Modelling and simulation of a porous core photonic crystal fibre for terahertz wave propagation

Abstract

A porous core photonic crystal fibre based on conventional hexagonal lattice cladding is proposed for propagating terahertz radiation. The structure is designed and theoretically investigated using full vectorial finite element method. Simulation results show that at 300 µm core diameter, with a high porosity of 85%, and an operating frequency of 1.3 THz, the proposed fibre reduces the bulk absorption loss of cyclic olefin copolymer (TOPAS) by about 81%, which corresponds to an ultra-low effective material loss value of 0.039 cm−1. Furthermore, the proposed fibre shows near zero dispersion coefficient of 0.47 ps/THz/cm with an extremely small variation of 0.05 over a broad 1.3 THz bandwidth; with confinement and bending losses investigated and found to be negligibly low. It is anticipated that the proposed waveguide can potentially be used for short range transmission of terahertz radiation in the communication window.

Full text

Vol.:(0123456789)
Optical and Quantum Electronics (2019) 51:122
https://doi.org/10.1007/s11082-019-1832-x
1 3
Modelling andsimulation ofaporous core photonic crystal
bre forterahertz wave propagation
IzaddeenK.Yakasai1 · PgEmeroylarionAbas1· SharafatAli2· FerozaBegum1
Received: 2 January 2019 / Accepted: 25 March 2019
© Springer Science+Business Media, LLC, part of Springer Nature 2019
Abstract
A porous core photonic crystal fibre based on conventional hexagonal lattice cladding is
proposed for propagating terahertz radiation. The structure is designed and theoretically
investigated using full vectorial finite element method. Simulation results show that at
300µm core diameter, with a high porosity of 85%, and an operating frequency of 1.3THz,
the proposed fibre reduces the bulk absorption loss of cyclic olefin copolymer (TOPAS) by
about 81%, which corresponds to an ultra-low effective material loss value of 0.039cm−1.
Furthermore, the proposed fibre shows near zero dispersion coefficient of 0.47ps/THz/cm
with an extremely small variation of 0.05 over a broad 1.3THz bandwidth; with confine-
ment and bending losses investigated and found to be negligibly low. It is anticipated that
the proposed waveguide can potentially be used for shortrange transmission of terahertz
radiation in the communication window.
Keywords Terahertz· Porous core photonic crystal fibre· Effective material loss·
Dispersion
1 Introduction
Terahertz (THz) radiation is typically understood to be electromagnetic radiation in the
frequency range from roughly 0.1–10 THz (Ghann and Uddin 2017). Such frequen-
cies are higher than those of radio waves and microwaves, but lower than those of infra-
red light. THz waves have drawn significant research attention over the past decade due
to their potential applications in various fields such as medicine (Siegel 2004), commu-
nications (Nagatsuma etal. 2013), spectroscopy (Tian and Ni 2015), oil and gas amongst
others (Pawar et al. 2013). Transmitting waves belonging to this bandwidth relies on
free space as its low loss transmission channel. Unfortunately, free space transmission is
marred by problems such as sender-receiver misalignment, complex integration with other
* Izaddeen K. Yakasai
17h0892@ubd.edu.bn
1 Faculty ofIntegrated Technologies, Universiti Brunei Darussalam, Jalan Tungku Link,
Gadong1410, BruneiDarussalam
2 Department ofMechanical & Electrical Engineering, School ofFood & Advanced Technology,
Massey University, Auckland, NewZealand

