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A Novel Low Loss, Highly Birefringent Photonic Crystal Fiber in THz Regime
Hasanuzzaman, G. K. M.; Rana, Sohel; Habib, Selim
Published in:
IEEE Photonics Technology Letters
Link to article, DOI:
10.1109/LPT.2016.2517083
Publication date:
2016
Document Version
Peer reviewed version
Link back to DTU Orbit
Citation (APA):
Hasanuzzaman, G. K. M., Rana, S., & Habib, S. (2016). A Novel Low Loss, Highly Birefringent Photonic Crystal
Fiber in THz Regime. IEEE Photonics Technology Letters, 28(8), 899-902.
https://doi.org/10.1109/LPT.2016.2517083
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1
Abstract—
We report on a new kind of dual-hole unit based
porous-core hexagonal photonic crystal fiber (H-PCF) for low-
loss guidance of THz radiation. The proposed fiber can offer
simultaneously high birefringence and low effective material loss
(EML) in the frequency range of 0.5-0.85 THz with single mode
operation. An air-hole pair is used inside the core instead of
elliptical shaped air-holes to introduce asymmetry for attaining
high birefringence; where the birefringence can be enhanced by
rotating the dual-hole unit axis of orientation. The proposed H-
PCF provides a birefringence of ~0.033 and an EML of
0.43dB/cm at operating frequency of 0.85 THz.
Index Terms—Photonic crystal fiber; Terahertz; High
birefringence; Effective material loss.
I. I
NTRODUCTION
ecently, the limelight has turned towards the latest hot
topic terahertz (THz) band ranging from 0.1 to 10 THz
due to its enormous applications in the field of sensing [1],
imaging [2], security [3], biotechnology [4], spectroscopy [5]
and astronomy [6]. Although, there has been a remarkable
technological advancement in THz wave generation and
detection techniques, still to date most of the THz systems that
are commercially available are based on free space
propagation due to the lack of low loss, flexible and
commercially available waveguides [7, 8]. Albeit, dry air
exhibits lowest absorption and dispersion than other material
in THz band, free space propagation is not enough convenient
due to unavoidable losses introduce during coupling,
transporting and managing THz beam [7-10]. Moreover,
waveguides are indispensable in certain cases; when the
application point is inaccessible, it is required to interact with
the sample strongly and to confine or focus to a smaller spot
size [9]. Still, it is a challenge to implement flexible, efficient
and low-loss transmission of broadband THz waves for long
length delivery. In order to lower the propagation loss of a
THz waveguides, an effective approach is to confine large part
of radiation in air while propagate small portion to material
[11,12].
Different types of THz waveguides have been addressed
both theoretically and experimentally based on metal wires
The authors are with the Department of Electrical and Electronic
Engineering, Rajshahi University of Engineering and Technology, Rajshahi-
6204, Bangladesh (g.kibria82@yahoo.com, selim041073@yahoo.com).
Md. Selim Habib is also with the DTU Fotonik, Department of Photonics
Engineering, Technical University of Denmark, DK-2800 Kgs. Lyngby,
Denmark. (e-mail: seha@fotonik.dtu.dk).
