International Journal of Engineering Trends and Technology (IJETT) – Volume 11 Number 8 - May 2014
Pi Phase Fiber Bragg Grating Sensitivity
Jyotsnarani Mahapatra
Mrs.Manisha Chattopadhyay
Dept. of E and TC Engg.
VESIT, Chembur, Mumbai-400 074, India
Dept. of E and TC Engg.
VESIT, Chembur, Mumbai -400 074, India
Abstract— In this paper we performed simulation of both
uniform & pi phase fiber Bragg grating sensitivity due to
ultrasonic pressure ,Metal of fiber Core. It is shown that the
wavelength sensitivity of Pi phase Fiber Bragg Grating is better
than uniform Fiber Bragg grating..our simulations are based on
Hooke’s Law, Stress Strain relationship etc. Our analysis shows
that the sensitivity not only changes due to pressure but also
change due to Metal used in the optical fiber core & will be
useful in the design of fiber-optic ultrasonic sensors that use a
πFBG as the sensing element.
Index Terms—Uniform FBG, Pi phase FBG, ultrasonic wave,
Wavelength Sensitivity.
counterparts. They are Tolerant of Harsh Environments,
Electrical Immunity, Remote Sensing, Long term Stability,
Miniature Size, Multiplexing, Ease and Cost of Installation[ .
This paper organized as follows. In Section II, we study the
modelling & methods of Mathematical derivation for design
of different types of FBG sensing methods .In section III, we
present the result of our simulation that is how the sensitivity
of FBG changes according change of ultrasonic frequency &
metal of optical core.
II. MODELLING & METHODS
I. INTRODUCTION
Optical fibers (or optical fibres) are transparent fibers, usually
made of glass or plastic, for transmitting light. They are
flexible strands roughly the diameter of a human hair. With
the use of this latest technology, large amounts of data can be
transmitted over long distances. During several years the
optical fibers are used to broadcast light signals and audio
signals, producing distortion-free sound[1]. Though fiber
optics was first invented in the 1930s, the use of this
technology barely started in the late 1960s. Both multi-mode
and single-mode fibers are used in communications, with
multi-mode fiber used mostly for short distances (up to 500
m), and single-mode fiber used for longer distance links.
Compared to the copper wires, optical fibers are less
expensive, thinner, have higher carrying capacity, less signal
degradation, carry digital signals, and are non-flammable,
lightweight, and flexible. now disadvantages of optical fiber is
Installation costs are high, Special test equipment is often
required, Susceptibility to physical damage, Wildlife damage
to fiber optic cables. To avoid allthese draw backs a new type
of fibero optic is fiber bragg grating used from 1979. Optical
fiber gratings are important components in fiber
communication and fiber sensing fields. Fiber Bragg grating
are widely used in many optical systems as band filters,
dispersion compensators, in-fiber sensors or fiber grating
lasers and amplifiers. The principle of the fiber grating is in
core refractive index modulation. So The FBG works on the
principle that when ultraviolet light (UV) illuminates a certain
kind of optical fiber, the refractive index of the fiber is
changed permanently, this effect is called photosensitivity.
this ultrasonic wave can be used sensing technology also.
Ultrasonic sensor applications are found in a variety of areas
such as non destructive structural health monitoring and
medicine[2]. Traditional ultrasonic sensors are typically based
on piezoelectric ceramics. Fiber-optic ultrasonic sensors
particularly fiber Bragg grating (FBG)-based ultrasonic
sensors, offer many advantages compared to their electronic
ISSN: 2231-5381
An The goal of this chapter is to establish a mathematical
model of ultrasonic pressure waves, and introduce an efficient
numerical method to simulate the response of FBGs. we have
done simulation on sensor sensitivity due to to ultrasonic
waves. The first is called “wavelength sensitivity,” which is
defined by the maximum spectral shift of the uniform or
πFBG Bragg wavelength caused by an ultrasonic wave [4].
Fig.1 Schematic of a ultrasonic wave propagating in the
optical fiber.
.So now Types of effect for wavelength sensitivity on FBG
due to ultrasonic wave[5].
(A)geometric effect:For change in grating period or grating
length of optical fiber.
(B)Elasto-optic effect:For change in refractive index of
fiber core.