I.K.Yakasai et al.
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122 Page 2 of 16
components, extreme absorption losses instigated by unfavourable atmospheric conditions.
As such, extensive researches have been going on in relation to the guiding of THz waves,
both theoretically and experimentally.
THz wave guides may be loosely grouped into metallic and dielectric waveguides.
Metallic THz waveguides are derived from already popular guiding structures in micro-
wave and radio frequency spectrums. Some examples of THz metallic waveguides include
hollow rectangular/circular waveguides (Gallot et al. 2000), metallic slits waveguides
(Wächter etal. 2007), and coaxial transmission lines (Jeon and Grischkowsky 2004). How-
ever, metallic waveguides are highly dissipative and typically produce high losses (Ata-
karamians etal. 2013). On the other hand, dielectric waveguides or Photonic Crystal Fibers
(PCFs) may be classified into hollow core (Hidaka etal. 2001), solid core (Han etal. 2002)
and porous core waveguides (Atakaramians et al. 2008). Light guidance in hollow-core
PCFs is obtained through a photonic band gap (PBG) effect. The disadvantages of hollow
core PCFs include the restriction of light propagation to only the bandwidth for which the
waveguide was designed, and the exhibition of high propagation losses due to their design
inflexibility (Vincetti 2009). Hence, this type of waveguide is unsuitable for efficient THz
wave propagation. Solid Core PCFs (SC-PCFs) may be viewed as the opposite of hollow
core PCFs. In SC-PCFs, light is guided by modified total internal reflection (MTIR). The
core is typically made of polymer materials while the cladding is made of a material with a
lower refractive index than the polymer, typically air (Atakaramians etal. 2013). Although
SC-PCFs exhibit lower propagation loss than hollow core PCFs, it is still excessively high
for implementation in the THz regime. Moreover, PCFs have also been utilised for several
sensing applications in near, mid and far infrared spectral regions (Islam etal. 2018a, b,
f, 2019). A good choice of polymer material with high transparency in the THz regime
and other favourable optical and physical properties has been shown to reduce the material
absorption losses of SC-PCFs to some degree. Notable materials include Polytetrafluoro-
ethylene (PTFE), popularly known as Teflon (Goto etal. 2004), Polymethyl Methacrylate
(PMMA) (Ziemann etal. 2008), and Cyclic Olefin Copolymer (COC) popularly known as
TOPAS (Johnson etal. 2011). Another way to reduce the absorption loss is by introducing
sub-wavelength air holes in the solid core region to give porous core PCFs (PC-PCFs).
Several designs and characterisations of PC-PCFs for THz wave guidance with core and
cladding structures of different shapes and sizes have been reported in the literature. A
significant progress has been made in enhancing the important guiding characteristics of
PC-PCFs such as the Effective Material Loss (EML), confinement loss and chromatic dis-
persion. However, there is still room for improvement, as some of the proposed PC-PCFs
have shown relatively high attenuation losses and dispersions.
Islam etal. (2018e) reported a modified hexagonal PC-PCF with EML of 0.065cm−1,
Sultana etal. (2018) also proposed an elliptical core PC-PCF with an EML of 0.05cm−1.
Besides the fact that the EML values are comparably high, important PC-PCF proper-
ties such as power fraction and bending loss have also not been investigated in the papers.
Moreover, the flattened dispersion spectrum was also not specified (Islam et al. 2018e).
A hybrid core PC-PCF with 81% porosity has been proposed in Islam etal. (2017a), the
fibre shows poor dispersion of 1.25 ± 0.10 ps/THz/cm within a small 0.2 THz bandwidth
is obtained. Moreover, the bending loss has not been investigated by the authors. Another
PC-PCF comprising of circular cladding and a combination of a rotated hexagonal and
rectangular lattice shapes forming a hybrid structure in the core has been reported in Islam
etal. (2018d). Similarly, the dispersion of the fibre is high with flattened variation over
0.43 THz bandwidth only. Another drawback of the proposal is that the cladding refractive
index has not been exactly calculated but rather speculated around the refractive index of

