Journal of Computer and Communications, 2013, 1, 9-13
Published Online December 2013 (
Open Access JCC
The Circular Biref ri n genc e -Insensitive FBG Sensor for
Weak Pressu r e
Hui Peng, Bi-hua Zhou, Li-hua Shi, Cheng Gao
National Key Laboratory on Electromagnetic Environment Effects and Electro-optical Engineering, PLA University of Science and
Technology, Nanjing, Jiangsu, China.
Received August 2013
The influence of the circular birefringence on the measurement performance was analyzed based on the Polarization
Properties of FBG in this paper. Due to the circular birefringence, the linear relationship between the max of PDL and
pressure has been broken down. To estimate the cross sensitivity, a new parameter named relative peak of PDL (RPPDL)
is proposed. Under different circular birefringence, the same pressure sensitivity of sensor has been achieved. The theo-
retical analysis and experiment results prove that transverse strain sensor of FBG is insensitive to the circular birefrin-
gence by applying the RPPDL. This res e a rch can be provide d to useful and practical application .
Keywords: Circularly Birefringence; Polarization Propertied; FBG Weak Pressure S ensor; The Relative Peak of PDL
1. Introduction
For both telecommunications and sensing purposes, FBG
thus becomes important to characterize the polarization
properties of FBG and their dependence on the wave-
length [1-3]. Furthermore, this study can lead to the de-
velopment of a new demodulation technique for FBG-
based sensors. Caucheteur et al. have used polarization
dependent loss (PDL) for transverse strain measurements
[4,5]. The polarization dependent properties are also used
for the magnetic field sensor [6].
Either way, there exist cross-sensitivity problems. In
wavelength detection, the centre wavelength will change
not only with the strain, but also with the temperatur e [7].
Similarly, in polarization detection, the polarization pro p -
erties are influenced by the linear and circular birefrin-
gence [8,9]. Hence, we must take various kinds of meas-
ures to compensate or distinguish the cross-sensitivity
problems. A number of techniques addressing this issue,
such as dual-wavelength superimposed grating, two FBGs
in different diameter fiber, hybrid FBG/long period grat-
ing, superstructure FBG and Fabry-Perot cavity method,
have be en reported [10-12]. Those methods provided some
approaches to distinguish cross-sensitivity e ffect, b ut most
of them needed specific gratings and special technique.
In this paper, the influence of the circular birefrin gence
on the measurement performance was analyzed based on
the polarization properties o f FBG. To estimate the cross
sensitivity, a new parameter named relative peak of PDL
(RPPDL) is proposed. The simulation and experiment re-
sults proved that the relative peak of PDL (RPPDL) could
effectively reduce the influence of circular birefringence.
2. Theoretical Models
2.1. Principle of Measurement
The polarization property of FBG has been widely used
in the field of measurement. Here, we shortly introduce
the principle of measurement.
The applied force causes a birefringence Δn, which is
defined as the difference in refractive index between two
orthogonal polarization modes called x and y modes (or
eigenmodes). Due to the Δn, the x and y modes undergo
different couplings through the grating. The total trans-
mitted signal is the combination of th e x and y mode sig-
nals. If there is only the linear birefringence, the Jones
vector associated to the FBG transmitted signal is given
by [5]:
, ,,
, ,,
txixx ix
  
= =
  
  
Where (Ei,x, Ei,y)T is the Jones vector of the input signal
and tx(y) denotes the transmission coefficient of x(y) mode
FBG [13].
Polarization Dependent Loss (PDL) is defined as the
The Circular Birefringence-Insensitive FBG Sensor for Weak Pressure
Open Access JCC
maximum change in the transmitted power by the grating
as the input state of polarizatio n is varied over all polari-
zation states.
In this paper, the input signal is the linear state at π/4
between the x(y) mode, Ei,x = Ei,y. In the case of Bragg
gratings, it is easy to show that the PDL for the transmit-
ted signal is given by [17]:
1010 2
( )10log10log
() ()
= =
2.2. The Effect of Linear Birefringence
The study of Caucheteur et al. demonstrated that there is
linear relationship between the peak of PDL and pressure
[5]. But in practice, the fiber has intrinsic circular bire-
fringence in the manufacturing process. Moreover, the
induced circular birefringence can be caused by the shape,
twisting and axial magnetic field of the fiber materials.
The effect of circular birefringence must be taken into
account when researching the performance of FBG weak
pressure sensor based on the polarization properties.
Due to the circular birefringence, the Equation (1) will
be modified as [18,19]:
, ,,
, ,,
txixx ix
 