and dielectric sub-wavelength fibers. These include dielectric
metal-coated tubes, metallic wires, Bragg fibers, and all-
dielectric sub-wavelength polymer fibers [13-18]. Though
sub-wavelength fibers and metallic wires exhibit low
absorption loss in THz range, most of the field propagates
outside the waveguide core, thus resulting in strong coupling
to the environment. On the contrary solid core of the
conventional photonic crystal fibers (PCFs) shows a high
material absorption loss [18], which is almost equal to the bulk
material absorption loss. Recently the spotlight has turned to
porous-core photonic crystal fiber, which offers relatively
lower absorption loss than a PCF with porous cladding or
porous-core fiber with air cladding [7,8,11,12]. Along with the
low loss property, high birefringence is also desired in
numerous applications like sensing, communications, and
polarized terahertz filters [10,19]. Two popular methods are
mainly used to achieve high birefringence in porous fibers just
like as conventional PCFs. One is to break the symmetry of
the fiber cladding and another is to introduce asymmetry to the
fiber core [10]. For the first time, Atakaramians et al. [20]
designed and fabricated Polymethyl-methacrylate (PMMA)
based rectangular porous fibers to achieve low loss and high
birefringence. The reported value of birefringence is 0.012 at
f= 0.65 THz. A birefringence level of 10
-2
has been achieved
by Chen et al. [21] by means of a squeezed lattice elliptical-
hole. As elliptical air-holes introduce additional fabrication
challenge and reduce coupling efficiency, this kind of porous
fiber is inconvenient for practical application [10]. A Topas
based porous fiber with a hexagonal array of sub-wavelength
elliptical holes have been identified as a means of achieving
low loss, high birefringence and single mode THz guidance by
Chen et al. [10]. Numerical investigations in [10] show that
birefringence can be enhanced by rotating the major axis
direction of the elliptical air-holes and there exists an optimal
rotating angle at 30°. At this optimal angle a birefringence as
high as 0.0445 can be obtained at a frequency range from 0.73
to 1.22 THz. However, this kind of elliptical air-hole based
fiber is difficult to fabricate and a certain amount of power is
propagating outside the fiber structure due to air cladding.
In this paper, we have demonstrated a novel and relatively
simple technique of attaining high birefringence and low loss
simultaneously without using elliptical air-holes as most of
literature used to achieve high birefringence properties. The
proposed PCF incorporates both a porous-core and also a
porous-cladding of hexagonal array structure. Instead of
inserting single elliptical air-hole we introduced two circular
A Novel Low Loss, Highly Birefringent
Photonic Crystal Fiber in THz Regime
G.K.M. Hasanuzzaman, Student Member, IEEE, Sohel Rana, Md. Selim Habib, Student Member,
IEEE
R
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2
air-holes of same size inside the core, thereby the proposed
fiber provides important manufacturing benefits and we define
the air-hole pair as dual-hole unit. The axis of orientation of
the dual-hole unit is rotated to obtain high birefringence.
Numerical simulations show that rotation angle of 30° exhibits
optimal results at which the fiber exhibits high birefringence
and considerable low absorption loss with single mode
operation.
II. G
EOMETRY
O
F THE PROPOSED DESIGN
The proposed H-PCF is based on a dual-hole unit where the
two small air-holes in one unit can be effectively viewed as an
elliptical air-hole as shown in Fig.1. Hexagonal lattice of three
air-hole rings have been used in both core and cladding to
reduce complexity. In the cladding region, the spacing
between two adjacent air-holes on two adjacent rings is
denoted as Λ
s
. D
core
denotes the core diameter, where diameter
of the core and cladding air-holes are labeled as d
c
and d
respectively (see Fig.1). Λ
c
stands for unit to unit distance
whereas H is the centre to centre distance between two air-
holes of a dual-hole unit. The air-hole diameter to pitch ratio
in the cladding d/Λ
s
is kept 0.90 throughout the simulation.
Furthermore, the orientation of air-holes inside the core at
different rotation angle of the proposed porous-core hexagonal
PCF is depicted in Fig.2. The size and the rotation angle of the
air-holes in the core have a large contribution for attaining
high birefringence and low absorption loss. The parameters
used for the simulations are D
core
=350 µm, d= 286 µm, Λ
s
=
318 µm, Λ
c
=49.3 µm, d
c
= 22.68 µm and H=24.5µm. We used
a cyclic-olefin copolymer (COC) with the trade name TOPAS
as background material. The selection based on of its unique
and beneficial properties which include low bulk material loss
of 0.2 cm
-1
[8], constant refractive index n = 1.5258 in the
THz spectrum which is beneficial for near zero dispersion
[22], humidity insensitivity [12], chemically inertness with
special bio-sensing properties and does not absorb water [12].
Fig. 1. Cross section of proposed hexagonal structure with three air-hole rings in the cladding and three air-hole rings in the core at the rotation angle 90
0
.