Modelling andsimulation ofaporous core photonic crystal fibre…
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Page 3 of 16 122
air, and the bending loss of the fibre has also not been investigated. The hybrid PC-PCFs
proposed in Islam etal. (2017b) and Sultana etal. (2017) failed to investigate bending loss
and core power fraction.
In the designs and investigations of PC-PCFs, it is crucial that all important parameters
of the fibre are investigated to ensure suitability for different applications. The PC-PCF
must also yield minimal losses as well as a near zero dispersion, and flattened over a wide
frequency bandwidth. Depending on the application, concentrated power in the core is also
a desirable property. More recently in 2019, Habib and Anower (2019) reported a PC-PCF
with 8 circular air holes in a single layer circular cladding and 13 elliptical air holes in the
core. The PC-PCF demonstrated a high EML of αeff = 0.07cm−1, and comparatively high
dispersion variation of 0.32ps/THz/cm.
In this paper, a single mode PC-PCF incorporating a hexagonal cladding lattice struc-
ture is reported. The objectives of the proposal are to obtain strong modal confinement and
low effective material and bending losses at 1.3THz operating frequency with the majority
of useful power transmitted through the core air holes. Near zero flattened intra modal dis-
persion over a wide frequency bandwidth is also targeted by increasing air filling fraction
and porosity of the core. These important parameters shall allow the fibre to be potentially
used in terahertz communication and single-mode terahertz imaging.
2 Design oftheproposed PC‑PCF
Physical geometry of the proposed structure is shown in Fig.1, consisting of 3 layers; Per-
fectly Matched Layer (PML), porous cladding and porous core on the outermost, middle
and innermost regions, respectively. The polymer materials used in designing SC-PCFs
are also applicable to PC-PCFs. However, TOPAS is used as background material of the
proposed PC-PCF, considering it has a nearly fixed refractive index (n = 1.53) within
0.1–2 THz, which is crucial in achieving negligible material dispersion and comparably
Fig. 1 Cross section of proposed PC-PCF with an enlarged view of the hexagonal core

I.K.Yakasai et al.
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122 Page 4 of 16
low bulk absorption loss of 0.2cm−1 (Cunningham etal. 2011). Other interesting proper-
ties of Topas are its water non-absorbance property (Johnson etal. 2011), insensitivity to
humidity (Yuan etal. 2011) and photosensitivity (Johnson etal. 2011).
As a boundary condition, a cylindrical PML with a thickness of 8% of the total fibre
radius is introduced to prevent reflection of light back onto the fibre. Moreover, the PML is
excluded throughout the iterative computation. The total diameter of the fibre is approxi-
mately 3.3 mm. All 90 air holes in the cladding, arranged in a hexagonal pattern, have
the same diameter d, and with the distance between two adjacent air holes in the cladding
referred to as its pitch Ʌ. A hexagonal lattice pattern is chosen for the cladding to keep the
proposed fibre compact and subsequently, improve confinement of light. Cladding air fill-
ing fraction is given by Fcl = d/Ʌ; with Fcl fixed at a high value to make the air holes com-
pact within the cladding whilst at the same time, preventing overlapping of air holes which
may lead to difficulties during fabrication.
The entire core of the proposed structure is designed inside a circle with diameter Dcore.
As cladding air filling fraction is kept constant, increasing Dcore increases both the diameter
d and pitch Ʌ of air holes in the cladding, and vice versa. Within the core, pitch and diam-
eter of air holes are denoted by Ʌc and dc, respectively. A total of 43 circular-shaped air
holes are introduced in the core; composed of 37 air holes arranged in rotated hexagonal
lattice pattern forming 3 rings, and 6 air holes that have been strategically added and also
arranged in a hexagonal pattern to reduce the amount of material in the core and, by exten-
sion, reducing the overall production cost of the fibre.
The core pitch Ʌc is made proportional to the core diameter, with Ʌc = Dcore/6.8 whilst
air holes diameter dc in the core is determined by the core porosity, expressed as a fraction
of total area of air holes in the core region to the total area of the whole core region. Core
air filling fraction is given by Fco = dc/Ʌc. As such, for a given core diameter Dcore, increas-
ing core porosity increases air holes diameter dc in the core, with core pitch Ʌc remaining
constant and consequently, core air filling fraction Fco also increases. Alternatively, Dcore
may be varied whilst fixing core porosity to a constant value. Increasing Dcore increases Ʌc
and accordingly, reducing core air filling fraction Fco.
The complete finer mesh consists of 154,64 triangular elements, 12,419 boundary ele-
ments, and 540 vertex elements. The total mesh area is 9,775,000µm2 while the average
element quality is 0.96.
3 Numerical characterisation
To theoretically characterize the proposed waveguide, several important optical properties
have to be investigated in relation to different geometrical adjustments. This would help in
the optimisation of parameters of the fibres for potential fabrication. The main properties
investigated are effective material loss (EML), confinement loss, bending loss, core power
fraction, a region of single-mode operation and chromatic dispersion.
3.1 Eective material loss (EML)
The minimisation of effective material loss (EML), which refers to attenuation loss of the
transmitting light due to material absorption, is among the main objectives of designing
PC-PCF. This is because the background material in itself absorbs light in THz frequencies

