This article appeared in a journal published by Elsevier. The attachedcopy is furnished to the author for internal non-commercial researchand education use, including for instruction at the authors institution

and sharing with colleagues.

Other uses, including reproduction and distribution, or selling orlicensing copies, or posting to personal, institutional or third party

websites are prohibited.

In most cases authors are permitted to post their version of thearticle (e.g. in Word or Tex form) to their personal website orinstitutional repository. Authors requiring further information

regarding Elsevier’s archiving and manuscript policies areencouraged to visit:

http://www.elsevier.com/copyright

Author's personal copy

Extremely large birefringence and shifting of zero dispersion wavelengthof photonic crystal fibers

Rakhi Bhattacharya, S. Konar n

Department of Applied Physics, Birla Institute of Technology, Mesra-835215, Ranchi, Jharkhand, India

a r t i c l e i n f o

Article history:

Received 23 December 2011

Received in revised form

28 February 2012

Accepted 29 February 2012Available online 22 March 2012

Keywords:

Photonic cryatal fibers

Dispersion

Birefringence

a b s t r a c t

Three different types of photonic crystal fibers have been investigated which promise very large

birefringence. The first type fiber is band gap guiding, the second index guiding, while the third type is

index guiding with high refractive index circular and elliptical regions in the innermost ring. The

birefringence, group velocity dispersion, modal effective index and mode field area of these fibers have

been numerically estimated by employing finite difference time domain method. When elliptical

regions are introduced in the first and second rings with the combination of small circular regions, each

of these proposed fibers exhibits large birefringence with shifted zero dispersion point. Among these

three different types of fibers, the band gap guiding photonic crystal fiber promises the largest

birefringence (�5.45�10�2) reported so far. The value of the birefringence and group velocity

dispersion of these fibers can be controlled by controlling the hole pitch. Largest birefringence is

achieved with a specific value of hole pitch.

& 2012 Elsevier Ltd. All rights reserved.

1. Introduction

The excellent propagation properties of photonic crystal fibers(PCFs) have attracted considerable attention since their firstfabrication in 1996 [1]. Many research groups all over the worldare making tremendous efforts to establish the superiority of PCFsover conventional fibers because of their novel optical character-istics. PCFs can be made from single material such as silica, withan array of air holes running along the length of the fiber [1–6].PCFs generally guide light by two different guiding mechanismsi.e., index guiding [1] and band gap guiding [7]. In index guidingPCFs, similar to conventional fibers, light is guided in a high indexcore by modified total internal reflection from a low effectiveindex cladding. On the other hand, in band gap guiding PCFs, lightis confined in a low index core by reflection. Because of theirnovel guiding mechanisms and diversity in design, PCFs have anumber of novel properties and significant applications. For indexguiding PCFs, these properties include endlessly single modeness[5], large mode area [8], high numerical aperture [9], highbirefringence [10], high nonlinear coefficient [11] and tailorablelarge dispersion [12]. Different types of band gap fibers such aslow loss air core [13], all solid [14] have been also designed whichfind important applications that includes CO2 laser beam trans-mission [15], gas sensing etc.

One of the potential applications of PCFs is that, they can bedesigned to exhibit high birefringence. Maintenance of state ofpolarization of optical field is very important property which isuseful for coherent optical communication and fiber optic sen-sors. Conventional single mode fibers with circular symmetriccore cannot maintain polarization state of the electromagneticfield due to several factors, such as, random irregularities alongthe length of the fiber, stress, twists and bends. Polarization statesof optical fields can be maintained by introducing modal birefrin-gence. Several authors have investigated birefringence of indexguiding PCFs in which the birefringence is introduced either byasymmetric core design, change of size of a few air holes [10,16]or by using squeezed crystal lattice, which means that the air holediameter along two orthogonal axes are different [17]. Somepolarization maintaining fibers employ elliptical air holes toproduce high birefringence [18,19,26]. Saitoh et al. [20] havestudied birefringence in a band gap guiding PCF with asymmetricair core. Experimental results of high birefringence (�10�3)at wavelength 1.55 mm in bandgap guiding PCFs have beenreported [21]. Wang et al. [22] have proposed bandgap guidingPCFs with elliptical air holes. Recently Lungso et al. [23] havereported two different types of polarization maintaining solidPCFs that guide light by a combination of a photonic band gap andtotal internal reflection. They have studied group and phasebirefringence experimentally and numerically, whose value�10�4. Cho et al. [24] have reported highly birefringent terahertzpolarization maintaining plastic PCFs which exhibit an extremelylarge birefringence (2.1�10�2).

