In this work, we report detailed numerical analysis of the nearelliptic core indexguiding triangularlattice and squarelattice photonic crystal fiber (PCFs); where we numerically characterize the birefringence, single mode, cutoff behavior and group velocity dispersion and effective area properties. By varying geometry and examining the modal field profile we find that for the same relative values of
d
/
Λ
, triangularlattice PCFs show higher birefringence whereas the squarelattice PCFs show a wider range of singlemode operation. Squarelattice PCF was found to be endlessly singlemode for higher airfilling fraction (
d
/
Λ
). Dispersion comparison between the two structures reveal that we need smaller lengths of triangularlattice PCF for dispersion compensation whereas PCFs with squarelattice with nearer relative dispersion slope (RDS) can better compensate the broadband dispersion. Squarelattice PCFs show zero dispersion wavelength (ZDW) redshifted, making it preferable for midIR supercontinuum generation (SCG) with highly nonlinear chalcogenide material. Squarelattice PCFs show higher dispersion slope that leads to compression of the broadband, thus accumulating more power in the pulse. On the other hand, triangularlattice PCF with flat dispersion profile can generate broader SCG. Squarelattice PCF with low Group Velocity Dispersion (GVD) at the anomalous dispersion corresponds to higher dispersion length (L
_{D}
) and higher degree of solitonic interaction. The effective area of squarelattice PCF is always greater than its triangularlattice counterpart making it better suited for high power applications. We have also performed a comparison of the dispersion properties of between the symmetriccore and asymmetriccore triangularlattice PCF. While we need smaller length of symmetriccore PCF for dispersion compensation, broadband dispersion compensation can be performed with asymmetriccore PCF. MidInfrared (IR) SCG can be better performed with asymmetric core PCF with compressed and high power pulse, while wider range of SCG can be performed with symmetric core PCF. Thus, this study will be extremely useful for designing/realizing fiber towards a custom application around these characteristics.
I. INTRODUCTION
Photonic Crystal Fiber (PCFs)
[1

2]
, which offers a great flexibility to vary the design parameters (
i.e.
, airhole diameter “
d
” and holetohole separation
Λ
) at the fabrication stage, provides the freedom to design the PCF for a number of unique and useful applications like dispersion tailoring, wideband singlemode operation, controlling losses, achieving higher effective area for handling high power applications like supercontinuum generation etc. which are not achievable in standard step index silica fibers. Importantly, with their remarkable and extraordinary features in lightguiding, PCFs are found to be absolutely unique in many applications in the field of photonics. Wellmatured technology is now developed in telecommunication and signal processing applications, metrology, instrumentation, medical surgery and imaging spectroscopy
[3]
.
Some of the unusual and exciting characteristics that have revolutionized the lightguiding features of PCFs are highbirefringence
[4

15]
, endlessly singlemode operation
[16]
, high effective nonlinearity
[17]
and tailoring of Group Velocity Dispersion (GVD)
[18]
. Essentially these characteristics dictate most of today’s fiberbased device applications, in particular the nonlinear fiber devices. For example, a proper study of highly birefringent fiber is extremely necessary for its many applications such as sensing
[19

21]
, long period grating devices
[22]
, fiber ring laser
[23]
, phase matching for fourwave mixing
[24]
, parametric amplifier
[25

28]
etc. In PCF, a very high index contrast is available between silica and airholes. This property, when combined with a large anisotropic geometry, will produce a huge amount of birefringence. For this purpose of anisotropy geometry, several approaches have been followed such as altering the associated structural parameters namely, asymmetric core
[10]
, elliptical airholes
[9]
, different sized airholes
[5
,
13]
and airholes filling with selective liquids along one of their diagonals
[11
,
15]
. Out of the above methods, asymmetric core PCF is the most studied one. Asymmetric core PCF can be created with two adjacent airholes missing in the core region. The concept has been extensively studied and demonstrated for triangularlattice PCF
[8
,
10]
. Similar perception can be applicable for squarelattice PCF with “
Λ
” as the holetohole spacing both in horizontal and vertical directions in the PCF and “
d
” as the diameter of the air holes. To realize asymmetric core squarelattice PCF, two adjacent airholes can be removed from the core region to induce the ellipticity. Symmetric core PCFs are termed as endlessly singlemode upto a certain
d
/
Λ
. The values are 0.406 for a triangular one and 0.446 for a squarelattice one. The above values of cutoff between singlemode and multimode regions cannot be the same for elliptical core PCF. The exact value of the cutoff between single mode and multimode is an important parameter for applications like high power laser delivery in singlemode regime
[29

32]
, to maximize the overlap amongst signal power, pump power and doped region at the core of an amplifier fiber
[33