Modelling andsimulation ofaporous core photonic crystal fibre…
1 3
Page 5 of 16 122
and the loss through this absorption represents a major portion of loss from the fibre. EML
of a PC-PCF may be determined by(Kaijage etal. 2013);
where, ε0 and µ0 are permittivity and permeability of free space, respectively. As TOPAS is
used as background material, nmat and αmat represent the refractive index and bulk material
absorption loss of TOPAS, respectively. E is the modal electric field and Sz is the z compo-
nent of the Poynting vector. PC-PCFs with low EML are needed for potential long-distance
terahertz transmission.
3.2 Connement loss
The confined light in PC-PCFs is characteristically leaky, owing to the finite extent of the
cladding rings. Light is better confined in the core when there are more cladding rings.
However, adding more rings to the cladding structure will make the fibre thicker which
may lead to fabrication complexities. Confinement of light in the core depends on the
imaginary part of the complex effective refractive index and can be estimated using the fol-
lowing equation (Kaijage etal. 2013);
where f is the operating frequency of the fundamental mode, c is the velocity of light in
free space and Im (neff) is the imaginary part of the complex effective refractive index,
neff of the fibre. High confinement loss in THz PC-PCFs could potentially be damaging to
the transmission of THz waves over long and moderate distances as the intensity of light
reduces. In other words, the lower the confinement loss, the better the MTIR guidance and
hence, the greater the light intensity at the receiving end of the transmission.
3.3 Bending loss
Long-haul transmission of electromagnetic waves may require the fibre to be twirled
around a tight spool. A small bend radius may force the angle of incidence to be smaller
than the critical angle; breaking the total internal reflection guiding mechanism, and conse-
quently losing a significant portion of the transmitted THz radiation. Radiation losses that
occur due to bending contribute towards a loss of modal confinement and overall perfor-
mance of an optical fibre. Evaluating actual bending loss is cumbersome, so an analytical
approximation is normally used instead (Kaijage etal. 2013):
where
F(x)=x
−
1
2
e
−
x
,
𝛽
=
2𝜋n
co
𝜆
and
𝛽cl
=
2𝜋ncl
𝜆
are the propagation constants of the core and
cladding, respectively.
nco
is the refractive index of the core whilst ncl is the refractive index
of the cladding. Aeff represents an effective modal area of the fibre.
(1)
α
eff =
√
ε0
μ0
(
∫mat nmat
|
E
|
2αmatdA
∫All SzdA
)
cm−
1
(2)
L
c=8.686

2𝜋f
c
Im

neff

×10−2cm−
1
(3)
α
BL =
1
8

2π
3
1
Aeff
1
𝛽
F




2
3
R

𝛽2−𝛽2
cl
3
2
𝛽2




cm−
1

I.K.Yakasai et al.
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122 Page 6 of 16
Unlike the core refractive index
nco
which may be directly obtained from the simulator, sev-
eral researchers have assumed the cladding refractive index ncl to be unity. However, it cannot
be unity in real sense since there are deposits of TOPAS in the cladding pitch. In general, for a
PC-PCF with cladding air filling fraction Fcl, and background material refractive index ns, the
exact refractive index of the cladding may be calculated using the following expression (Islam
etal. 2017b; Sultana etal. 2017);
The effective modal area Aeff is an estimation of the total area covered by the Gaussian
profile of the fundamental mode, and calculated using the following expression (Islam etal.
2017a):
where I(r) is the electric field intensity in the fibre cross-section.
3.4 Power fraction
Another important criterion that aids in evaluating the performance of PC-PCF is power frac-
tion, which represents the amount of useful power propagated through the core within the
fibre. This important property can be calculated using the following expression (Islam etal.
2017b);
where Sz is the z component of the Poynting vector. As the aim is to determine the percent-
age of power transmitted through the core air holes, the numerator is only integrated over
the core air holes region indicated by x whilst the denominator is integrated over all air
holes and TOPAS regions. A high percentage of power transmission through the core air
holes illustrates that the THz light is confined to the core region, in the low index air holes
inside the core, allowing the intensity of the beam to be concentrated within the core. This
may suggest possible applications of the fibre in THz medical equipment for single mode
imaging.
3.5 Single mode region
It is important to determine the regions for which the proposed fibre supports only one fun-
damental mode per polarization. Single mode propagation is particularly crucial for long-
haul data transmission as it does away with intermodal dispersion issues. For this purpose,
V-parameter or normalised frequency equation is used; which must not exceed 2.405 for single
mode operation (Birks etal. 1997);
(4)
n
cl =
√
Fcl +
(
1−Fcl
)
ns
(5)
Aeff =[∫I(r)rdr]
2
∫I
2
(r)rdr
μm
2
(6)
𝜂
�=
∫
x
S
z
dA
∫
all
S
z
dA ×
100
(7)
V
=
2𝜋rf
c√
n2
co −n2
cl

