Long Period Grating in Multicore Optical Fiber:
an Ultra-Sensitive Vector Bending Sensor for Low
Curvatures
Pouneh Saffari,
1
Thomas Allsop,
2
Adedotum Adebayo,
2
David Webb,
2
Roger Haynes,
1
Martin M. Roth
1
1
Leibniz-Institut für Astrophysik Potsdam (AIP), An der Sternwarte 16, D-14482 Potsdam, Germany
2
Aston Institute of Photonic Technologies, Aston University, Aston Triangle, Birmingham, B4 7ET, UK
Long period grating were UV inscribed into a multi-core fiber consisting of 120 single mode cores. The multi-core fiber that
hosts the grating was fusion spliced into single mode fiber at both ends. The splice creates a taper transition between the two
types of fiber that produces a non-adiabatic mode evolution; this results in the illumination of all the modes in the multi-core
fiber. The spectral characteristics of this fiber device as a function of curvature were investigated. The device yielded a
significant spectral sensitivity as high as 1.23 nm/m
-1
and 3.57 dB/m
-1
to the ultra-low curvature values from 0 to 1 m
-1
. This
fiber device can also distinguish the orientation of curvature experienced by the fiber by the long period grating attenuation
bands producing either a blue or red wavelength shift. Finite Element Method model was used to investigate the modal
behaviour in multi-core fiber and to predict the phase-matching curves of the long period grating inscribed into multi-core
fiber.
Long Period Grating (LPG) is a large scale (10 µm to
1 mm) periodic perturbation of the refractive index of
the core of a photosensitive single mode optical fiber [1].
The conventional LPG couples the core mode to various
forward propagating cladding modes that fulfill the
phase-matching condition of the grating. Since the
cladding modes suffer from high attenuation as they
are mainly absorbed by the coating layer of the fiber or
scattered out, the transmission spectrum of LPG
consists of a series of attenuation bands [1]. LPGs have
shown potentials in the field of telecommunications [2]
and are a topic of research in environmental sensing
through their sensitivity to strain, bending,
temperature, and the refractive index of surrounding
medium [3]. The LPG’s response to the mentioned
stimuli can manifest itself in two ways: first the
spectral shift of its associated attenuation band
(wavelength shift of stop-bands) and second the change
in the spectral transmission profile of the attenuation
band. Comparing to the traditional Fiber Bragg
Gratings (FBGs), that are more sensitive to the axial
strain and almost insensitive to the curvature
measurements, LPGs are very sensitive to the applied
bending. However, the bending sensitivity of
conventional uniform LPGs, which are written in
standard step index single mode fibers [3], are
independent of the bending orientation. On the other
hand, the ability to determine the direction of the
deformation can be very important for sensors used in
structural health monitoring applications including
monitoring the condition of bridges, cranes, blades of
wind turbines, etc. Therefore there is a high demand
for developing sensors with the ability of measuring
both direction of bend and its amplitude. There are
many successful examples in the literature of
employing standard LPGs in various radially
asymmetric fibers [4-8] or inscribed asymmetric
gratings in radially symmetric fiber [9-16] to create a
directional bend sensor. However, none of the
introduced sensors shows a high sensitivity to small
curvatures and strong directional sensitivity.
Furthermore, complexity and expensive fabrication
approach, as well as the difficulty of splicing some of
these fibers to the ordinary fibers, are considered as
significant drawbacks of these approaches. In this
paper, for the first time to our knowledge, we present a
UV inscribed LPG written into a Multi-Core Fiber
(MCF), which is highly sensitive to bending at low
curvatures and can also sense the orientation of the
curvature. Comparing with the LPGs written in
standard step index fibers no splitting effect,
originating from the induced birefringence [17], was
observed from this device. A Finite Element Method
(FEM) was used to investigate the modal behavior of
MCF, spectral characteristics of the LPG device, and to
predict the phase matching curve and fabrication
design parameters of the LPG device.
