Design of High Birefringence Photonic Crystal

Fiber with Three Ring Circular Air Holes in

Fiber Cladding and Two Ring Elliptical

Air Holes in Fiber Core

Yuan-Fong Chau

Abstract— Photonic crystal fibers (PCFs)- a silica–air

microstructure consisting of air hole arrays running along its length-

have attracted much attention for fiber device application in recent

years because of its unusual optical properties that are not realized in

conventional optical fiber, such as high birefringence, high

nonlinearity, low confinement loss and tailorable chromatic

dispersion. High birefringent PCF can be designed by breaking the

circular symmetry and implementing asymmetric defect structures

such as dissimilar air hole diameter, varying the number of circular

and elliptical air holes. This paper proposes a highly birefringent

PCF with ultra-low confinement loss by introducing three ring solid

core hexagonal structure which having circular three ring air holes in

fiber cladding and introducing two ring smaller elliptical air holes in

the fiber core region for making the asymmetry. The modal

birefringence and confinement loss are calculated by using Finite

element method (FEM). An endlessly single mode, high birefringent

(6.25×10-3) and a low confinement loss (4.84×10-15 dB/km) found at

the excitation wavelength of λ=1550nm.

Keywords- Photonic crystal fibers; high birefringence; low

confinement loss; Finite element method.

I. INTRODUCTION

HOTONIC crystal fiber (PCF) with silica–air

microstructures has received increasing attention since it

was first proposed in 1995 [1]. Its novel guiding

properties, namely high birefringence, high nonlinearity, low

confinement loss, chromatic dispersion tailoring, a wide

single-mode wavelength region, a large effective mode area,

and a small bending loss, suggest the possibility of diverse

applications to optical transmission [2–4]. Among the features

of PCFs, birefringence is one of the most interesting

characteristics. Birefringence in PCFs usually results from

intentionally reducing the rotational symmetry of the fiber

structure.

The effect of the birefringence is more obvious if the index

contrast between the core-cladding is high. Because of the

symmetry in PCFs is broken by some environmental factors,

such as small changes in the glass composition,

microbendings and twists, or by stresses, the degeneracy is

Yuan-Fong Chau , Department of Electronic Engineering Chien Hsin

University of Science and Technology, Zhongli City, Taoyuan County 32097, Taiwan 320, R.O.C. yfc01@uch.edu.tw

lifted and the real parts of the effective indices (neff ≡ λβ/2π)

of the degenerate modes separate by an amount termed modal

birefringence.

These perturbations couple the modes that lead to different

phase velocities, with the consequence that the polarization of

light would be poorly controlled after a short distance. High

birefringence PCFs are more flexible to such external factors. Based on our previous works [5,6] and considered the

drawback of the fabrication process (needs a careful control) of elliptical air-hole in PCF cladding, in this paper, we would like to report a easy design of high birefringence and ultra-low confinement loss PCF. The birefringence of our structure is a result of the core region asymmetry. The fiber core is a point defect, which is formed by the omission of one circular air hole in the PCF center, which the mode field is well confined in the core region; thus, it is possible to create a high birefringence and low loss PCF. Together with the technological advancement in the fabrication of PCFs [7], it is possible to fabricate our suggested PCF.

II. SIMULATION METHOD

In this paper, we employ a full-vectorial finite-element

method (FEM) with hexagonal structure for the analysis of

birefringence PCFs. Its fiber cross-sectional representation is

very accurate when the domain is divided into sub-domains

with a triangular or quadrilateral shape. This method has been

successfully applied to investigate dispersion properties of

hexagonal and cobweb PCFs [8]. FEM simulations are

performed by the commercial package Comsol Multiphysics

[9]. The Maxwell equations with a magnetic field

formulation can be presented as followed:

1 2

r 0 r( H) k H 0

(1)

Where H is the magnetic field, r and r are the relative dielectric permittivity and magnetic permeability,

respectively, and

0k 2 /

is the wave number in

vacuum, being the wavelength. The magnetic field of the

modal solution is expressed as H h(x,y)exp( j z)

,

where h(x,y) is the field distribution on the transverse

P

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http://dx.doi.org/10.15242/ IJCCIE.E0913049 43

plane and

r ij

is the complex propagation constant

with i the attenuation constant and

r the phase constant.

In order to evaluate confinement loss of the mode, an anisotropic perfectly matched layer is employed as a boundary condition at computational domain edges.

