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Simulation and calculation of the parameters of PCF under terahertz wave band.

INTRODUCTION

A PCF is an optical fiber that achieves its waveguide properties not from a spatially variable glass structure but from planning of very small and closely spaced air holes which go through the whole length of fiber [1-3]. Photonic-crystal fiber (PCF) is a novel class of optical fiber based on the properties of photonic crystals. Because of its ability to confine light in hollow cores or with confinement characteristics not possible in conventional optical fiber, PCF is now finding applications in fiber optic communications, fiber lasers, nonlinear devices, high-power transmission, highly sensitive gas sensors and other areas [4, 5]. Additional specific classes of PCF include photonic band gap fiber, holey fiber, hole-assisted fiber and Bragg fiber [6, 7]. PCF fibers may be measured a subcategory of a more general class of micro structured optical fibers, where light is directed by essential adjustments and not only by refractive index differences [8]. The PCF can freely control the motion of photons which give us a lot of room for designing and constructing, making PCF possess many more attractive features than electron crystal material. It gave a technology and has become a big hot spot in photoelectron research in recent years [9, 10]. Terahertz wave frequency range is 0.1THz~10THz, located midway between the microwaves infrared light. This bandwidth is also recognized as the THZ gap because it is noticeably underutilized. Because terahertz waves are electromagnetic waves with frequencies higher than microwaves but lower than. infrared radiation and visible light. PCF applied in THZ bands has the advantage of easy preparation and etc. because its size is in millimeters magnitude [11-17]. The reaction of the refractive index of LC to the change of the external electric field is more sensitive than others, so we can adjust the parameters of the PCF through infiltrating the air holes with the LC selectively and changing the voltage of applied electric field [18, 19].

Refractive Index of Lc:

LC is an intermediate state between liquid and crystal, also called the fourth state of substance. A liquid crystal having both the flow ability and orderly crystal-like structure, it like liquid on the mechanical properties and like the crystal on the optical properties, so we also called it liquid crystal [20]. In this paper, heating cyanobiphenyl (CB) nematic liquid crystal (LC) and change the refractive index of LC By changing the external electric field have been used. When there is no applied electric field, the LC molecules are similar to the uniaxial crystal. The direction of Z axis is consistent with the direction of LC molecular alignment as shown in Figure 1. It's equivalent that light spread in the isotropic material, so the transmitted light is ordinary light and the refractive index of LC is no. When the applied voltage is greater than the threshold voltage, the LC molecules will begin to spin. The angle between long axis's direction of LC molecules and PCF axis direction is 0 as shown in Figure 2. It's similar as that light spread in the anisotropic medium. In the process of voltage increase, the polarized light in X axis direction will keep unchanged light refractive index. The polarized light in Y axis direction will change with the impressed voltage [21, 22].

T he polarized retractive index of LC molecules in the direction along the X-axis and Y -axis can be obtained by the following formula [23, 24]:

[n.sub.x] = [n.sub.0] (1)

[n.sub.y] = [([sin.sup.2][theta]/[n.sub.e.sup.2] + [cos.sup.2][theta]/[n.sub.o.sup.2]).sup.1/2] (2)

The refractive index of extraordinary light and ordinary light of LC 5CB at 25[degrees]C are around 1.77 and 1.58 in the frequency range of 0.2 to 1.0 THz, respectively [25, 26] where 0 is determined by:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)

Where Eeff is the effective voltage, which interacts with LC molecules and controls molecular sorting Ec is the threshold voltage, which is only related to the LC molecules itself.

Numerical Simulation And Analysis:

We use polyethylene as a material of PCF, which can be easily got. The refractive index of this material is 1.5. We chose the structure shown as Figure 3 and fill the marked air holes with 5CB LC. The radius of the cladding holes are 30 nm, 40 nm, 50 nm, 60 nm respectively. The air hole spacing in the cladding is 1.45mm and the input frequency is 0.7THZ.

The Effective Refractive Index:

The effective refractive index is an important parameter of PCF. It is closely related to other characteristics of the PCF such as chromatic dispersion. Using COMSOL Multiphysics, we can directly acquire PCF's effective refractive index in different modes. Figure 4 shows the curve of effective index varies with impressed voltage.

As what can be seen from the Figure 4, at the same applied voltage, when he hole center distance and input frequency unchanged but the pore radius increases, the fundamental mode effective index increases, and it increases more and more slowly. When the pore radius is constant, the fundamental mode effective index is proportional to the applied voltage. And the greater the voltage is, the faster the fundamental mode effective index increases. The fundamental mode effective index is proportional to the holes' radius. When pore radius is constant, the effective refractive index of the fundamental mode increases with the applied voltage increasing. The increasing trend is growing. Meanwhile, the fundamental mode effective index of four different structures does not overlap nor intersect. They almost have the same growth trend.