Contents lists available at SciVerse ScienceDirect

journal homepage: www.elsevier.com/locate/optlastec

Optics & Laser Technology

0030-3992/$ - see front matter & 2012 Elsevier Ltd. All rights reserved.

http://dx.doi.org/10.1016/j.optlastec.2012.02.036

n Corresponding author.

E-mail address: swakonar@yahoo.com (S. Konar).

Optics & Laser Technology 44 (2012) 2210–2216

Author's personal copy

In this paper, we have investigated three different types ofPCFs which promise extremely large birefringence. In the firstdesign, the fiber is composed of seven rings of air holes, the holesare arranged in triangular lattice formation with some selected airholes of elliptical shape. The central air hole acts as the core of thefiber whose air hole diameter and pitch are adjusted to ensureband gap guiding. The second fiber is very similar to the first oneexcept it has a solid core ensuring index guiding. The third type offiber is also index guiding, having similar structure, with anoticeable difference that a selected few elliptical air holes inthe innermost ring is replaced by a medium of refractive index1.48. We have investigated important optical properties such asbirefringence, dispersion characteristics, effective refractiveindex, effective V parameter and mode field pattern of thesefibers. We have also compared optical properties of these fibers.The present investigation reveals that the birefringence of theband gap guiding PCFs is �5.45�10�2, which to the best of ourknowledge is much larger than the birefringence reported so far.

2. Modeling method

In order to study optical properties of the designed fibers, wehave employed finite difference time domain (FDTD) method [25]which is based on direct discretization of Maxwell’s equations. Inorder to absorb outgoing waves without reflection, special con-ditions are required on the boundaries of the computationaldomain. To absorb these outgoing waves without reflection, wehave used perfectly matched layers. Starting from a given fielddistribution, the time-evolution of the electromagnetic field iscalculated over a given spatial domain. This makes FDTD methoda tool that is suitable for investigating the electromagnetic wavepropagation in complicated structures. The FDTD computer codeis derived by the discretization of Maxwell’s equations using Yee’sspace cell [25,28]. The FDTD approximations to the fields Hx

(x-component magnetic field) and Ex (x-component electric field)obtained from Maxwell’s equations in the computational domain.The FDTD approximations to other field components can beobtained in a similar manner. Once necessary information suchas permittivity, permeability, conductivity and the initial distri-bution of the source fields are known at each space grid point, thetime evolution of the fields can be obtained by using leapfrogtime-step. For fixed number of time steps, the computational timeis proportional to the number of discretization points in thecomputational domain. To keep the method stable, the time stepsshould follow:

Dtr1

vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

1Dx2 þ

1Dy2 þ

1Dz2

q , ð1:1Þ

where Dx,Dy, Dz are the space steps in three different directions,respectively, Dt is the time step and v is the speed of light in thelayout. In order to verify accuracy and authenticity of the FDTDcode, we have confirmed that the code is able to reproduce well-known results reported elsewhere [27].