Propagating incident light through the anisotropic materials

will result in the splitting or decomposition of the light into

two parts. Conventional materials with uniaxial anisotropy--

have an axis of symmetry with unequal axis in the plane

perpendicular to it-- exhibits this optical phenomenon. This

axis of symmetry is termed as optical axis of a particular

material. Incident light with linear polarizations in parallel

and perpendicular direction will show unequal effective

refractive indices ne and no for extraordinary and ordinary

emerging lights respectively. If an un-polarized incident light

penetrates a material with a nonzero sharp angle to the optical

axis, the perpendicularly polarized component will refract at

an angle as per the standard law of refraction and its

complementary component at a non-standard angle

determined by the difference between the two effective

refractive indices known as the birefringence magnitude [5].

Δn = ne - no

(2)

The difference between the real part value of the effective

indices of the pronounced fundamental core Eigen modes

along x and y axis- LP01x and LP01

y

The birefringence of a PCF is determined by the difference

between the effective indices of two orthogonal polarization

modes, yx

eff effB n n (3)

where

xeffn

and

yeffn

are the refractive indices of the x- and

y- polarized fundamental modes of the PCF, respectively.

The presence of finite air holes in the core region causes

leakage of optical mode from inner core region to outer air

holes is unavoidable which results in confinement losses. The

confinement loss of the fundamental mode is calculated from

the imaginary part of the complex effective index nieff, using

Confinement loss 102 10 2

Im[ ] dBm/km(i=x,y)ln10

i

effn

(4)

Where Im[ ] i

effnis the imaginary part of effective index on

the guided mode.

III. MODELS, RESULTS AND DISCUSSIONS

Hexagonal pattern of PCF design is known to be the best

structure for obtaining high birefringence, and comparatively

low confinement loss. Here, a high birefringence hexagonal

solid core PCFs with three rings was been modeled for

comparison. The material used here is pure silica with

refractive index 1.45. Two different structures (i.e., case A

and case B) as shown in Figs. (a) and (b) were designed and

compared for various parameters. The case A (see Fig. 1(a)) is a conventional pattern with a

three ring circular air holes in fiber cladding whereas the case B (see Fig. 1(b)) comprises the same structure as the case A but with two ring smaller elliptical air holes in the fiber core region. The key intension of such a design for case B is to break the structural symmetry making a commendable effective index difference between two polarization modes lying orthogonal to each other and is been well analyzed by our previous work [5,6].

Two structures were analyzed for the comparison of its

structural properties. The pitch (center-to-center distance

between the air holes) of air holes in fiber cladding is kept Ʌ

=1.9 μm throughout this paper. The fiber cladding in Case A

consists of circular air holes with varying diameter dc=(0.8,

0.825, 0.85, 0.9) Ʌ for comparison. Case B is the same as case

A but with two ring elliptical air holes with half minor axis

a=163 nm and half major axis b=135 nm respectively in the

fiber core region.

Fig. 1 Schematic plot of simulation models. (a) case A,

and (b) case B.

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Fig. 2 x- and y- polarized mode field patterns with varying dc of

cases A at the excitation wavelength of λ=1550 nm. (a) dc=0.8 Ʌ, (b)

dc=0.825 Ʌ, (c) dc=0.85 Ʌ, and (d) dc=0.9 .

FEM electromagnetic module is particularly well adapted

to solve PCF problems. The fiber cross section is divided into

the so-called elements. For each element, the wave equation is

solved. Simulated the case A structure for different dc values

with a defined PML thickness of 2μm using COMSOL

simulating tool. The resultant 2D view of the simulation is

given which shows high confinement of light beam defined.

To illustrate the field profile of case A, the x- and y- polarized

mode field patterns with varying dc at the excitation

wavelength of λ=1550 nm is shown in Figs. 2(a)-2(d), which

show the different patterns of confinement light in the PCF

core region. In these cases, the electric field is well confined

in the solid core, as shown in Fig. 2. This observation is

confirmed by the calculation of the confinement loss. A

circular PML is applied. The fundamental mode is strongly

bonded in the high-index core region with the effective

indices

Fig. 3 (a) Plots of birefringence as a function of wavelength with

varying dc in fiber cladding for case A. (b) Plots of confinement loss

as a function of wavelength with varying dc in fiber cladding for

case A.

neffx and neff

y, giving a birefringence B = |neff

x- neff

y |. It is

evident for the cases shown in Figs. 2(a)-(d) that the intensity

of the x-polarized mode is higher than that of the y-polarized

mode owing to the x-polarized states having a lower air filling

fraction than the y-polarized states. This implies that the

asymmetry by introducing air holes in core region is one of

the key factors in determining the localization extent of the

transverse mode.

