fiber under load,

*b*is the radius of the optical fiber, and

*v*is the Poisson’s ratio. The refractive index changes within the loaded zone in response to the applied load are derived from photoelastic theory described by Eqs. (2) and (3):

*E*is the Young’s modulus,

*p*and

_{11}*p*are the strain-optic coefficients;

_{12}*n*is the average effective refractive index.

_{0}13. T. Erdogan, “Fiber Grating Spectra,” J. Lightwave Technol. **15**(8), 1277–1294 (1997). [CrossRef]

*m*uniform subgratings and the load applied on each subgrating can be treated as uniform. Based on the transfer matrix method, a

*2x2*matrix is identiðed for each subgrating, and then multiplying all of these matrices together could obtain a single

*2x2*matrix which describes the whole grating. Define

*R*and

_{i}*S*to be the field amplitudes after traversing the section

_{i}*i*. And then the propagation through each uniform section can be described by a matrix

*T*defined such that:where

_{i}*“dc”*coupling coefficient corresponding to the

*x*and

*y*modes, and

*k*is

*“ac”*coupling coefficient,

*△z*is the length of each subgrating and because the FBG is under plane strain state (

*ε*= 0), so

_{z}*△*z =

*L/m*. Once all of the matrices for the individual sections are known, the output amplitude is:

*F = F*,

^{(m)}·F^{(m-1)}·…·F^{(i)}·…·F^{(1)}*R*and

_{0}*S*describe boundary conditions and

_{0}*R*= 1,

_{0}*S*= 0. The refractive index of the subgrating within the loaded zone should be substituted by (2) and (3) to modify the transfer matrix, leading to the simulation of the spectrum response of the FBG. The amplitude and power transmission coefficients of the

_{0}*x*and

*y*modes

*t*and

_{x(y)}= S_{m}/R_{m}*T*= |

_{x(y)}*t*|

_{x(y)}^{2}can be derived from Eq. (6). PDL is defined as the maximum change in the transmitted power when the input state of polarization is varied over all polarization states:

*t*|

_{max}^{2}and |

*t*|

_{min}^{2}denote the maximum and minimum power transmitted through the component. In the case of FBG, the final expression of PDL for transmission is:

## 3. Numerical simulation and experimental investigation

*L*is 1cm,

*n*1.5,

_{0}=*E*= 74.52

*Gpa*,

*v*= 0.17,

*p*

_{11}= 0.121 and

*p*= 0.270. A simple experiment was also carried out to verify the simulated model and results.

_{12}### 3.1 Effect of the transverse load magnitude

*pi*. In this case, the PDL spectrum will be symmetrical. As the localtransverse load changes, the transmission notch will moves to longer or shorter wavelengths since the phase shift is not equal to

*pi*. Then the PDL spectrum will be no longer symmetrical, which cause the observed asymmetry between the two main lobes of PDL. For the same reason, the characterization of quasi periodic variations in PDL is also predicable since the phase shift is periodic and strain dependent, which will lead to repetitive behaviors in amplitude spectrum and eventually in PDL spectrum. Figure 2(b) depicts the maximum PDL amplitudes and their corresponding wavelengths of the FBG with respect to the local transverse loads magnitudes. As seen in Fig. 2(b), the variation of the maximum PDL values is similar to an inverted power function curve with slowly decreasing amplitude. The wavelengths corresponding to the max PDL values increase gradually with the load increase in a period of about 10N, however, the peak envelope of the wavelengths decreases slowly with the load increase. The simulated results could be efficiently used for recovering the local transverse load magnitude based on detecting both the maximum PDL amplitudes and their corresponding wavelengths.

### 3.2 Effect of the position of the load

### 3.3 Effect of the loaded length

### 3.4 Experimental investigation

## 4. Conclusion

## Acknowledgments

## References and links

1. | A. D. Kersey, M. A. Davis, H. J. Patrick, M. LeBlanc, K. P. Koo, C. G. Askins, M. A. Putnam, and E. J. Friebele, “Fiber Grating Sensors,” J. Lightwave Technol. |

2. | Y. Wang, N. Chen, B. Yun, and Y. Cui, “Use of Fiber Bragg Grating Sensors for Determination of a Simply Supported Rectangular Plane Plate Deformation,” IEEE Photon. Technol. Lett. |

3. | Y. Wang, M. Wang, and X. Huang, “High-sensitivity fiber Bragg grating transverse force sensor based on centroid measurement of polarization-dependent loss,” Meas. Sci. Technol. |

4. | S. Oh, W. Han, U. Paek, and Y. Chung, “Discrimination of temperature and strain with a single FBG based on the birefringence effect,” Opt. Express |

5. | C. Caucheteur, S. Bette, R. Garcia-Olcina, M. Wuilpart, S. Sales, J. Capmany, and P. Mégret, “Transverse strain measurements using the birefringence effect in fiber Bragg gratings,” IEEE Photon. Technol. Lett. |

6. | S. Bette, C. Caucheteur, M. Wuilpart, and P. Mégret, “Theoretical and experimental study of differential group delay and polarization dependent loss of Bragg gratings written in birefringent fiber,” Opt. Commun. |

7. | D. Wang, M. R. Matthews, and J. F. Brennan III, “Polarization mode dispersion in chirped fiber Bragg gratings,” Opt. Express |

