Ultra-high negative dispersion and nonlinearity based single mode photonic crystal fiber: design and analysis

Abstract

In this article, we have proposed a large negative dispersion coefficient and highly nonlinear polarization maintaining single mode square photonic crystal fiber. The proposed design is extremely attractive for compensation of chromatic dispersion of − 1052.60 ps/(nm km) to − 2421.90 ps/(nm km) around 1340–1640 nm wavelength band. Guiding characteristics are investigated applying finite element method containing perfectly matched layer boundary condition. Simulation outcomes ensure the possibility of large negative dispersion coefficient and low confinement loss of − 2015.30 ps/(nm km) and 3.41 × 10¹ dB/m respectively, at 1550 nm wavelength. The proposed fiber also exhibits highly nonlinear coefficient of 99.73 W⁻¹ km⁻¹ at the same wavelength. Moreover, V parameter assures the single mode operation of the structured fiber over the whole band of interest. The structural diameter variation of ± 2% over the optimum value is simulated and reported to explore the practical feasibility. Besides, effective area is also presented and explained. From overall investigations, it can be reported that the proposed fiber will be an attractive candidate in high-speed transmission system for broadband dispersion compensation, nonlinear optics and sensing applications as well.

Full text

RESEARCH ARTICLE
Ultra-high negative dispersion and nonlinearity based single mode
photonic crystal fiber: design and analysis
Md. Ibadul Islam
1
•Kawsar Ahmed
1,2
•Bikash Kumar Paul
1,2,3
•
Sawrab Chowdhury
1
•Shuvo Sen
1
•Md. Shadidul Islam
1
•Sayed Asaduzzaman
1,2,3
•
Ali Newaz Bahar
1
Received: 8 March 2017 / Accepted: 27 November 2018 / Published online: 4 December 2018
ÓThe Optical Society of India 2018
Abstract In this article, we have proposed a large negative
dispersion coefficient and highly nonlinear polarization
maintaining single mode square photonic crystal fiber. The
proposed design is extremely attractive for compensation
of chromatic dispersion of -1052.60 ps/(nm km) to
-2421.90 ps/(nm km) around 1340–1640 nm wavelength
band. Guiding characteristics are investigated applying
finite element method containing perfectly matched layer
boundary condition. Simulation outcomes ensure the pos-
sibility of large negative dispersion coefficient and low
confinement loss of -2015.30 ps/(nm km) and
3.41 910
1
dB/m respectively, at 1550 nm wavelength.
The proposed fiber also exhibits highly nonlinear coeffi-
cient of 99.73 W
-1
km
-1
at the same wavelength. More-
over, Vparameter assures the single mode operation of the
structured fiber over the whole band of interest. The
structural diameter variation of ±2% over the optimum
value is simulated and reported to explore the practical
feasibility. Besides, effective area is also presented and
explained. From overall investigations, it can be reported
that the proposed fiber will be an attractive candidate in
high-speed transmission system for broadband dispersion
compensation, nonlinear optics and sensing applications as
well.
Keywords Ultra-high negative dispersion Nonlinear
coefficient Dispersion compensating S-PCF Effective
area Single mode fiber Confinement loss
Introduction
In recent years, microfibers have allured more and more
attention due to their extended applications in nonlinear
optics, evanescent wave sensors, micro-scale photonic
devices, couplers for micro-cavities and so on [1]. A lot of
experimental and numerical outcomes in the published
article exhibit that microfibers have different excellent
characteristics like high birefringence [2], high nonlinear
coefficient [3], confinement loss [1], chromatic dispersion
coefficient [4–6] and strong evanescent fields [7] and tight
optical confinement [8]. Among these properties, nonlin-
earity is one of the most significant characteristics. In
microfibers, high nonlinear coefficient can be perceived by
alleviating the fiber diameter or applying soft glass mate-
rials including high nonlinearity [9]. Currently, nonlinear
microfibers are essential candidates for numerous practical
applications such as supercontinuum generation, optical
parametric amplification and all-optical wavelength con-
version [10,11]. Another parameter, effective mode area is
inversely proportional to nonlinear coefficient. High non-
linear coefficient produces small affective area [3]. Due to
small effective mode area, the evanescent field cannot be
confined properly into core region which leads to penetrate
the light into cladding region [1].
Photonic crystal fibers (PCFs) guide the electromagnetic
field arranging of air holes that run down the entire fiber
&Kawsar Ahmed
kawsar.ict@mbstu.ac.bd; k.ahmed.bd@ieee.org;
kawsarit08050@gmail.com;
http://mbstu.ac.bd/depts/ict/index.html
1
Department of Information and Communication Technology
(ICT), Mawlana Bhashani Science and Technology
University (MBSTU), Santosh, Tangail 1902, Bangladesh
2
Group of Bio-photomativ, Tangail, Bangladesh
3
Department of Software Engineering (SWE), Daffodil
International University, Shukrabad, Dhaka 1207,
Bangladesh
123
J Opt (March 2019) 48(1):18–25
https://doi.org/10.1007/s12596-018-0499-1

