The document describes a novel design of a hexagonal photonic crystal fiber (PCF) with anomalous dispersion and high birefringence. The PCF structure consists of six rings of circular air holes of varying diameters. Simulation results show the designed PCF exhibits very low dispersion of 7 ps/nm/km at 850nm, making it suitable for optical communications. It also shows high birefringence of 3×10−3 at the first optical window, making it useful for fiber optic sensors. The PCF has low confinement loss of 6×10−6 and normalized frequency less than 4.1, confirming it is a single mode fiber. This novel PCF design could be used for applications like supercontinuum generation

1. Photonic crystal fiber with anomalous dispersion
behavior and high birefringence
Abstract— A novel design of hexagonal PCF has been
investigated with variation in areas of circular air holes. The
structure consists of six rings. The three outermost ring has
largest circular air holes. The immediate two rings next to the
innermost ring consists of smallest circular air holes. The
innermost ring consists of circular air holes whose area is lesser
than the three outermost rings but larger than the second and
third ring. The designed fiber reports a very low dispersion.
Moreover a high birefringence is observed at the first optical
window. Besides, normalized frequencies and confinement loss is
also studied. This fiber can be used for generation of broadband
supercontinnum and soliton based devices.
Index Terms—Photonic crystal fiber, dispersion, birefringence,
normalized frequency.
I. INTRODUCTION
At certain wavelength due to the periodic arrangement of a
dielectric, the propagation of light can be suppressed. Basically
in that frequency range even spontaneous emission is not
possible. Periodic arrangement of such dielectric is called
photonic crystal. With the help of technique employed for
making conventional fiber, a two dimensional structure
silica/air were manufactured [1]. Later three dimensional PCFs
were developed [2]. Core cladding silica glass optical fiber has
brought a revolution in communication system. In this regard
PCFs has been superior to conventional fiber. PCFs due to its
various unique properties like birefringence [3], dispersion [4],
endlessly single mode fiber [5], normalized frequency and
other non-linear properties has been a burning topic of
research. Basically PCFs is a special class of fiber or micro-
structured fiber, which allows the light to confine in solid and
hollow cores. The light guiding mechanism in PCFs is of two
types : index guiding [6] and photonic bandgap [7]. In index
guiding mechanism a defect has been created at the centre of
fiber. In photonic bandgap an index contrast between air and
silica is created, for propagation of light. The arrangement of
air holes acts to lower the effective refractive index in the
cladding region and hence the light is confined to the solid
core. As mentioned earlier, PCFs guide light due to index
contrast between solid core and arrangement of air holes in the
cladding region. These holes have great effect on the properties
of PCFs [8]. The number of holes and their sizes effects guided
light, relative to its wavelength in the fiber. Thus it became
possible to design PCFs with some unique properties. PCFs
can be structurally modeled. These structure modification is
made by varying pitch factor, which is hole to hole spacing,
increasing or decreasing diameter of air holes and number of
air holes in the cladding region. In index guided PCFs,
cladding configuration strongly influenced dispersion. These
influence are more intense when the core is made small and
cladding region is made on the scale of wavelength of light [9].
Normal dispersion generally reduces the impact of coherence
degradation [10] for a non-linear device. Hence low value
dispersion is favorable for optical thresholding device. Zero
dispersion are also found to be widely used in pulse
compression [11], optical switching [12], optical parametric
amplification [13]. Asymmetry and imperfections in fiber
profile along with large index contrast structure and small
scale structure leads to birefringence [14]. Birefringence can
also be obtained intentionally by manipulating structure of core
and cladding of fiber [15-16]. Basically two types of
birefringence are observed : phase birefringence and
wavelength dependent birefringence. Highly birefringence
fibers are used for sensor and communication purposes [17-
18]. All guided mode are laky modes. Even PCFs with true
bounded modes, suffer from confinement loss [19-20].
We have investigated a hexagonal six ring PCF structure. The
structure consists of circular air holes of different area. The
simulation results shows that the designed fiber can be used for
communication, high data rate transfer and sensing
applications.
II. PROPOSED STRUCTURE
We have investigated a PCF structure with variation in area of
circular air holes. The structure consists of circular air holes of
three different areas. The arrangement of circular air holes is
such that the inner most ring consist of circular air holes of
largest area. The two rings immediate next to inner most rings
consist of circular air holes of smallest area. The intension for
choosing such a structure is to shape the dispersion curve.
The group velocity of light depends on the optical wavelength
of light and this phenomenon is called dispersion. It can be
obtained by the second order derivative of the real part of the
effective refractive index. However the mathematical
expression to calculate dispersion is [21]:
2
2
( )effd n
D
c d
λ
λ
= − (1)
Where λ is wavelength, c is velocity of light and effn is the
effective refractive index.
Pranaw Kumar, Priyanka Das,
School of Electronics Enginnering
KIIT University, Bhubaneshwar
Kumarpranaw9@gmail.com , dpriyanka752@gmail.com