Modelling andsimulation ofaporous core photonic crystal fibre…
1 3
Page 7 of 16 122
where r is the distance from the core center to the additional core air hole radius and c is
the velocity of light in free space. nco is taken to be the effective refractive index of the fun-
damental mode while ncl, on the other hand, is calculated from Eq.(4).
3.6 Chromatic dispersion
Chromatic dispersion is a major contributing factor to signal quality degradation in optical
fibres and it occurs due to pulse broadening of signals during transmission. It is defined as the
summation of material and waveguide dispersions. However, material dispersion is normally
ignored when TOPAS is used as background material as its value is negligibly low within the
0.1 and 2 THz frequency range (Cunningham etal. 2011). As pulse broadening may result in
high bit error rate of transmission, dispersion of the proposed fibre needs to be sufficiently low
for it to be useful for data transmission. The dispersion of a PC-PCF may be calculated by the
following (Islam etal. 2017b);
where neff is the effective refractive index and ω = 2πf is the angular frequency. Dispersion
is measured in pulse spreading per unit frequency per unit transmitted distance.
It is required that the dispersion profile is sufficient for a PC-PCF to allow pulses transmit-
ted within a wide range of frequency to propagate with almost equal pulse spreading. Low
dispersion PC-PCFs are also crucial for applicability in terahertz sensing and filtering applica-
tions (Aljunid etal. 2016).
4 Simulation results anddiscussions
Finite element method (FEM) with ‘finer mesh’ meshing type was used to investigate the
transmission characteristics of the proposed PC-PCF (Uthman etal. 2012). Figure2a depicts
the distribution of THz light in the core region at frequency f = 1.3 THz, Dcore = 300µm for
80%, 85% and 90% porosity levels. It can be seen that light is more confined to the core at 80%
porosity level, with increased light scattering out from the core as porosity is increased. This
is due to an increase in the amount of air in the core at higher porosities, thereby reducing its
effective refractive index. As a result, light scatters out from the core towards the cladding.
Figure 2b shows the distribution of THz light in the core region at operating frequency of
0.7THz, 1THz, and 1.3THz with core diameter and porosity level kept constant at 300µm
and 85%, respectively. It is shown that more light scatters out of the core at lower operating
frequency than it does at a higher frequency. Given that frequency is directly proportional to
effective refractive index, 1.3THz operating frequency amounts to higher core-cladding index
difference which makes the core optically denser and therefore confines more light.
4.1 Impact ofcore diameter andporosity ontransmission losses
4.1.1 Eective material loss
The relationship between EML and core diameter, for different porosity values at 1.3THz
frequency, is shown in Fig. 3. EML is seen to linearly increase with an increase in core
(8)
𝛽
2=2
c
dneff
d𝜔
+𝜔
c
d
2
neff
d𝜔
2ps∕
THz/cm