length. The air holes decrease the average index around the
solid core in the holey fibers, and the guidance can be
credited to the total internal reflection. PCFs provide
flexibility in tuning dispersion which is important in
designing dispersion compensating fiber design. Nowa-
days, PCFs have diverse applications in sensors, interfer-
ometry, telecommunications, lasers, soliton, medical
instrumentations and various polarization sensitive devices,
etc. However, PCFs boost either single mode or multimode
operation. Thus, it is likely important to assure the single
mode operation to ignore multimode dispersion together
for dispersion compensating PCF with large negative dis-
persion and low confinement loss [12]. For long-distance
optical data communication system to confine the broad-
ening of pulse, it is necessary to compensate the dispersion.
The way to understand this is to practice the dispersion
compensating fibers (DCFs) taking large negative disper-
sion. To reduce the insertion loss and cost, the coefficient
of negative dispersion must be as large as possible at the
same the DCFs should be as small as possible. The nega-
tive dispersion of DCFs should broaden a wide spectrum to
properly compensate the dispersion at all the frequencies of
dense wavelength division multiplexing (DWDM).
Chromatic dispersion is one of the most important
characteristics. Dispersion is one of the significant prob-
lems in wavelength division multiplexing (WDM) and
high-speed transmission systems because it broadens the
optical pulse as well as limits the bandwidth of the system
[4]. Dispersion compensating fiber including large negative
dispersion is used to reject the deposited positive disper-
sion coefficient of single mode fibers (SMFs) [13]. PCFs or
holey fibers deal with pliability in fine-tuning dispersion
coefficient, because by varying the size of air holes
diameter as well as their position, the dispersion behavior
can be checked [14] which are essential for dispersion
compensating fiber design. Typically, conventional fibers
offer about -100 ps/(nm km) to -300 ps/(nm km) neg-
ative dispersion coefficient at 1550 nm wavelength [15].
There are many attempts have been offered by various
groups to gain large negative dispersion and an eligible
band for dispersion compensation [16]. For example, DC-
HyPCF design in 2014 [17] showed negative dispersion
coefficient of -555.93 ps/(nm km) with high birefrin-
gence of 3.79 910
-2
. In 2015, a simple MHF structure
had been demonstrated by Md Aminul Islam [18] which
improved dispersion with negative dispersion coefficient of
-610 ps/(nm km) but low birefringence of order
2.10 910
-2
compared to [17]. Another PCF design was
suggested by Mejbaul Haque et al. [12] which provided
negative dispersion coefficient of -650 ps/(nm km) at
1550 nm with nonlinear coefficient of 45.50 W
-1
km
-1
.In
2016, HyPCF was presented by Hasan et al. [19] with
negative dispersion coefficient of -578.50 ps/(nm km)
including low confinement loss of 8.13 910
-3
dB/m. To
reduce the limitations of previous articles Halder et al. [1]
proposed hexagonal microstructure optical fiber (H-MOF)
which provided high birefringence of 3.373 910
-2
. The
proposed fiber obtained large negative dispersion coeffi-
cient of -837.80 ps/(nm km) and also high nonlinear
coefficient of 53.45 W
-1
km
-1
at 1550 nm wavelength.
In this study, we have proposed an S-PCF that assures
the broadband dispersion compensation efficiency with
high nonlinearity. According to investigation, it is seen that
the designed S-PCF acts as a single mode fiber around
E?S?C?Lbands and offers a large negative disper-
sion of -2015.30 ps/(nm km) at 1550 nm wavelength.
The proposed structure also provides high nonlinear coef-
ficient of 99.73 W
-1
km
-1
at the same wavelength. The
fundamental advantages of our proposed design are the
structural simplicity and large negative dispersion. It is
greatly expected that S-PCF would be effectible in lofty
speed DWDM optical transmission systems for efficient
dispersion compensation and nonlinear optics applications.
Geometry
The schematic view of the proposed square-lattice PCF (S-
PCF) with air hole distribution has been shown in Fig. 1.
To achieve large negative dispersion as well as high non-
linearity, adjacent air holes in the entire cladding region are
transformed to circular air hole. It is known that the dis-
persion characteristic is influenced by the size of the air
holes near core region [20]. Moreover, by using a tradi-
tional PCF topology, it is difficult to engineer a large
negative dispersion and inspect nonlinear coefficient, dis-
persion slope and polarization maintaining properties
d0
Λ
d
d
d
d3
d
d
Λc
Air hole
Fig. 1 Transverse cross-sectional view of proposed square PCF
J Opt (March 2019) 48(1):18–25 19
123

