Table of Content

1.1	State of the art

1.1.1

Fiber Bragg gratings

1.1.2

Local characterization of fiber Bragg gratings

1.1.3

Optical low coherence reflectometry

1.2	Motivation and thesis outline

1.3	References

Chapter 2 : Fiber Bragg Gratings

2.1	Optical fiber

2.1.1

Optical fiber principle

2.1.2

Types of optical fibers

2.1.3

Fiber Parameters

2.2	Fiber Bragg grating

2.2.1

Bragg reflections

2.2.2

Photosensitivity in fibers

2.2.3

FBG fabrication

2.3	FBG properties

2.3.1

Refractive index profile

2.3.2

FBG types

a-b	FBG types (Homogeneous, apodized)

c-f	FBG types (Chirped, blazed, with phase shifts, arbitrary)

2.3.3

Temperature and strain sensitivity

2.4	Experimental results

2.4.1

FBG fabrication

2.4.2

Spectral characterization

2.4.3

Bragg wavelength determination

2.4.4

Characterization of the photosensitivity

2.5

Summary

2.6	References

Chapter 3 : FBG simulation and reconstruction

3.1	FBG spectral response simulation in the coupled-mode formalism

3.1.1

Coupled-mode equations

3.1.2

Analytic solution for homogeneous FBGs

3.1.3

Numerical solution of the Riccati equation for non-homogeneous FBGs

3.1.4

T-matrix method

3.1.5

Causal T-matrix method

3.2	FBG synthesis and reconstruction

3.2.1

Overview of reconstruction methods

3.2.2

Discrete Layer-peeling

3.2.3

Reconstructed FBG interpretation

3.3	Calculated FBG spectral and impulse responses

3.3.1

Homogeneous FBG examples

a	Homogeneous FBG examples (Constant length)

b	Homogeneous FBG examples (Constant refractive index modulation amplitude)

c	Homogeneous FBG examples (Constant product fo the length and the refractive index modulation amplitude)

3.3.2

Non homogeneous FBG examples

a	Non homogeneous FBG examples (With discontinuities and ramps)

b	Non homogeneous FBG examples (Period step-chirped)

3.3.3

Source effect

a	Source effect (Bandwidth)

b	Source effect (Detuning)

3.4	Reconstruction examples

3.4.1

Reconstruction limits

Reduction of the Gibb's effect

3.4.5

Reconstruction from the complex spectral response

3.4.6

Reconstruction from the complex impulse response

3.5	Methods for characterizing FBGs with loss or with refractive index and period chirp components

3.5.1

Characterization of FBGs with loss

3.5.2

Method to distinguish period chirp and DC refractive index chirp

3.6

Summary

3.7	References

Chapter 4 : FBG characterization by optical low coherence reflectometry

4.1	Methods for measuring the complex impulse response of a grating

4.2	OLCR measurement of the complex impulse response

4.2.1

Overview

4.2.2

Temporal coherence in vacuum

4.2.3

Propagation in vacuum

a	Propagation in vacuum (Michelson interferometer example)

b	Propagation in vacuum (Phase decorrelation view)

c	Propagation in vacuum (Coherence time and coherence length)

4.2.4

Propagation in dielectric materials

a	Propagation in dielectric materials (Dielectric material without dispersion)

b	Propagation in dielectric materials (Dielectric material with dispersion)

4.2.5

OLCR measurement of FBG

4.3	New OLCR set-ups

4.3.1

Time multiplexing OLCR design

4.3.2

Measurement principle

4.3.3

Balanced detection scheme

4.3.4

Polarization effects

4.3.5

Wavelength multiplexing OLCR design

4.3.6

Discussion on the different OLCR designs

4.3.7

Time multiplexing design in OFDR use

4.3.8

Transmission impulse response OLCR set-up

4.4	Reconstruction process

4.4.1

Complex OLCR signal reconstruction

4.4.2

Complex FBG spectral response calculation

4.4.3

Complex coupling coefficient reconstruction

4.5	Reconstructed FBG

4.5.1

Homogeneous FBG

4.5.2

Non-homogenous grating

4.5.3

Fiber Bragg grating with excess loss

4.6

Summary

4.7	References

Chapter 5 : FBG strain sensors

5.1	Axial strain field distribution measurements

5.1.1

Axial stress effect on fiber Bragg gratings

5.1.2

Experiment description

Reconstruction of the complex coupling coefficient

5.1.6

Finite element simulations

5.1.7

Conclusion

5.2	Characterization of a Fiber Bragg Grating under Diametric Loading

Diametric Load of low-birefringent fiber

5.2.4

Diametric Load of Polarization Maintaining Fiber

5.2.5

Study on the PM fiber strain anisotropy sensitivity

5.2.6

Conclusions

5.3	References

Chapter 6 : FBG based humidity and temperature sensor

6.1	Influence of humidity and temperature on polyimide-coated fiber Bragg gratings

6.1.1-2

Influence of humidity and temperature on polyimide-coated fiber Bragg gratings (Abstract, Introduction)

6.1.3

Influence of humidity and temperature on polyimide-coated fiber Bragg gratings (Experiment)

6.1.4

Influence of humidity and temperature on polyimide-coated fiber Bragg gratings (Results and discussion)

6.1.5-6

Influence of humidity and temperature on polyimide-coated fiber Bragg gratings (Conclusion, References)

6.2	Relative Humidity Sensor Using Optical Fiber Bragg Gratings

Chapter 7 : OLCR based picometric vibration sensor

7.1	Sub-pN shear-force feed back system in air and liquid

7.2	References

Chapter 8 : Conclusions and future work

8.1	Conclusions

8.2	Future work

Appendix : A, B, C, D and E

A	Slab waveguide and circular core fiber

A.1.1

Slab waveguide (Maxwell's equations and solutions)

A.1.2

Slab waveguide (Fundamental mode propagation constant and dispersion)

A.2.1-2

Optical Fiber Waveguide (Comparison with a slab waveguide, Maxwell's equations)

A.2.3

Optical Fiber Waveguide (Fundamental mode HE11)

B	Modified phase mask technique description

B.1	Introduction

B.2	Ray optic concatenation of lenses

B.3	Modified phase mask technique

C	Coupled-mode description of FBG

C.1	Scalar wave approximation

C.2	Coupled mode equations

C.3	Physical interpretation

C.4	References

D	Fourier Transforms, Gaussian Function and FFT requirements for complex impulse response calculation

D.1	Fourier Transforms

D.2	Gaussian Function

D.3.1

Matlab FFT and Gaussian example (Theory)

D.3.2

Matlab FFT and Gaussian example (Example)

D.4	References

E	Polarization rotation effect on OLCR measurements

E.1	OLCR set-up

E.2	Interference intensity

Other parts

i	Remerciements

ii	List of publications

iii	Curriculum vitae