International Conference on Electrical, Electronics, Signals, Communication and Optimization (EESCO) - 2015
PCF with low Dispersion and high Birefringence Pranaw Kumar*, Ruplata Kumari**, Satya Sourav Nayak*, Pratik Swarup Mund* * School of Electronics Engineering, KIIT University, Bhubaneshwar. ** Department of Applied Physics, BIT Mesera, Ranchi.
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[email protected] Abstract—Photonic Crystal Fibers (PCFs) structure with unique arrangement of circular air holes has been investigated. The structure has circular air holes of different areas and those air holes are arranged in a unique fashion. Both TE and TM mode has shown zero dispersion. A very low loss and high birefringence was observed for the structure. Normalized frequency and confinement loss for the structure has also been observed. Index Terms—Dispersion, Birefringence, Confinement loss, Vparameter.
I. INTRODUCTION Presently PCFs has become a source of attraction for the researchers. It consists of periodic arrangement of air holes which runs along the length of the fiber with a defect in its centre[1]. PCFs allows single mode guidance throughout the visible and near IR region. Based on the guiding mechanism, PCFs can be catagorised in two types: index guided fiber and photonic bandgap fibers[2]. Index guided fibers are those fibers in which the light rays propagate by the phenomenon of total international reflection. Similarly photonic bandgap fibers in which light is propagated by photonic bandgap effect in low index core region. The novel optical characterstics of PCFs has made it superior over conventional optical fibers. The optical properties of PCFs like chromatic dispersion, highly birefringent, large effective area and endlessly single mode fiber has made it a point of attraction for the researchers[3-5]. Dispersion refers to spreading of pulses during its propagation[6]. Dispersion is basically of two types : waveguide dispersion and material dispersion. Different modes propagate with different velocities which cause waveguide dispersion. Moreover for a given mode the propagation constant is wavelength dependent. As we know a pulse of light is superposition of range of frequencies centered on the frequency of modulated source,in material dispersion where the refractive index are wavelength dependent, each spectral components of the given pulse propagate at different velocities. Dispersion has flexibility in its values. Its positive value shows anamolous behavior, where as negative dispersion regime is considered to be normal[7]. Highly birefringent PCFs have find its application in signal processing, optical communication system and specifically in sensing applications. Large index contrast in combination with asymmetric core design are responsible for high modal birefringence[8]. Besides these two unique properties, normalised frequency and confinement loss are also important parameters to be studied. Several flexibility in design of PCFs has been observed. The variation in designs includes refrective index value, diameter of the air holes and by varying the pitch factor[9-12]. The pitch
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factor is the distance between two centres of air holes. Besides silica fibers, various non-silica fibers are also being employed[13]. In this paper we have reported a PCF structure with unique arrangement of circular air holes of different areas. The structure has two rings of larger circular air holes at four sides (A, B, D, and E) of hexagonal structure as shown in Fig. 1(b),whereas, the other two sides (C and F) of hexagonal structure has circular air holes of area in between the larger and smaller area circular air holes as shown in Fig. 1(b). The circular air holes of two rings adjacent to the air holes at four sides (B, C, E, and F ) of hexagonal structure has smallest area shown in Fig. 1(b). It has the circular air holes of smaller area at its two sides (A and D) of hexagonal structure as shown in Fig. 1(b). The innermost ring has circular air holes of larger area. The intention of designing such a fiber is to shape the dispersion. The rest of the paper is organized in other three sections. The second section elaborates the proposed structures and their results can be analysed in third section. Finally we conclude in last section. II. PROPOSED STRUCTURE PCF structures have been investigated with unique arrangement of circular air holes of different areas. PCF structure have five rings of circular air holes. We have used FDTD simulation method. Non-uniform stress experienced by the core of the fiber and the variation in shape of the core along the length of the fiber are the two important parameters for which the cylindrical symmetry of the fiber is broken. These factors remove the degeneracy between two perpendicular polarized mode and thus gain birefringence. Birefringence is determined by
B = η x −η y Where
η x and η y are
(1) the effective modal index number for
transverse electric and magnetic field respectively. Single mode PCFs has an advantage that intermodal dispersion is almost zero. It is due to the fact that the energy of the pulse is carried by only one mode. But as we know the fundamental mode is frequency dependent, different spectral component of the pulse travel at slightly different group velocity, which results group velocity dispersion (GVD). Dispersion (D) can be written as the sum of material dispersion and waveguide dispersion (14). DT = DM + DW . (2)
D=
d 1 ( ) d λ vg
Where
(3)
vg is the group velocity.