34]
. The dispersion properties of this fiber; especially the tailoring of zero dispersion wavelength (ZDW) is extremely useful for numerous applications like broadband supercontinuum generation (SCG)
[35]
, ASE (Amplified Spontaneous Emission) suppressed amplifier
[34]
, reduction of soliton fission in SCG
[36]
and different sources for Infrared (IR) applications
[37]
. The above features of PCF are primarily owed to the photonic lattice structure of the fiber. There are two competing technologies available in realizing these microstructured fibers, the triangularlattice
[1

2
,
18]
and squarelattice transverse geometry
[38

39]
. Both the structural approaches have certain advantages and disadvantages. In view of these facts, in this paper, we describe our investigations on the comparative assessment of these key modal properties, namely, birefringence, cutoff and dispersion characteristics of the asymmetric core PCFs with triangularlattice and squarelattice structure with C
_{2}
v symmetry. C
_{n}
symmetry implies that the structure remains unchanged after a rotation of 2π/
n
. The symbol C
_{n}
stands for both a particular symmetry operation and the collection of all symmetry operations based on it. The term C
_{n}
v means that the structure also includes
n
number of planes of reflection symmetry along with the
n
fold rotational symmetry. For our case
n
=2. A detail of the symmetry can be obtained from McIssac
[40]
.
Figures 1(a)
and
(b)
respectively show the triangularlattice and squarelattice cladding structures with two adjacent central holes missing in a silica matrix background. In the analysis of both the structures, we use the conventional notations of airhole diameter as “
d
” and holetohole distance as “
Λ
”. However, we use
Λ
as the holetohole spacing both in horizontal and vertical direction in the PCF with squarelattice air holes and
d
as the diameters of the air holes. The modal field, the dispersion and cutoff calculation are calculated by using CUDOS MOF Utilities
[41]
that simulates PCFs using the multipole method
[42

43]
along with MATLAB
^{®}
for numerically calculating modes, the dispersion relation and cutoff parameter.
Cross section of the designed PCF, the gray area denotes pure silica; the white area denotes air holes. 1(a) triangular lattice PCF and (b) square lattice PCF.
In this present study, we have shown that for the same values of normalized airhole diameter, triangularlattice PCFs show higher birefringence whereas the squarelattice one shows wider range of singlemode operation. We need smaller lengths of triangular PCF for dispersion compensation whereas PCFs with squarelattice can better compensate the broadband dispersion because of their nearmatching dispersion slope with the existing inline fiber. The effective area of squarelattice is always greater than its triangular counterpart, making it better suitable for high power application.
II. MODAL PROPERTIES
 2.1. Birefringence Properties
The availability of large refractive index contrast between core and cladding, and flexibility to engineer the PCF geometrical parameters have made PCF a great candidate for achieving highly birefringent
[4

15]
fiber compared to conventional stepindex fibers. Highly birefringent PCFs can be used as polarization maintaining fibers, which can stabilize the polarization states of the guided light.
Theoretically predicted birefringence for a series of fibers with different airhole size is computed as a function of normalized frequency
Λ
/λ and is shown in
Fig. 2 (a)
triangularlattice airholes
(b)
squarelattice airholes. From
Fig. 2
, we can see that birefringence is strongly improving with the increase of airhole size. From
Fig. 2(a)
, we can see that the maximum birefringence of PCF with triangularlattice air holes is 8.52×10
^{3}
at normalized frequency
Λ
/λ=0.5 and
d
/
Λ
=0.7, which is almost 2 orders of magnitude higher that of the classical fiber. From
Fig. 2(b)
, we can see that the maximum birefringence of PCF with squarelattice air holes is 6.03×10
^{3}
at normalized frequency
Λ
/λ=0.486 and
d
/
Λ
=0.7. From the other values of
d
/
Λ
that we have studied, it is observed that the maximum birefringence is obtained for PCF with triangularlattice for the same
d
/
Λ
value; whereas the maximum birefringence is available for a smaller value of normalized frequency
Λ
/λ for PCF with squarelattice.
Estimated birefringence as a function of Λ/λ with d/Λ as parameter. Arrow sign gives the transition between the first and second mode (a) triangular lattice PCF and (b) square lattice PCF.
An interesting observation can be observed in the above figure for smaller values of airfilling fraction. For smaller values of
Λ
/λ, the birefringence reaches a minimum and then starts increasing again for further reduction of
Λ
/λ. As we go on decreasing the normalized frequency (higher wavelength), the refractive index difference between the two orthogonal modes decreases, subsequently reducing the birefringence. After a certain wavelength (equivalent
Λ
/λ) the effective indices of the two orthogonal modes crossover each other and after that they start to separate away from each other, thereby increasing the birefringence again. We should remember that we are actually calculating absolute difference of the effective indices (abs (
n_{x}