FEM modeling (Comsol software) was used to
investigate the possible core and cladding modes that
the MCF would support. A series of simulations were
conducted over a range of wavelengths to obtain the
effective indices of the core and cladding modes.
Fig. 1 (a-d) illustrate the two distinctive classes of
modes: one where most of the light propagates in the
cores, i.e. the “core modes” [presented in Fig. 1 (a, b)];
the other where the light propagates more uniformly
over the whole core and cladding region i.e. the
“cladding modes”, [shown in Fig. 1 (c, d)]. FEM
simulation generated a series of core and cladding
modes. By visual inspection of the generated modes
and using conventional waveguide theory [18], it was
decided that modes with the radial symmetry of the
electric field are the real solutions for FEM model.
Effective index values of approximately 1.45 for the
core and 1.44 to 1.4426 for the cladding modes were
decided for the MCF and used to predict the possible
phase matching condition between core modes, core to
cladding modes, and cladding to cladding modes. Using
the above premises, we obtained 110 core modes and
investigated the coupling coefficients for all of the
modes. It was found that only relatively few significant
coupling between core modes occur and no core modes
coupling meet the phase matching conditions in the
wavelength range of interest.
Fig. 1. Images of modes constructed from FEM modeling
(a) core mode with effective index of 1.44709 (b) core
mode with effective index of 1.44788 (c) cladding modes
with effective index of 1.44261 (d) cladding modes
effective index of 1.44003 at a wavelength of 1500 nm.
The phase matching condition between the guided
mode and the forward propagating cladding modes in
LPG is given by:
(1)
Where and are the propagation constant of
the core mode and cladding modes respectively.
denotes the periodicity of the grating required to
couple the fundamental mode to the n
th
cladding mode.
One can predict the wavelength at which the mode
coupling occurs from the grating period [1]. FEM
simulations were used to predict the phase matching
curves that are presented in Fig. 2 (a) and we can
choose the desired coupling wavelength region of the
LPG by selecting the grating period from these curves.
The MCF employed for the experiment consists of 120
Ge doped silica single mode cores. Each core has a
diameter of 3.9 µm and the distance between the
adjacent cores is 16 µm. The fiber cladding is pure silica
and has an outer diameter of 230 µm. A 10 cm long
length of MCF was first fusion spliced, at both ends, to
the SMF and then the unit was hydrogen loaded at 120
bar and room temperature for a period of two weeks.
LPG was written into the MCF in a single exposure
using a CW- 244 nm frequency-doubled Ar
+
laser
operating at ~ 95 mW. The spot diameter of the laser
beam at the position of fiber was ~120 µm and only
partially covered the cross section of cores within the
MCF (~180 µm). For the LPG fabrication, we employed
point-by-point inscription technique with the scan
velocity of 0.10 mm/s. The respective length and period
of LPG were designed to be 50 mm and 325 µm. The
LPG period was specifically selected for mode coupling
at 1500 nm region. The attenuation band of the LPG
was characterized by employing an Optical Spectrum
Analyzer (OSA) with a resolution of 0.2 nm and a
BroadBand light Source (BBS). Fig. 2 (b) shows the
transmission spectrum of the fabricated device.
Fig. 2. (a) Phase matching curve for LPG written in
MCF using core mode (0) over the wavelength range of
interest (b) Experimental transmission profile of LPG
written in MCF.
