Journal of Computer and Communications, 2014, 2, 36-41
Published Online May 2014 in SciRes. http://www.scirp.org/journal/jcc
http://dx.doi.org/10.4236/jcc.2014.27006
How to cite this paper: Urban, F. (2014) Optimization of the Tilted Fibre Bragg Gratings for the Fibre Accelerometric Sensor.
Journal of Computer and Communications, 2, 36-41. http://dx.doi.org/10.4236/jcc.2014.27006
Optimization of the Tilted Fibre Bragg
Gratings for the Fibre Accelerometric Sensor
Frantisek Urban1,2
1Dept of Microelectronics, Brno University of Technology, FEEC, Brno, Czech Republic
2Network Group, s.r.o., Brno, Czech Republic
Received January 2014
Copyright © 2014 by authors and Scientific Research Publishing Inc.
This work is licensed under the Creative Commons Attribution International License (CC BY).
http://creativecommons.org/licenses/by/4.0/
Abstract
The presentation shows the principle and construction of the fibre optic accelerometric sensor.
The sensor element is based on the use of the tilted fibre Bragg grating (TFBG) that is imprinted to
the bend insensitive single-mode telecommunication grade fibre. The fibre section with TFBG is
then coupled to the evaluation fibre circuit with the cladding-core mode conversion element that
provides the core re-coupling of the optical power injected by TFBG to the fibre cladding. The
cladding-core mode conversion efficiency is sensitive to the acceleration generated fibre bending.
It is shown that the sensitivity of the device depends on the rate of the main core reflection versus
cladding ghost reflection induced by the grating. The analysis of the core reflection power coupl-
ing on the angle of the grating tilt and the analysis of the cladding ghost reflection power coupling
on the angle of the grating tilt is presented and the optimal parameters of the tilt and refractive
index modulation are derived. The presentation gives the experimental results of the TFBG sensor
prepared according to the optimization process.
Keywords
Optical Fibre, Tilted Fibre Bragg Grating, Accelerometric Sensor, Cladding Modes, Reflected
Spectrum
1. Introduction
Fibre optic accelerometric sensors are one of the applications of the optical fibres where the tilted Bragg gratings
can find the utilization. The principle of the fibre optic accelerometric sensor with the tilted Bragg grating is
shown in the Figure 1.
The sensor element is based on the use of the tilted fibre Bragg grating (TFBG) that is imprinted to the bend
insensitive single-mode telecommunication grade fibre. The fibre section with TFBG is then coupled to the

F. Urban
37
evaluation fibre circuit with the cladding-core mode conversion element that provides the core re-coupling of the
optical power injected by TFBG to the fibre cladding. As the mode conversion element the section of the graded
index multimode fibre with core/cladding diameters of 62.5/125 microns and the specific length was selected.
The cladding-core mode conversion efficiency of the light passing through the multimode fibre section is sensi-
tive to the acceleration generated fibre bending and for suitable length of the multimode section it grows with
the angle γ. Similarly, the transmission of TFBG reflected core mode through the multimode section is inversely
affected by the angle γ. Thus, the use of TFBG allows for relative signal amplitude evaluation where the bending
angle γ is derived from either the ratio of the cladding and reflected core mode powers or from the ratio of the
ghost and reflected core mode powers. The powers of light confined in reflected core mode, ghost and cladding
modes are spectrally separated, as shown in the Figure 2, and can be measured individually. The relative signal
amplitude measurement allows for the elimination of any light source intensity noise or instabilities and gives
increased sensibility. On the other hand, the relative measurement requires the design of TFBG that gives com-
parable amplitudes of core reflection versus the ghost or the cladding modes. The following paragraphs deal
with that issue.
2. Tilted Grating Reflections
The behaviour of the TFBG with broadband incident light represents a complex issue. First, the core reflection
propagating opposite to the incoming incident core mode still exists and its amplitude changes with the grating
tilt. The maximum amplitude is obtained when the grating planes are perpendicular to the fibre axis. The grating
tilt α also causes the frequency shift of the core reflection λα that migrates towards the longer wavelengths.
0
2
cos
α
λα
⋅Λ
=
Then, the tilted planes of the grating reflect some spectral parts of the coming light to the first order cladding
mode called “ghost” and to the series of higher order cladding modes. Dislike the core reflection that propagates
along the axis of the fibre, the ghost and cladding modes have each other their own angle of propagation βi with
respect to the fibre asis. These angles are pertinent to the fibre core/cladding structure and are only weekly af-
fected by the grating. Both the ghost and the cladding modes are shifted towards the shorter wavelengths, the
shorter the higher is the mode characteristic angle of propagation
Figure 1. Principle of Accelometric sensor.
Figure 2. Spectrum view of reflected light in SM-MM-TFBG structure.