The Normalized Frequency:

The normalized frequency of PCF has connection with the input frequency, radius of the air holes, core effective refractive index and the cladding effective refractive index. That determined by the equation (4):

[V.sub.eff] = 2[pi]R/[lambda] [([n.sup.2.sub.core] - [n.sup.2.sub.clad]).sup.1/2] (4)

Where define Veff <2.55 as the cut-off frequency. of second order mode. The curve of normalized frequency of PCF filled with LC versus by voltage is showed in Figure 5.

Single-mode transmission can be occurring when the radius of the air holes is 30 nm and the change is gradual. The normalized frequency can be increases when the voltage is increasing. Under the same applied, Voltage the larger the radius of air holes, the larger the normalized frequency. The tendency becomes more apparent because of cladding effective refractive index changes very slowly as the voltage changing. We achieved the larger of radius of the air holes is, the less obvious change. Therefore the greater the radius of the air hole is, the effective mode has more similar curve with the effective refractive index.

The Effective Mode Area:

The effective mode area of PCF filled LC is measured by PCF's structure and useful voltage. We can get the large range of variation of effective mode area by choosing pertinent structure of PCF. We should project PCF with the various effective mode areas according to the required nonlinear effect. The effective mode area is demonstrated as:

[A.sub.eff] = [[[integral][integral][[absolute value of (E(x,y))].sup.2]dxdy].sup.2]/[integral][integral][[absolute value of (E(x,y))].sup.4]dxdy (5)

Here, E(x,y) represents electric mode field distribution, we select all areas of PCF materials as domain of integration.

As shown in Figure 6, when the voltage is fixed, the mode field area increases with increase of air hole radius; when air hole radius is constant, the effective mode area increases with the applied voltage reducing. Meanwhile, the larger the radius of the air holes is effective mode area of PCF is more stable and the value of nonlinear effects is more stable. We can choose appropriate size of the structure parameters and applied voltage to control the size of the required effective mode area. And thus we can improve the nonlinear or single-mode transmission characteristics of PCF.

Numerical Aperture:

NA is the important parameter which react the light collecting capability of PCF, which is defined as:

NA sin [[theta].sub.a] = sin (tan-1([lambda]/[pi][omega])) [approximately equal to] [(1 + [pi][A.sub.eff]/[[lambda].sup.2]).sup.-1/2] (6)

Figure 7 shows the numerical aperture increases as the voltage amplifying when the input frequency is constant and the radius of the air hole is fixed. The numerical aperture changes gradually as the applied voltage changing and the radius of air holes increasing. The numerical aperture reduces with the radius increasing when the voltage is fixed. We can achieve the desired numerical aperture through designing different fiber structures and the adjusting applied voltage on PCF.

Conclusion:

In this paper, we used COMSOL and MATLAB received the performance parameters of the PCF infiltrated by LC 5CB under various voltage. These properties include effective refractive index, the normalized frequency, the effective mode area, numerical aperture, waveguide dispersion. Results indicated that both single-mode transmission and ultra-flat dispersion can be achieved under the appropriate voltage and suitable structure. Moreover, stable nonlinear effect is appeared at the large radius of air holes. It provides references to design voltage sensing terahertz waveguide device for corresponding demand.

ARTICLE INFO

Article history:

Received 4 September 2014

Received in revised form 24 November 2014

Accepted 8 December 2014

Available online 16 December 2014

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(1,2) A. Afroozeh, (3,4) S.E. Pourmand, (5) A. Zeinalinezhad

(1) Young Researchers and Elite Club, Jahrom Branch, Islamic Azad University, Jahrom, Iran.

(2) The Department General of Fars Province Education, Iran

(3) Department of Optics and Lasers Engineering, Estahban Branch, Islamic Azad University, Estahban, Iran.

(4) Young Researchers and Elite Club, Estahban Branch, Islamic Azad University, Estahban, Iran.

(5) Chemistry Department, Anar Branch, Islamic Azad University, Anar, Iran.

Corresponding Author: Abdolkarim Afroozeh, Young Researchers and Elite Club, Jahrom Branch, Islamic Azad University, Jahrom, Iran.

E-mail: afroozeh155@yahoo.com.
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Author:Afroozeh, A.; Pourmand, S.E.; Zeinalinezhad, A.
Publication:Advances in Environmental Biology
Article Type:Report
Date:Oct 1, 2014
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