Design and optimization of photonic crystal fiber for liquid sensing applications
Citation: Md. Faizul Huq ARIF, Kawsar AHMED, Sayed ASADUZZAMAN, and Md. Abul Kalam AZAD, “Design and Optimization
of Photonic Crystal Fiber for Liquid Sensing Applications,” Photonic Sensors
Design and Optimization of Photonic Crystal Fiber for Liquid Sensing Applications
Corresponding author: Kawsar AHMED 2
Md. Faizul Huq ARIF 1 2
Kawsar AHMED 1 2
Sayed ASADUZZAMAN 1 2
Md. Abul Kalam AZAD 0 2
0 Department of Material and Metallurgical Engineering (MME), Bangladesh University of Engineering and Technology
1 Department of Information and Communication Technology (ICT), Mawlana Bhashani Science and Technology
2 University (BUET) , Dhaka-1000 , Bangladesh
This paper proposes a hexagonal photonic crystal fiber (H-PCF) structure with high relative sensitivity for liquid sensing; in which both core and cladding are microstructures. Numerical investigation is carried out by employing the full vectorial finite element method (FEM). The analysis has been done in four stages of the proposed structure. The investigation shows that the proposed structure achieves higher relative sensitivity by increasing the diameter of the innermost ring air holes in the cladding. Moreover, placing a single channel instead of using a group of tiny channels increases the relative sensitivity effectively. Investigating the effects of different parameters, the optimized structure shows significantly higher relative sensitivity with a low confinement loss.
Photonic crystal fiber (PCF); liquid sensor; microstructure core; sensitivity; confinement loss
The field of fiber optics is no longer limited into
telecommunication and medical science only; it has
been developing in an incredible pace with large
dimensions of applications. Fiber optic technologies
have made a revolutionary change after the
invention of photonic crystal fiber (PCF). PCF is a
new class of optical fiber which is one of the recent
inventions in the field of fiber optics. PCF can be
used as a transmission media as well as optical
functional devices. In contrast to the conventional
optical fiber, PCFs have additional design features,
such as air-hole diameter, pitch size, and number of
rings, which offer to overcome many limitations of
Due to the well-known advantages, such as
enhanced design freedom, low cost, short-time
detection, small size, robustness, and high sensitivity
and flexibility PCFs have received considerable
attention in developing optodevices and sensors.
Photonic crystal fibers (PCFs) have been attracted a
great deal of attention for its incredible performance
and large variety of applications. PCF can be used as
], switches [
], electro-optical modulators
], polarization converters [
], sensors [
etc. PCF based sensors are smart applications in
fiber optic technology which have been
investigating and developing since last decade. A
wide range of sensing applications of PCF are
available, such as temperature sensors [
index (R.I) sensors [
], chemical sensors [
mechanical sensors [
], pressure sensors [
], stress sensors , pH sensors [
liquid sensors [
], biosensors [
], and so on. An
ideal candidate of optical sensors is index guiding
PCF. The sensing mechanism of index guiding PCF
is evanescent interaction between the optical field
and the analyte to be sensed. The evanescent field
based PCF sensors have been developing rapidly for
chemical and biomedical applications due to their
Highly sensitive chemical (liquid and gas)
sensors are playing an important role in the
industrial processes [
] especially for detecting
toxic and flammable chemicals (e.g., toxic gasses or
liquids) to overcome the safety issues. So it has
become one of the key challenges to enhance the
performance of liquid and gas sensors. In recent
years, researchers are keeping much interest on the
development of photonic crystal fiber (PCF) based
sensors for environmental and safety monitoring [
] issues. Photonic crystal fiber based liquid and
gas sensors through the evanescent field show
excellent performance in terms of sensitivity,
because core of the PCF directly interacts with the
material to be analyzed.