DT = −
2 λ d neff c dλ2
(4)
Where c is the velocity of light, λ is the operating wavelength and neff is the modal index number. An important parameter which play a vital role in determining the cut-off condition is normalized frequency or V parameter. The Veffective parameter of a PCF structure is determined by(15) :
Veff = (2π / λ ) ∧ n1 2Δ
(5)
Fig. 1(b) Geometrical presentation of designed PCF.
n1 is the refrective index of core, Δ is the relative refrective index difference of core and cladding , ∧ is the pitch factor ( ∧ = 1) and λ is the wavelength.
Where
The core and microstructured cladding have almost the same refrective index. The core of PCFs are not insulated from the microstructured cladding (surrounding matrix material) by the cladding. As we know the holes do not get merge with their neighbours and thus the matrix is connected with the core and the exterior as well. As a result a loss is expected when the light leaks from the core of PCFs to the exterior through the bridges between holes . This loss is confinement loss ( Lc ) . It is calculated by(16):
Lc = 8.686k0 (Im(neff )) Where
(6)
k0 is the free space number given by k0 =
2π
λ
, is and
Im(neff ) is the imaginary part of the effective modal index number.
III. SIMULATION RESULTS We have investigated a PCF structure with variation in areas as well as their arrangements in the five ring hexagonal struture. The structure can be explained as follows. The structure has two rings of larger circular air holes at four sides (A, B, D, and E) of hexagonal structure as shown in Fig. 1(b),whereas, the other two sides (C and F) of hexagonal structure has circular air holes of area in between the larger and smaller area circular air holes as shown in Fig. 1(b). The circular air holes of two rings adjacent to the air holes at four sides (B, C, E, and F ) of hexagonal structure has smallest area shown in Fig. 1(b). It has the circular air holes of smaller area at its two sides (A and D) of hexagonal structure as shown in Fig. 1(b). The innermost ring has circular air holes of larger area. The diameter of the largest air holes is 1.6 μ m . And the smaller air holes have
1.2 μ m . At last the smallest air holes have diameter 0.8μ m . The wafer is made of silica with refractive index of n = 1.46 . The length is chosen of 32 μ m and width is of 30 μ m . The structures consist of circular air holes whose diameter is 1μ m . OptiFDTD software has been used diameter of
for the simulation and analysis purpose.
Fig. 1(a) PCF structure . Fig. 2(a) Dispersion behaviour of the TM mode.
The structure has reported almost zero dispersion for a wide range of wavelengths. . A zero dispersion was observed near all optical windows. Even the TE mode also has reported zero
dispersion. We can thus say that the designed fiber can be used for communication purposes.
Fig. 5(a) Effective V parameter of the structure
As we know that for Veff ≤ 4.1 , the PCFs will have single
Fig. 2(b) Dispersion behaviour of the TE mode.
mode propagating inside the core. The effective V parameter shows that both the proposed PCFs structure are endlessly single mode fibers. IV. CONCLUSION Thus we have investigated the propagation characterstics of PCF structure. The structure was found to be a good candidate for optical communication purposes. However the PCF structure reports very low dispersion. The structure also reports high birefringence and thus can be used for sensor. Infine it can be said that both the structures are good for high data rate transfer. Fig. 3(a) Birefringence of the PCF structure.
REFERENCES
The birefringence reported for the structure is of the order of
10−4 . However the structure reports comparatively high birefringence at all optical windows. Moreover at 1.55μ m also the birefringence observed is very high. It can be used for sensor purposes. The confinement loss reported for structure is very low. The −6
order of loss reported for the structures is 10 .
Fig. 4(a) Confinement loss of the structure.
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