Figure 3(a) shows plots of birefringence as a function of

wavelength with varying dc in fiber cladding for case A. The

corresponding maximum birefringence at an excitation

wavelength λ= 1550 nm are as follows: for dc=0.8 Ʌ, B=9×10-

6; for dc=0.825 Ʌ, B=9.7×10

-4; for dc=0.825 Ʌ, B=1.066×10

-3;

and for dc=0.9 Ʌ, B=1.145×10-3

. It can be clearly seen in Fig.

3(a) that the birefringence of case A with dc=0.9 Ʌ is higher

than those of other dc values at an excitation wavelength λ=

1.55 m. The birefringence increases significantly as the

wavelength increases and birefringence of the order of 10−3

is

attainable with the case of dc=0.85 Ʌ and dc=0.9 Ʌ. Note that

the birefringence can be increased as the circular air holes in

fiber cladding is increased.

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FEM with PMLs, which are placed before the outer boundary,

can be used to calculate the confinement loss of PCFs. The

imaginary part of the complex effective index represents the

loss. As described in refs. [6], for small holes and a few rings

of holes, the confinement loss is huge, but decreases rapidly

as the air hole diameter increases or as more rings of holes are

employed. The FEM with PMLs is used to calculate the

confinement loss of the fundamental modes in the four cases

of PCFs, and the results are plotted in Fig. 3(b). Figure 3(b)

shows confinement loss as a function of wavelength with

varying dc in fiber cladding for case A. It can be predicted that

more rings are used to achieve a low confinement loss of

PCF. The confinement losses of the case A structure with

varying dc at a wavelength of 1.55μm are 5.83×10-14

dB/km

for dc=0.8 Ʌ, 4.86×10-16

dB/km for dc=0.825 Ʌ, 3.61×10-16

dB/km for dc=0.85 Ʌ, and 6.25×10-18

dB/km for dc=0.9 Ʌ when

the number of air hole rings N = 3. To explain this

phenomenon, the confinement field of the case A structure is

assigned to the PCF core, which is surrounded by adjacent air

holes near the core and gives rise to more fields confined in

the core region. It can also be observed from Figs. 2(a)-2(d)

that the mode field patterns are effectively enclosed by air

holes near the PCF cores.

Now we investigate the case B structure which modifies

from the case A structure by introducing two ring additional

elliptical air holes into the fiber core region, the high

birefringence PCF is obtained and birefringence of the order

of 10−3

is attainable with the case of dc in the range of 0.85 Ʌ

-0.9 Ʌ as shown in Fig. 4(a). The two ring smaller elliptical air

holes in the fiber core region provides the asymmetry and it

significantly increase the birefringence. This is because a fiber

core with two ring elliptical air holes will cause the structure

to be more nonsymmetrical. Normally, the fourfold symmetry

of the PCFs guarantees the degeneracy of the fundamental

modes. For PCFs with circular air holes in fiber cladding,

higher birefringence emerges due to the introduction of the

smaller circular air holes in fiber core region. In Fig. 3(a) for

case B PCF, the corresponding maximum birefringence at an

excitation wavelength λ= 1550 nm are as follows: for dc=0.8

Ʌ, B=5.48×10-3

; for dc=0.825 Ʌ, B=3.838×10-3

; for dc=0.825

Ʌ, B=6.873×10-3

; and for dc=0.9 Ʌ, B=6.725×10-3

,

respectively. Note that the high birefringence of case B PCF

with cladding air hole of dc=0.9 Ʌ is 5.87 time than that of the

birefringence obtained from the case B PCF.

Figure 4(b) also shows confinement loss as a function of

wavelength with varying dc in fiber cladding for case B. The

confinement losses of the case B structure with varying dc at a

wavelength of 1.55μm are 5.09×10-11

dB/km for dc=0.8 Ʌ,

4.72×10-12

dB/km for dc=0.825 Ʌ, 6.22×10-13

dB/km for

dc=0.85 Ʌ, and 4.84×10-15

dB/km for dc=0.9 Ʌ when the

number of air hole rings N = 3. The large diameter circular

air holes in the fiber cladding region provide strong

confinement ability. Confinement loss decreases with

decreasing dc values for both the cases as shown also it

increases with increasing wavelength.

Typical x- and y- polarized mode field patterns of cases B

at the excitation wavelength of λ=1550 nm are shown in Figs.

5(a)-(d), respectively. Highly birefringence structures are

obtained in these different patterns of two spot mode by

introducing two ring smaller elliptical air holes in the fiber

core region.

Fig. 4 (a) Plots of birefringence as a function of wavelength with

varying dc in fiber cladding for case B. (b) Plots of confinement loss

as a function of wavelength with varying dc in fiber cladding for

case B.