simultaneously. Consequently, it is necessary to incorpo-
rate a design with a higher degree of independence
regarding overall geometrical structure parameters. Hence,
the proposed design parameters are defined as pitch K, air
hole diameters d
0
,dand d
3
. The proposed PCF consists of
six air hole layers in square manner, and the air holes
diameters at third layer are defined as d
3
and rest of the air
holes diameters are same denoted as d. The diameter of
tinny air holes near core region is defined as d
0
. In this
case, the square-lattice geometry of the proposed PCF, the
hole-to-hole spacing both in horizontal and vertical direc-
tions [21,22] is denoted as Kand the distance of tinny air
holes from center is defined as K
c
. To form inner core, the
central air holes are omitted which offers to achieve large
negative dispersion. This type of structure offers high
nonlinear coefficient and large negative dispersion which
have great impact on high-speed optical transmission sys-
tem. Due to effect on the dispersion properties, only a
single material usually silica is set as background material
for the proposed PCF. The refractive index of silica has
been calculated through Sellmier’s equation.
Synopsis of numerical methods
The modal analyses have been simulated on the cross
section in the X–Yplane of the PCF as the wave is prop-
agating in the z-direction. The finite element method
(FEM) including a circular perfectly matched layer (PML)
boundary condition is applied to carry out the numerical
investigations for analyzing the guiding properties of the
proposed design for dispersion compensation. By using
FEM, Maxwell’s vectorial equation [23] is solved to best
approximate the value of modal effective refractive indices
n
eff
. Once, the modal effective indexes (n
eff
) are measured
by Eq. (2). Moreover, the dispersion coefficient (D(k)),
nonlinear coefficient (c), effective area (A
eff
) and effective
Vparameter (V
eff
) can be determined by using the Eqs. (3)–
(6) illustrated in [24,25]. To explore the modal charac-
teristics of the proposed PCF, commercial full vector finite-
element software (COMSOL 4.2) is used. The background
of the proposed square-lattice fiber usually is taken to be
silica whose refractive index has been obtained through the
following Sellmier’s equation [26]:
nkðÞ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1þB1k2
k2C1
þB2k2
k2C2
þB3k2
k2C3

sð1Þ
The model effective indexes (n
eff
) are obtained as the
function of wavelength and material dispersion (n
m
(k)). So
that [25].
neff ¼bk;nmkðÞðÞ=k0ð2Þ
where bis the propagation constant, k
0
=2p/kis the wave
number of free space and n
m
(k) can be estimated by using
the Sellemeier’s formula.
The dispersion characteristics can be easily controlled
by changing the shape, size and pitch of the air holes. The
dispersion coefficient D(k) is calculated from the effective
index of the fundamental mode n
eff
versus the wavelength
using the following equation [27]:
DkðÞ¼
k
c
d2Re neff
½
dk2ps/(nm km) ð3Þ
where kis the wavelength, cis the velocity of light in
vacuum, Re neff
½is the real part of effective indices
obtained from simulations.
However, the nonlinear coefficient cis evaluated as [1]:
c¼2p
k
n2
Aeff
 ð4Þ
where A
eff
is the effective area which can be determined by
the following equation [24].
Aeff ¼RR E
jj
2dxdy