3. Band gap guiding PCF: Birefringence and dispersion

In order to design band gap guiding PCFs for device and systemapplications, it is essential to establish a detail understanding ofthe polarization properties of these fibers. For example, it isimportant to know how fiber structure affects birefringence andpolarization mode dispersion. In our first attempt in this direc-tion, we have considered a PCF where air holes are arranged intriangular lattice pattern with air filling fraction f¼70%. The airfilling fraction is defined as the total area of the air holes in a unit

cell relative to the total unit cell area. The proposed fiber is shownin Fig. 1, which has seven rings of air holes in the cladding region.The inner most ring is composed of two large elliptical air holesand four small circular air holes. The second ring is also composedof circular and elliptical air holes. The major axes of all ellipticalholes are in the same direction. From subsequent investigations ithas been verified that elliptical air holes at the first and secondring ensure high birefringence. The air hole at the centre makesthe fiber band gap guiding. The diameter of circular air holes is d

and the centre to centre distance between two air holes i.e., holepitch is L. The length of the major and minor axes of the ellipseare dL and dS, respectively. Diameter of the small air holes at thefirst ring is d1 and diameter of the air holes at the centre is dcore.To begin with, we have investigated a band gap PCF in whichL¼1.8 mm and d¼0.7�L¼1.26 mm. Length of the major andminor axes of the elliptical air holes are dL¼0.8�L¼1.44 mm anddS¼0.5�L¼0.9 mm, respectively. Diameter of the small air holesin the first ring is d1¼0.4�L¼0.72 mm and that of the core isdcore¼sqrt(f)�L¼1.50 mm, respectively. We have calculated thevariation of effective refractive indices as a function of wave-length of the two orthogonal polarization modes i.e., horizontalpolarization mode and vertical polarization mode. The modalbirefringence B is defined as the difference of refractive indices ofhorizontal and vertical polarization modes. The variation of modalbirefringence with operating wavelength l has been demon-strated in Fig. 2. The figure demonstrates quite a large value ofbirefringence. As an illustration, consider the curve (a) in Fig. 2which shows modal birefringence �5.45�10�2 at l¼1.55 mm.It is worth pointing out that this is the largest value of birefrin-gence reported till date. From figure it is obvious that the modalbirefringence increases with increasing l. Another importantpoint to note is that L¼1.8 mm is the optimum value of holepitch for achieving large birefringence. If we increase L further,then the value of birefringence decreases with the increase in thevalue of L. As an example, for L¼2.0 mm, the value of birefrin-gence is less in comparison to its value at L¼1.8 mm.

Fig. 1. Cross section of the proposed highly birefringent band gap guiding PCF

which consists of seven rings of air holes. Air holes are arranged in the triangular

lattice formation with elliptical and circular air holes in two inner rings.

L¼1.8 mm, d¼0.7�L¼1.26 mm, length of the horizontal and vertical axes of

the elliptical air holes are dL¼0.8�L¼1.44 mm and dS¼0.5�L¼0.9 mm, respec-

tively. Diameter of the small air holes in the first ring and center are

d1¼0.4�L¼0.72 mm and dcore¼sqrt(0.7)�1.8¼1.50 mm, respectively.

R. Bhattacharya, S. Konar / Optics & Laser Technology 44 (2012) 2210–2216 2211

Author's personal copy

We have calculated the dispersion of two polarization states ofthe fundamental mode. The effective refractive index of the fiberfundamental mode is given by neff¼l/2pb, where b is thepropagation constant. The waveguide dispersion Dw(l) of thePCF can be directly calculated from the modal effective index neff

over a range of wavelength using the relationship

DwðlÞ ¼ �lc

d2neff

dl2,

where c is the velocity of light in vacuum [2]. The total dispersioncoefficient D(l) is calculated as a sum of waveguide dispersionand material dispersion i.e., D(l)¼Dm(l)þDw(l). The materialdispersion Dm(l) has been obtained directly from the Sellmeier’sequation which is

n2ðoÞ ¼ 1þXm

j ¼ 1

Bjo2j

o2j �o2

:

For bulk fused silica B1¼0.6961663, B2¼0.4079426,B3¼0.8974794, l1¼0.0684043 mm, l2¼0.1162414 mm and l3¼

9.896161 mm, where lj¼2pc/oj, oj is the resonance frequency.An important parameter which characterizes the fiber is theV-parameter whose effective value is Veff. The effectiveV-value for an index-guiding PCF was first introduced by Birkset al. [5] which can be calculated by using

