Engineering, 2010, 2, 608-616
doi:10.4236/eng.2010.28078 Published Online August 2010 (http://www.SciRP.org/journal/eng).
Highly Nonlinear Bending-Insensitive Birefringent
Photonic Crystal Fibres
Huseyin Ademgil, Shyqyri Haxha, Fathi AbdelMalek
Broadband and wireless communication group, School of Engineering and Digital Arts, University of Kent,
Canterbury, UK
Received May 20, 2010; revised July 21, 2010; accepted July 23, 2010
Abstract
Highly nonlinear birefringent Photonic Crystal Fibre (PCF) that exhibits low losses and small effective mode
area across a wide wavelength range has been presented. The effects of angular orientation on bending losses
of the proposed PCFs have been thoroughly investigated by employing a full vectorial finite element method
(FEM). It has been demonstrated that it is possible to design a bending-insensitive nonlinear PCF with a bi-
refringence in the order of 10-2 and a nonlinear coefficient of 49 W-1km-1 at the wavelength of 1.55 μm. Also,
significant improvements on key propagation characteristics of the proposed PCFs have been demonstrated
by carefully altering the desired air hole diameters and the hole-to-hole spacing. It is demonstrated that two
zero dispersion wavelengths can be achieved by the proposed design.
Keywords: Nonlinear Coefficient, Effective Mode Area, Confinement Loss and Birefringence
1. Introduction
Photonic Crystal Fibers consisting of a central defect
region in a regular lattice of air holes have attracted sig-
nificant research attention. These fibers provide extra
degrees of freedom in manipulating optical properties
[1-2]. PCFs can be divided into two categories according
to the mechanism used to guide the light: photonic-band-
gap (PBG) guidance and effective index guidance. The
PBG fibers use a perfectly periodic structure exhibiting a
PBG effect of the crystal lattice at the operating wave-
length to guide light in a low-index core region. In PBG
fibres, the core can be created from the lower refractive
index material, which could be solid glass or a large air
hole (in the case of an air-glass PCF) [3-5]. On the other
hand, the effective index-guiding PCFs rely on total in-
ternal reflection (TIR) to confine light in the region of
missing air hole forming a central core. The presence of
air holes decreases the effective index of the cladding,
making light guidance possible by TIR. This guiding
method is more analogous to the operation of a conven-
tional step-index fibre [1,3,6].
PCFs have remarkable properties, strongly depending
on the design details such as low sensitivity to bend loss-
es even for high mode areas, where, low or high mode
areas leading to very strong or weak optical nonlineari-
ties. PCF technology, now allows the fabrication of fi-
bers with very tightly confined modes, and thus very
high optical nonlinearities per unit length. Indeed, index-
guided PCFs can have nonlinearity 10-100 times that of a
conventional silica fiber [7,8]. Birefringent PCFs can
simply be realised [9] compared to conventional fibres,
since the refractive index contrast between the core and
the cladding is higher than the refractive index contrast
of conventional fibres. Additionally to nonlinearities,
growing interest is being shown in birefringence study in
PCFs. There are different ways of designing birefringent
fibres, such as use of anisotropic materials. However, for
nominally isotropic silica fibres, the usual method is to
create a spatial asymmetry in the index or shape profile
by applying a stress to the fibre [9-11].
Birefringence is used in many sensing applications and
in applications where light is required to maintain a lin-
ear polarization state. In this regard, PCFs are considered
to be good candidates for applications requiring high
temperature insensitivity and high birefringence [12-13].
Indeed, PCFs can have birefringence much larger than
that of the conventional PANDA fibres [10]. To increase
the effective index difference between the two orthogo-
nal polarization modes and achieve birefringent PCFs the
structural asymmetry can be achieved by altering the air
hole sizes near the core area [6,14]. Alternatively, by
distorting the shape of the air holes (elliptical air holes)
[11-12] birefringence can be achieved. Previously pub-

