effect of lattice constant and air hole diameter on the ... · physics, electronics and ......

Abstract— A photonic crystal fiber (PCF) presents a new

way to guide light. The air holes in the fiber work as a cladding,

but provide much more flexibility in the design. In this paper the

mode profile in square and triangular lattice Phonic Crystal

Fiber (PCF) is investigated for different lattice constant and air

hole diameter of PCF using a 3D Mode Solver. The effect of

variation in lattice constant and air hole diameter on the mode

profile is analyzed and good optical confinement with increasing

air filling faction at THz regime is obtained.

Index Terms— Air Hole Diameter(d), Air Filling Faction, 3D

Mode Solver, Effective Refractive index(nnff), Lattice Constant

(Λ), Photonic Crystal Fiber (PCF).

I. INTRODUCTION

Photonic crystal fibers (PCFs) are characterized by an array

of air holes running along the entire fiber length, which

provides for the confinement and guidance of light. Owing to

the huge variety of air-hole arrangements, PCFs offer many

possibilities for controlling the refractive index contrast

between the core and the microstructured cladding and, as a

consequence, offer novel and unique optical

properties[1],[2]

.Photonic crystal fibers (PCFs) with a pe-riodic

transverse microstructure have been in practical existence as

low-loss waveguides since early 1996[3]

. Classical optical

Manuscript received July17, 2010

Md. Omar Faruk is a researcher in the Dept. of Applied

Physics, Electronics and Communication Engineering, University of

Dhaka. (e-mail: [email protected]).

Mahmud ul Aftab is a researcher at Advance Electronics Lab in the Dept.

of Applied Physics, Electronics and Communication Engineering,

University of Dhaka. (e-mail: [email protected]).

Rajib Ahmed is a member of OSA, researcher in Semiconductor & Optics

in the Dept. of Applied Physics, Electronics and Communication

Engineering, University of Dhaka. (e-mail: [email protected]).

Md. Belayat Hossain* is a researcher in the Dept. of Applied Physics,

Electronics and Communication Engineering, University of Dhaka.

(Corresponding author, phone: 880-1717616181; fax: 880-2-8615583;

e-mail: [email protected]).

Md. Shafiul Islam is a researcher in the Dept. of Applied

Physics, Electronics and Communication Engineering, University of

Dhaka. (e-mail : [email protected]).

Saadia Binte Alam is a researcher in International University of Business

Agriculture and Technology; email: [email protected]

fibers perform very well in telecom and non-telecom

applications, but there is a series of fundamental limits related

to their structures. The fibers have rigid design rules to fulfill:

limited core diameter in the single-mode regime, modal cutoff

wavelength, limited material choice (thermal properties of

core glass and cladding glass must be the same).

The design of PCFs is very flexible. There are several

parameters to manipulate: lattice constant or pitch, air hole

shape and diameter, refractive index of the glass, and type of

lattice. The simplest (and most often used) types of PCF are

triangular and square lattice of air holes, with one hole

missing at centre acts as core, shown in Fig. 1.

Fig.1. Photonic crystal Fiber (a) Triangular lattice (b) Square lattice

The light guides through these fibers by principal of Total

Internal Reflection (TIR) between the core and cladding

region. Single mode property of a PCF is very useful for

communication system application.

In this paper the PCF is analyzed using effective index

method [7]

. Here by changing the lattice constant (Λ) and air

hole diameter (d) the effective refractive index of cladding

region is calculated and the mode profiles are obtained, which

could be a great help in the fabrication of PCF.

II. LAYOUT DESIGNING OF THE BOTH PCF

The both PCF are formed by a 5 rings triangular and square

pattern of air holes in hexagonal and square layout

respectively. The wafer chosen for both of them is of pure

GaAs with refractive index 3.41917. The air holes, with

refractive index 1, are of radius d/2=0.60µm and the centre

to centre spacing between two nearest air holes is referred as

the lattice constant or pitch Λ of 2.4 µm. The core of pure

GaAs with refractive index ncore is surrounded by the cladding

of effective refractive index neff..

The number of guided modes is obtained by the V-number (or

normalized frequency) defined as [6]

Effect of Lattice Constant and Air Hole

Diameter on the Mode Profile in Triangular and

Square Lattice Photonic Crystal Fiber at THz

Regime

Md. Omar Faruk, Mahmud ul Aftab, Rajib Ahmed, Member, OSA, Md. Belayat Hossain*, Md. Shafiul

Islam, Saadia Binte Alam

Proceedings of the World Congress on Engineering and Computer Science 2010 Vol II WCECS 2010, October 20-22, 2010, San Francisco, USA

ISBN: 978-988-18210-0-3 ISSN: 2078-0958 (Print); ISSN: 2078-0966 (Online)

WCECS 2010

mailto:[email protected]






V= √ (ncore 2 - neff

2 ) …..(1)

The confinement loss of the fundamental modes can be

deduced from the value (imaginary part) of the complex

effective index (neff -c) of the fundamental mode of the optical

fiber, which is given by[5]

α=8.686×Im( neff-c)………(2)

The confinement loss CL of the mode is deduced from the

attenuation constant α as

CL = 20α log10 e =8.686α (dB/m)…..(3)

III. VARIATION IN LATTICE CONSTANT

The variation in lattice constant or pitch (Λ) in the

simulating region results the change in the air fill faction [4],[8]

for both of triangular and square lattice fiber with constant air

hole diameter as shown in Table I.

The mode field should be sun flower like pattern for triangular

lattice PCF and a rectangular with extended tail like pattern

for square lattice PCF and for better optical confinement the

entire field should be concentrated in the core and should not

leak in the cladding.