2
RR E
jj
4dxdyð5Þ
where Eis the electric field.
Now, it was consciously investigated the mode property
of the proposed PCF. According to effective Vparameter, it
is seen that single modeness of the fiber is changed inside
the telecom bands. V
eff
parameter for the PCF can be cal-
culated by applying the following equation [28].
Veff ¼2pK
kffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
n2
co n2
cl
qð6Þ
Equation (6) is applied to verify the single mode
behavior of the proposed design where 2pK
kdenotes the
wave number in the free space and Kis the pitch; n
co
and
n
cl
represent the refractive indices of core and cladding,
respectively.
Numerical results and discussion
Figure 2shows the fundamental mode field profile of the
proposed design at 1550 nm wavelength for both x- and y-
polarization modes. From Fig. 2, it is visualized that the
mode field is well confined in the core region with proper
arrangement of the air holes in cladding region. The optical
field is properly absorbed into the core region due to high-
index contrast in the center than the cladding. The pro-
posed PCF exhibits tumid design pliability in tailoring
dispersion and nonlinear coefficient in an advanced way
compare to standard SMF.
20 J Opt (March 2019) 48(1):18–25
123

Figure 3exhibits the effect of variation of air hole
diameter d
1
located at first layer on the dispersion when the
other parameters are kept constant. From the figure, it can
be seen that dispersion coefficient negatively promotes by
enhancing the air holes diameter d
1
. Due to this, the optical
field is tightly bounded into the core region which leads to
obtain highly negative dispersion as well as very high
nonlinear coefficient than [29]. However, the designed fiber
represents dispersion coefficient of about -1779.20 ps/
(nm km), -2015.30 ps/(nm km) and -2335.40 ps/
(nm km) over 1340–1640 nm wavelength for the variation
of d
1
as 0.75 lm, 0.76 lm, 0.77 lm, respectively. Large
negative dispersion is an important parameter in designing
the fiber that should be as large as possible. Therefore, it is
necessary to take into consideration the dispersion in
drawing PCF for dispersion compensation and also for
diameter optimization [30].
A general step by step procedural technique is followed
for optimization of parameters of the proposed S-PCF
geometry. The normalized air filling ratio d
3
/Kis subjected
as 0.86, 0.88 and 0.89 while keeping the others parameters
constant throughout the investigation. The resulting dis-
persion curve is shown in Fig. 4. The decrement of nor-
malized air filling ratio d
3
/Kmakes the dispersion
coefficient to be more negative. As a result, d
3
/K= 0.88 is
chosen as optimum which offers large negative dispersion
that is effectible for dispersion compensation applications.
According to the variations of d
3
as 0.69 lm, 0.70 lm and
0.71 lm, the evaluated dispersion coefficients at the wave-
length 1550 nm of -2184.10 ps/(nm km), -2015.30 ps/
(nm km) and -1888.30 ps/(nm km) are achieved, respec-
tively. From above observation, it is reported that dispersion
negatively promotes by alleviating the air holes diameter d
3
.
As a result, the optical field is strongly absorbed into the core
Fig. 2 Field distributions of
fundamental modes at
wavelength 1550 nm for ax-
polarization and by-
polarization
1.34 1.4 1.46 1.52 1.58 1.64
−3000
−2700
−2400
−2100
−1800
−1500
−1200
−900
Wavelength,λ (μm)
Dispersion D[ps/(nm.km)]
d1/Λ = 0.94, d1 = 0.75 μm
d1/Λ = 0.95, d1 = 0.76 μm
d1/Λ = 0.96, d1 = 0.77 μm
Fig. 3 Dispersion coefficient versus wavelength for the proposed
S-PCF for the design parameters: K= 0.80 lm; K
c
= 0.40 lm;
d
0
= 0.30 lm; d
1
= 0.75 lm, 0.76 lm, 0.77 lm; d
3
= 0.70 lm
1.34 1.4 1.46 1.52 1.58 1.64
−2700
−2400
−2100
−1800
−1500
−1200
−900
Wavelength,λ (μm)
Dispersion D[ps/(nm.km)]
d3 = 0.69 μm, Λ = 0.80 μm
d3 = 0.70 μm, Λ = 0.80 μm
d3 = 0.71 μm, Λ = 0.80 μm
Fig. 4 Dispersion coefficient versus wavelength versus wavelength
for the proposed S-PCF for the design parameters: K= 0.80 lm;
K
c
= 0.40 lm; d
0
= 0.30 lm; d= 0.76 lm; d
3
/K= 0.86, 0.88 and
0.89
J Opt (March 2019) 48(1):18–25 21
123