F. Urban
38
0
cos
2cos
i
i
β
β
λα = Λ
Maximum amplitude of the light reflected to the ghost or cladding mode is achieved when the tilt of the grat-
ing planes coincides with the optimum tilt angle αopt = β/2. The situation is shown in the Figure 3. When the re-
flecting planes do not posses the angle αopt then the reflected light from the different sections of the cross section
of the fibre core gets the phase shifts that, conclusively, leads to the decreasing of the energy coupling from the
incident core mode to the desired reflected mode.
3. Cladding Coupling Models
The cladding mode coupling efficiency is affected by the above mentioned cross section phase shift and by the
cross section mode field intensity distribution. To simplify the calculation we have set three model of the fibre
fundamental core mode distribution and from these premises we have figured out the expressions giving the
relative reflection efficiency against the grating tilt angle α.
The first model counts with the equal distribution of the incident mode light intensity within the interval
<-a/2|x, y a/2>, where a variable represents the physical diameter of the fibre core, see the Figure 4. The cou-
pling efficiency factor for this supposition is:
22
00 0
2
cos sin
aa
a
K dxy
πα

=
Λ

∫∫
The second model is represented by the cosine intensity distribution in the fibre core, again in the interval
22
00 0
ππ 2πsin
coscos cos
aa
b
Kxdxyy dy
aa
α


= ⋅⋅
  Λ
 
∫∫
Figure 3. Reflected wave from tilted gratings.
Figure 4. Model 1—incident light intensity distribution.

F. Urban
39
<-a/2|x, y|a/2>,, see the Figure 5. The coupling efficiency factor for this supposition is:
The third model uses the modification of the second one. The cosine core intensity distribution is cut to the
area of rhomb as seen in the Figure 6. The coupling efficiency factor for this supposition is:
22
00 0
ππ 2πsin
coscos cos
aa
y
c
Kxdxyy dy
aa
α
− 
= ⋅⋅
  Λ


∫∫
The resulting curves for the coupling efficiencies to the core reflection mode for all three models with respect
to the tilt angle α are shown in the Figure 7. Experimental results obtained by analysing the TFBGs exposed to
Figure 5. Model 2—incident light inten-
sity distribution.
Figure 6. Model 3—incident light inten-
sity distribution.
Figure 7. Coupling efficiency evaluation.

F. Urban
40
the hydrogenated G.657A fibres with different angles showed the best match of the second model.
Using the second model, we have evaluated the graphs of the coupling efficiency to the core reflection, ghost
and dominant higher order cladding mode. The curves depend greatly on the fibre core diameter, and it is seen
clearly from the comparison of the curve sets for 10µ and 7.5µ fibre cores, see Figure 8 and Figure 9 that the
high efficiency of coupling to the high order modes can be strongly boosted when selecting the tiny core fibre
where the higher tilt angles of the TFBG make sense.
4. Conclusions
According to the results obtained by the above analysis we have selected the optimum angle of tilt for the TFBG
used in the design of the fibre vibration sensor with relative amplitude evaluation. So that to get the Ghost to
Core reflection intensity rate of 2:1 ve have selected the tilt angle of 2˚. The Figure 10 shows the resulting
transmission spectrum of the FTBG designed and exposed accordingly.
Figure 8. Coupling coefficients for 10µ fibre core.
Figure 9. Coupling coefficients for 7.5µ fibre core.

F. Urban
41
Figure 10. Resulting transmission spectrum of the FTBG.
Acknowledgements
This research has been supported by Technology Agency of the Czech Republic under contract TA03010835
“Fiber optic sensors for industrial applications”.
References
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[2] Jacques, A., Shao , L.Y. and Caucheteur, C. (2013) Tilted fiber Bragg Grating Sensor. Laser Photonics Reviews, 7, 83-
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[3] Kashyap, R. (1999) Fiber Bragg Gratings. Academic Press, Sand Diego.
[4] Othonos, A. and Kalli, K. (1999) Fiber Bragg Gratings, Fundamentals and Applications. Artech House, Notwood.