n_{y}
)) of the two orthogonal modes. So, the absolute birefringence reaches a minimum (at the cross over point) and then starts increasing again as can be observed with smaller
d
/
Λ
values for both types of geometry.
Figure 3
shows the maximum birefringence variation with
d
/
Λ
for PCFs with both triangularlattice and squarelattice. We can clearly see that the birefringence is increasing with the increase of
d
/
Λ
. With the same value of
d
/
Λ
, PCFs with triangularlattice are having higher values of birefringence than those of PCFs with squarelattice. The fact can be explained by the concept of airfilling fraction. For a triangularlattice type of arrangement, the airfilling fraction is given by
whereas for a squarelattice arrangement
. From the two formulas, we can see that the airfilling fraction of PCFs with triangularlattice has higher filling fraction than that of the PCFs with squarelattice. Therefore the higher value of airfilling fraction causes the PCFs with triangularlattice to have higher value of birefringence.
Maximum birefringence as a function of d/Λ for both types of PCFs.
Figure 4
shows the normalized frequency
Λ
/λ corresponding to maximum birefringence as a function of
d
/
Λ
. We can see that the normalized frequency
Λ
/λ corresponding to maximum birefringence decreases with the increase of
d
/
Λ
. At the same value of
d
/
Λ
, the normalized frequency
Λ
/λ corresponding to maximum birefringence of PCFs with triangularlattice is higher than that of PCFs with squarelattice.
Normalized frequency (Λ/λ) as a function of d/Λ for both types of PCFs.
 2.2. Cutoff Properties and Single Mode Region
Triangularlattice PCFs with a symmetric core are endlessly single mode for normalized hole sizes up to a value as large as
d
/
Λ
=0.406
[44

45]
, where as the symmetric core PCF with rectangularlattice is endlessly single mode for normalized hole sizes up to a value as large as
d
/
Λ
=0.442
[46]
. This cannot be the case for the present fibers as the core region for the structure under concern is different from a normal one. We performed the cutoff analysis according to Kuhlmey
et al
[44]
and Poli
et al
[46]
. The multipole method
[42

43]
that has been used for the development of CUDOS MOF utilities has the unique ability to calculate both the modes and their losses accurately. In
Fig. 5
we have shown the variation of the imaginary part of
n
_{eff}
(Im(
neff)) with
λ/
Λ
. Im(
neff
) is given by Eqn. (1)
where β is the complex propagation constant and
κ_{0}
is the freespace wave number for the second mode. The figure represents Im(n
_{eff}
) variation in a MOF with 3 rings (42 holes) for three different values of
d
/
Λ
, respectively 0.25, 0.30 and 0.40. Im(
n
_{eff}
) is linked to the geometrical losses
L
(dB/km) through Eqn. (2) such that the loss and Im(
n_{eff}
) are proportional at a fixed wavelength.
Im(n_{eff}) as a function of λ/Λ for the PCF structure with triangularlattice.
A clear shift from the regular variation can be observed as we increase the airfilling fraction (
d
/
Λ
). The figure shows a sharp transition in the ratio of Im(
n
eff) (loss equivalent) versus λ/
Λ
for
d
/
Λ
>0.25, whereas for
d
/
Λ
≤0.25 the transition becomes increasingly gradual. With the increase of
d
/
Λ
(
d
/
Λ
=0.3 and 0.4), the transition becomes more and more acute. With the increase of airfilling fraction, the curve deviated more and more from the original regular path signifying the PCF to be of multimode at higher λ/
Λ
(or smaller
Λ
/λ).
The transition can be studied with some other parameters as well
[44