PCF technologies allow for the accurate tuning
of fiber through changing the air hole shape, size,
and their position. A wide variety of PCF based
sensing techniques have been reported by changing
different geometric parameters of the PCF to gain
sensitivity at a maximum and confinement loss at a
minimum satisfactory level in liquid and gas sensing
applications. J. Park et al. [
] enhanced relative
sensitivity for chemical sensing, using a hexagonal
PCF with a hollow high indexed ring defect. In the
hollow core PCF, the direct interaction between light
and the analyte in the hollow channel is higher than
the index-guided PCFs. Recently, the idea of filling
core or cladding holes with various liquids or gases
has been attracted much to the researchers. Cordeiro
et al. [
] proposed a microstructure core PCF
infiltrated with liquid analyte which enhanced the
evanescent field. This concept introduced the
sensing potentiality with infiltrated microstructure
core. PCF of microstructure core offers to sense low
indexed material because of the highly interaction of
evanescent fields with the analyst to be sensed. A
large number of published papers investigated and
enhanced the performance of PCF based gas and
liquid sensors with microstructure core [
In recent study, higher sensitivity and lower
confinement loss of microstructure core PCF for
liquid sensing have been attempted by using
octagonal cladding structure [
]. Reference 
suggested 5-ring octagonal PCF for higher
sensitivity and lower confinement loss; but in
practical manufacturing octagonal structure requires
extra more capillaries than the hexagonal structure.
Keeping large number of capillaries will make high
cost to fabricate. In this point of view, liquid sensing
using a single infiltrated channel may also reduce
the complexity of the core. To the best of our
knowledge, no studies have been done in analyzing
the sensitivity performance of PCF with a liquid
filled core of a single channel.
In this research work, we have proposed and
optimized simple evanescent hexagonal structure of
PCF (H-PCF) with microstructure core and cladding
for liquid sensing, which shows high relative
sensitivity as well as low confinement loss. We have
also explained the effect of single infiltrated channel
replacing the microstructure core by proposing
another structure of PCF, which achieved more
enhancements of relative sensitivity and simplicity
in design. We have not used any defect around the
hollow core; though one of the previous articles [
enhanced relative sensitivity by using a ring defect
around the core. The relative sensitivity and
confinement loss against different liquids (water,
ethanol, and benzyne) have been investigated and
compared. Although we have chosen water, ethanol,
and benzyne as the targeted chemical species for
characterization of our structures but these structures
and the mechanism can be applied for all fluids and
gases based on the absorption line of the targeted
2. Design principle
Figure 1 shows the transverse cross sectional
view of the four stages of our proposed PCF
structure. The proposed PCF contains only four
layers of air holes in the cladding. The distance
between center and center of two adjacent air holes
(pitch distance) has been denoted by . The
diameters of air holes in the innermost ring, second
ring, third ring, and outermost ring are d1, d2, d3, and
d4, respectively. In PCF1, the diameter of all air
holes is equal, where d1=d2=d3=d4.
In our numerical investigation, we found that the
outermost ring holes diameter has greater impact on
the confinement loss, and then we have come into
PCF2. In PCF2, d1=d2=d3<d4. Another result of our
numerical investigation shows that larger diameter
of the innermost ring holes enhances the sensitivity
and we have turned into PCF3. In PCF3, optimized
values of air holes diameter have been kept as
d2=d3<d1=d4. However, we have turned into PCF4
and achieved higher sensitivity by replacing the
group of tiny holes with a single hollow core filled
with same analyte to be detected. The hollow core
area is same as the area covered by supplementary
tiny holes. In the PCF1, PCF2, and PCF3, the core is
designed with some tiny holes in circular form
which are filled with various liquid samples: water,
ethanol, and benzyne for this study. These
supplementary core holes are arranged with the hole
to hole pitch distance denoted by a. Figure 2
visualizes the enlarged view of core of PCF1, PCF2,
PCF3, and the replacement of hollow channel instead
of using a group of tiny channels in PCF4. Diameter
of the hollow channel is D2=1.70 m, which is same
as the diameter of the region of supplementary holes
in the core (D1=D2).
Figure 3 shows the computational region of the
proposed PCF3 and PCF4, which is divided into
homogeneous triangular pieces forming a mesh.
Each of the PCFs has two orthogonal sides of the
computational region which are assigned with two
artificial boundary conditions: perfect electric
conductor (PEC) and perfect magnetic conductor
(PMC). Perfectly matched layer (PML) is used as a
boundary condition. Thickness of the PML is fixed
to 10% of the radius of the proposed PCFs for
efficient calculation of confinement loss [
d4 d3 d2 d1
d4 d3 d2 d1
Fig. 1 Transverse cross sectional view of (a) PCF1, (b) PCF2,
(c) PCF3, and (d) PCF4.
Fig. 2 Enlarged view of core region of (a) PCF1, PCF2, and
PCF3 and (b) PCF4.