IV. CONCLUSION

In conclusion, we have successfully demonstrated high birefringence and low confinement loss PCF with three ring circular air holes in fiber cladding and two ring elliptical air holes in core region. It has been shown that the cladding of our Proposed case B PCFs is completely birefringent, though it is only formed by circular air-holes in fiber cladding and smaller elliptical air holes in core region. The obtained results show that the birefringence of our proposed case B PCF significantly increases and birefringence of the order of 10

−3 is attainable

which is much higher than the conventional circular air holes PCF which birefringence is of the order of 10

-4. Another merit

of our proposed case B PCF is the low confinement loss, which is close to 4.84×10

-15 dB/km for only three rings of air

holes in the PCF cladding. As a result, the design of forming the point defect by the omission of one air hole in highly birefringent PCFs with whole asymmetry cladding is illustrated to reduce confinement loss and increase birefringence. As only two ring small elliptical air holes are

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included in the fiber core region, our proposed PCF in this paper is easy to fabricate. The merit of the designed PCFs is that their optimum birefringence and confinement loss can be easily achieved by introducing the smaller elliptical air holes in the core area. Our simulation result is useful and provides a simple concept for designing high birefringence and low loss PCF with good performance.

Fig. 4 x- and y- polarized mode field patterns of cases B at the

excitation wavelength of λ=1550 nm. (a) dc=0.8 Ʌ, (b) dc=0.825 Ʌ,

(c) dc=0.85 Ʌ, and (d) dc=0.9 Ʌ.

ACKNOWLEDGMENT

The author acknowledges the financial support from the National Science Council of the Republic of China (Taiwan) under Contract No. NSC 99-2112-M-231-001-MY3.

REFERENCES

[1] T. A. Birks, P.J. Roberts, P. St. J. Russell, D.M. Atkin, and T. J.

Shepherd, "Full 2-D photonic bandgaps in silica/air structure," Electron.

Lett. vol. 31 pp. 1941–1943, 1995.

http://dx.doi.org/10.1049/el:19951306

[2] A. Ortigosa-Blanch, J. C. Knight, W. J. Wadsworth, J. Arriaga, B. J. Mangan, T. A. Birks, and P. St. J. Russell, "Highly birefringent

photonic crystal fibers," Opt. Lett. vol. 25 (18). pp. 1325–1327, 2000.

http://dx.doi.org/10.1364/OL.25.001325 [3] K. Suzuki, H. Kubota, S. Kawanishi, M. Tanaka, and M. Fujita, "High-

speed bi-directional polarization division multiplexed optical

transmission in ultra low-loss (1.3 dB/km) polarization-maintaining photonic crystal fibre," Electron. Lett. vol. 37 (23), pp.1399–1401,

2001.

http://dx.doi.org/10.1049/el:20010964 [4] T. A. Birks, J. C. Knight, and P. St. J. Russell, "Endlessly single-mode

photonic crystal fiber," Opt. Lett. vol. 22 (13), pp.961–963, 1997.

http://dx.doi.org/10.1364/OL.22.000961 [5] Yuh-Sien Sun, Yuan-Fong Chau, Han-Hsuan Yeh, and Din Ping Tsai,

"Highly Birefringent Index-Guiding Photonic Crystal Fiber with

Squeezed Differently Sized Air-Holes in Cladding," Japanese Journal of

Applied Physics Vol. 47, pp. 3755–3759, 2008.

http://dx.doi.org/10.1143/JJAP.47.3755

[6] Y. S. Sun, Y. F. Chau, H. H. Yeh, L. F. Shen, T. J. Yang, D. P. Tsai. High birefringence photonic crystal fiber with a complex unit cell of

asymmetric elliptical air hole cladding, Appl. Opt., vol. 46, pp. 5276-

5281, 2007. http://dx.doi.org/10.1364/AO.46.005276

[7] A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov,

I. Y. Khrushchev, and J. Pertrovic,― Nanofabricated media with negative permeability at visible frequencies,‖ Nature, vol. 438, No. 17,

pp. 335- 338, 2005.

http://dx.doi.org/10.1038/nature04242 [8] Y. C. Liu, and Y. Lai, ―Optical birefringence and polarization

dependent loss of square- and rectangular-lattice holey fibers with

elliptical air holes: numerical analysis, Opt. Exp., Vol. 13, pp. 225-235, 2005.

http://dx.doi.org/10.1364/OPEX.13.000225

[9] http://www.comsol.com/

[10] A. Proulx, J.-M. Ménard, N. Hô, J. M. Laniel, R. Vallée, and C. Paré,

―Intensity and polarization dependences of the supercontinuum

generation in birefringent and highly nonlinear microstructured fibers,‖ Opt. Express, vol. 11, no. 25, pp. 3338–3345, Dec. 2003.

http://dx.doi.org/10.1364/OE.11.003338

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