2. Birefringence is obtained by the difference between the
effective refractive index of the perpendicular polarization
modes. The following mathematical expression can be used to
obtain birefringence [22]:
x y
eff effB n n= − (2)
x
effn and
y
effn are the effective index number in x and y
directions (TE and TM mode).
With the help of the imaginary parts of the effective refractive
index the confinement loss can be obtained for the
corresponding mode. Mathematically:
2
8.868Im( )effCL n
π
λ
= (3)
λ is wavelength and Im( )effn is the imaginary part of
modal index number.
The number of mode of PCF is determined by V number. For a
single mode fiber. The value of V number should be less than
4.1. Normalized frequency can be calculated [23]:
2 2
2eff core effV n nπ
λ
∧
= − (4)
∧ is the pitch factor, coren is the refractive index of core,
effn is the modal index number and λ is wavelength.
Fig. 1(a) PCF structure.
III. SIMULATION RESULTS
A full vector method finite element method has been used
to simulate the design fiber. We have employed optiPDTD
software for simulation proposes. The smallest circular air hole
has a diameter of 0.6 mμ . Circular air holes of largest area
used in the fiber have diameter of 1.4 mμ whereas the other
air holes are of diameter 1 mμ . The refractive index of wafer
taken is 1.46. The pitch factor, center to center spacing of 2
circular air holes, is considered to be 2 mμ . The mess size for
simulation is 0.027 mμ and 0.0291 mμ along x and y
direction respectively.
Fig. 2(a) Dispersion behaviour
The designed fiber reports a very low dispersion at first
optical window. A dispersion of 7 / /ps nm km has been
found at wavelength of 850mm . The low value of dispersion
enables the fiber to be employed for optical communication
purpose.
Fig. 2(b) Birefringence relation.
PCF with higher birefringence have various applications in
fiber optic sensors interferometric system and optical devices.
The investigated fiber reports a birefringence of the order of
3
10−
at the first optical window.
Fig. 2(c) The confinement loss at different wavelength .
The low value of confinement loss assures the ability of
confinement light in PCF is stronger. The result of the
simulated design PCF reports a very low confinement loss. The
reported loss is of order of
6
10−
.
The decrease in the value of normalized frequency or V
number along with increase in wavelength, shows a proper
design which can be fabricated easily. The reported V number
is less than 4.1 proves the PCF to be single mode fiber.

3. Fig. 2(d) The normalised frequency vrs wavelength.
Fig. 2(e) The mode field distribution.
It is to be noted that the mode field distribution of the
simulated fiber shows that the maximum power propagates in
the core of the fiber.
IV. CONCLUSION
Thus we have investigated a new PCF structure with
variation in the area of circular air holes. The arrangement of
circular air holes is made such that the three outermost ring of
the hexagonal structure consists of circular air holes of largest
area and the innermost ring has the circular air holes of
smallest area. Besides, these circular air holes, all the circular
air holes are smaller in size. However the designed fiber
reports a very low dispersion at the first optical window. The
birefringence is very high and is of the order of
3
10−
. Thus we
can conclude that the designed fiber is supposed to be eligible
for high data rate transfer, fiber optic sensor and optical
devices.
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