Veff ¼ 2pLl

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffin2

eff�n2cl

q,

where ncl is the effective refractive index of the cladding.The wavelength dependences of the total dispersion for horizon-tal and vertical polarization modes have been depicted in Fig. 3.The zero dispersion wavelengths for both vertical polarizationmode and horizontal polarization mode are at 0.85 mm. For bothcases, the value of group velocity dispersion initially increaseswith the increase in wavelength up to approximately 1.2 mm,beyond which the value of group velocity dispersion graduallysaturates. The dispersion curve is wavelength flattened over avery large wavelength range from 1.2 mm to 2 mm with negligiblepositive slope. Below 0.85 mm, the fiber is normal dispersivewhose magnitude decreases sharply with decrease in wavelength.Fig. 4 depicts variation of effective V-parameter with wavelength.The criterion [2,5] for single mode operation in a triangular latticePCF is Veffr4.2, hence, from figure it is obvious that the designedfiber is a single mode fiber at 1.55 mm. Band structure of theproposed fiber has been demonstrated in Fig. 5. In the bandstructure calculation of these fibers, the variation of wave vectorwas limited by first Brilluoin zone. All points inside the Brilluoin

zone can take a lot of time and is hard to analyze for computationof the band structure of these fibers. Instead of this, the highsymmetry points of the Brilluoin zone are only considered.Computation of band structure usually begins from the centre

0.6 0.8 1 1.2 1.4 1.6 1.8

0.02

0.04

0.06

0.08

λ (μm)

Bire

frin

genc

e

(a)

(e)

(d)(c)(b)

Fig. 2. Variation of modal birefringence with wavelength l. (a) L¼1.8 mm,

(b) L¼1.6 mm, (c) L¼1.4 mm, (d) L¼1.2 mm, (e) L¼2 mm.

0.6 0.8 1 1.2 1.4 1.6 1.8−200

−100

0

100

200

λ (μm)

D (p

s/nm

/km

)

(a)

(b)

Fig. 3. Variation of group velocity dispersion with wavelength l for two polariza-

tion states of the fundamental mode. L¼1.8 mm. Curve (a) represents vertical

polarization mode, curve (b) represents horizontal polarization mode.

0.8 1 1.2 1.4 1.6 1.8 21

2

3

4

5

λ (μm)

V eff (b)

(a)

Fig. 4. Variation of effective V-parameter with wavelength l for L¼1.8 mm. Curve

(a) represents horizontal polarization mode. Curve (b) represents vertical

polarization mode.

Hybrid Band Structure

Freq

uenc

y (k

0a=2

π a/λ

)

0

2

4

6

8

10

Γ M K Γ

Fig. 5. Band structure of the proposed band gap guiding PCF.

R. Bhattacharya, S. Konar / Optics & Laser Technology 44 (2012) 2210–22162212

Author's personal copy

of the Brilluoin zone. This point is designated by the Greek letter G.In this point, the wave vector equals to zero. Then computation iscarried out for all high symmetry points i.e., M and K, then returnsto the point G. The contour obtained by the connection of highsymmetry point is called k-path. It is evident that the bandstructure possesses extremum in these symmetry points andbetween these points it monotonically decreases or increases.Typical mode field pattern has been depicted in Fig. 6 which showsthat band gap guided mode is confined around the air core.

4. Index guiding PCF: Birefringence and dispersion

The cross section of the proposed index guiding PCF is shownin Fig. 7 which consists of seven rings of air holes. The first ring