(C)wavelength shift of FBG
We know that bragg wavelength is given by,
λ b=2neffĂ
Now
differenciating
d λ b=2Ădneff +2neffdĂ
(1)
eqn
(1)
we
Δ λ b=2Ă Δ neff +2neff Δ Ă
Δ λ b=2Ă(Δ neff +neff Δ Ă/ Ă)
Δ λ b=2 Ă neff{(Δ neff /neff)+( Δ Ă/ Ă)}

Δ λ b= λ b {(Δ neff /neff)+( Δ Ă/ Ă)}
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(2)
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got
International Journal of Engineering Trends and Technology (IJETT) – Volume 11 Number 8 - May 2014
Here ( Δ Ă/ Ă)=Geometric Effect
So now grating period or geometric effect (Δ L/L) =
Єzz )for piphase FBG is towards the Z-direction.so
(Δ L/L) = Єzz is given by
(Δ Ă/ Ă)= (Δ L/L) = Є = Єzz=
(7)
(Δneff/neff)=elasto-optic effect
Δ λ b = wavelength shift FBG
A.(1) Mathematical model of Geometric Effect for uniform
FBG:
We used hookes law for our derivation of geometric
effect,because geometric effect related to strain. Hooke’s law
gives relation between stress & strain.so using hooke’s law
stress (σ ) is given by
σ =E*є
(3)
h ere E=modulus of elasticsity,є=strain, σ=stress
now For 3D ,if directions are labeled (1),(2),(3)
respectively conducted x,y,z direction.So if a
material pulling to x direction,
Strain ,Єxx1 = σxx/ E , Єyy1 = -vσyy/E, Єzz1 = vσzz/E
for pulling a force or stress y direction
Єyy2 = σyy/E , Єxx2 = -v σyy/E , Єzz2 =-v σyy/E
for pulling a force or stress z direction
Єzz3 = σzz/E, Єyy3 =-v σzz/E, Єxx3 = -vσzz/E
In general case a cube is subjected to combine to
normal stress σxx, σyy, σzz.so combine strain can be
obtains[4]
Єxx = Єxx1 + Єxx2 + Єxx3
Єxx = 1/E(σxx -v σyy -v σzz)
Similarlly
Єyy = 1/E(-vσxx + σyy -v σzz)
Єzz = 1/E(-vσxx -v σyy + σzz)
For stress (σxx=σyy=σzz= -P)
Now strain=stress/E
Єxx = Єyy = Єzz = (1/E)*(1-2*v)*(-P ) (4)
We know that grating period or grating length= (Δ Ă/
Ă)= (Δ L/L) = Є = Єxx
so strain for uniform grating is
Єxx = (1/E)*(1-2*v)*(-P)
P=stress= σ,Z=P/V=σ*c
P=V* σ*c ,P= V* σ* f*λ
V=velocity of particle for the medium
C=velocity of wave=f*λ
ρ= density of particle
A.(2) Mathematical model of Geometric Effect for Pi
phase FBG:
pi phase
means elliptical polarization that is the direction of
light or electric field is opposite to each other.so if
the stress(P) applied to Z-direction,the pressure of X
&Y direction is zero.
Stress vector= σ =
We σ=
=
(5)
B(1): Mathematical model of Elasto-Optic Effect for
uniform FBG:
The effect of refractive index due to ultrasonic wave
is called elasto-optic effect.now the indicatrix is
represented as
(8)
Here
x1
x2
x3
(
So,
)2  ( )2  ( )2  1
n1
n2
n3
(1/ ni )= Bij
B11x12 + B22x22+ B33x32=1
=1
ΔBij=Bij’-Bij
now according to theory of photoelasticity proposed
by pockel s,this change in index as a result of
stress/strain.so according to pockels theory
ΔBij =
ΔBij =
=Δ(
i
So, ΔBij=Bij’-Bij=(ni2-n’i2)/(ni*ni’)
ΔBij=Bij’-Bij=-(
=Δ(
(9)
So according to optical properties ,for isotropic solid
for considering fused quartz ,the photo elastic
Tensor(Pij) is given by
Pij
Now put the value of Pij in below equation
ΔBij =
=Δ(
i=-(
-(
*
-(
*
ISSN: 2231-5381
(6)
(11)
So eqn (12) is the elasto Optic Effect of uniform
FBG.
=(
*(1-2*v)*(p11+212)*P (12)
B(1) Mathematical model of Elasto-Optic Effect for
piphase FBG:
We know that
=
(10)
=
So using the above derivation, we got from eqn (10)
is given by
(
=(
*(1-v)*(p12-vp 11)*P (13)
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International Journal of Engineering Trends and Technology (IJETT) – Volume 11 Number 8 - May 2014
So eqn(13) is elasto optic effect for piFBG
C(1): wavelength for uniform FBG
Now using above two effects wavelength shift FBG
due to ultrasonic wave for uniform FBG.For a FBG
response to strain arised due to both change in the
refractive index & grating period from eqn(2).this
can be written as mathematically
Δ λ b= λ b {(Δ neff /neff)+( ΔL/ L)}
Now put the value of Δ neff /neff= Δ n/n & ΔL/ L from
above eqns(4) &(12)
So now wavelength shift or sensitivity for uniform FBG= Δ
λ b is given by
usage of sensitivity technology ,for uniform FBG ,
there is wavelength shift from ( Fig.2 ) dλ=-.018nm
for 2Mhz ultrasonic frequency. So Change in design
wavelength
(λb
)
is
(1558-.018)
nm=1557.982nm.This consumes a higher frequency
which is not desirable.
(b)Fig .3 shows the refractivity of FBG with respect to
wavelength. From Fig. 3 we got 80% refractivity or output of
a uniform FBG for 1558nm.
C(2): wavelength shift FBG due to ultrasonic wave for
piphase FBG:
We know, Δ λ b= λ b {(Δ neff /neff)+( ΔL/ L)}
Now put the value of Δ neff /neff= Δ n/n & ΔL/ L from
above eqns (7) &(13).
