Optics and Photonics Journal, 2013, 3, 225-228
http://dx.doi.org/10.4236/opj.2013.33036 Published Online July 2013 (http://www.scirp.org/journal/opj)
Pressure Sensor Based on Mechanically Induced LPFG in
Novel MSM Fiber Structure
Sunita Ugale, Vivekanand Mishra
Department of Electronics and Communication Engineering, S. V. National Institute of Technology, Surat, India
Received January 1, 2013; revised February 12, 2013; accepted February 20, 2013
Copyright © 2013 Sunita Ugale, Vivekanand Mishra. This is an open access article distributed under the Creative Commons Attribu-
tion License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly
cited.
ABSTRACT
We have proposed and demonstrated experimentally a novel and simple pressure sensor based on mechanically induced
long period optical fiber gratings. We report here for the first time to our knowledge the characterization of mechani-
cally induced long period fiber gratings in novel multimode-singlemode-multimode fiber structure. The MLPFG in-
duced in single mode fiber and multimode fibers are studied separately and the results are compared with MLPFG in-
duced in MSM fiber structure. MLPFG in MSM structure has much greater sensitivity. We have obtained maximum
transmission loss peak of around 18 dB, and the sensitivity of pressure sensor is 8 dB/Kg.
Keywords: Mechanically Induced Grating; Pressure Sensor; Sensitivity
1. Introduction
Fiber optics sensors based on gratings are still in the de-
velopment stage in laboratories and lot of work is needed
to be done to promote and develop their use in advanced
applications. In-fiber grating sensor technology has be-
come one of the most rapidly progressing sensing topics
of this decade in the field of optical fiber sensors. These
sensors are currently emerging from the laboratory to
find practical applications. Rapid progress has been made
in both sensor system developments and applications in
recent years.
The spectral characteristic of Long period optical fiber
grating (LPFG) is more flexible as compared to fiber
Bragg grating (FBG). LPFG have low insertion loss and
low back reflection. It can offer the advantages of abso-
lute measurement, high sensitivity, all-fiber in-line, small
size, etc. The other advantages of LPFG sensor include
simple fabrication and easiness in adjusting the resonant
wavelength well within the spectrum of optical source by
simply adjusting the grating period. All these attractive
features of LPFGs are the strong points to push towards
detail study of this device. Because of much longer Pitch
Λ (almost 100 times that of FBG) the forward propagat-
ing core bounded modes and cladding-bounded modes
couple to each other. Therefore there are several resonant
peaks depending on the involved number of cladding
modes in the interesting wavelength range and the core
mode is coupled to several copropagating cladding modes.
Many methods have been demonstrated for the fabri-
cation of LPFG. The techniques can be divided into two
groups: the one that enables the fabrication of permanent
gratings, and the other that allows the fabrication of re-
versible or mechanically induced gratings, i.e. by remov-
ing the external perturbation the grating disappears [1].
As the period of LPFG is of the order of micrometers, it
can be induced through microbending using various me-
chanical means. The important advantage of this tech-
nique over other techniques is that it can be applied to
any kind of fiber and is also simple, flexible and low-cost.
These are very sensitive to external pressures enabling a
good control over their transmission characteristics [2,3].
2. LPFG Mathematical Model
If a periodical pressure is applied on the waveguide, a
long period grating is formed owing to the photo elastic
effect and the microbending effect. The energy of the
core mode LP01 is coupled into that of the cladding mod-
es LP1m if the phase matching condition as follows is
satisfied [4].
22 2
co cl
eff eff
nn




 (1)
where : is the effective index of the core mode, :
Is the effective index of cladding mode.
co
eff
ncl
eff
n
C
opyright © 2013 SciRes. OPJ

S. UGALE, V. MISHRA
226
For a given periodicity Λ one can induce mode-coupl-
ing between the fundamental mode and several different
cladding modes, a property that manifests itself as a set
of spiky losses at different wavelengths in the transmis-
sion spectrum. In design of optical filters concatenation
of gratings are required and the relatively close spaced
resonance peaks of cladding modes can cause serious
difficulties to generate a desired spectrum.
The coupled mode equations describe their complex
amplitude, Aco(z) and Acl(z) [5].
  
  
2
2
de
d2
de
d2
co iz
co cococo clcl
cl iz
cl clclcl coco
Az s
iKAzi KAz
z
Az s
iKAzi KAz
z







(2)
where Aco and Acl are the slowly varying amplitudes of
the core and cladding modes, Kco-co, Kcl-cl and --co clclco
are the coupling coefficients, s is the grating modulation
KK


depth and 1
co cl
eff eff
nn



 




is the detuning from
the resonant wavelength. The coupling is determined by
the transverse fields of the resonant modes EI and the
average index of the grating nI
 
0d
4
iji j
n
K
nrE rErr



 (3)
According to coupled mode theory, grating transmis-
sion is a function of coupling coefficient Kij
Assuming the detuning from resonant wavelength is
balanced by the dc coupling, simplified expression for
grating transmission is given by