3. Principles of operation
PCFs act as a waveguide, and in this wave guide,
d4 d3 d2 d1
d4 d3 d2 d1
and the targeted analyte and light interact with each
other. We have analyzed the evanescent field
distribution of the proposed PCFs. Using the finite
element method (FEM), the properties of
propagating mode of the proposed PCFs is
numerically investigated. We have considered
circular perfectly matched layer (PML) as a
boundary condition. The cross sections of the
proposed PCFs are divided into homogeneous
triangular subspaces using mesh analysis shown in
Fig. 3. The liquid filled air holes’ region is then
divided into many sub-domains which are either
triangular or quadrilateral in shape. Using FEM,
Maxwell’s equations are solved by accounting
neighboring subspaces. As the wave propagates
through z direction, the modal analysis has been
performed in the x-y plane of the PCF structure. The
following vectorial wave equation can be derived
from the Maxwell’s equation [
Fig. 3 FEM meshes and boundary conditions for
computation of (a) PCF3 and (b) PCF4.
(S1 E) k02n2SE 0
where S represents the PML matrix of 3×3 and
S1 is the inverse of S matrix. The symbol E
denotes the electric field vector, n is the refractive
index of the domain, K0 is the wave number in free
space, and is the operating wavelength. The
propagating constant is represented by the
Due to the finite number of air holes in the
cladding part, there may cause leakage of light. The
leakage of light from core to exterior materials
results in confinement loss (dB/m) which can be
obtained from the imaginary part of neff by using the
following equation [
Lc 8.868 K0 Im[neff ]dB/m .
However, this leakage of light energy can be
omitted by using an infinite number of air holes. But
in practical, the number of air holes is finite.
The relative sensitivity coefficient measures the
interaction between the light and the analyte to be
sensed. This interaction is measured through the
absorption coefficient at a particular wavelength.
According to the Beer-Lambert law, light is
attenuated by the intensity of absorption of
evanescent wave [
I( ) I0( ) exp[r mlc ] (4)
The absorbance of the sample to be detected is
defined by the following equation [
A lg I0 r mlc (5)
where I and I0 are the input and output intensities,
respectively, and c is the concentration of absorbing
material. The length of the channel is l. The function
of absorption coefficient is m( ) , and r is the
relative sensitivity coefficient, which can be defined
by the following equation [
r nnerff f (6)
where nr refers to the refractive index of the sample
to be sensed, and neff is the effective index of the
guided mode. f is the fraction of total power located
in the core, and it is also known as a power
distribution function [
] by using Poynting’s
theorem which can be expressed as the following
f holes Re(ExH y EyH x )dxdy
total Re(ExH y EyH x )dxdy
where Ex and Hx are transverse electric field and
PCF1, n=1.330, X-polarization
PCF2, n=1.330, X-polarization
PCF3, n=1.330, X-polarization
1.340.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6
Fig. 4 Effective index curves of the fundamental mode for
the X-polarization with =2.4 m, d=0.45 m. PCF1:
d1=d2=d3=d4=1.9 m; PCF2: d1=d2=d3=1.9 m and d4=
2.15 m; PCF3: d2=d3=1.9 m and d1=d4=2.15 m.
4. Results and discussion
This section describes the numerical analysis of
propagation characteristics in fundamental mode and
some higher order modes of the proposed PCFs.
Three liquid analytes, water, ethanol, and benzyne,
have been selected for filling the supplementary core
holes. Here, it has been considered X-polarization of
fundamental mode for this investigation. The initial
analysis has been performed by assuming the
geometric parameters of PCF1: d1=d2=d3=d4=1.9 m;
PCF2: d1=d2=d3=1.9 m and d4=2.15 m; PCF3:
d2=d3=1.9 m and d1=d4=2.15 m. The
supplementary holes pitch ratio is d/a=0.70. The
center-to-center air holes distance is =2.4 m at the
cladding, which has been kept fixed for all of the
proposed PCFs. The simulation has been performed
at a wide range of wavelength from 0.6 m to 1.6 m.