H. ADEMGIL ET AL. 609
lished results by Yue et al. [11] and Sun et al. [12] have
demonstrated that it is possible to design PCFs with rela-
tively large birefringence in the order of 10-3-10-2. To our
knowledge proposed PCFs with elliptical air holes [11-
12] exhibit the highest birefringence to date. However,
fabrication becomes challenging by the use of several
rings of elliptical air holes in cladding region. Moreover,
controlling the elliptical air holes during the fabrication
process might be difficult [10,15].
The design of PCF structures with small mode areas
that lead to high nonlinear coefficient γ, is an ongoing
challenge. By varying the size of the air holes in the
cladding region and the hole to hole spacing, desired
effective mode areas can be obtained [7,8]. Small core
diameter that leads to low effective mode area can be
reduced by having a relatively small hole to hole spacing.
Previously published results such as Poli et al. [16] and
Saitoh et al. [17] have demonstrated theoretically, that it
is possible to design PCFs with nonlinear coefficients of
about 30 and 44 W-1km-1, respectively, at 1.55 μm tele-
communication wavelength. However, these structures
are purely theoretical and the hole to hole spacing, Λ, is
around 0.9 μm. From the point of view of fabrication,
small hole to hole spacing might be problematic to
manufacture.
In recent years, highly birefringent PCFs with nonlin-
ear properties have received growing attention in tele-
communication and supercontiniuum applications [7,18-
19]. Previously published results by Lee et al. [7] and
Yamamoto et al. [18], have experimentally demonstrated
that it is possible to design highly nonlinear PCFs with a
relatively large birefringence in the order of 10-3 at 1.55
μm telecommunication wavelengths. Lee et al. [7] has
demonstrated a birefringent PCF having nonlinear coef-
ficient γ, of 31 W-1km-1 for the use of optical code-divi-
sion multiple access (OCDMA) applications. Similarly,
Yamamoto et al. [18] has demonstrated highly birefrin-
gent PCF with Ge-doped core having nonlinear coeffi-
cient, γ, of 19 W-1km-1.
Moreover, recently published papers such as Kudlinski
et al. [20] and Cumberland et al. [21] have shown that
PCFs with two zero dispersion wavelengths (ZDW)
demonstrate stronger power spectral densities than single
ZDW PCFs. Therefore PCFs with two ZDW can be be-
neficial in supercontinuum applications. Kudlinski et al.
[20] have demonstrated that it is possible to design two
ZDW PCF with a nonlinear coefficient of 31 W-1km-1.
For many applications it is essential to design PCFs
that exhibit simultaneous high birefringence, low losses,
and high nonlinear coefficient across a wide wavelength
window. Additionally, bending losses can be a critical
issue in the sensing and communication applications [22].
Bending is one of the important issues regarding the
practical development of PCFs. When an optical fibre is
bent, the field profile deforms outwards in the direction
of the bend and radiation losses occur. Since there are
more holes around the core of the holey fiber, the effect-
tive refractive index can be designed more flexibly than
that of conventional optical fibers by adjusting the hole
diameter and hole to hole spacing [22-23].
Figure 1 presents our proposed design which looks
similar to a design proposed by Saitoh et al. [24]. How-
ever, our design differs from this design in a number of
key areas. In our design we have shifted the first row of
air holes outwards by Λ/2. We have also used different
hole to hole spacing and diameters that in combination
improve the birefringence and reduce the confinement
losses. In ref. [24] the birefringence is around 4 × 10-3
and the losses are around 0.1 dB/km at 1.55 μm wave-
length. Compared to ref. [24], at the same wavelength,
lower confinement losses (≈ 0.001 dB/km) and higher
birefringence (≈ 8 × 10-3) can be achieved with our pro-
posed design. Additionally, in our design only 5 air hole
rings are used which makes the design less complex and
potentially easier to fabricate.
The main purpose of the proposed PCF structure is to
simultaneously achieve high birefringence, low confine-
ment loss and a high nonlinear coefficient. In this paper,
we propose a novel type of bending-insensitive highly
birefringent nonlinear PCF. High birefringence in PCFs
can be produced by combining the asymmetric core and
the large core-cladding index contrast. As shown in Fig-
ure 1, in order to destroy the symmetry of the fiber core,
the first row of the central air hole group is shifted out-
wards by Λ/2. Additionally, different air-hole diameters
along the two orthogonal axes are used in the core region.
All the air holes in the cladding region have the same
diameter except for the outermost ring which has larger
air holes in order to reduce the confinement losses. The
current progress in PCF (nanophotonics) technology [15,
25], has demonstrated that fabrication of our proposed
Figure 1. Schematic cross section of PCF, dm/Λ = 0.941,
d/Λ = 0.588, d5/Λ = 0.764.