The fusion splicing between the SMF and MCF was
visually inspected and the physical dimensions from
SMF to MCF was measured using a microscope system
(Axioskop, Zeiss); it was found that the transition
between the two fibers produced a taper (Fig. 3(a)). The
fiber taper effect on the evolution of the cladding modes
and the core modes (adiabatic or non-adiabatic) across
the taper length was investigated using the slowness
criterion [19-22]. This is done by considering the
magnitude of the rate of change of the radius as a
function of the beat length between the modes being
investigated. These values were compared to the ratio
of taper’s radius to beat lengths of the modes along the
taper length that is shown in Fig. 3 (b). Slowness
criterion for adiabatic mode evolution is given by [18]:
(2)
Where z
b
is the beat length between two modes with
propagation constant of ß
1
and ß
2
, r is the radius of the
fiber along the taper and r/z
b
is the adiabatic length
scale criteria. The modes chosen for analysis were
selected from the phase matching curve shown in Fig. 2
(a) and the satisfied matching condition around the
spectral location of 1500 nm. Three limit curves shown
in Fig. 3 (b) correspond to the particular mode
propagation constants with the larges beat lengths that
were calculated along the taper length using FEM
simulation (Comsol) for the investigated wavelengths :
1400 nm (dotted line), 1500 nm (dashed line) and,1650
nm (solid line). The section lengths of the taper for the
simulation were chosen to ensure that the E-fields do
not significantly change their phase along that section
compared to the light guided in a non-tapered fiber of
the same initial diameter [21].
Tapering caused an overall reduction in the radius of
the MCF from 115 mm to 62.5 mm. Hence, it was
assumed that there was a reduction in the radius of the
cores from 4 µm to 2.1 µm and core separation from 16
µm to 7.8 µm. Therefore, there will be 7 cores from
MCF with direct coupling to the SMF core. Also each
core in the MCF yields a V parameter of ~1.44; this
results in approximately 52% of the intensity
distribution extending out of the cores with an effective
radius of ~ 5 m carrying the major part of the energy.
This implies a significant coupling between cores and
2
)(
01
n
cl
n
cl
01
21
2
,
b
bb
z
z
r
z
r
the cladding especially when the slowness criteria is
investigated and the beat length between the core and
cladding modes ranges upward from 10 m. As shown
in Fig. 3 (a), the taper length is approximately 50 m
thus the beat length is short compared to the length of
the taper and significant coupling occurs across the
cores. Inspecting Fig. 3 (b), section B of the taper
exhibits the condition of non-adiabatic mode evolution;
therefore strong coupling occurs between the core
modes to the cladding modes and the cladding to the
cladding modes whilst sections A and C have adiabatic
condition that implies a negligible power transfer
between the core and the cladding modes. Overall the
section B explains the observed low-loss fiber device
(measured for several prepared samples ~ 2 dB)
created by the union of these two fibers.
Fig. 3 (a). Typical measured geometric profile of a
conical taper/splice between the SMF and MCF (b) The
ratio of taper’s radius to beat lengths of the modes along
the taper length (three slowness criterion- limit curves
for the largest beat lengths calculated for three
wavelengths: 1400 nm (dotted line), 1500 nm (dashed
line) and, 1650 nm (solid line)).
Four fiber devices were fabricated and all subjected
to the bending measurements. For this purpose,
devices were clamped mid-way between two towers on
a flexible V-groove; both clamps were mounted on
translation stages, which were moved inwards to
induce a bend in the groove and hence the attached
device. It should be noted that in order to prevent the
strain cross sensitivity [23] for this set of
measurements, the samples were attached to the
groove from one end while its other end was free.
Furthermore, rotation of the LPG sensors was
performed on this rig by subjecting the sensors to a
series of known curvatures while rotating the sensor
around its clamp. The tags on the fibers were used to
ensure that there was no twist in the fibers during the
experiments and also to indicate the orientation of the
fibers. The experimental setup for bending
measurements is presented in Fig. 4. The light from
the BBS was passed through a broadband polarizer
before illuminating the LPG device. The device’s
curvature is calculated by [6]:
(3)
where L is the half distance between the edges of the
two towers and d is the deflection at the center of the
LPG.
Fig. 4. Schematic diagram of the experimental setup for
bending measurements.
The devices were subjected to a range of curvatures
from 0 to 1 m
-1
and the transmission spectra were
collected using an OSA with the resolution of 0.2 nm.
