Experimental and theoretical study of locally transverse
loaded fibre Bragg gratings for pressure sensing applications
Ricardo Correia, Edmon Chehura, Stephen W. James and Ralph P. Tatam
Optical Sensors Group, School of Engineering, Cranfield University, Bedford MK43
0AL, UK
s.w.james@cranfield.ac.uk
Abstract. An experimental and theoretical study of locally transverse loaded fibre Bragg
gratings (FBGs) for pressure sensing purposes is presented. When a load is applied to a small
section of a FBG, a spectral hole is generated in the reflection spectrum, which moves to
higher wavelengths as the load is increased. This has been modelled using Rouard’s method
and experimentally tested under the same FBG parameters and load conditions. The FBG was
interrogated using a tunable external cavity laser and a polarisation maintaining fibre network
that allows the two orthogonally polarised signals reflected from the FBG to be detected
independently and simultaneously. The experimental results were consistent with the
theoretical predictions and demonstrate potential for high resolution pressure sensing.
1. Introduction
Since the discovery of the fibre Bragg grating (FBG) in 1978 [1], they have been widely used for
sensing and optical fibre communications purposes [2]. Their ability to measure static or dynamic
fields such as temperature, strain and pressure, the fact that the information is wavelength encoded,
and the ease with which FBG sensor elements can be multiplexed, have made them the subject of
intense research within the fibre optic sensor community [3]. When an FBG is subject to a transverse
load, deformations of the dielectric waveguide and anisotropic changes in the refractive index occur,
leading to the creation of birefringence. When a transverse load is applied uniformly along the axis of
an FBG fabricated in single mode (SM) optical fibre, the introduction of birefringence causes a
splitting of the Bragg peak. In the case of FBGs fabricated in linear highly birefringent (HiBi) optical
fibre, the separation of the central wavelengths of the two orthogonally polarised Bragg peaks
increases or decreases, depending upon the orientation of the load with respect to the birefringent axes
of the fibre. Detailed studies of the response transverse loading of FBGs fabricated in different types
of HiBi fibres have shown that, generally, the highest sensitivity is obtained when the load is applied
along the eigen-axes of the HiBi fibre [4-6].
Recent studies showed that non-uniform transverse loading of a FBG introduces a spectral hole
within the bandwidth of the FBG [7-9] due to a local change of the refractive index within the loaded
region (Figure 1), creating a phase shift. This paper presents the analysis of that effect, with the aim of
developing a pressure sensor that tracks the wavelength shift of the spectral hole as a function of the
applied load. A theoretical study of the reflection spectrum of an SM fibre subject to a transverse load
was undertaken and experimentally verified. An experimental investigation of the effect using HiBi is
also presented.
Figure 1. Diagram illustrating the local change of the refractive index within the loaded region.
2. Theoretical analysis
Rouard’s method was used to simulate the spectral response of an FBG subject to a transverse load
applied to a section of the FBG. Rouard’s method is a recursive technique commonly used in the
design of thin-film coatings that was modified by Weller-Brophyand Hall for the analysis of
diffraction gratings [10]. According to this method, each grating period is treated as a layer in a thinfilm coating and its reflection coefficient is calculated. Using a recursive technique the entire
reflection coefficient of the grating is calculated. The methodology used was described [11], where
half grating periods are considered as uniform layers, leading to a square index modulation within the
period of the grating. The refractive index within the loaded zone is substituted by the new one,
leading to the simulation of the spectrum response of the FBG.
Changes in refractive index in response to the applied load are derived from photoelastic theory
[12] described by Equations 1 and 2:
(neff ) x  
n03
{( p11  2p12 ) X  [(1  ) p12 p11]( y   z )}
2E
n03
(neff ) y  
{( p11  2p12 ) y  [(1  ) p12 p11 ]( x   z )}
2E
(1)
(2)
Where E is the Young’s modulus,  the Poisson’s coefficient of the fibre, p11 and p12 the
photoelastic constants and  x and  y the stress components in the x and y direction, respectively.
3. Experiment
For the experimental test, FBGs with centre wavelength 1550 nm were fabricated in photosensitive
single mode (SM) optical fibre (fibercore PS1250) and in hydrogen loaded linear HiBi bow-tie optical
fibre (Fibercore HB1500). The FBGs were of length of 6mm and 3mm respectively. The experimental
arrangement used to interrogate the transversely loaded FBG written in HiBi fibre is shown
schematically in Figure 2. The wavelength range of interest was scanned with a resolution of 3 pm
using a tunable external cavity laser (TUNICS-Plus CL) coupled to a Polarisation Maintaining (PM)
coupler. The FBG was attached to one output arm of the PM coupler while the other output was
immersed in an index matching gel. The light reflected from the FBG was directed to a polarisation
selective coupler. The orthogonal linearly polarised outputs of the two arms of the coupler were
recorded separately by two photo-detectors via a data acquisition (DAQ) card. For experiments
undertaken on the FBGs fabricated in SM fibre, a single mode coupler was used in place of the PMC
in figure 2, and a single detector was used to monitor the reflected spectrum.