H. ADEMGIL ET AL. 610
PCF structure is not an issue. Theoretical and experi-
menttal investigations by Suzuki et al. [10] have shown
that it is possible to fabricate even complex PCF struc-
tures by adapting conventional stack and draw methods.
However, stack and draw methods [15] are limited to
closely-packed geometries such as triangular or honey-
comb lattices and cannot easily generate different geom-
etries. Alternatively, drilling methods allow great flexi-
bility for both the hole size and spacing, but the struc-
tures are generally limited to a small number of holes.
Another alternative fabrication method is to use the sol-
gel method which allows for independent adjustment of
the hole size and spacing. The sol-gel method [15] pro-
vides additional design flexibility that will be neces-
sary for such PCF structures. Additionally, recently pub-
lished results by Vu et al. [22] demonstrated experiment-
tally, that the fabrication of bending insensitive PCFs is
possible and that these fibers are robust against high
amounts of bending.
In this work, we have employed full vectorial finite
element method (FEM) to investigate key modal proper-
ties of the proposed index guided PCF. The modal solu-
tion approach based on FEM is more flexible and reliable
than other techniques. It can represent any arbitrary
cross-section more accurately and has been widely used
to find the modal solutions of a wide range of optical
waveguides [6,26]. The FEM formulation for modal
analysis based on anisotropic perfectly matched layers
(PML) is capable of handling as many modes as required
and analyse leaky modes. By using PMLs boundary con-
dition, propagation characteristics and optical properties
of leaky modes in PCFs, it can be precisely evaluated
[27]. The modal analysis has been applied on the cross-
section in the x-y plane of the PCF as the wave is propa-
gating in the z direction.
In this study, birefringence, confinement loss, effec-
tive mode area, nonlinear coefficient properties of the
proposed PCFs are reported thoroughly. Also, significant
improvements of propagation characteristics of the PCFs
are demonstrated. Following this introduction, a brief
theoretical analysis is provided in Section 2. The simula-
tion results are reported in Section 3 and, finally, conclu-
sions are drawn in the last section.
2. Theory
The PCF cross section of Figure 1, with a finite number
of air holes is divided into homogeneous subspaces
where Maxwell’s equations are solved by accounting for
the adjacent subspaces. These subspaces are triangles
that allow a good approximation of the circular structures.
Using the anisotropic PML [6-26] from the Maxwell
equations the following vectorial equation is derived:
 (E) - 22
0
kn E = 0 (1)
where E is the electric field vector, k0 (= 2π/λ) is the
wave-number in the vacuum, n is the refractive index of
the domain, [s] is the PML matrix, [s]-1 is an inverse ma-
trix of [s] and λ is the operating wavelength.
2.1. Confinement and Bending Loss
Due to a finite number of layers of air holes, it is
inevitable that the optical mode will leak from the core
region into the outer air hole region. Considering the fact
that the jacket of the PCF is far from cladding and core
regions, the light guidance in the core region is exclu-
sively due to a finite number of layers of air holes in the
silica extending to infinity. The amount of leakage
constitutes the confinement loss. The confinement loss is
calculated from the imaginary part of the complex
effective index, neff using [5,6,26]:


3
40
..Im 10
ln 10eff
ConfLossn


 [dB/km] (2)
where Im is the imaginary part of the neff.
The calculations of the bending loss were carried out
using the same formulation. We assume a circular bend
structure where the PML is used along the radiation di-
rection (+x direction) for suppressing spurious reflection.
The curved fiber is replaced by a straight fiber with an
equivalent refractive index distribution defined by [9,22-
23].
neq = n (x,y)exp
x
R