8. | S. Bette, C. Caucheteur, M. Wuilpart, P. Mégret, R. Garcia-Olcina, S. Sales, and J. Capmany, “Spectral characterization of differential group delay in uniform fiber Bragg gratings,” Opt. Express |

9. | Y. Wang, B. Yun, N. Chen, and Y. Cui, “Characterization of a high birefringence fiber Bragg grating sensor subjected to non-homogeneous transverse strain fields,” Meas. Sci. Technol. |

10. | J. F. Botero-Cadavid, J. D. Causado-Buelvas, and P. Torres, “Spectral Properties of Locally Pressed Fiber Bragg Gratings Written in Polarization Maintaining Fibers,” J. Lightwave Technol. |

11. | R. B. Wagreich, W. A. Atia, H. Singh, and J. S. Sirkis, “Effects of diametric load on fiber Bragg gratings fabricated in low birefringent fiber,” Electron. Lett. |

12. | R. Gafsi and M. A. E. Sherif, “Analysis of induced-Birefringence Effects on Fiber Bragg Gratings,” Opt. Fiber Technol. |

13. | T. Erdogan, “Fiber Grating Spectra,” J. Lightwave Technol. |

**OCIS Codes**

(060.2370) Fiber optics and optical communications : Fiber optics sensors

(230.1480) Optical devices : Bragg reflectors

**ToC Category:**

Fiber Optics and Optical Communications

**History**

Original Manuscript: October 14, 2011

Revised Manuscript: November 19, 2011

Manuscript Accepted: November 22, 2011

Published: November 30, 2011

**Citation**

Yiping Wang, Ming Wang, and Xiaoqin Huang, "Spectral characterization of polarization dependent loss of locally pressed fiber Bragg grating," Opt. Express **19**, 25535-25544 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-25-25535

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### References

- A. D. Kersey, M. A. Davis, H. J. Patrick, M. LeBlanc, K. P. Koo, C. G. Askins, M. A. Putnam, and E. J. Friebele, “Fiber Grating Sensors,” J. Lightwave Technol. 15(8), 1442–1463 (1997). [CrossRef]
- Y. Wang, N. Chen, B. Yun, and Y. Cui, “Use of Fiber Bragg Grating Sensors for Determination of a Simply Supported Rectangular Plane Plate Deformation,” IEEE Photon. Technol. Lett. 19(16), 1242–1244 (2007). [CrossRef]
- Y. Wang, M. Wang, and X. Huang, “High-sensitivity fiber Bragg grating transverse force sensor based on centroid measurement of polarization-dependent loss,” Meas. Sci. Technol. 21(6), 065304 (2010). [CrossRef]
- S. Oh, W. Han, U. Paek, and Y. Chung, “Discrimination of temperature and strain with a single FBG based on the birefringence effect,” Opt. Express 12(4), 724–729 (2004). [CrossRef] [PubMed]
- C. Caucheteur, S. Bette, R. Garcia-Olcina, M. Wuilpart, S. Sales, J. Capmany, and P. Mégret, “Transverse strain measurements using the birefringence effect in fiber Bragg gratings,” IEEE Photon. Technol. Lett. 19(13), 966–968 (2007). [CrossRef]
- S. Bette, C. Caucheteur, M. Wuilpart, and P. Mégret, “Theoretical and experimental study of differential group delay and polarization dependent loss of Bragg gratings written in birefringent fiber,” Opt. Commun. 269(2), 331–337 (2007). [CrossRef]
- D. Wang, M. R. Matthews, and J. F. Brennan, “Polarization mode dispersion in chirped fiber Bragg gratings,” Opt. Express 12(23), 5741–5753 (2004). [CrossRef] [PubMed]
- S. Bette, C. Caucheteur, M. Wuilpart, P. Mégret, R. Garcia-Olcina, S. Sales, and J. Capmany, “Spectral characterization of differential group delay in uniform fiber Bragg gratings,” Opt. Express 13(25), 9954–9960 (2005). [CrossRef] [PubMed]
- Y. Wang, B. Yun, N. Chen, and Y. Cui, “Characterization of a high birefringence fiber Bragg grating sensor subjected to non-homogeneous transverse strain fields,” Meas. Sci. Technol. 17, 939–942 (2006). [CrossRef]
- J. F. Botero-Cadavid, J. D. Causado-Buelvas, and P. Torres, “Spectral Properties of Locally Pressed Fiber Bragg Gratings Written in Polarization Maintaining Fibers,” J. Lightwave Technol. 28(9), 1291–1297 (2010). [CrossRef]
- R. B. Wagreich, W. A. Atia, H. Singh, and J. S. Sirkis, “Effects of diametric load on fiber Bragg gratings fabricated in low birefringent fiber,” Electron. Lett. 32(13), 1223–1224 (1996). [CrossRef]
- R. Gafsi and M. A. E. Sherif, “Analysis of induced-Birefringence Effects on Fiber Bragg Gratings,” Opt. Fiber Technol. 6(3), 299–323 (2000). [CrossRef]
- T. Erdogan, “Fiber Grating Spectra,” J. Lightwave Technol. 15(8), 1277–1294 (1997). [CrossRef]

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