46]
. The transition can be better viewed if we plot the second derivative of the logarithm of the imaginary part of the effective index with respect to the wavelength, the Q parameter (specified by Eqn. (3)) as shown in
Fig. 6
[44]
.
Variation of the Q factor (3) during the transition for the PCF with triangularlattice.
The approach has been a little different than which has been followed in their work. The wavelength has been changed in place of pitch for our study. The Q parameter shows a sharp negative minimum, giving an accurate value for the transition.
Figure 6
clearly shows a distinct minimum for
d
/
Λ
values of 0.30 and 0.40, whereas no minimum would be observed for
d
/
Λ
value of 0.25. So whereas the regular PCF with triangularlattice is singlemode up to a value of
d
/
Λ
=0.4, the present design is indeed found to support a secondorder mode with a cutoff
Λ
/λ=1.19 for the same value of
d
/
Λ
. The fibers support secondorder modes with a holesize as small as
d
/
Λ
=0.3.We have studied the cutoff analysis of the PCF structure for triangularlattice for
d
/
Λ
values of 0.3, 0.4, 0.5, 0.6 and 0.7 and the second order cutoffs are marked with arrows in the
Fig. 2
. Our study reveals that this fiber structure of PCF with triangularlattice with holesize
d
/
Λ
=0.25 or smaller may be classified as endlessly singlemode.
With the same analogy as that of the PCF with triangularlattice, we have studied the cutoff properties of the PCF with squarelattice as well.
Figure 7
shows Im(n
_{eff}
) of the second mode of the PCF with squarelattice. It is clearly visible that a transition is taking place for
d
/
Λ
values greater than 0.28. Similarly to
Fig. 5
, with the increase of airfilling fraction, the loss curve deviated more and more from the original regular path signifying that the PCF, at higher λ/
Λ
(or smaller
Λ
/λ), is becoming multimode. For an accurate determination of the transition point between the singlemode and multimode we have plotted the
Q
parameter (Eqn. (3)) for the second mode of the PCF with squarelattice as shown in
Fig. 8
. It is clearly shown that there is no minimum for the Q parameter for the
d
/
Λ
value of 0.28.
Im(_{neff}) as a function of λ/Λ for the PCF structure with squarelattice.
Variation of the Q factor (3) during the transition for the PCF with squarelattice.
Similar to the PCF with triangularlattice, we have studied the cutoff analysis of the PCF with squarelattice for
d
/
Λ
values of 0.3, 0.4, 0.5, 0.6 and 0.7 and the second mode cutoff regions are marked with arrows in the
Fig. 2 (b)
. Our study reveals that this fiber structure of PCF with squarelattice with holesize
d
/
Λ
=0.28 or smaller may be classified as endlessly singlemode for PCFs with squarelattice.
Figure 9
shows the cutoff normalized frequency
Λ
/λ as a function of d/
Λ
for PCF with both triangularlattice and squarelattice. We can see that the cutoff normalized frequency
Λ
/λ for the PCFs decreases with the increase of d/
Λ
. At the same value of d/
Λ
, the normalized frequency
Λ
/λ corresponding to maximum birefringence of PCFs with triangularlattice is lower than that of PCFs with squarelattice. So PCF with squarelattice is single mode for higher values of d/
Λ
.
Normalized cutoff frequency Λ/λ as a function of d/Λ for both types of PCFs.
 2.3. Dispersion Properties
PCFs possess the attractive property of great controllability in waveguide dispersion
[18]
. The dispersion property for both the PCFs with triangularlattice and squarelattice can be controlled by varying the airhole diameter
d
and pitch
Λ
. Controllability of waveguide dispersion in PCFs is an important issue for applications to optical communications, dispersion compensation, nonlinear applications, etc. We have calculated the dispersion of the structures through Eqn. (4).
Figure 10
shows the dispersion properties of the PCF with triangularlattice and squarelattice for xpolarized component for different values of airfilling fraction (
d
/
Λ
) with
Λ
=1 μm. It can be observed that for both types of fibers dispersion slope is always positive for smaller values of airfilling fraction (0.3 and 0.4). With the increase of
d
/
Λ
value to 0.5 the dispersion values change drastically and the slope is always negative throughout the wavelength range we considered. As we go still further for higher values of
d
/
Λ
, though the slope is negative the effective dispersion values become more and more positive. So both types of fiber with moderate value of airfilling fraction (0.5 here) can better compensate the dispersion. When
Λ
becomes larger the effect of waveguide dispersion decreases and material dispersion dominates the dispersion for both regular triangularlattice PCFs
[18
,
47]
and for squarelattice PCF
[38