(3)
where n (x,y) is the refractive index profile of the straight
fiber and R represents the bend radius.
2.2. Effective Mode Area and Nonlinear
Coefficient
Another key factor in designing PCFs is the effective
mode area. The effective mode area, Aeff is related to the
effective area of the core area, which is calculated using
[9,26];


2
2
4
eff
Edxdy
A
Edxdy

 (4)
where E is the amplitude of the transverse electric field
propagating inside the fibre.
Study of Aeff is thus an important starting point in the
understanding of the nonlinear phenomena in PCFs. Due
to the high index contrast between silica and air, PCF
technology offers the possibility of much tighter mode
confinement and thereby a lower effective mode area
compared to conventional fibres. An important value for
the calculation of the strength of nonlinear effects, is the
ratio between the nonlinear refractive-index coefficient,
n2 (Kerr constant), and the effective area for a given
wavelength of the optical field. The nonlinear coefficient

H. ADEMGIL ET AL. 611
is inversely proportional to the effective mode area and
can be calculated from [7,16-18];
2
2
() ()
eff
n
A




 (5)
where n2 is the nonlinear refractive-index coefficient (n2
= 2.76 × 10-20 m2/W) [27].
2.3. Chromatic Dispersion
Chromatic dispersion is one of the most important modal
properties of the PCFs. It is the main contributor to opti-
cal pulse broadening. Chromatic dispersion is caused by
the combined effects of material and waveguide disper-
sion. Moreover, the chromatic dispersion consists of ma-
terial dispersion and waveguide dispersion, which can be
calculated from the real part neff values against the wave-
length. The material dispersion given by Sellmeier’s
formula is directly included in the calculation [2,6].


2
2
Re
Deff
n
λ
cλ

  (6)
where c is the velocity of light and Re(neff ) is the real
part of the neff. Material dispersion refers to the wave-
length dependence of the refractive index of material
caused by the interaction between the optical mode and
ions, molecules or electrons in the material.
3. Simulation Results
In Figure 1, the proposed PCF design with an in-
dex-guiding core surrounded by a triangular array of air
holes is presented. The diameter of air holes and hole-to-
hole spacing is denoted by d and Λ, respectively. The
refractive index of pure silica is set equal to 1.45. In or-
der to reduce the confinement losses, five rings of air
holes are considered.
Previously published results by Ortigosa et al. [14]
have shown that, by varying the hole diameters along the
two orthogonal axes high birefringence can be achieved.
Therefore, in our design in order to achieve ultrahigh
birefringence, the air hole diameter sizes, d1, along the
x-direction are increased. To enhance the birefringence
further, the first column of the air hole group is shifted
outwards by Λ/2. As a result, the PCF core becomes
more asymmetrical which results in a significant increase
in the birefringence.
In order to keep the birefringence at the optimum level
and reduce confinement losses, we next investigate the
size of the air holes in the cladding region. It is known
that confinement losses [2,26] can be reduced by in-
creasing the size of the air holes in the inner cladding
area, d. However, according to our simulations this has a
negative effect on the birefringence. Hence, there is a
tradeoff between ultrahigh birefringence and low con-
finement losses. Alternatively, by increasing the number
of air hole rings [26], ultra low confinement losses can
be realized with negligible reduction in the birefringence.
Next, in order to control the dispersion, a dispersion
management technique [2] is also applied to proposed
PCF design. With this technique different air hole di-
ameters are used in each ring to control the chromatic
dispersion across a wide wavelength range. On the other
hand, it is well known that by altering Λ and d, ZDW can
be controlled [20-21]. Also, control of ZDW is much ea-
sier when hole to hole spacing is small [2]. In this regard,
the desired properties of birefringence, nonlinearities,
chromatic dispersion and confinement losses have been
simultaneously achieved in the PCF structure configura-
tion, shown in Figure 1, where, dm/Λ = 0.941, d/Λ =
0.588 and d5/Λ = 0.764.
The polarization dependent confinement losses still
need to be evaluated before one can conclude the fiber
structures to be practical. The confinement losses stron-
gly depend on the number of air hole rings, air hole di-
ameter and hole-to-hole spacing. Due to the number of
air hole rings and their diameters used in our proposed
PCF design, confinement losses are minimized. The con-
finement feature of the mode to the core region is di-
rectly linked to how much the mode is ‘leaking’ into the
outer air hole region.
Our proposed PCF supports the fundamental mode and
some higher-order modes. In order to clarify this, the
confinement losses of fundamental and first order modes
are investigated and presented in Figure 2. These modes
are approximately linearly polarized and, by analogy to
the elliptical core fiber and other asymmetric waveguides,
may be labeled as LP modes, such as in this case the
fundamental 01 LP mode which corresponds to an11
H
E.
In this regard, variation of confinement loss as a function
of hole-to-hole spacing Λ, when dm/Λ = 0.941, d/Λ =
0.588, d5/Λ = 0.764 at the operating wavelength λ = 1.55
μm, is shown in Figure 3. The confinement losses for both
Figure 2. Variation of Confinement losses as a function of
the hole to hole spacing, Λ, where λ=1.55 μm.