Table I. Variation in lattice constant or pitch, Λ

Configuration Air hole

diameter , d µm

Lattice constant,

Λ µm

Air fill faction, d/Λ

I 1.2 2.40 0.5

II 1.2 2.00 0.6

III 1.2 1.71 0.7

IV 1.2 1.50 0.8

IV. VARIATION IN LATTICE CONSTANT

The variation in air hole diameter in the simulating region

results the change in the air fill faction for both of triangular

and square lattice fiber with constant lattice constant Λ as

shown in Table II.

Table II. Variation in air hole diameter, d

Configuration Air hole

diameter , d µm

Lattice constant,

Λ µm

Air fill faction, d/Λ

I 1.20 2.4 0.5 II 1.44 2.4 0.6 III 1.68 2.4 0.7 IV 1.92 2.4 0.8

V. RESULTS

The mode field patterns corresponding to the variation of

lattice constant these PCF layouts and the 3D field intensity

plots of the propagated light in PCF is also shown in Fig. 2.

Using these values and equation the normalized frequency V

is plotted in Fig.3.The figures in Fig 3. Clearly specify that as

the lattice constant or pitch(Λ) is decreased, the V number

decreases almost linearly, hence the lowest order mode

doesn’t leak in cladding region and this will go towards the

single mode operation.

Triangular lattice PCF

Square lattice PCF

(a)



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Square lattice PCF

(b)


Square lattice PCF

(c)




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Square lattice PCF

(d)

Fig. 2 Mode profile of PCF with the variation in lattice constant (Λ) at

wavelength 0.55µm (a) Configuration I (b) Configuration II (c)

Configuration III (d) Configuration VI as per Table II

Fig 3. V number VS. Lattice constant or Pitch, Λ

The mode field patterns corresponding to the variation of

the air hole diameter, d of these PCF layout and the 3D field

intensity plots of the propagated light in both type of PCF

fiber is shown in Fig 4. The figures in Fig 5 clearly specify

that air hole diameter, d is increased, the confinement loss

decreases almost logarithmically, hence the lowest order

mode doesn’t leak in cladding region and this will go towards

the single mode operation.

Triangular Lattice PCF

Square lattice PCF

(a)




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Square lattice PCF

(b)


Square lattice PCF

(c)


Square lattice PCF

(d)

Fig. 4 Mode profile of PCF with the variation in air hole diameter, d at

wavelength 0.55µm (a)Configuration I (b) Configuration II (c)

Configuration III (d) Configuration VI as per Table II.



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Fig 5 Leakage loss as a function of the air-hole diameter d normalized to the

pitch Λ = 2.4 µm for ring number 6 (triangular lattice) and 8(square lattice).

VI. DISCUSSION

As shown in above results, as the lattice constant or pitch

Λ is decreased, it is clearly visible from the Fig 2 that the

confinement of light is increased and at the same time when

we compare this result with the theoretical values of V

number (Fig 3), we get a very good agreement. Similarly

when we increase the air hole diameter, d the confinement of

light increases which is clearly visible from Fig 4 and the

confinement loss also stats to decrease exponentially (Fig 5.)

.So we get a very good agreement with our theoretical and

experimental result. In both cases configuration VI is most

appropriate for manufacturing purpose.

VII. CONCLUSION

Here two types of PCF with varying lattice constant or

pitch Λ and air hole diameter d have been analyzed in terms of

optical confinement and attenuation properties. From where

we can design these parameters (Λ & d) such that the

propagating field will more confine to the core region. This

will help the manufacturer, to design the lattice constant Λ

and air hole diameter d that would help to more confine the

light into the core section of the fiber.

.

REFERENCES

[1] G F. Poli, A. Cucinotta, S. Selleri, Photonic Crystal Fibers

(Springer,2007).

[2] F. Poli, M. Foroni, M. Bottacini, M. Fuochi, N. Burani, L. Rosa, A.

Cucinotta, and S. Selleri, ―Single-mode regime of square-lattice

photonic crystal fibers‖ J. Opt. Soc. Am. A, Vol. 22, No. 8,August

2005.

[3] Philip St.J. Russell, ―Photonic-Crystal Fibers‖ Lightwave Technology,

Journal OF, VOL. 24, NO. 12, DECEMBER 2006.

[4] D. Chen, M.-L. V. Tse, and H. Y. Tam, ―Super-Lattice Structure

Photonic Crystal‖, Progress In Electromagnetic Research M, Vol. 11,

53-64, 2010.

[5] ] D. Chen, M.-L. V. Tse and H. Y. Tam, ―Optical properties of

photonic crystal fibers with a fiber core of arrays of sub-wavelength

circular air holes: birefrin-gence and dispersion‖, Progress In

Electromagnetics Research, Vol. 105, 193-212, 2010.

[6] Niels Asger Mortensen , Jacob Riis Folkenberg, ―Modal cut-off and the

V –parameter in photonic crystal fibers‖, arXiv:physics/ 0307010v1

[physics.optics] 2 Jul 2003.

[7] Yanfeng Li, Changlei Wang, Ning Zhang, Ching-yue Wang, and

Qirong Xing,‖ Analysis and design of terahertz photonic crystal fibers

by an effective-index method‖, APPLIED OPTICS, Vol. 45, No. 33, 20 November 2006.

[8] ] Masashi Eguchi,Yasuhide Tsuji,‖ Single-mode single-polarization

holey fiber using anisotropic fundamental space-filling mode‖, OPTICS LETTERS, Vol. 32, No. 15, August 1, 2007.



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