region which offers to achieve highly negative dispersion
than (approximately -555.93 ps/(nm km)) [17].
Figure 5points out the effect of don the dispersion
coefficient. From this figure, it is clearly evident that dis-
persion coefficient negatively enhances by increasing the
air holes diameter d. The variations of das 0.75 lm,
0.76 lm and 0.77 lm, the calculated dispersion coeffi-
cients of -1933.90 ps/(nm km), -2015.30 ps/(nm km)
and -2101.70 ps/(nm km) are gained respectively at the
operating wavelength 1550 nm. There is a great impact of
large negative dispersion on optical amplification applica-
tions. Generally, long traditional optical fiber links do not
maintain linear polarization; the Raman gain defines an
average value, which is to be about half of the corre-
sponding polarized gain. Thus by maintaining linear
polarization, gain efficiency may be improved by approx-
imately a factor of 2 [31]. The proposed PCF exhibits large
negative dispersion, which governs to a relatively small
fiber length required to acquire dispersion compensation.
Hence, it is expected that the proposed PCF will be capable
to sustain linear polarization. From Fig. 6, it is also noticed
that the dispersion coefficient negatively increases by
enhancing the diameter of tinny air holes near core region
and vice versa. According to the variation of tinny air hole
diameter, the dispersion coefficients of -1732.50 ps/
(nm km), -2015.30 ps/(nm km) and -2400.90 ps/
(nm km) are gained at 1550 nm wavelength. By comparing
Figs. 5and 6, it is observed that dispersion coefficient
negatively enhances with the increment of air hole diam-
eter close to core but decreases with the enhancement of air
hole diameter located far layers from first layer.
In Fig. 7, it is illustrated the influence of pitch variation
on dispersion behavior by keeping constant the other
parameters as K
c
= 0.40 lm, d= 0.76 lm, d
3
= 0.70 lm,
d
0
= 0.30 lm. From above investigations, it is noticed that
the large negative dispersion can be achieved by reducing
pitch for wideband dispersion compensation. It is also
reported that the PCF can compensate the dispersion
coefficient about 3.48 times than [19] which is compatible
in optical communication.
Veffective (V
eff
) parameter is used to examine the single
mode operation of the proposed PCF. Figure 8describes
the wavelength dependent V
eff
parameter with optimized
design parameters of K= 0.80 lm; K
c
= 0.40 lm;
d=0.76lm; d
3
= 0.70 lm; d
0
= 0.30 lm. It has been
used FEM at the outer enclosure to perceive the index of
space-filling mode with approximate perfect electric and
magnetic conductor boundary condition [28]. In
1.34 1.4 1.46 1.52 1.58 1.64
−2600
−2300
−2000
−1700
−1400
−1100
−800
Wavelength,λ (μm)
Dispersion D[ps/(nm.km)]
d/Λ = 0.94, d = 0.75 μm
d/Λ = 0.95, d = 0.76 μm
d/Λ = 0.96, d = 0.77 μm
Fig. 5 Wavelength dependent dispersion coefficient of the proposed
S-PCF for the design parameters: K= 0.80 lm; K
c
= 0.40 lm;
d
0
= 0.30 lm; d= 0.75 lm, 0.76 lm and 0.77 lm; d
3
= 0.70 lm
1.34 1.4 1.46 1.52 1.58 1.64
−3000
−2700
−2400
−2100
−1800
−1500
−1200
−900
Wavelength,λ (μm)
Dispersion D[ps/(nm.km)]
d0 = 0.28 μm, d0/Λc = 0.70
d0 = 0.30 μm, d0/Λc = 0.75
d0 = 0.32 μm, d0/Λc = 0.80
Fig. 6 Dispersion coefficient versus wavelength of the proposed PCF
for the design parameters: K= 0.80 lm; K
c
= 0.40 lm;
d
0
= 0.28 lm, 0.30 lm, 0.32 lm; d= 0.76 lm; d
3
= 0.70 lm
1.34 1.4 1.46 1.52 1.58 1.64
−2600
−2300
−2000
−1700
−1400
−1100
−800
Wavelength,λ (μm)
Dispersion D[ps/(nm.km)]
d/Λ = 0.94, Λ = 0.81 μm
d/Λ = 0.95, Λ = 0.80 μm
d/Λ = 0.96, Λ = 0.79 μm
Fig. 7 Dispersion coefficient versus wavelength for the proposed
S-PCF for the design parameters: K
c
= 0.40 lm; d= 0.76 lm;
d
3
= 0.70 lm; d
0
= 0.30 lm; K= 0.79 lm, 0.80 lm and 0.81 lm
22 J Opt (March 2019) 48(1):18–25
123