H. ADEMGIL ET AL. 612
Figure 3. Variation effective mode area, Aeff of the funda-
mental mode as a function of the operating wavelength.
fundamental and first order modes reduce with increas-
ing hole-to-hole spacing.
As expected, losses of higher order modes are much
higher than the fundamental mode. It is worth noting that,
confinement loss for y-polarized mode of both funda-
mental and first order mode are higher than x-polarized
mode. In this study we mainly concentrate on the beha-
vior of the fundamental modes. Therefore, further analy-
sis of propagation properties focuses on the fundamental
modes.
Figure 3 shows the variation of effective mode area as
a function of wavelength. It can be noted that Aeff is in-
creasing with the increasing hole to hole spacing. The
effective mode area steadily increases when the wave-
length increases. It is worth noting that the effective area
is much smaller than that of the conventional fibres at
1.55 μm wavelength. This would contribute to increase
the nonlinearities produced by refractive index power de-
pendence [1].
Having the freedom to control the optical properties of
the PCF by hole to hole spacing and placement whilst
maintaining strong confinement of the mode, allows for
the realization of high nonlinear effects. With ultra-high
nonlinearities, we can generate supercontinuum with re-
latively low pumping power. This is a very important
advantage. The devices can be made smaller, cheaper
and become more portable [28].
Variation of the nonlinear coefficient as a function of
wavelength is presented in Figure 4. As presented in
Equation (5) the nonlinear coefficient is inversely pro-
portional to the effective area. Small effective mode area
leads to high nonlinear coefficient that would be useful
in the context of supercontiniuum generation and soliton
pulse transmission [7,9]. In this regard, the nonlinear
coefficient steadily increases when the wavelength and
hole to hole spacing, Λ decreases. Our design shows that
the nonlinear coefficient, γ, for Λ = 1.7 μm and Λ = 2 μm
at 1.55 μm operating wavelength is 26 W-1km-1 and 20
W-1km-1, respectively.
Figure 4. Variation of nonlinear coefficient γ, as a function
of the operating wavelength.
Due to the low effective mode area, our proposed PCF
is expected to be insensitive to bending. Also it is known
that, low effective mode area has a positive effect on
bending loss [9]. Moreover, the impact of angular orien-
tation on bending losses is a critical issue in PCFs.
Figure 5 shows variation of the confinement losses as
a function of bending radius at different angular orienta-
tions of the fibre with respect to the bending plane,
where, Λ = 1.9 μm at operating wavelength 1.55 μm. As
can be seen from figure, three angular orientations φ = 0°,
φ = 15° and φ = 30° are investigated and these orienta-
tions has a critical effect on the proposed PCF losses
when the fibre is bent. As the bending radius increases,
the effect of φ increases. According to our simulations,
the effect of angular orientation on confinement losses is
related to core size. As expected, when φ increases, con-
finement losses increase marginally. However, the effect
of angular orientation on losses is similar for all values
of bending radii. One can see that, as hole to hole spac-
ing increases (core size increases) the effect of angular
Figure 5. Variation of confinement losses of the11
x
HE mode
as a function of the bending radius, R, for three different
angular orientation, when Λ = 1.9 μm and λ = 1.55 μm.