consists of four small circular air holes and two elliptical air holes.The refractive index of the air holes is 1 and the refractive index ofthe background material is 1.45. The missing air hole at the centreacts as fiber core. The diameter of circular air holes is di and thehole pitch is Li. The length of major (horizontal) and minor(vertical) axes of the elliptical air holes are diL and diS, respec-tively. To continue our investigation, we take Li¼4 mm,di¼2.8 mm, diL¼3.2 mm and diS¼2 mm. Diameter of small circularair holes in the first ring is dsmall¼0.4�Li¼1.6 mm. We havecalculated effective refractive indices of the two orthogonalpolarization modes as a function of wavelength. Four differentvalues of hole pitch, in particular L¼2.5 mm, 3 mm, 3.5 mm and4.5 mm have been chosen for our investigation. The variations ofmodal birefringence with wavelength for different hole pitch havebeen depicted in Fig. 8. The modal birefringence attains a value of1.15�10�2 at the wavelength 1.55 mm. From this figure it isevident that modal birefringence is high at higher wavelength.We conclude that birefringence can be increased by increasingthe value of hole pitch till L¼4 mm. Beyond L¼4 mm, birefrin-gence decreases with the increase in the value of hole pitch whichis evident from the curve labeled (e).

The dispersion of two polarization states of the fundamentalmode has been calculated. Fig. 9 depicts the total dispersion of thebirefringent PCF. From figure it is clear that the zero dispersionpoint has been shifted to 0.96 mm. The fiber has normal dispersionbelow 0.96 mm whose magnitude increases with the decrease inwavelength. Fig. 10 shows the variations of effective V-parameterwith wavelength of the vertical and horizontal polarization mode.It is clear from the figure that Veff is always less than 4.2 whichensures single modeness. Therefore, the proposed fiber remainssingle mode over a range of wavelength from 0.8 mm to 2 mm.Fundamental mode field pattern is shown in Fig. 11, whichindicates that the fundamental mode is always confined to thefiber core.

5. Index guiding PCF with high refractive index materials inthe first ring

In this section we have investigated an index guided PCF withseven rings of air holes which are arranged in triangular latticeformation. A schematic of the fiber is shown in Fig. 12, which hasa missing air hole at the centre that acts as fiber core. Theinnermost ring consists of two large elliptical regions and foursmall circular regions all of which are made of high indexmaterial. In the second ring two air holes are elliptical while

Fig. 6. Mode field pattern of the proposed highly birefringent band gap guiding

fiber.

Fig. 7. Cross section of the proposed fiber with seven rings of air holes which are

arranged in a triangular lattice formation; two inner rings are composed of

elliptical and circular air holes. Li¼4 mm, di¼0.7�Li¼2.8 mm, length of the

horizontal and vertical axes of the elliptical air holes are diL¼0.8�Li¼3.2 mm and

diS¼0.5�Li¼2 mm. Diameter of the small air holes in the first ring

dsmall¼0.4�Li¼1.6 mm.

0.6 0.8 1 1.2 1.4 1.6 1.8

0.005

0.01

0.015

0.02

λ (μm)

Bire

frin

genc

e

(a)

(d)

(c)(b)

(e)

Fig. 8. Variation of modal birefringence with wavelength l of the index guiding

PCF. (a) Li¼4 mm, (b) Li¼3.5 mm, (c) Li¼3 mm, (d) Li¼2.5 mm, (e) Li¼5 mm.

R. Bhattacharya, S. Konar / Optics & Laser Technology 44 (2012) 2210–2216 2213

Author's personal copy

remaining air holes are circular. The refractive index of theelliptical and circular regions in the innermost ring is 1.48. Therefractive index of the background region and center is 1.45,

whereas refractive index of air holes is 1. The length of major andminor axes of elliptical regions are same as in the previous sectioni.e., dL¼3.2 mm and dS¼2 mm, respectively. Hole pitch L¼4 mm,diameter of air holes d¼2.8 mm and diameter of small holes withhigh index in the first ring is dsmall¼1.6 mm. Birefringence ofthis fiber has been demonstrated in Fig. 13. The thick solid curve(a) in the figure demonstrates the variation of birefringence forL¼4 mm which attains a value 3.02�10�3 at 1.55 mm. Othercurves in this figure show the birefringence for different values ofhole pitch. The value of birefringence decreases with the decreas-ing vale of hole pitch. From this figure we can conclude thatfiber birefringence can be increased by increasing the value ofhole pitch till L¼4 mm. Beyond L¼4 mm, birefringence againdecreases with the increase in the value of hole pitch which isevident from the curve labeled (e).