electromagnetic investigation, some optical power pene-
trates into the outer boundary of the innermost core region.
As a result, it produces some undesirable nonphysical
radiation. For this reason, an absorption boundary PML has
been added to outside of the cladding region for getting
accurate result. This PML acts as absorption boundary
condition (ABC) or perfect electric and magnetic conduc-
tor boundary condition. The V
eff
parameter for a single
mode fiber (SMF) is V
eff
B2.405 [29]. The Vparameters
of 1.47–1.03 are achieved from ranging of 1340–1640 nm
wavelength. According to simulation, it is clearly reported
that the proposed PCF acts as a SMF around the entire
bands.
Figure 9exhibits the effective area as well as nonlinear
coefficient of the proposed PCF as a function of wave-
length for the optimized parameters. The figure also rep-
resents that effective area increases according to the
increase of wavelength. The mode power closely confined
in the core region at the longer wavelength, so the guiding
waves spread largely. The effective area of our proposed
design is 1.26 lm
2
at 1550 nm. It is also regarded that
small effective mode area has a crucial effect on bending
loss [27]. Due to low effective area, the nonlinear coeffi-
cient of 99.73 W
-1
km
-1
is very high which is also rep-
resented in Fig. 9. It is also visualized that the nonlinear
coefficient reduces with the increment of wavelength. The
higher nonlinear characteristic is very suitable in pulse-
forming, self-phase modulation for switching, supercon-
tinuum generation, wavelength conversion applications for
frequency metrology, spectroscopy or optical coherence
tomography, etc. [32]. Besides, PCF with higher nonlin-
earity is to be eligible for dispersion compensation, where
four-wave mixing is prone to appearing [33].
At time of the fabrication process, ±1% variations of
global diameters may occur in a standard fiber draw [14].
To confirm dispersion tolerance, there may need an accu-
racy of ±2%. In the proposed PCF, global parameters are
varied up to 2% to gain better dispersion accuracy which is
exhibited in Table 1. At the wavelength 1550 nm, the
dispersion coefficients of -1923.40 ps/(nm km),
-1830.70 ps/(nm km) and -2105.30 ps/(nm km),
-2211.23 ps/(nm km) are achieved by increasing and
decreasing the global parameters order of 1% and 2%,
respectively.
A comparison is shown between characteristics of the
PCF and some other prior design for dispersion compen-
sation applications. From Table 2, it is clearly visualized
that our proposed PCF provides superior result both dis-
persion and nonlinear coefficient. Thus, it definitely
describes that the proposed PCF is better for dispersion
compensation as well as high nonlinear coefficient than
prior PCFs. Our proposed PCF also exhibits simplicity in
design compare with prior PCFs [17,29].
The structured S-PCF provides design flexibility in tai-
loring the chromatic dispersion as well as nonlinearity
which are required to gain application specific properties
from the fiber. At first, the wavelength dependence nature
of chromatic dispersion for optimized parameters
K= 0.80 lm; K
c
= 0.40 lm; d
0
= 0.30 lm; d= 0.76 lm
and d
3
=70lm is simulated and shown optical fields in
Fig. 10. A negative dispersion coefficient of -2015.30 ps/
(nm km) at the operating wavelength of 1550 nm is
investigated for x-polarized mode. The dispersion values
vary from -1052.60 ps/(nm km) to -2421.90 ps/
(nm km) for x-polarization over the spectral range of
1340–1640 nm. It is found out x-polarized mode to achieve
optimum result such as large negative dispersion that
overcomes the limitation of [30] which contained low
dispersion coefficient (approximately -1054.40 ps/
(nm km).
Finally, it has been explored the fabrication simplicity of
the proposed structure. The traditional stack and draw
technique is applied for fabrication of PCF because this
method gives a better degree of exactness for closed
packed geometry like honeycomb or triangular lattice [30].
Another technique, the drilling method provides adjust-
ment of both holes size and spacing as well as can pro-
create circular shapes perfectly. However, by recently
advanced technology the proposed structure can be fabri-
cated for technological advancement in the fabrication of
PCFs. The sol–gel technique offered by Bise et al. [34]is
used to fabricate the PCFs with all structures and they also
offer the freedom to adjust air hole size, shape and spacing.
In addition, the sol–gel casting method provides design
flexibility that will be perfect for the proposed PCF. Our
1.34 1.4 1.46 1.52 1.58 1.64
0.8
1
1.2
1.4
1.6
1.8
2
2.2
2.4
2.6
Wavelength (µm)
Veff
2.405 Multi−mode
Single Mode
Fig. 8 V parameter of the proposed S-PCF as a function of
wavelength for K= 0.80 lm; K
c
= 0.40 lm; d= 0.76 lm;
d
3
= 0.70 lm; d
0
= 0.30 lm
J Opt (March 2019) 48(1):18–25 23
123