 
= =
 
 
 
 
cos( )sin( )
= +
2sin( )
(2 )
Φ=+ Ω
(3 -3)
( )
δ ββ
= −
Where Φ, 2Ω and Δ are the phase shift of elliptically,
circularly and linear polarized light, respectively. And we
use the L and R subscripts to indentify the eigenmodes
corresponding to the left and circularly polarized light.
According to th e Equations (2) and (3), we will under-
stand more clearly the effects of circular birefringence on
the evolut ions of PDL.
3. Simulation Results
We design a FBG with 1.455 of neff, 535 nm of Λ, 4mm
of L and 1 × 10 4 of Δn. According to the given data, the
simulation results can be got to analyze the influence of
circular birefringence on the performance of proposed
FBG sensor.
For purposes of analysis, some abbreviations were de-
fined, such as BPDL(the value of PDL that outside the
FBG band), PPDL(the peak value of PDL).
According to the Equations (1) and (2), Figure 1
presents the PDL as a function of pressure. As expected,
the increase of pressure leads to a general increase of
PDL amplitudes. The PPDL increase linearity with the
pressure without circular ly b irefringen ce, which is shown
in Figure 2.
Considering the influence of circular birefringence, the
evolutions of PDL spectrums with pressure and circular
birefringence are shown in the Figure 3. Due to the cir-
cular birefringence, the BPDL is no longer zero and changed
non-linearly with the circularly birefringence. Hence, the
PPDL does not increase linearly with the increasing of
pressure, as shown in Figure 3. From Figure 3, it also
can be seen that the PPDL is influenced by the combina-
tion of circular and linear birefringence.
Up until now, it can be seen clearly that the linear rela-
tionship [5] between PPDL and pressure was broken be-
cause of circular birefringence. In order to eliminate the
effect, a new parameter named the relative peak of PDL
(RPPDL) is defined. The RPPDL refers to the difference
between the BPDL and PPDL. Without circular birefrin-
gence, the RPPDL and PPDL are the same.
Figure 1. PDL versus wavelength at pressure without cir-
cularly birefringence.
Figure 2. PPDL versus pressure without circularly birefrin-
The Circular Birefringence-Insensitive FBG Sensor for Weak Pressure
Open Access JCC
Figure 3. the evolutions of PDL at different circularly bire-
fringence and pressure (CB = circular birefringence).
Under circular birefringence, the evolutions of RPPDL
were shown in Figure 4. From which it can be seen that
the four RPPDL lines were almost coincided under differ-
ence circular birefringence (solid, dash, dot and dash dot).
Figure 4 means that the RPPDL is insensitive to the circu-
lar birefringence. Hence, the influence of circular bire-
fringence on the performances of the FBG pressure sen-
sors can be eliminated by using the RPPDL.
4. Experiment Results
The experimental data were then compared to theoretical
evolutions. For that purpose, the experiment system was
set up. The optical vector analyzer (OVA) is regarded as
a light source, detector and processor. The FBG that used
in experiment was designed and fabricated by our project
group. The parameters of FBG are: neff = 1.455, Λ = 535
nm, Δn = 5e5 and L = 10 mm. The width of glass plate is
the same size as the length of FBG. The fixture was used
to generate the random circular birefringence by twisted
the FBG, in this way, only the qualitative method can be
used to analyze the circular birefringence. Due to the
experimental condition limitations, the applied pressure
was in the range 1 ~ 10 N by steps of 1 N. The results
under two random conditions with different circular bire-
fringence were calculated and analyzed in this section.
Using the optical vector analyzer whose precision is