39]
. The same is confirmed for both types of structures as shown in
Fig. 11
where we have considered higher values of
Λ
for both elliptical core triangularlattice and squarelattice PCFs in
Fig. 11(a)
and
11(b)
, respectively, as we increase the
Λ
to 2 μm.
Figure 11
shows the dispersion properties of the structures for x polarized component for higher values of
Λ
(
Λ
=2 μm). When the
d
/
Λ
is very small and
Λ
is large, the dispersion curve is close to that of the material dispersion of pure silica. As the airhole diameter is increased, the influence of waveguide dispersion becomes stronger. We can see that it is possible to shift the zero dispersion wavelength from visible to nearinfrared (IR) by appropriately changing the geometrical parameters such as
Λ
and
d
for both type of PCFs with triangularlattice and squarelattice. For even higher values of
Λ
(=3 μm, not shown here) the dispersion values are all positive with a higher positive slope than with
Λ
=2 μm. A comparison of the two types of PCFs with higher
Λ
(=2.5 μm) and
d
/
Λ
=0.4 has been considered for a wideband wavelength range as shown in
Fig. 12
. The two dotted lines show the ZDW corresponding to the two different PCF structures. The graph establishes some significant outcomes as explained below. First of all, with the similar geometrical parameters, the ZDW of the squarelattice PCF is redshifted which is preferable for midIR SCG, especially those using nonsilica high nonlinear chalcogenide PCFs. Secondly, the dispersion profile of the squarelattice PCF shows a higher slope (
i.e.
the curve is less flat) than the dispersion characteristics revealed by similar type regular triangularlattice structures. The high slope in the dispersion curve leads to compression of the generated broadband accumulating more power in the supercontinuum pulse. On the other hand, with flatter slope with triangular PCF, we could have a wider range of SCG. Thirdly, squarelattice PCF has low GVD at the anomalous dispersion region which corresponds to higher Dispersion Length (L
_{D}
) and higher degree of solitonic interaction. The effective area corresponding to the above structure has been presented in
Fig. 13
which clearly shows that squarelattice PCF has a higher amount of effective area which is preferable for high power applications as the larger core can accumulate a higher amount of power. Also higher effective area means a higher threshold power limit before material damage occurs.
Comparison of the D parameter for both types of PCFs with different value of d/Λ with Λ=1 μm for (a) triangularlattice PCF and (b) squarelattice PCF.
Comparison of the dispersion parameter values D for both the polarization for both types of PCFs with Λ=2 μm for (a) triangularlattice PCF and (b) squarelattice PCF.
Comparison of the dispersion properties (xpolarization) of triangularlattice and squarelattice PCFs with d/Λ=0.4, for Λ=2.5 μm. ZDWs for both the structures are shown by the dotted lines.
Comparison of the effective area variation of both types of PCFs keeping Λ=2.5 μm with d/Λ=0.4.
A comparison for dispersion compensation has been carried out in
Fig. 14
, where we have taken
Λ
=1μm and
d
/
Λ
=0.5. The graph clearly indicates that both types of fibers can be useful for dispersion compensation while higher values of negative dispersion can be achieved with the triangular one. However, the relative dispersion slope (RDS) value, which is very important for broadband dispersion compensation
[48]
, is better for the squarelattice with RDS of 0.00175 nm
^{1}
, whereas for the triangular one the value is 0.00113 nm
^{1}
at 1550 nm with the RDS value of the standard SMF28 at this wavelength is 0.0036 nm
^{1}
.
Comparison of the dispersion variation for both types of PCFs keeping Λ=1 μm with d/Λ=0.5.
 2.4. Single Mode Properties Comparison
A final analysis on the properties of both types of elliptical core PCFs is reported in
Fig. 15
for different values of
Λ
values namely 1 μm and 2 μm. We have taken
d
/
Λ
values to be 0.3 for our study such that both the elliptical core PCFs remains singlemode in the whole wavelength considered. As we have already observed that elliptical core squarelattice is endlessly single mode upto a
d
/
Λ
value of 0.28, where as the elliptical core triangular PCFs are endlessly singlemode for
d
/
Λ
value upto 0.25. We have observed that cutoff normalized frequency (
Λ
/λ) for elliptical core triangularlattice PCF and square–lattice PCF are 1.785 and 2.041, respectively for
d
/
Λ
=0.3. Taking into consideration of the above values we have restricted our study for single mode operation. Squarelattice PCF has higher
D
values than triangular PCF for larger values of
Λ
(
i.e.
2 μm) in the wavelength range considered. An interesting fact can be observed from the figure that squarelattice PCF has higher