I.K.Yakasai et al.
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122 Page 8 of 16
diameter at a fixed operating frequency of 1.3THz. Another noticeable trend from the same
figure is the increase in EML with decreasing porosity levels, particularly at small core
diameters. To explain the first behaviour, increasing Dcore implies increasing the amount of
TOPAS in the core and thus more light is absorbed by the abundant bulk material at high
Dcore values, resulting in higher EML. On the other hand, increasing porosity from 80 to
90% for any particular Dcore, effectively replaces some portion of TOPAS with air and thus,
reducing the amount of TOPAS. Consequently, less light in the core is absorbed, reducing
EML.
For 90% porosity level, the PC-PCF experiences a dramatic rise in EML from around
375–450µm. This is due to breakage in the MTIR guidance as a result of very small core-
cladding index contrast, which consequently allows the guided mode to spread to the clad-
ding area and hence, absorbed by both the material in the core and the affected sections of
the cladding.
Fig. 2 Mode field distribution of THz light in the proposed PC-PCF for different a porosity levels at
Dcore = 300 µm and operating frequency of 1.3 THz, b operating frequencies for Dcore = 300µm and poros-
ity = 85%
Fig. 3 EML of the proposed PC-
PCF for different Dcore and poros-
ity values at 1.3THz operating
frequency

Modelling andsimulation ofaporous core photonic crystal fibre…
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Page 9 of 16 122
4.1.2 Connement loss
Confinement loss is investigated for varying core diameters Dcore and for three porosity
values in Fig.4. It is shown that confinement loss reduces with increased core diameter
and increases with increased core porosity. Both behaviours are connected to the core-
cladding refractive index contrast. When the core diameter is large, the amount of TOPAS
increases in the core. Since TOPAS has higher refractive index than air, more TOPAS in
the core increases the effective refractive index and consequently the index contrast—with
the cladding refractive index remaining constant. High core-cladding index contrast makes
the guidance of light by TIR mechanism stronger and hence, reduces confinement loss. On
the contrary, increasing porosity reduces the amount of TOPAS in the core and therefore,
reduces effective refractive index. This then makes the index contrast very small and, as a
result, weakens the MTIR mechanism which increases confinement loss. For 90% porosity
level, the abundance of low index dry air overcomes the presence of TOPAS even at higher
Dcore values, with confinement loss remaining high even at large core diameter.
4.1.3 Bending loss
The effect of changing core diameters and porosity levels on the bending loss of the PC-
PCF is shown in Fig.5 depicting bending loss at different Dcore for 80%, 85% and 90%
porosity levels, at a fixed operating frequency and bend radius Rb of 1.3 THz and 1 cm,
respectively. The critical bend radius is chosen to be 1cm due to the requirement of exces-
sive force and heat that may distort the fibre geometry if it were to be less than 1cm. Bend-
ing causes the light to escape out of the core with increased bending loss as core diameter
is decreased. 80% porosity level gives the lowest bending loss for all examined core diam-
eters, from the 3 porosity levels considered.
4.1.4 Core power fraction
The percentage of power transmitted through core air holes of the proposed PC-PCF at
1.3 THz operating frequency and different porosity levels across a wide Dcore range is
shown in Fig.6. Figure4 also show that increasing the core diameter increases core-clad-
ding index contrast which improves MTIR guidance mechanism and consequently, reduces
the confinement loss. In terms of core power fraction, this manifests itself in higher core
power fraction as core diameter is increased, as can be seen in Fig.6. Core power fractions
Fig. 4 Confinement loss of the
proposed PC-PCF for differ-
ent Dcore and porosity values at
1.3THz operating frequency

I.K.Yakasai et al.
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122 Page 10 of 16
for both 80% and 85% porosity levels peak at about Dcore = 350µm and remain reasonably
flat for the rest of the examined Dcore range. This is due to the negligibly low confinement
losses within the aforementioned range. For 90% porosity level, core power fraction is very
small in the Dcore range considered in Fig.6, this result tallies the high confinement loss
experienced when the porosity is set to 90% in Fig.4. Although EML is reasonably low for
90% porosity, especially for small Dcore as shown in Fig.3, its confinement loss is almost
ten times the EML as shown in Fig.4. These explain the small percentage of light transmit-
ted through the core air holes at these parameters and hence, the low core power fraction
values. From the 3 porosity levels considered, 80% porosity level exhibits the highest core
power fraction; due to 80% porosity exhibiting the lowest confinement loss.
4.2 Selection ofoptimal design parameters
Given that reducing transmission loss is the major objective of this paper, it becomes
necessary to optimise the geometrical configuration of the proposed fibre. The geometri-
cal parameters need to be fine-tuned in order to optimise the optical characteristics and
enhance propagation of terahertz radiation. Particularly, the optimal core diameter Dcore
and porosity need to be determined, which in turn shall determine other parameters of the
fibre.
To achieve an optimised set of design parameters, the two transmission losses namely;
EML and confinement loss have been summed up to produce a total loss of the fibre.
Fig. 5 Bending loss of the pro-
posed PC-PCF for different Dcore
and porosity values at 1cm bend
radius and 1.3THz operating
frequency
Fig. 6 Core power fraction of the
proposed PC-PCF for differ-
ent Dcore and porosity values at
1.3THz operating frequency