2
cosTZ KZ (4)
Cross coupling coefficient к depends on the grating
index profile and field profiles of the resonant modes.
The analysis given by Erdogan (Erdogan 1997) [6] is
followed for the calculation of core and effective clad-
ding refractive index.
Consider a step index fiber with three layers: central
core with refractive index n1, cladding with refractive
index n2 and the external medium with refractive index
n3 is considered. The core radius is a and the cladding is
assumed to extend to infinity.
Variation of effective index of fundamental LP01
guided mode as a function of wavelength in a fiber
shown in Figure 1 is calculated by using the following
equations.
co
eff
n
Figure 1. Multimode-Single mode-Multimode (MSM) Fiber
Structure.
The normalized frequency of the fiber is given by V.
22
12
Vn n

2a

 (5)
Normalized index difference
12
1
nn
n

 (6)
The approximate value of index as a function of wave-
length is given by Sellmeier equation

2
2
22
1
1
Mi
ii
A
n





 
 (7)
The commonly used waveguide parameters u and w
are
22
10
uk 1

 (8)
22
01 2
w  k

 (9)
where
12
12 01
2
22
,,
co
eff
n
nn
kk





  (10)
The characteristic equation for a LP0m guided propaga-
tion in a weakly guiding fiber (n1 ≈ n2) is given by





11
00
11
J
uak wa
uJ uawk wa
 (11)
where m is radial order of mode. Jp, kp are Bessel and
modified Bessel functions of order p.
Calculation of effective indices of the circularly sym-
metric, forward propagating cladding modes.
Consider a multimode step index structure ignoring the
presence of core.
The Eigen value equation for the LP0m cladding mode
can then be approximated by that of a uniform dielectric
cylinder surrounded by an infinite medium.


 


 



 



 






2
2
111
122
12 22
111 1
1
mmm
mm
clcl cl
cl cl
mmm mmmm mmm
cl clclclcl clclclcl cl
JubJub Kwb
Kwb KK b
uJub wKwbuJubwKwbuw


 



 
  


 

  
 

 



(12)

S. UGALE, V. MISHRA 227

m
cl
u and are the waveguide parameters for clad-
ding

m
cl
w
 

2
2
2
m
cl
uk  
m
(13)
 

22
3
mm
cl
w  k (14)
 
2m
mcl
n



 (15)
and

22
2
22
cl m
eff jm
nn b

 

 

 
(16)
where jm are the roots of the Bessel function of order
zero (J0(jm) = 0).
3. Experiment and Results
The Reversible LPFG with period of 600 μm and length
= 70 mm is induced in single mode fiber in Multimode-
Single mode-Multimode (MSM) structure. Light is laun-
ched from a broadband source to the lead-in MMF,
through the device (MLPFG) to the lead-out MMF and
spectrally resolved using an optical spectrum analyzer
(OSA) (Prolite60).
A schematic diagram of the MSM structure used in
experiment is shown in Figure 1. The sample is prepared
by splicing a 15 cm long section of SMF (SMF-28™)
using a Sumitomo Type39 fusion splicer in between two
MMFs (62.5/125). The loss at both splices was 0.02 dB.
The MLPFG induced in single mode fiber and multi-
mode fibers are also studied separately. It is observed
that single mode grating produced resonant loss peaks of
up to ~7 dB and multimode grating produced resonant
loss peaks of up to ~5 dB. The transmission spectrum of
MLPFG in MSM structure is plotted in Figure 2, the
input power spectrum is also shown for comparison pur-
pose. The peak loss of around 17 - 18 dB is obtained,
which is much greater than MLPFG in Single mode and
multimode fiber.
Thus the MSM structure has a higher sensitivity than
just writing the MLPFG the single mode or multimode
fiber individually.
The transmission spectra of the MLPFG in SMS struc-
ture with periods of 600 μm and length L = 70 mm for
different pressure applied on it is shown in Figure 3. We
can see that a high pressure has a deep notch in the trans-
mission spectrum and the high coupling efficiency at the
resonant wavelength. The results of those measurements
are given in Table 1, and plotted in Figure 4.
The curve fitting polynomial P for pressure sensor is
32
0.20870.94422.6336 0.0449Px xx.
Resonant loss peaks with strengths of up to 17 dB
have been generated in the MLPFG in MSM structure.
There is no change in resonance wavelength with exter-
nal applied pressure. Therefore MLPFGs, can find appli-
cation as pressure gauges.
Sensitivity of pressure sensor = Change in transmis
Figure 2. Spectral response of MLPFG in MSM fiber struc-
ture.
Figure 3. Complete transmission spectrum of MLPFG in
MSM structure (Λ = 600 µm) with different pressures
Table 1. Transmission loss to applied pressure.
Applied Weight (Kg) Transmission loss (dBm)
0 45.0
2.0 48.5
3.5 51.0
4.0 53.5
4.4 56.7
4.6 57.8
4.8 59.3
5.0 60.8
5.2 62.0

S. UGALE, V. MISHRA
228
Figure 4. Response of grating to external applied pressure.
sion loss/ change in applied weight
56.7 53.53.28dB Kg
4.4 4.00.4
S 

4. Conclusion
We report here, for the first time to our knowledge, the
characterization of mechanically induced LPFGs in MSM
fiber structure. MLPFG in MSM structure gives single
transmission dip. Resonant loss peak strength is around
18 dB, which is much greater than maximum loss of 8
dB in Single mode MLPFG and 5 dB in multimode
MLPFG. The MLPFG in MSM structure with  = 600
μm and length = 70 mm can be used as a pressure sensor.
5. Acknowledgements
This work is partially supported by the Department of
Science and technology of India.
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