D
values than triangular PCF for smaller values of
Λ
(
i.e.
1 μm) but the values crossover and reverse phenomenon took place after crossover. The dispersion slope has been affected a little with the geometrical characteristics of the lattice. With the increase of the
Λ
values the slope almost vanishes as we move towards the higher wavelength ranges. PCFs with squarelattice always have higher effective area than triangular one for both the pitches as shown in
Fig. 15(b)
.
Comparison of (a) dispersion variation (b) effective area of the two types of PCFs when they are under single mode operation.
 2.5. Comparison with Symmetricalcore PCF
We have performed a comparative analysis of dispersions properties of the triangular lattice PCF between the symmetriccore and the asymmetriccore geometry. As we have already observed that the best performance in terms of broadband dispersion compensation with elliptical core PCF can be achieved with
Λ
=1 μm and
d
/
Λ
=0.5 (
Fig. 10
), we have considered the above parameters (
Λ
= 1 μm with
d
/
Λ
=0.5) for both the cores to have a comparison with the regular triangularlattice PCF. The findings are demonstrated in
Fig. 16
. It can be observed from the figure that regular symmetriccore PCF has higher negative value of dispersion at the communication wavelength of 1550 nm, which clearly indicates that we need smaller length of the fiber for total dispersion compensation. However, the slope of the dispersion curve for symmetriccore PCF around 1550 nm of wavelength is positive. It is well known that dispersion accumulates due to propagation of light in the existing inline fiber (SMF28 is) is positive with a positive slope. Therefore, to compensate the broadband dispersion, our dispersion compensating fiber should consist of negative dispersion with a negative slope. So, broadband dispersion compensation can’t be possible with the above geometrical parameter with symmetriccore PCF. Consequently, for broadband dispersion compensation, ellipticalcore PCF with negative dispersion and negative slope with
Λ
=1 μm and
d
/
Λ
=0.5 will be a better choice.
Comparison of the dispersion properties for symmetriccore and asymmetriccore PCFs with Λ=1μm and d/Λ=0.5.
In another comparison, we have considered higher
Λ
(=2.5 μm) and smaller
d
/
Λ
(=0.4) for both types of symmetriccore and asymmetriccore PCFs. The comparative study has been demonstrated in
Fig. 17
with the value of the ZDW presented with the vertical dotted line. The figure clearly presents that the ZDW of the asymmetriccore PCF is redshifted compared to that of symmetriccore PCF, which in turn establishes that midIR SCG can be better performed with elliptical core PCF with the same geometrical parameters.
Comparison of the dispersion properties for symmetriccore and asymmetriccore PCFs with Λ=2.5 μm and d/Λ=0.4. ZDWs for both the structures are shown by the dotted lines.
It is also interesting to note that the dispersion profile of the asymmetriccore PCF shows a higher slope (
i.e.
the curve is less flat) than the dispersion characteristics revealed by similar type regular symmetriccore PCF structures. The higher slope in the dispersion curve leads to compression of the generated broadband accumulating more power in the supercontinuum pulse. On the other hand, with flatter slope with symmetriccore PCF, we could have a wider range of SCG.
III. CONCLUSION
We have shown that a high birefringence of the order of 10
^{2}
can be achieved in both the PCFs with triangularlattice and squarelattice airhole arrangement in the cladding and a silica core of the PCFs that is formed by removing two adjacent holes in the center of the fiber. Our numerical calculations establish that maximum birefringence can be achieved with PCFs with triangularlattice, where as wider range of single mode operation is possible for PCFs with squarelattice. Triangularlattice PCF was found to be endlessly singlemode for an airfilling fraction (
d
/
Λ
) of 0.25, whereas the squarelattice PCF was found to be endlessly singlemode for higher
d
/
Λ
of 0.28. A comparison regarding the dispersion characteristics of the two structures reveal that, we need smaller length of triangularlattice PCF for dispersion compensation, whereas PCFs with squarelattice can better compensate broadband dispersion compensation due to the better matching of the RDS with the existing SMF28. In addition to the above, squarelattice PCFs show ZDW redshifted making it preferable for midIR SCG with chalcogenide material. Also its dispersion profile with higher dispersion slope leads to compression of the broadband accumulating more power in the pulse. On the other hand, triangularlattice PCF with flat dispersion profile can generate broader SCG. Squarelattice PCF with low GVD at the anomalous dispersion corresponds to higher dispersion length (L