H. ADEMGIL ET AL. 613
orientation becomes the same for all bending radii. This
phenomenon can be linked to the effect of the core size.
On the other hand, due to leaky nature of the fibre, the
effective mode area plays a key role in confinement. It is
well known that small mode areas are usually the conse-
quence of strong guiding where bend losses and other
effects of external disturbances are weak. Therefore, in
our case it is evident that low effective mode areas mi-
nimize the bending effects on the confinement losses. In
other words, our PCF design is insensitive to bending.
Recently, published results by Vu et al. [22] demon-
strated experimentally, that fibres can be bent up to 3
mm radius. In our design, fibre size compared to their
design [22] is much smaller and for this reason our pro-
posed fibre can be anticipated to be more flexible and
may be bent further.
Next, we have investigated birefringence properties of
the proposed structure. Our simulated results indicate
that the effective index of the 11
x
H
E mode is larger than
that of the 11
y
H
E mode. Figure 6 illustrates the varia-
tion of the modal birefringence as a function of wave-
length for different hole-to-hole spacing. As can be ob-
served from this figure, relatively large birefringence of
the order of 10-3-10-2 is achieved. It can clearly be seen
that the birefringence is sensitive to the varying wave-
length λ. It can be anticipated that as hole-to-hole spac-
ing Λ decreases, the birefringence increases. It can be
noted that birefringence for Λ = 1.7 μm and Λ = 2 μm at
1.55 μm operating wavelength is 9 × 10-3 and 7.3 × 10-3,
respectively. Highly birefringent PCFs provide several
advantages for supercontinuum generation. Specifically,
all the spectral components exhibit the same linear po-
larization and also the power required to generate the
continuum is reduced compared to non-birefringent
PCFs. In addition, the fibre allows for simultaneous gen-
erations of two different continua due to the large differ-
ence between two polarization modes [19].
Figure 6. Variation of birefringence as a function of the
wavelength.
As can be seen from Figure 3, effective mode area can
be minimized by reducing the hole to hole spacing.
Therefore, nonlinear coefficient of proposed PCF can be
improved by reducing the hole to hole spacing. Moreover,
significant increase on birefringence can be observed by
reducing the hole to hole spacing. In this regard, in order
to improve the birefringence and nonlinear coefficient,
the proposed PCF is investigated for different design
parameters (smaller hole to hole spacing). The nonlinear
coefficient of the proposed PCF is illustrated in Figure 7.
It can be seen that, the nonlinear coefficient steadily in-
creases when the wavelength and hole to hole spacing, Λ,
decreases. Our simulations show that, the highest non-
linear coefficient corresponding to effective area, eff
A
=
2.28 μm2 at λ = 1.55 μm, is equal to 49 W-1 km-1 for Λ =
1 μm.
Next, we have investigated the birefringence proper-
ties of the proposed PCF, shown Figure 8. Our simulated
results indicate that the effective index of the 11
x
H
E
mode is larger than that of the 11
y
H
E mode. As can be
observed from this figure, relatively high birefringence
Figure 7. Variation of nonlinear coefficient γ, as a function
of the operating wavelength.
Figure 8. Variation of birefringence as a function of the
wavelength.