Dispersion profiles of the horizontal and vertical polarizationmodes of the proposed fiber are shown in Fig. 14. Due to thepresence of circular regions with high refractive index in the firstring, refractive index difference between core and claddingincreases, therefore, the zero dispersion wavelength shiftstowards higher wavelength side. The zero dispersion wavelengths

0.6 0.8 1 1.2 1.4 1.6 1.8−200

−100

0

100

200

λ (μm)

D (p

s/nm

/km

)

(a)

(b)

Fig. 9. Variations of group velocity dispersion of the two polarization states of the

fundamental mode with wavelength l of index guiding PCF for L¼4 mm. Curve

(a) represents vertical polarization; curve (b) represents horizontal polarization.

0.8 1 1.2 1.4 1.6 1.8 20

1

2

3

4

5

6

λ (μm)

V eff (b)

(a)

Fig. 10. Variations of effective V-parameter with wavelength l for L¼4 mm. Curve

(a) represents horizontal polarization mode and curve (b) represents vertical

polarization mode.

Fig. 11. Mode field pattern of the proposed highly birefringent index guiding fiber.

Fig. 12. Cross section of the proposed seven ring triangular lattice birefringent

index guiding PCF with high refractive index regions in the innermost ring.

Li¼4 mm, di¼0.7�Li¼2.8 mm. Length of the horizontal and vertical axes of the

elliptical air holes are diL¼0.8�Li¼3.2 mm and diS¼0.5�Li¼2 mm. Diameter of

the small air holes in the first ring dsmall¼0.4�Li¼1.6 mm.

0.6 0.8 1 1.2 1.4 1.6 1.8

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

λ (μm)

Bire

frin

genc

e (a)

(d)

(c)(b)

(e)

Fig. 13. Variation of modal birefringence with wavelength l of the index guiding

PCF with high refractive index regions in the innermost ring. (a) Li¼4 mm,

(b) Li¼3.5 mm, (c) Li¼3 mm, (d) Li¼2.5 mm, (e) Li¼5 mm.

R. Bhattacharya, S. Konar / Optics & Laser Technology 44 (2012) 2210–22162214

Author's personal copy

for both vertical polarization mode and horizontal polarizationmode are at 1.4 mm. For both cases, the group velocity dispersionvalue initially increases with the increase in wavelength up toapproximately 1.6 mm, beyond which the group velocity disper-sion increases very slowly. The variation of effective V-parameterwith wavelength has been depicted in Fig. 15. From Fig. 15, it isclear that the proposed fiber is single mode over a range ofwavelength from 0.8 mm to 2 mm. Fundamental mode field isdepicted in Fig. 16 in which the mode field is confined within thehigh index elliptical regions.

6. Comparisons

We have designed three different types of PCFs i.e., band gapguiding, index guiding and index guiding with higher refractiveindex circular and elliptical regions in the first ring. Fiber parameterssuch as hole diameter, hole pitch, major and minor axes length ofelliptical regions are same in the cases of two types of index guidingPCFs and different in the case of band gap guiding PCF. From ourinvestigation it is evident that the expected birefringence of theband gap fiber is larger at 1.55 mm in comparison to two other PCFsand it is also larger than the birefringence reported till now. InFig. 17, we have compared dispersion profiles of the horizontalpolarization modes of these three types of PCFs. From this figure it isamply clear that zero dispersion wavelengths have been shifted inall the three cases. The curve (a) of above figure shows thedispersion profile of band gap PCF for which zero dispersion is atwavelength 0.85 mm, curve (b) depicts the dispersion profile ofindex guiding PCF and curve (c) shows the dispersion profile ofindex guiding PCF with higher refractive index material in theinnermost ring. The zero dispersion wavelength of the index guidingPCF with high refractive index regions in the innermost ring hasbeen shifted to1.4 mm i.e., towards higher wavelength side. There-fore, introduction of high refractive index region in the inner ringcan be used to shift the zero dispersion wavelength of the PCFtowards higher wavelength.