_{D}
) and higher degree of solitonic interaction. The effective area of squarelattice PCF is always greater than its triangularlattice counterpart making it better suitable for high power accumulations and enhanced threshold power limit for material damage. We have also performed a comparison of the dispersion properties of between the symmetriccore and asymmetriccore triangular lattice PCF. While we need smaller length of symmetriccore PCF for dispersion compensation, broadband dispersion compensation can be performed with asymmetriccore PCF with
Λ
=1 μm and
d
/
Λ
=0.5. MidIR SCG can be better performed with asymmetric core PCF with compressed broadband that can accumulate high power in the pulse because of higher slope, while on the other hand symmetric core PCF can generate a wider range of SCG because of its flatter slope. Thus, these analyses will be extremely useful for realizing fiber aiming towards a custom application around these characteristics.
Acknowledgements
The authors would like to thank Dr. Boris Kuhlmey, University of Sydney, Australia for providing valuable suggestions during the designing and studying of the properties of the structure.
Broeng J.
,
Mogilevstev D.
,
Barkou S. E.
,
Bjakle A.
1999
“Photonic crystal fibers: A new class of optical waveguides,”
Opt. Fiber Tech.
5
305 
330
Knight J. C.
2003
“Photonic crystal fibers,”
Nature
424
847 
851
Cerqueira S. A.
2010
“Recent progress and novel applications of photonic crystal fibers,”
Rep. Prog. Phys.
73
1 
21
OrtigossBlanch A.
,
Knight J. C.
,
Wadsworth W. J.
,
Arriaga J.
,
Russel P. St. J.
2000
“Highly birefringent photonic crystal fiber,”
Opt. Lett.
25
1325 
1327
Suzuki K.
,
Kubota H.
,
Kawanishi S.
,
Tanaka M.
,
Fujita M.
2001
“Optical properties of a lowloss polarizationmaintaining photonic crystal fiber,”
Opt. Express
9
676 
680
Simpson J. R.
,
Stolen R. H.
,
Sears F. M.
,
Pleibel W.
,
Macchesney J. B.
,
Howard R. E.
1983
“A singlepolarization fiber,”
J. Lightwave Technol.
LT1
370 
374
Kubota H.
,
Kawanishi S.
,
Koyanagi S.
,
Tanaka M.
,
Yamaguchi S.
2004
“Absolutely singlepolarization photonic crystal fiber,”
IEEE Photon. Technol. Lett.
16
182 
184
Roychoudhuri P.
,
Poulose V.
,
Zhao C.
,
Lu C.
2004
“Near elliptic core polarization maintaining photonic crystal fiber: Modeling birefringence characteristics and realization,”
IEEE Photon. Techol. Lett.
16
1301 
1303
Steel M. J.
,
Osgood R. M.
2001
“Polarization and dispersive properties of ellipticalhole photonic crystal fibers,”
J. Lightwave Technol.
19
495 
503
Hansen T. P.
,
Broeng J.
,
Libori S. E. B.
,
Enudsen E.
,
Bjarklev A.
,
Jensen J. R.
,
Simpson H.
2001
“Highly birefringent indexguiding photonic crystal fibers,”
IEEE Photon. Technol. Lett.
13
588 
590
Liou J. H.
,
Huang S. S.
,
Yu C. P.
2010
“Lossreduced highly birefringent selectively liquidfilled photonic crystal fibers,”
Opt. Commun.
283
971 
974
Saitoh K.
,
Koshiba M.
2003
“Singlepolarization singlemode photonic crystal fibers,”
IEEE Photon. Technol. Lett.
15
1384 
1386
Cho T. Y.
,
Kim G. H.
,
Lee K.
,
Lee S. B.
2008
“Study on the fabrication process of polarization maintaining photonic crystal fibers and their optical properties,”
J. Opt. Soc. Korea
http://dx.doi.org/10.3807/JOSK.2008.12.1.019
12
(1)
19 
24
Lee S. G.
,
Lim S. D.
,
Lee K.
,
Lee S. B.
2010
“Broadband singlepolarization singlemode operation in highly birefringent photonic crystal fiber with a depressedindex core,”
Jpn. J. Appl. Phys.
49
12 
Maji P. S.
,
Roy Chaudhuri P.
2014
“Tunable selective liquid infiltration: Applications to low loss birefringent photonic crystal fibers (PCF) and its single mode realization,”
Journal of Photonics and Optoelectronics
2
27 
37
Birks T. A.
,
Knight J. C.
,
Russell P. St. J.
1997
“Endlessly singlemode photonic crystal fiber.”
Opt. Lett.
22
961 
963
Dudley J. M.
,
Taylor J. R.
2009
“Ten years of nonlinear optics in photonic crystal fibre,”
Nature Photonics
3
85 
90
Kuhlmey B.
,
Renversez G.
,
Maystre D.
2003
“Chromatic dispersion and losses of microstructured optical fibers,”
Appl. Opt.
42
634 
639
Dong B.
,
Zhao Q.
,
Lvjun F.
,
Guo T.
,
Xue L.
,
Li S.
,
Gu H.
2006
“Liquidlevel sensor with a highbirefringencefiber loop mirror,”
Appl. Opt.
45
7767 
7771
Hu S.
,
Zhan L.
,
Song Y. J.
,
Li W.
,
Luo S. Y.
,
Xia Y. X.
2005
“Switchable multiwavelength erbiumdoped fiber ring laser with a multisection highbirefringence fiber loop mirror,”
IEEE Photon. Technol. Lett.
17
1387 
1389
Yange L.
,
Bo L.
,
Xinhuan F.
,
Weigang Z.
,
Guang Z.
,
Shuzhong Y.
,
Guiyun K.
,
Xiaoyi D.
2005
“Highbirefringence fiber loop mirrors and their applications as sensors,”
Appl. Opt.
44
2382 
2390
Zhang L.
,
Liu Y.
,
Everall L.
,