H. ADEMGIL ET AL. 614
of the order of 10-2 is achieved. The birefringence is sen-
sitive to the varying wavelength, λ and it increases as the
wavelength increases. It can be noted that the birefrin-
gence for Λ = 1 μm and Λ = 1.6 μm at 1.55 μm operating
wavelength is 2.65 × 10-2 and 1.01 × 10-2, respectively.
Finally, the chromatic dispersion profile can be easily
controlled by varying the hole diameter and the hole to
hole spacing [28]. Controllability of chromatic dispersion
in PCFs is a very important problem for practical appli-
cations to optical communication systems, dispersion
compensation, and nonlinear optics [12]. At short wave-
length, the modal field remains confined to the silica
region, but at longer wavelengths the effective cladding
index decreases. Thus, as we change the size of air hole d
or the separation between them Λ, ZDW can be altered
to any value. This unusual dispersion characteristic of
PCFs allows them to be used in non-linear fiber optics.
One can see that it is possible to shift the zero dispersion
wavelength from visible to near-infrared (IR) regions by
appropriately changing the geometrical parameters (d
and Λ).
At short wavelength, the modal field remains confined
to the silica region, but at longer wavelengths the effec-
tive cladding index decreases. Thus, as we change the
size of air hole d or the separation between them Λ,
ZDW can be altered to any value. This unusual disper-
sion characteristic of PCFs allows them to be used in
non-linear fiber optics. One can see that it is possible to
shift the zero dispersion wavelength from visible to
near-infrared (IR) regions by appropriately changing the
geometrical parameters (d and Λ). As may be seen from
Figure 9 when hole to hole spacing, Λ = 1 μm and Λ =
1.2 μm the proposed PCF has a single ZDW, 0.8 μm and
0.84 μm respectively. On the other hand, when Λ = 1 μm
and Λ = 1.2 μm two ZDW is achieved. The first ZDW
for both cases is around 0.8 μm. However, according to
simulation results the second ZDW for Λ = 1 μm and Λ
Figure 9. Variation of the chromatic dispersion of 11
x
H
E
modes as a function of the wavelength for different hole to
hole spacing.
= 1.2 μm is found as 1.36 μm and 1.67 μm, respectively.
PCFs that have two ZDW have been used previously for
high power supercontinuum generation applications
[20-21]. Also, Cumberland et al. [21] have shown that
two ZDW PCFs can be used to control the long wave-
length edge of the continuum when needed for specific
applications.
In nonlinear optics, to maximize the spectral broaden-
ing, it is advantageous to have a polarization maintaining
(PM) nonlinear fiber (birefringent nonlinear fiber).
Pumping a PM fiber with the pump source polarization
aligned to one of the principle axes in the fiber yields a
power advantage close to a factor of two compared to a
non-PM fiber. Moreover, the output from the fiber is also
polarized, increasing the usability of the generated light.
Therefore, highly birefringent nonlinear PCFs can be
useful in SC and nonlinear applications.
The birefringence and nonlinear coefficient properties
of the proposed PCF reported in this paper are much lar-
ger than that of the conventional fibres. These fibres are
useful to improve the capabilities of optical fibre com-
munication systems and new types of optoelectronic de-
vices. Nonlinear PCFs with highly birefringence and low
confinement losses can be widely used for polarization
control in fibre-optic sensors, precision optical instru-
ments, ultra-short solution pulse transmission and four-
wave mixing [8,18-19]. Moreover, reported results can
be useful for optical communication systems [10], opti-
cal switching and OCDMA applications [7]. From ex-
perimental point of view, the sol-gel fabrication method
offers flexible design freedom with such a lattice struc-
ture and is robust against high degrees of bending. This
fabrication method allows the experienced manufacturer
to produce low cost highly advanced PCF structures tai-
lored to the desired propagation properties.
4. Conclusions
In summary, we have presented a highly nonlinear bire-
fringent PCF. Simultaneous, birefringence, and nonlinear
(coefficient) properties of the proposed PCF have been
reported in this paper that to the best of our knowledge,
are much higher than any other results published so far in
literature. Moreover, two ZDW that is beneficial for su-
percontiniuum applications has been achieved. Also, it is
shown that a low effective area has a positive effect on
the bending losses and the proposed structure is bending
insensitive. The proposed PCF structure configuration is
straightforward when compared to many fabricated PCF
structures in literature. Therefore, fabrication of the pro-
posed PCFs is believed to be possible and is not beyond
the realms of today’s existing PCF technology. These
reported results can be widely used for the supercon-
tinuum generation, polarization control in fiber-optic
sensors and telecommunication applications.

H. ADEMGIL ET AL. 615
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