7. Conclusion

We have investigated the optical properties of three differenttypes of PCFs i.e., band gap guiding, index guiding andindex guiding with high refractive index regions in the inner

0.8 1 1.2 1.4 1.6 1.8 2−200

−100

0

100

200

λ (μm)

D (p

s/nm

/km

)

(a)

(b)

Fig. 14. Variations of group velocity dispersion of the two polarization states of

the fundamental mode with wavelength l for L¼4 mm. Curve (a) and curve

(b) represent vertical polarization mode and horizontal polarization mode,

respectively.

0.8 1 1.2 1.4 1.6 1.8 21

2

3

4

5

λ (μm)

V eff

(b)

(a)

Fig. 15. Variations of effective V-parameter with wavelength l of index guiding

PCF with high refractive index regions in the inner ring. L¼4 mm. Curve (a) and

curve (b), respectively represents vertical polarization mode and horizontal

polarization mode.

Fig. 16. Mode field pattern of the proposed birefringent index guiding fiber with

high refractive index regions in the innermost ring.

0.6 0.8 1 1.2 1.4 1.6 1.8−200

−100

0

100

200

λ (μm)

D (p

s/nm

/km

)

(a) (c)(b)

Fig. 17. Comparison of dispersion profiles of the vertical polarization mode of

three different types of PCFs. Curve (a) is for band gap guiding PCF with

L¼1.8 mm, curve (b) is for index guiding PCF with L¼4 mm, and curve (c) is for

index guiding PCF having high refractive index regions in the innermost ring with

L¼4 mm.

R. Bhattacharya, S. Konar / Optics & Laser Technology 44 (2012) 2210–2216 2215

Author's personal copy

ring. In all the three cases the air holes are arranged in triangularlattice formation. The birefringence, dispersion characteristics,effective index, the fiber V-parameter and mode field of thefundamental mode have been numerically investigated usingfinite difference time domain method. The proposed band gapPCF promises very large birefringence (�5.45�10�2) at 1.55 mm,which is the largest value reported till date. We have identifiedthat the value of the hole pitch L¼1.8 mm yields the optimumvalue of birefringence in case of band gap fiber. The dispersioncharacteristics of these fibers show that zero dispersion wave-length have been shifted in all the three cases. The proposedfibers could be useful in designing fiber optic sensors which relyon fiber birefringence. High value of birefringence will be usefulin maintaining polarization of electric fields, thus, making thesefibers attractive in the fabrication of different fiber optic sensorssuch as strain, temperature, pressure, humidity, acoustic waveetc. These fibers may be also useful in optical communicationsand fabrication of polarization controllers.

Acknowledgement

We thank gratefully anonymous referee for insightful com-ments and valuable suggestions. We agree that his/her commentshave improved the quality of the manuscript. This work issupported by the Department of Science and Technology (DST),Government of India through the R&D grant SR/S2/LOP-17/2010.One of the authors, Rakhi Bhattacharya would like to thank theCouncil of Scientific and Industrial Research (CSIR), Governmentof India, for providing a Senior Research Fellowship.

References

[1] Knight JC, Birks TA, Russell PStJ, Atkin DM. All-silica single-mode optical fiberwith photonic crystal cladding. Optics Letters 1996;21:1547.

[2] Bjarklev A, Broeng J, Bjarklev ASC. Photonic Crystal Fibers. Kluwer AcademicPublishers. 2003.

[3] Broeng J, Magilevslev D, Borkou Stig E, Bjarklev. A. Photonic crystal fibers:a new class of optical waveguides. Optical Fiber Technology 1999;5:305.

[4] Reeves WH, Knight JC, Russell PStJ. Demonstration of ultra-flattened disper-sion in photonic crystal fibers. Optics Express 2002;10:609.

[5] Birks TA, Knight JC, Russell PStJ. Endlessly single mode photonic crystal fiber.Optics Letters 1997;22:961.

[6] Saitoh K, Koshiba M. Leakage loss and group velocity dispersion in air-corephotonic bandgap fibers. Optics Express 2003;11:3100.