Williams J. A. R.
,
Bennion I.
1999
“Design and realization of longperiod grating devices in conventional and high birefringence fibers and their novel applications as fiberoptic load sensors,”
IEEE J. Select. Topics Quantum Electron.
5
1373 
1378
Chen L. R.
2004
“Tunable multiwavelength fiber ring lasers using a programmable highbirefringence fiber loop mirror,”
IEEE Photon. Technol. Lett.
17
410 
412
McKinstrie C.
,
Kogelnik H.
,
Jopson R.
,
Radic S.
,
Kanaev A.
2004
“Fourwave mixing in fibers with random birefringence,”
Opt. Express
12
2033 
2055
Xu Y. Q.
,
Murdoch S. G.
,
Leonhardt R.
,
Harvey J. D.
2009
“Ramanassisted continuouswave tunable allfiber optical parametric oscillator,”
J. Opt. Soc. Am. B
26
1351 
1356
Guasoni M.
,
Kozlov V. V.
,
Wabnitz S.
2012
“Theory of polarization attraction in parametric amplifiers based on telecommunication fibers,”
J. Opt. Soc. Am. B
29
2710 
2720
Drummond P. D.
,
Kennedy T. A. B.
,
Dudley J. M.
,
Leonhardt R.
,
Harvey J. D.
1990
“Crossphase modulational instability in highbirefringence fibers,”
Opt. Commun.
78
137 
142
Stéphane C.
,
Lun C. A. H.
,
Rainer L.
,
Harvey J. D.
,
Knight J. C.
,
Wadsworth W. J.
,
Russell P. St J.
2002
“Supercontinuum generation by stimulated Raman scattering and parametric fourwave mixing in photonic crystal fibers,”
J. Opt. Soc. Am B
19
753 
764
Limpert J.
,
Schmidt O.
,
Rothhardt J.
,
Röser F.
,
Schreiber T.
,
Tünnermann A.
,
Ermeneux S.
,
Yvernault P.
,
Salin F.
2006
“Extended singlemode photonic crystal fiber lasers,”
Opt. Express
14
2715 
2720
Knight J. C.
2007
“Photonic crystal fibers and fiber lasers,”
J. Opt. Soc. Am. B
24
1661 
1668
Fabian S.
,
Florian J.
,
Tino E.
,
Alexander S.
,
Cesar J.
,
Jens L.
,
Andreas T.
2011
“High average power largepitch fiber amplifier with robust singlemode operation,”
Opt. Lett.
36
689 
691
Platonov N. S.
,
Gapontsev D. V.
,
Gapontsev V. P.
,
Shumilin V.
2002
“135W CW fiber laser with perfect single mode output,”
CLEO
in Proc. Conference on Lasers and ElectroOptics
2
CPDC3 
1~CPDC34
Mondal K.
,
Roy Chaudhuri P.
2011
“Designing high performance Er+3 doped fiber amplifier based on triangular lattice photonic crystal fiber,”
Optics and Laser Technology
43
1436 
1441
Varshney S. K.
,
Saitoh K.
,
Koshiba M.
,
Pal B. P.
,
Sinha R. K.
2009
“Design of Sband Erbiumdoped, concentric dualcore photonic crystal fiber amplifiers with ASE and SRS suppression,”
J. Lightwave Technol.
27
1725 
1733
Roy S.
,
Chaudhuri P. R.
2009
“Supercontinuum generation in visible to mid infrared region in squarelattice photonic crystal fiber made from highly nonlinear glasses”
Opt. Commun.
282
3448 
3455
Baili A.
,
Cherif R.
,
Zghal M.
2012
“New design of As2Se3based chalcogenide photonic crystal fiber for ultrabroadband, coherent, midIR supercontinuum generation,”
Proc. SPIE
8564
856409 
1
Eggleton B. J.
,
LutherDavies B.
,
Richardson K.
2011
“Chalcogenide photonics,”
Nature Photonics
5
141 
148
Bouk A. H.
,
Cucinotta A.
,
Poli F.
,
Selleri S.
2004
“Disperson properties of squarelattice photonic crystal fibers,”
Opt. Express
12
941 
946
Im J.
,
Kim J.
,
Paek U. C.
,
Lee B. H.
2005
“Guiding properties of squarelattice photonic crystal fibers,”
J. Opt. Soc. Korea
http://dx.doi.org/10.3807/JOSK.2005.9.4.140
9
(4)
140 
144
McIsaac P. R.
1975
“Symmetryinduced modal characteristics of uniform waveguides. I. Summary of results,”
IEEE Trans. Microwave Theory Tech.
MTT23
421 
429
CUDOS MOF utilities
available online: http://www.physics.usyd.edu.au/cudos/mofsoftware/
White T. P.
,
Kuhlmey B. T.
,
PcPhedran R. C.
,
Maystre D.
,
Renversez G.
,
de Sterke C. M.
,
Botten L. C.
2002
“Multipole method for microstructured optical fibers. I. Formulation,”
J. Opt. Soc. Am. B
19
2322 
2330
Kuhlmey B. T.
,
White T. P.
,
PcPhedran R. C.
,
Maystre D.
,
Renversez G.
,
de Sterke C. M.
,
Botten L. C.
2002
“Multipole method for microstructured optical fibers. II. Implementataion and results,”
J. Opt. Soc. Am. B
19
2331 
2340
Kuhlmey B. T.
,
PcPhedran R. C.
,
de Sterke C. M.
2002
“Modal cutoff in microstructured optical fibers,”
Opt. Lett.
27
1684 
1686
Kuhlmey B. T.
,
PcPhedran R. C.
,
de Sterke C. M.
,
Robinson P. A.
,
Remversez G.
,
Maystre D.
2002
“Microstructured optical fibers: Where’s the edge?,”
Opt. Express
10
1285 
1290
Poli F.
,
Foroni M.
,
Bottacini M.
,
Fuochi M.
,
Burani N.
,
Rosa L.
,
Cucinotta A.
,
Selleri S.
2005
“Single mode regime of squarelattice photonic crystal fibers,”
J. Opt. Soc. A
22
1655 
1661
Maji P. S.
,
Chaudhuri P. R.
2013
“A new design of ultraflattened nearzero dispersion PCF using selectively liquid infiltration,”
Photonics and Optoelectronics
2
24 
31
Poli F.
,
Cucinotta A.
,
Fuochi M.
,
Selleri S.
2003
“Characterization of microstructured optical fibers for wideband dispersion compensation,”
J. Opt. Soc. Am. B
20
1958 
1962