Modelling andsimulation ofaporous core photonic crystal fibre…
1 3
Page 11 of 16 122
Figure7 shows total losses at different Dcore and porosity values, with the inset highlight-
ing the 80% and 85% porosity lines. It can be seen from the figure that 90% porosity level
yields extremely high total loss and as such, may be excluded from consideration. From the
inset, it can be clearly seen that Dcore = 300µm and 85% porosity, results in the lowest total
loss, and thus, is selected as the optimal design parameter of the proposed fibre.
Although confinement loss at 85% porosity value is higher than that with 80% porosity
value, as seen from Fig.4, EML is lower at 85% porosity than at 80% porosity over the
entire Dcore range showed in Fig.5. As the bulk of the losses of the fibre at Dcore ≥ 300µm
come from EML, total loss of the fibre at 85% porosity is consequently lower than at 80%
porosity. It is noted that at the optimal parameter, the majority of the total loss comes from
EML with negligibly low confinement loss.
Figures8, 9 and 10 show the behaviour of EML, confinement and bending losses, total
loss as well as the core power fraction across a wide range of operating frequencies at
optimal design conditions. EML increases with frequency in Fig.8 because more terahertz
light is incident on the absorbent TOPAS in the core at higher frequencies. Also, experi-
mental evidence has shown that the bulk absorption loss of TOPAS and EML increments
as the frequency is increased (Johnson etal. 2011; Yuan etal. 2011) Relationship of con-
finement loss with frequency is also depicted in Fig.8; showing confinement loss reducing
with an increase in frequency. The presence of higher frequency THz light in the core gives
rise to the higher refractive index of the core, which in turn increases core-cladding index
contrast. As a result, confinement loss reduces at higher operating frequencies. Figure9
shows the bending loss of the fibre at two different bending radii over different frequen-
cies. It can be seen that bending loss reduces as the frequency is increased. Also, a smaller
bend radius produces higher bending loss due to disruption of the MTIR mechanism within
the fibre. It is noted that bending loss is negligibly low as compared to EML and confine-
ment loss, and as such may be overlooked. EML, confinement loss and bending loss at
1 cm bending radius, for 1.3 THz operating frequency at optimal design conditions are
0.03906cm−1, 7.8 × 10−4cm−1, and 1.05 × 10−5cm−1, respectively.
Total loss and core power fraction against frequency, are plotted in Fig.10. The fibre
experiences high total loss for operating frequencies below 1 THz as a result of high con-
finement loss in those frequencies. At higher frequency, confinement loss reduces to negli-
gibly low value, with most of the loss coming from EML, resulting in a lower total loss. On
the other hand, core power fraction increases with frequency. As frequency is increased,
most of the power is confined to the core due to the reduction in confinement loss, resulting
Fig. 7 Total loss of the proposed
PC-PCF for different Dcore and
porosity values at 1.3THz oper-
ating frequency