These measurements were repeated for two opposite
bending directions, convex and concave. A typical
experimental results for a single fiber device are shown
in Fig. 5 (a and b). Inspecting Fig. 5 (a and b), the LPG
attenuation bands exhibit either blue or red
wavelength shift depending on the direction of the
applied curvature while their optical strength reduce
with the increase in curvature value.
Fig. 5. The transmission spectra of the proposed sensor
while it was subjected to a range of (a) convex and, (b)
concave bending curvature from 0 to 1 m
-1
.
Fig. 6 (a) shows the spectral sensitivity of the sensor
when subjected to a range of curvatures in both of the
convex and concave directions. The device exhibits
different linear spectral responses to the convex and
concave curvatures as a result of the asymmetric
inscription of the LPG structure. This leads to the
respective blue and red shift in the central wavelength
of its stop-bands, as seen in Fig. 6 (a). As previously
mentioned, the full cross section of the MCF core
region, ~ 180 µm, is significantly larger than the
inscription beam diameter (~120 µm) resulting in LPG
inscription in only 46 cores of the MCF. Hence the
LPG was written across an asymmetric cross section of
the MCF cores. This device also shows a linear
response to both concave and convex curvatures with
the change in its optical strength shown in Fig. 6 (b).
The device shows the respective sensitivity of 3.57
dB/m
-1
and 3.15 dB/m
-1
for the concave and convex
curvatures. The device yielded a bending sensitivity of
+0.49 nm/m
-1
and 1.23 nm/m
-1
to a low range value (up
to 1 m
-1
) of convex and concave curvatures respectively.
A theoretical investigation into the spectral sensitivity
as a function of curvature was performed using Comsol
(FEM software package) and conformal mapping
technique and found a reasonable agreement with
experimental investigation. The spectral sensitivities of
this sensor are significantly greater in the lower
curvature regime than any other researchers’
published results.
)(
2
22
Ld
d
R
Fig. 6. Response of the proposed sensor to convex and,
concave curvatures in form of (a) wavelength shift (b)
optical strength variation of LPG peak.
The spectral behavior of the sensors in the literature
[6, 7, 10, 11, 14-16] show limited sensitivities in the low
curvature regime, but there are only a few number of
data points resulting in some uncertainty in the
sensitivity measurement in this range [12, 13]. Fig. 6 (a
and b) show a difference in the magnitude of the
device’s sensitivity to the applied convex and concave
curvatures. Considering the large diameter of the
MCF, when it is subjected to a bend, there is a rather
noticeable difference between the amount of curvature
which is experienced by the inner and the outer bend.
The asymmetric structure of the device and also the
inscription orientation of the LPG (realized from the
attached tags on the fiber) suggest that for the concave
measurements the LPG was mainly located at the
inner bend while over the convex measurements it was
situated mostly at the outer bend. As a result, the
spectral sensitivity of LPG, for which the wavelengths
shift of the central LPG peak is measured, for the
convex curvature is almost half of the correspondent
measured value for the concave bending. This suggests
that the LPG was experiencing a larger curvature
during the concave bending measurements. This
argument is further supported by the rate of the optical
intensity variations of the LPG with the applied convex
and concave curvatures; in this case, the bending
sensitivity of the device for convex measurements is
smaller than the concave measurements indicating
that less curvature being experienced by LPG over the
convex measurement.
In this paper, we have introduced a multi-core fiber
based LPG bending sensor with an ultra-high
sensitivity to the applied low curvature values and
capability of detecting the bending orientation. The
fabrication of the LPG was by UV inscription into an
MCF containing 120 photosensitive single mode cores,
for the first time to our knowledge. The detailed
theoretical investigation of mode excitation in MCF is
studied for an MCF that has been fusion spliced to the
SMF-28 at both ends; also the splicing condition and
mode evolution in the tapered region has been
discussed. This fiber sensor has the compelling benefit
of a simple and robust structure, capability of detection
of small deflections with a high resolution and
indicating the direction of the applied bend
simultaneously.
Authors acknowledge the University of Bath for
providing the MCF.
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