The simulation process has been down using
COMSOL Multiphysics 4.2 by selecting a fine mode
of mesh size. The convergence error seems very low
of proposed PCFs about 3.55×10−5% and 3.50×
10−5 % for PCF3 and PCF4, respectively.
magnetic field respectively; Ey and Hx are
longitudinal electric field and magnetic field
respectively. Using FEM the mode field pattern and
effective index are obtained. During the simulation,
we have considered the material dispersion of silica
background using the Sellmeier equation [
Initially, Fig. 4 shows the effective index profile
of PCF1, PCF2, and PCF3. It is clear from Fig. 4 that
the effective indices decrease linearly with an
increase in wavelength. It can be evidently seen that
the PCF1 shows higher effective index values among
the first three proposed PCFs.
PCF1, d1/=d2/=d3/=d4/=0.83, n=1.366
10 PCF2, d1/=d2/=d3/=0.83, d4/=0.93, n=1.366
PCF3, d2/=d3/=0.83, d1/=d4/=0.93, n=1.366
0.6 0.7 0.8 0.9 1W.0avele1n.g1th (m1.)2 1.3 1.4 1.5 1.6
Fig. 5 Comparison of the relative sensitivity of PCF1, PCF2,
and PCF3 for (a) water, (b) ethanol, and (c) benzyne, where
=2.4 m, d=0.45 m. PCF1: d1=d2=d3=d4=1.9 m; PCF2:
d1=d2=d3=1.9 m, and d4=2.15 m; PCF3: d2=d3=1.9 m, and
PCF1, d1/=d2/=d3/=d4/=0.83, n=1.33
PCF2, d1/=d2/=d3/=0.83, d4/=0.93, n=1.33
PCF3, d2/=d3/=0.83, d1/=d4/=0.93, n=1.33
0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6
PCF1, d1/=d2/=d3/=d4/=0.83, n=1.354
PCF2, d1/=d2/=d3/=0.83, d4/=0.93, n=1.354
PCF3, d2/=d3/=0.83, d1/=d4/=0.93, n=1.354
0.6 0.7 0.8 0.9 1W.0avele1n.g1th (m1.)2 1.3 1.4 1.5 1.6
Figure 5 presents the relative sensitivity curves
of PCF1, PCF2, and PCF3 for the three analytes as a
function of wavelength. There is no significant
change in sensitivity for PCF1 and PCF2 in all
wavelengths. Therefore, no significant impacts on
sensitivity have been observed with increasing
diameters of outer rings holes. However, the relative
sensitivity of PCF3 is greatly enhanced. At the
wavelength =1.33 m, for water, ethanol, and
benzyne, the calculated sensitivity of PCF3 is 30%,
32.5%, and 33.67%, respectively and the
confinement loss is 3.25×10−10 dB/m,
2.95×10−10 dB/m, and 2.31×10−10 dB/m, respectively.
The reason behind the enhanced sensitivity of PCF3
is that the increment of the inner ring holes diameter
leads them closer to the core area and the fraction of
evanescent field penetrates to the holes increase and
relative sensitivity of the PCF3 increases
consequently. It is also clear that higher index
material shows higher relative sensitivity.
Figure 6 illustrates the relative sensitivity
performance of PCF3 varying the diameter (d) of the
supplementary holes in the core region. According
to this inquiry, the sensitivity increases with the
increment of the diameter of supplementary holes.
From Fig. 6, we have found the highest relative
sensitivity when d=0.55 m. For this value of the
supplementary holes diameter, PCF3 shows relative
sensitivity 48.50% and 47.78%, and confinement
loss 1.28×10−10 dB/m and 5.37×10−11 dB/m for
ethanol and water, respectively, at the wavelength
To achieve much more relative sensitivity, we
have proposed PCF4 replacing a single hollow
channel instead of using supplementary tiny holes.
In PCF4, the diameter of the hollow channel is
D2=1.70 m. Figure 7 depicts the comparative
performance of sensitivity of the last two proposed
PCFs: PCF3 and PCF4 for all types of analytes used
in this study. According to Fig. 7, PCF4 shows great
enhancement of relative sensitivity. At the
wavelength =1.33 m, PCF4 exhibits the relative
sensitivity 50%, 55.83%, and 59.07%, confinement
loss 4.25×10−10 dB/m, 8.72×10−10 dB/m, and
2.56×10−10 dB/m for water, ethanol, and benzyne,
d1/=d4/=0.93, d2/=d3/=0.83, n=1.354, d=0.45 m
d1/=d4/=0.93, d2/=d3/=0.83, n=1.354, d=0.50 m
d1/=d4/=0.93, d2/=d3/=0.83, n=1.354, d=0.55 m
0.6 0.7 0.8 0.9 1W.0avele1n.g1th (m1.)2 1.3 1.4 1.5 1.6
d1/=d4/=0.93, d2/=d3/=0.83, n=1.33, d=0.45 m
d1/=d4/=0.93, d2/=d3/=0.83, n=1.33, d=0.50 m
d1/=d4/=0.93, d2/=d3/=0.83, n=1.33, d=0.55 m
0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6
Fig. 6 Comparison of relative sensitivity of PCF3 as a
function of operating wavelength for (a) ethanol (b) water;
where d=0.45 m, d=0.50 m, d=0.55 m, and rest of the
parameters are fixed as before.