105 (dB) in our experiment [20], the PDL evolutions for
different pressure under two cases (different circular bi-
refringence) are got and shown in Figure 5. The PPDL
becomes more and more obvious along with the increase
of pressure. To observe Figures 3 and 4, the simulation
results and experiment results were similar.
Based on different pressure and circular birefringence,
the experimental data of the BPDL, PPDL and RPPDL values
respectively are given in Table 1.
From the Figure 6, we can find that the two set of data
about RPPDL and their fitting curves have a good agree-
ment, which demonstrates that the RPPDL is not influ-
Figure 4. the evolutions of RPPDL at different circularly bi-
refringence with same pressure (CB = circular birefrin-
(a) case 1
(b) case 2
Figure 5. PDL versus wavelength at pressure for two cases.
enced by the circular birefringence. In addition, due to
the values of the fitting curves are increase monotonical-
ly with pressure, the RPPDL can be used to retrieve the
pressure. Based on calculations, the pressure sensitivity
are same 0.229 dB/N. Figure 6 also presents the theoret-
ical results, the pressure sensitivity of which is 0.291
dB/N. The error between the experiment and theoretical
results is caused by the manufacturing error of the FBG,
such as the photo-induced birefringence [21,22]. The
1547.2 1547.4 1547.6 1547.8 1548.0 1548.2 1548.4
Wavel ength( nm)
0 N
5 N
1547.2 1547.4 1547.6 1547.8 1548.0 1548.2 1548.4
Wavel e ngth(nm)
0 N
5 N
The Circular Birefringence-Insensitive FBG Sensor for Weak Pressure
Open Access JCC
Table 1. the experimental results for two cases.
Pressure/N Case 1 Case 2
0 10.94447 11.60567 0.6612 13.35158 14.01735 0.66577
1 9.7146 10.36974 0.65514 11.3351 12.0727 0.7376
2 6.94343 7.77878 0.83535 7.40321 8.23232 0.82911
3 6.7089 8.0723 1.3634 7.5258 8.8028 1.277
4 7.69596 9.12483 1.42887 8.1061 9.5944 1.4883
5 5.79927 7.7797 1.98043 6.86557 8.69737 1.8618
7 5.8658 7.91799 2.05219 6.98792 9.12278 2.13486
8 6.37788 8.56389 2.18601 7.97609 10.19856 2.2225
9 5.35373 7.74207 2.38834 6.08897 8.56583 2.47686
10 6.3616 9.35989 2.99829 7.97609 10.95309 2.977
Figure 6. Evolution of RPPDL in response to a change of
initial value of RPPDL both are 0.66 under two conditio ns
because of the intrinsic birefringence. The theoretical
analysis and experiment results prove that the errors
caused by the circular birefringence can be effectively
elimi na t e d by using t he RPPDL.
5. Conclusion
By analyzing the influences of the circular birefringence
on the performance of the FBG pressure sensor, it is
known that the nonlinear relationship between the PPDL
and the pressure can be caused by the circular birefrin-
gence, which affects the accuracy of the FBG pressure
sensor based on the PPDL. For overcoming this weakness,
the parameter denoted by RPPDL is proposed in this paper
which can ensure the linear relationship between the
RPPDL and the pressure under the different circular bire-
fringence, thus the pressure can be retrieved by the val-
ues of the RPPDL. Th e theoretical analysis and experiment
results prove that the errors caused by the circular bire-
fringence can be effectively eliminated by using the
RPPDL. This research is helpful to the practical applica-
tion of the FBG weak pressure sensor, such as underwa-
ter acoustic and liquid level measurement, etc.
6. Acknowledgements
This work was supported by the National Natural Science
Foundation of c hina under GRANT 61271106, the Jiangsu
Province Natural Science Foundation BK2012508 and
China Postdoctoral Science Foundation funded project
(2012M521850). We would like to thank Prof. Xiangfei
Chen of Nanjing University for providing OVA in expe-
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