I.K.Yakasai et al.
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122 Page 12 of 16
in higher core power fraction. The total loss for 1.3 THz operating frequency at optimal
design parameters is 0.03985cm−1; which is lower than previously proposed PC-PCFs in
references (Islam etal. 2018e; Sultana etal. 2018), with about 43% of total power transmit-
ted through the low index air holes in the core.
The operating frequencies supporting single mode operation for the proposed fibre at
optimal design parameters is shown in Fig.11; with V-parameter less than the threshold
Fig. 8 EML, confinement and
bending losses at optimal design
parameters
0.6 0.9 1.2 1.5 1.8
0.00
0.02
0.04
0.06
0.08
EML (cm
-1
)
Frequency (THz)
EML
10
-6
10
-4
10
-2
10
0
10
2
L
c
Confinement Loss (cm
-1
)
Fig. 9 Bending loss of the pro-
posed fibre for different operating
frequencies at optimal design
parameters and RB = 1 and 2cm
0.6 0.9 1.2 1.5
1.8
10-20
10-15
10-10
10-5
100
Bending Loss (cm
-1
)
Frequency (THz)
R
B
= 1 cm
R
B
= 2 cm
Fig. 10 Total loss and power
fraction for different operating
frequencies at optimal design
parameters
0.6 0.9 1.2 1.5 1.8
0.0
0.4
0.8
1.2
1.6
Total Loss
Total Loss (cm
-1
)
Frequency (THz)
0
20
40
60
Core Power Fraction
Core Power Fraction (%)

Modelling andsimulation ofaporous core photonic crystal fibre…
1 3
Page 13 of 16 122
for single mode operation within 0.5–1.5THz frequency range. Although the V-param-
eter calculation indicate that higher order modes may exist at operating frequencies
above 1.5THz, modal simulation results indicate that those higher order modes propa-
gate through the cladding region and only fundamental mode will be localised at the
core region (Islam etal. 2018b, c). Therefore, it can be said that the fibre operates as a
single mode PC-PCF and can, therefore, be potentially used for single-mode terahertz
industrial applications.
Dispersion of the proposed PC-PCF at different frequencies at optimal design condi-
tions is given in Fig.12. It is observed that dispersion is close to zero and ultra-flattened
across a wide frequency bandwidth, with a dispersion of β2 = 0.4725ps/THz/cm, and a
variation of 0.0584ps/THz/cm within 0.4–1.7 THz frequency range (1.3 THz frequency
bandwidth). The dispersion characteristics is better than previously proposed PC-PCFs
in references (Habib and Anower 2019; Islam etal. 2017a, b, 2018e, d; Sultana et al.
2017, 2018). At operating frequency of 1.3 THz, dispersion of the PC-PCF is 0.5203ps/
THz/cm. Moreover, a comparison with some recently published PC-PCF structures is
presented in Table1. It can be observed from the table that the proposed PC-PCF dem-
onstrates superior near-zero ultra-flattened dispersion variation and comparably low
EML. Moreover, the extent of the proposed fibre’s flexibility has been ascertained. The
bending profile of the fibre may be integrated into compact terahertz systems such as
THz endoscopy system (Grischkowsky 2014).
Fig. 11 V-parameter of the pro-
posed fibre for different operating
frequencies at optimal design
parameters
0.6 0.9 1.21.5 1.
8
0.5
1.0
1.5
2.0
2.5
3.0
3.5
V Parameter
Frequency (THz)
Optimal
V = 2.405
Fig. 12 Dispersion variation of
the proposed PC-PCF at optimal
design conditions
0.6 0.9 1.2 1.5
1.8
-1
0
1
2
3
4
5
Dispersion (ps/THz/cm)
Frequency (THz)
Optimum
0.05 ps/THz/cm

I.K.Yakasai et al.
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122 Page 14 of 16
5 Conclusion
A hexagonal cladded porous core photonic crystal fibre with TOPAS as background mate-
rial was proposed, resulting in extremely low total loss of about 0.04 cm−1 at an operat-
ing frequency of 1.3 THz. 300µm core diameter and 85% porosity were shown to be the
optimal parameters for the designed fibre. It has been shown that 43% of useful power is
propagated through the core air holes with a reasonable low EML value of 0.039cm−1.
Confinement and bending losses have also been shown to be negligibly low with near-zero
flattened dispersion profile of 0.47 ± 0.05ps/THz/cm flattened over a wide 1.3 THz band-
width. This has the effect of improving the information capacity of the PC-PCF. It is envis-
aged that the proposed PC-PCF may potentially be used for long-haul transmission of tera-
hertz radiation in the communication window as well as for non-polarisation demanding
terahertz applications.
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