10 PCF4, n=1.354
Fig. 70.R6ela0t.7ive 0s.8ensi0t.9ivity1W.0avveelre1ns.gu1ths(wm1.)2avel1e.3ngth1.4 for1.5PCF13.6 a nd
PCF4 with =2.4 µm, d=0.55m, D2=1.70 m, d2=d3=1.9 m,
and d1=d4=2.15 m.
Figure 8 presents the confinement loss curves of
PCF3 and PCF4. With the investigation of Fig. 8, it
can be seen that PCF4 exhibits better performance in
terms of confinement loss for all types of analytes
used in this study. Therefore, it can be said that the
light mode is more confined in the core region for
the proposed PCF4 compared with the first three
proposed PCF structures. This may be linked to the
fact that the electromagnetic interaction between the
propagated light and analyte is higher which causes
an increase in relative sensitivity. In addition, from
Fig. 8, it can be found that lower confinement losses
are achieved with higher indexed liquids. According
to the overall discussion, PCF4 shows higher
sensitivity and lower confinement loss than PCF3.
10120.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6
Fig. 8 Confinement loss versus wavelength for PCF3 a nd
PCF4 with =2.4 µm, d=0.55 µm, D2=1.70 µm, d2=d3=1.9 m,
and d1= d4=2.15 m.
In order to support the numerical results reported
in the figures, the electric field distribution of the
proposed PCF3 and PCF4 has been illustrated in
Fig. 9, where the operating wavelength is set to
=1.33 m and the core holes are filled with ethanol.
It can be clearly seen that the fundamental mode of
our optimized PCFs (PCF3 and PCF4) is tightly
confined in the core region.
From the overall discussion, we have found that
our designed structures show better performance in
relative sensitivity with more design simplicity than
the prior structures [
] for liquid sensing.
Table 1 shows the comparative performance analysis
shape: 3 rings
shape: 5 rings
shape: 4 rings
shape: 4 rings
between prior PCFs and proposed PCFs for liquid
sensing at the wavelength =1.33 m. Tables 2 and 3
represent the sensitivity dependency on diameters
and global parameters variations, respectively.
Although, diameters are varied after fabrication but
it has no global effects on result of the proposed
Through the experimental point of view, the
fabrication feasibility of the proposed PCFs is an
important part. It seems that the fabrication process
of the micro cored region may not be easy. However,
due to the technological advancement, the
fabrication of our recommended PCFs is possible.
Micro core must be filled with the analyte without
damaging the fiber’s integrity. Now, several
techniques are available for filling the PCF holes
with analytes. Huang et al. [
] proposed a unique
method for selectively filling the all cladding holes
as well as micro core holes. The fabrication of PCF
with liquid filled core or cladding can be
accomplished with the same method [
applying the sol-gel technique  any kind of
complexity of fabrication of microstructure optical
fiber can be removed. In this regard, our proposed
PCF structures can be fabricated with the currently
available nanotechnology. Selective filling technique
] can be used for fill the analytes (gas or liquids)
at the core.
performance of the PCF based liquid sensor has
been done by our recommended two structures of
PCF, which are based on microstructure core and
hollow core, and infiltrated with the liquid to be
All of the
microstructure core and liquid core have better
guiding capability and the manufacturing of this
type of structure is possible with the current
nanofabrication techniques [
]. Our proposed
PCF provided higher relative sensitivity with tighter
confinement of optical field than the prior PCF
structures. Therefore, our proposed
successfully overcome the critical trade-off between
confinement loss and sensitivity, and it is assumed
that our proposed structures of PCF offer great
potentiality for toxic chemical and gas detection in
industrial safety purposes.
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indicate if changes were made.
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