So now wavelength shift or sensitivity for piphase FBG= Δ λ
b is given by
Δ λ b= λ b*{( +( {(1-v)*p12-v*p11}}*P
(15)
III. RESULT & DISCUSSION :
The model described above simulates the of effect
wavelength of FBGs by a ultrasonic pressure wave,
given by Eqn.(14) & (15), which allows us to study the
performance of uniform, pi FBGs when they are used as
ultrasonic sensors. The key parameters of sensor
performance for using glass as a fiber core material,
including V=velocity of molecules in That medium
V(glass)=2740m/sec, Density=2200kg/m^3, ultrasonic
lamda(λu)=310nm,design
wavelength(λb)=1558nm,P11=.121, p12=.270,E=70Gpa.we
used in our simulation ,ultrasonic frequency rangefor
uniform FBG is from 0-3 Mhz.
Fig.3 implementation
wavelength of FBG.
of
refractivity of
FBG
versus
(c) after used the sensitivity technology , we got the
wavelength decrease to 1557.982nm.
Now output of FBG reflector or refractivity is decreases to 25% that is 78-75%.shown in below Fig.4
(a)Now Fig .2shows that how is the wavelength shift or
sensitivityof uniform FBG for different ultrasonic wave
frequency
change.
sensitivity
Fig.4 implementation of refractivity of FBG versus design
wavelength of FBG(after sensitivity).
we used Wavelength for uniform FBG before usage
of sensitivity technology 1558nm.however with
(d)Now Fig .5 shows that how is the wavelength shift or
sensitivityof pi FBG for ultrasonic wave frequency change(05)Khz.
Fig: 2. Implementation of wavelength shift or
versus ultrasonic frequency.
ISSN: 2231-5381
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International Journal of Engineering Trends and Technology (IJETT) – Volume 11 Number 8 - May 2014
Fig. 5 Implementation of wavelength shift or sensitivity of pi
FBG versus ultrasonic frequency.
We used Wavelength for pi FBG before usage of sensitivity
technology 1558nm.However after used of sensitivity
technology ,for piFBG , there is wavelength shift from ( Fig.5)
dλ=0.08nm for 2khz ultrasonic frequency. So Change in
design wavelength (λD ) is (1558+0.08) nm=1558.08nm.
(e)Fig .6 shows the refractivity of piFBG with respect to
wavelength. From Fig. 6 we got 80% refractivity or output of
a piphase FBG for 1558nm.
Fig.6. implementation of refractivity of pi FBG versus
wavelength of FBG.
(f) after used the sensitivity technology , we got the
wavelength increase to 1558.08nm.Now output of FBG
reflector or refractivity is increases to 1-4% that is 8184%.shown in Fig.7
Fig. 8(a) piFBG sensitivity for glass material verus ultrasonic
frequency. (b) piFBG sensitivity for plastic material verus
ultrasonic frequency.
From figure 8(a) &(b) we got that plastic material shows
better sensitivity compare to glass material inside fiber core.
IV. CONCLUSIONS
A theoretical model has been established to simulate the
responses of FBGs impinged by ultrasonic pressure waves.
For simulation we used MATLAB software computer
program to implement our mathematical equation. Our
analysis shows that, for uniform FBG ,wavelength sensitivity
decreases when ultrasonic frequency increases,so after
wavelength shift decreases the output of FBG reflector or
refractivity of uniform of FBG also decreases or compress.but
for pi FBG ,wavelength sensitivity increases when ultrasonic
frequency increases,so after wavelength shift increases the
output of FBG reflector or refractivity of pi FBG also
increases .Pi FBG also require less frequency compare to
uniform FBG.now we can increase the sensitivity of PiFBG ,if
we use plastic for fiber core material.these piFBG design
methods can be use for fiber-optic ultrasonic sensors that use
a FBG as the sensing element.
ACKNOWLEDGMENT
I would like to express my thanks to Asst.Prof. Mrs Manisha
Chattopadhyay for overall support and valuable guidance.
REFERENCES
Fig.7. implementation of refractivity of pi FBG versus
wavelength of piFBG(after sensitivity).
(g) now Fig. 8 shows that how is the wavelength sensitivity of
pi FBG changes for change core material of FBG.
ISSN: 2231-5381
[1]wiki padia,optical fiber.
[2] Jyotsnarani Mahapatra , Asst.Prof. Manisha Chattopadhyay , Spectral
characteristic of Uniform Fiber Bragg Grating using couple mode theory,
International Journal of Electrical, Electronics and Data Communication
(IJEEDC),vol 1,issue 5, pp 40-44, july 13
[3] Analysis of π-Phase-Shifted Fiber Bragg Gratings for Ultrasonic
Detection,IEEE Sensors Journal, Vol. 12, No. 7, July 2012.
[4]Analysic of Fiber Brahh Grating for ultrasonic detection,Tongging LiU.
[5]strain effect,optoelectronics,chapter 5.
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