Fig. 2. Anti-clockwise rotation of the axis of orientation of dual-hole unit (a) 0
0
(b) 15
0
, and (c) 30
0
.
III. N
UMERICAL RESULTS AND DISCUSSION
In this paper, birefringence is obtained by introducing
asymmetry inside the core. The axis direction of dual-hole unit
might play an important role in introducing asymmetry [10]
and hence the birefringence might be varied when one rotates
the axis direction. Birefringence B can be obtained by the
following equation [12]
||
yx
nnB −=
(1)
where B is the birefringence, n
x
and n
y
are the refractive
indices of x- and y- polarization respectively. The
birefringence as a function of frequency at different rotation
angle is shown in Fig. 3. It is seen from Fig. 3 that the
birefringence increases gradually with the increase of rotation
angle. When the rotation angle becomes 30
0
, the birefringence
reaches the zenith point. Further increment of rotation angle,
there is a decrement of birefringence. The structure of the fiber
and the layout of air-holes in the core explain the angle-
dependent variation. For example, when the angle is rotated to
30°, there exists the most difference of the porosity between
the two orthogonal polarizations directions corresponds to the
maximal birefringence. It should be noted that, when being
rotated to 60°, the geometric configuration of the fiber is
(a) (b)
(c)
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identical to that of unrotated state owing to the six-fold
symmetry of the hexagonal porous fiber.
Fig. 3. Birefringence as function of frequency for different rotation angle.
All simulations in our design are performed under the single
mode condition which is determined by a parameter named V-
parameter expressed by [10]
405.2
2
22
≤−=
clco
nn
c
rf
V
π
(2)
where r is the radius of the fiber core, f is the frequency, c is
the velocity of light in vacuum and n
co
and n
cl
are the effective
indices of the fiber core and cladding respectively. As the
cladding structure is mostly holey, n
cl
can be approximated as
1. V-parameter versus as a function of frequency is depicted in
Fig. 4 which shows that the single mode cutoff frequency is
around 0.85 THz. Although single mode exists at a frequency
lower than 0.5 THz, due to the relatively low value of
birefringence in this band, simulations are performed over 0.5
to 0.85 THz frequency range.
Fig. 4. V-parameter as a function of frequency at optimal rotation angle 30
0
for x- and y- polarization.
Fig. 5. Frequency dependence of birefringence at optimal rotation angle.
Figure 5 depicts the birefringence as function of frequency.
The birefringence as high as ~ 0.033 is achieved at frequency
0.85 THz which is much higher compared with those reported
on Refs. [20-21]. Power flow distribution in the z-direction for
two orthogonal polarization modes at different rotation angle
is shown in Fig.6 at 0.85 THz. The figures indicate that the
mode power is well confined in the fiber core.
Fig. 6. Power flow distributions in the z direction for x- and y- polarization.
Power flow distributions are shown for fundamental modes at 0.85. THz. (a)
(b) and (c) for x-polarization at 0
0
, 15
0
, and 30
0
rotation angles respectively.
(d), (e) and (f) for y-polarization at 0
0
, 15
0
, and 30
0
rotation angle respectively.
Effective material loss (EML) or absorption loss (α
eff
) is
used to investigate the loss property of the PCFs for terahertz
frequencies. Effective material loss can be calculated by the
following equation [22]
∫
∫
=
all
z
A
mat
eff
dAS
dAEn
mat
mat
2
2/1
0
0
)(
2
1
α
µ
ε
α
(3)
where ε
o
and µ
o
are the permittivity and the permeability
respectively in the vacuum, α
mat
is the material absorption loss,
n
mat
is the refractive index of the background material. It
should be pointed out that, in Eq. (3), the integration in the
numerator is only performed over the solid material region
(A
mat
), whereas denominator is performed over all regions.