[7] Knight JC, Broeng J, Birks TA, Russell PStJ. Photonic band gap guidance inoptical fibers. Science 1998;282:1476.

[8] Knight JC, Birks TA, Cregan RF, Russell PStJ, de Sandro PD. Large mode areaphotonic crystal fibre. Electron Letters 1998;34:1347.

[9] Wadsworth W, Percival R, Bouwmans G, Knight J, Russell PStJ. High powerair-clad photonic crystal fibre laser. Optics Express 2003;11:48.

[10] Ortigosa-Blanch A, Knight JC, Wadsworth WJ, Arriaga J, Mangan BJ, Birks TA,et al. Highly birefringent photonic crystal fibers. Optics Letters 2000;25:1325.

[11] Petropoulos P, Monro TM, Belardi W, Furusawa K, Lee JH, Richardson DJ.2R-regenerative all-optical switch based on a highly nonlinear holey fiber.Optics Letters 2001;26:1233.

[12] Birks TA, Mogilevtsev D, Knight JC, Russell PSJ. Dispersion compensationusing single-material fibers. IEEE Photonics Technology Letters 1999;11:674.

[13] Smith CM, Venkataraman N, Gallagher MT, Muller D, West JA, Borrelli NF, et al.Low-loss hollow-core silica/air photonic bandgap fibre. Nature 2003;424:657.

[14] Laun F, George AK, Hadley TD, Pearce GJ, Bird DM, Knight JC, et al. All-solidphotonic bandgap fiber. Optics Letters 2004;29:2369.

[15] Temelkuran B, Hart SD, Benoit G, Joannopoulos JD, Fink Y. Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO2 lasertransmission. Nature 2002;420:650.

[16] Hansen TP, Broeng J, Libori SEB, Knudsen E, Bjarklev A, Jensen JR, et al. Highlybirefringent index-guiding photonic crystal fibers. IEEE Photonics TechnologyLetters 2001;13:588.

[17] Zhang L, Yang C. Photonic crystal fibers with squeezed hexagonal lattice.Optics Express 2004;12:2371.

[18] Steel MJ, Osgood Jr. RM. Elliptical-hole photonic crystal fibers. Optics Letters2001;26:229.

[19] Steel MJ, Osgood Jr. RM. Polarization and dispersive properties of elliptical-hole photonic crystal fibers. IEEE Journal of Lightwave Technology2001;19:495.

[20] Saitoh K, Koshiba. M. Photonic bandgap fibers with high birefringence. IEEEPhotonics Technology Letters 2002;14:1291.

[21] Chen X, Li MJ, Venkataraman N, Gallagher MT, Wood WA, Crowley AM, et al.Highly birefringent hollow-core photonic bandgap fiber. Optics Express2004;12:3888.

[22] Wang J, Jiang C, Hu W, Gao. M. High birefringence photonic bandgap fiberwith elliptical air holes. Optical Fiber Technology 2006;12:265.

[23] Lungso JK, Mangan BJ, Olaussan CB, Roberts. PJ. Stress induced birefringencein hybrid TIR/PBG guiding solid photonic crystal fibers. Optics Express2010;18:14031.

[24] Cho M, Kim J, Park H, Han Y, Moon K, Jung E, et al. Highly birefringentterahertz polarization maintaining plastic photonic crystal fibers. OpticsExpress 2008;16:7.

[25] Taflove, A and Hagness, SC, Computational Electrodynamics: The FiniteDifference Time Domain Method. 3rd edn., Artech House, Boston, London.

[26] Konar S, Ghorai SK, Bhattacharya R. Highly birefringent microstructured fiberwith zero dispersion wavelength at 0.64 mm. Fiber and Integrated Optics2009;28:138.

[27] Gerome F, Anguste J, Blondy JM. Design of dispersion-compensating fibersbased on a dual-concentric-core photonic crystal fiber. Optics Letters2004;29:2725.

[28] FullWAVE & BandSOLVE, RSoft Design Group Inc., USA, 2003.

R. Bhattacharya, S. Konar / Optics & Laser Technology 44 (2012) 2210–22162216