proposed S-PCF can be fabricated by sol–gel casting
method.
Conclusion
In summary, a single mode broadband dispersion com-
pensating fiber involving large negative dispersion and
high nonlinear coefficient has been proposed based on
square-lattice geometry. The numerical analysis represents
that the proposed structure offers high negative dispersion
as well as high nonlinear coefficient ranging from
-1052.60 ps/(nm km) to -2421.90 ps/(nm km) and
1.34 1.37 1.4 1.43 1.46 1.49 1.52 1.55 1.58 1.61 1.64
0.99
1.09
1.19
1.29
1.39
1.49
Aeff (μm2)
Wavelength (μm)
1.34 1.37 1.4 1.43 1.46 1.49 1.52 1.55 1.58 1.61 1.64
80
90
100
110
120
130
140
150
γ (W−1km−1)
Fig. 9 Effective area and
nonlinear coefficient for x-
polarization mode of the
proposed PCF as a function of
wavelength for K= 0.80 lm;
K
c
= 0.40 lm; d= 0.76 lm;
d
3
= 0.70 lm and d
0
= 0.30 lm
Table 1 Comparisons of
different index-guiding
properties for optimum design
parameters and also for fiber’s
global diameter variations of
order ±1–±2% around the
optimum value
Change in diameters (%) D(ps/(nm km)) A
eff
(lm
2
)c(W
-1
km
-1
)
2-1830.70 1.31 95.93
1-1923.40 1.29 97.41
Optimum -2015.30 1.26 99.73
-1-2105.30 1.25 100.53
-2-2211.23 1.24 101.34
Table 2 Comparison between properties of the proposed S-PCF and
prior PCFs at 1550 nm wavelength
PCFs D(ps/(nm km)) A
eff
(lm
2
)c(W
-1
km
-1
)
[17]-555.93 2.63 40.1
[19]-578.50 1.92 53.1
[18]-613.00 2.8 –
[12]-650.00 2.1 45.5
Proposed PCF -2015.30 1.26 99.73
1.34 1.4 1.46 1.52 1.58 1.64
−2600
−2400
−2200
−2000
−1800
−1600
−1400
−1200
−1000
Wavelength,λ (μm)
Dispersion D[ps/(nm.km)]
X−Polarization
Fig. 10 Dispersion coefficient versus wavelength for the proposed
S-PCF for the optimum design parameters: K= 0.80 lm; K
c-
= 0.40 lm; d
0
= 0.30 lm; d= 0.76 lm and d
3
= 0.70 lm
24 J Opt (March 2019) 48(1):18–25
123

145.36–83.05 W
-1
km
-1
respectively around wavelength
of 1340–1640 nm. Due to the excellent index-guiding
property, the proposed design will be suitable for broad-
band dispersion compensation and high-speed transmission
system applications. It is also expected that the proposed
PCF will be effective for a lot of future applications like
wideband dispersion compensation in high-bit-rate trans-
mission networks, PM devices and sensing systems.
Acknowledgements The authors are grateful to those who partici-
pated in this research work.
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