0.5 0.55 0.6 0.65 0.7 0.75 0.8
0.85
0.005
0.010
0.015
0.020
0.025
0.030
0.035
Frequency (THz)
Birefringence
θ
= 0
0
θ
= 15
0
θ
= 30
0
θ
= 45
0
0.5 0.55 0.6 0.65 0.7 0.75 0.8
0.85
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.6
Frequency(THz)
V parameter
x-polarization
y-polarization
Rotation angle
θ
= 30
0
0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85
0.016
0.018
0.020
0.022
0.024
0.026
0.028
0.030
0.032
0.034
0.036
Frequency (THz)
Birefringence
Rotation angle
θ
= 30
0
(a)
(b)
(c)
(d)
(e)
(f)
X- Pol.
Y- Pol.
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4
Fig. 7. Effective material loss as a function of frequency for x- and y-
polarization at optimal rotation angle
θ
=30
0
.
Figure 7 depicts the effective material loss as a function of
frequency at θ=30
o
. It can be seen that the EMLs of x- and y-
polarization modes are 0.43dB/cm and 0.54dB/cm,
respectively at 0.85 THz. Therefore, the loss of x- polarization
mode is decreased to 50% of its bulk material loss which is
good enough for practical applications. Moreover the EML of
x- polarization is smaller than that of y-polarization. More
electromagnetic fields exist in Topas for y- polarization since
y- polarization’s refractive index is higher than x-polarization.
The variation of refractive index as a function of frequency is
demonstrated in Fig. 8.
Fig. 8. Frequency dependence of effective refractive index for x- and y-
polarization at optimal rotation angle
θ
=30
0
.
Another kind of loss mechanism usually occurred in
photonic crystal fiber is known as confinement loss usually
occurs due to the finite extent of the periodic cladding and is
obtained from the imaginary part of the complex refractive
index, n
eff
is given by
)Im(
2
100
686.8
effCL
n
c
f
=
π
α
dB/cm (4)
where f the frequency of the light is, c is the speed of the light
in vacuum and Im(n
eff
) is the imaginary part of the refractive
index of the guided mode. Confinement loss as a function of
frequency at optimum rotation angle θ= 30
0
is shown in Fig. 9.
It can be observed that calculated value of confinement loss is
far below the level of effective material loss and hence can be
neglected.
Fig. 9. Confinement loss as function of frequency for x- and y-polarization at
optimal rotation angle
θ
=30
0
.
Another important property that represents the power flow
distribution of different regions named fraction of mode power
can be estimated by the following equation [10]
∫
∫
=
all
Z
X
Z
dAS
dAS
'
η
(5)
X may be one of three regions among air-holes in core,
background material and air cladding. Figure 10 shows the
fraction of power in different regions as functions of
frequency for two orthogonal polarization modes at optimum
rotation angle of 30
0
. It is seen from Fig. 10 that about 32.5%
of total power confines in core air-holes for x-polarization and
28% for y-polarization at operating frequency f = 0.85 THz.
One of the most noticeable points is that in this case all the
power is confined inside the waveguide whereas; a fraction of
light energy is transported outside the fiber for porous fiber
with air cladding [10].
Fig. 10. Fraction of power localized in air-core, air cladding and Topas for
both orthogonal polarization modes for 30
0
rotation angle within the single
mode operating region.
Finally, we would like to address the fabrication feasibility
of the proposed design. At present PCFs fabrication is no
0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85
0.30
0.35
0.40
0.45
0.50
0.55
Frequency (THz)
Effective material loss (dB/cm)
x-polarization
y-polarization
Rotation angle
θ
=30
0
0.5 0.55 0.6 0.65 0.7 0.75 0.8
0.85
1.12
1.14
1.16
1.18
1.20
1.22
1.24
1.26
1.281.28
Frequency (THz)
Effective Refractive Index (n
eff
)
x-polarization
y-polarization
Rotation angle
θ
= 30
0
0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85
10
-4
10
-3
10
-2
10
-1
10
0
Frequency (THz)
Confinement Loss (dB/cm)
x-polarization
y-polarization
0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85
10
15
20
25
30
35
40
45
50
55
60
Frequency (THz)
Fraction of power(%)
Rotation Angle = 30
0
Topas x-pol.
air core x-pol.
air cladding x-pol.
Topas y-pol.
air cladding y-pol.
air core y-pol.