Figure 2. Schematic diagram of the experimental arrangement
In order to apply the pressure to the fibre, a loading fixture designed to minimise the fibre twist (as
represented in Figure 3), and used previously to characterise the transverse load response of PM FBGs
[4], was employed. The test fibre and an identical support fibre located parallel to the first were loaded
transversally between the two metal stages that had been designed to apply a load to 1.05 mm of the
FBG. Each of the stages had three contact points, one located at the centre of the FBG, with a length
of 1.05 mm, and two other contact points, each of length 5mm, which were outside the FBG. The load
was applied to the fibres by rotating a screw, which was monitored by a load button with a capacity of
222 N and resolution of 0.1 N. The signal from the load button was recorded through a DAQ card. The
alignment of the Hi-Bi fibres polarisation axes within the loading fixture was achieved through two
rotational stages. The load in this case was applied along the slow axis.
Figure 3. Representation of the loading fixture
The centre of the FBG was approximately determined during the fabrication process and later
confirmed applying a fixed load at different positions along the FBG and analysing the reflected
spectrum. When the load was applied at the centre of the FBG, the spectral hole showed the largest
sensitivity.
4. Results and discussion
The theoretical simulation was compared with the experiment in terms of the spectral behaviour and
the sensitivity of the wavelength shift of the spectral hole to the applied load. The spectral response of
a 6 mm SM FBG was simulated under the same load conditions and with the same fibre parameters.
The parameters include the effective refractive index, diameter, E , , p11 and p12 .
4.1. Theoretical simulation
The results of the theoretical simulation show that the spectral hole exhibits a red shift with increasing
load (Figure 4). Once the spectral hole had traversed the FBG bandwidth, a new cycle starts, with the
spectral hole reappearing at the blue end of the spectrum.
Figure 4. Theoretical evolution of the reflection spectrum from a SM FBG subject to a local transverse load
applied along a 1.05 mm length, at the centre of the FBG.
4.2. Experimental results from the SM FBG
Figure 5 (a) shows the response of the spectrum of the SM FBG to the application of the transverse
load. The spectral hole tracks across the spectrum as theoretically simulated. The spectral features that
appear at the red end of the spectrum as the load is increased can be attributed to the introduction of
birefringence.
The experimental and theoretical sensitivities, 57.1 and 52.5 pm/(N/mm) respectively, determined
from the slope of the graphs in Figure 5 (b), show good agreement.
Experimental results
0.35
wavelength shift (nm)
Theorical results
0.3
0.25
0.2
0.15
0.1
0.05
0
0
(a)
1
2
3
Load (N/mm)
4
5
6
(b)
Figure 5. (a) Evolution of the reflection spectrum from a SM FBG subject to a local transverse load applied
along a 1.05mm length, at the centre of the FBG, (b) Experimental vs. theoretical dependence of the central
wavelength of the spectral hole to the applied load.
4.3. Experimental results from the HiBi FBG
To investigate the introduction of birefringence, an FBG fabricated in bow-tie HiBi fibres was used in
conjunction with the instrumentation illustrated in figure 2. On transversally loading the fibre along
the slow axis, the spectral hole appeared only along the loaded axis i.e. the slow axis of the FBG
spectrum, as illustrated in Figure 6(a), the fast axis remaining unperturbed. The sensitivity calculated
from the graph in Figure 6 (b) was 74.3pm/(N/mm).
The total length of fibre in contact with the metal stage was 11.01 mm. Thus the load imposed to
the 1.05 mm length of the FBG was only approximately 1/11 of the total load. The sensitivity could be
enhanced by decreasing the length of the contact points.
Wavelength shift (nm)
0.400
0.200
0.000
0.00
2.00
4.00
6.00
Load (N/mm)
(a)
(b)
Figure 6. (a) Evolution of the reflection spectrum from the slow axis of the HiBi FBG subject to a local
transverse load applied along a 1.05mm length, aligned with the slow axis. (b) Dependence of the central
wavelength of the spectral hole on applied load.
5. Summary
Local transverse loading of FBGs introduces a spectral hole into the Bragg spectrum. This effect was
theoretically analysed and experimentally tested for FBGs fabricated in SM optical fibre. The spectral
hole developed in the SM fibres showed that the experimental sensitivity and cyclical behaviour
reproduces the theoretically simulation. The investigation of locally loaded HiBi FBGs showed that
the spectral hole appears only in the Bragg reflection from the axis along which the load is applied.
6. Acknowledgements
The authors gratefully acknowledge the support of the Royal Society Paul Instrument Fund, UK
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