Photonic crystal fiber with anomalous dispersion

Photonic crystal fiber with anomalous dispersion behavior and high birefringence Pranaw Kumar, Priyanka Das School of Electronics Enginnering KIIT University, Bhubaneshwar [email protected] , [email protected] Abstract— A novel design of hexagonal PCF has been investigated with variation in areas of circular air holes. The structure consists of six rings. The three outermost ring has largest circular air holes. The immediate two rings next to the innermost ring consists of smallest circular air holes. The innermost ring consists of circular air holes whose area is lesser than the three outermost rings but larger than the second and third ring. The designed fiber reports a very low dispersion. Moreover a high birefringence is observed at the first optical window. Besides, normalized frequencies and confinement loss is also studied. This fiber can be used for generation of broadband supercontinnum and soliton based devices. Index Terms—Photonic crystal fiber, dispersion, birefringence, normalized frequency.

I. INTRODUCTION At certain wavelength due to the periodic arrangement of a dielectric, the propagation of light can be suppressed. Basically in that frequency range even spontaneous emission is not possible. Periodic arrangement of such dielectric is called photonic crystal. With the help of technique employed for making conventional fiber, a two dimensional structure silica/air were manufactured [1]. Later three dimensional PCFs were developed [2]. Core cladding silica glass optical fiber has brought a revolution in communication system. In this regard PCFs has been superior to conventional fiber. PCFs due to its various unique properties like birefringence [3], dispersion [4], endlessly single mode fiber [5], normalized frequency and other non-linear properties has been a burning topic of research. Basically PCFs is a special class of fiber or microstructured fiber, which allows the light to confine in solid and hollow cores. The light guiding mechanism in PCFs is of two types : index guiding [6] and photonic bandgap [7]. In index guiding mechanism a defect has been created at the centre of fiber. In photonic bandgap an index contrast between air and silica is created, for propagation of light. The arrangement of air holes acts to lower the effective refractive index in the cladding region and hence the light is confined to the solid core. As mentioned earlier, PCFs guide light due to index contrast between solid core and arrangement of air holes in the cladding region. These holes have great effect on the properties of PCFs [8]. The number of holes and their sizes effects guided light, relative to its wavelength in the fiber. Thus it became possible to design PCFs with some unique properties. PCFs can be structurally modeled. These structure modification is made by varying pitch factor, which is hole to hole spacing,

increasing or decreasing diameter of air holes and number of air holes in the cladding region. In index guided PCFs, cladding configuration strongly influenced dispersion. These influence are more intense when the core is made small and cladding region is made on the scale of wavelength of light [9]. Normal dispersion generally reduces the impact of coherence degradation [10] for a non-linear device. Hence low value dispersion is favorable for optical thresholding device. Zero dispersion are also found to be widely used in pulse compression [11], optical switching [12], optical parametric amplification [13]. Asymmetry and imperfections in fiber profile along with large index contrast structure and small scale structure leads to birefringence [14]. Birefringence can also be obtained intentionally by manipulating structure of core and cladding of fiber [15-16]. Basically two types of birefringence are observed : phase birefringence and wavelength dependent birefringence. Highly birefringence fibers are used for sensor and communication purposes [1718]. All guided mode are laky modes. Even PCFs with true bounded modes, suffer from confinement loss [19-20]. We have investigated a hexagonal six ring PCF structure. The structure consists of circular air holes of different area. The simulation results shows that the designed fiber can be used for communication, high data rate transfer and sensing applications. II. PROPOSED STRUCTURE We have investigated a PCF structure with variation in area of circular air holes. The structure consists of circular air holes of three different areas. The arrangement of circular air holes is such that the inner most ring consist of circular air holes of largest area. The two rings immediate next to inner most rings consist of circular air holes of smallest area. The intension for choosing such a structure is to shape the dispersion curve. The group velocity of light depends on the optical wavelength of light and this phenomenon is called dispersion. It can be obtained by the second order derivative of the real part of the effective refractive index. However the mathematical expression to calculate dispersion is [21]: 2 λ d (neff ) D=− c dλ2 Where λ is wavelength, c is

effective refractive index.

458

(1) velocity of light and

neff is the

Birefringence is obtained by the difference between the effective refractive index of the perpendicular polarization modes. The following mathematical expression can be used to obtain birefringence [22]:

B = neffx − neffy

simulation is 0.027 μ m and direction respectively.

0.0291μ m along x and y

(2)

neffx and neffy are the effective index number in x and y directions (TE and TM mode). With the help of the imaginary parts of the effective refractive index the confinement loss can be obtained for the corresponding mode. Mathematically:

CL = 8.868 Im(neff )

λ is

wavelength and

2π

λ

(3)

Im(neff ) is the imaginary part of

modal index number. The number of mode of PCF is determined by V number. For a single mode fiber. The value of V number should be less than 4.1 . Normalized frequency can be calculated [23]:

Veff = 2π

∧

λ

2 core

n

−n

2 eff

(4)

∧ is the pitch factor, ncore is the refractive index of core,

neff is the modal index number and λ is wavelength.

Fig. 1(a) PCF structure. III. SIMULATION RESULTS

Fig. 2(a) Dispersion behaviour

The designed fiber reports a very low dispersion at first optical window. A dispersion of 7 ps / nm / km has been found at wavelength of 850mm . The low value of dispersion enables the fiber to be employed for optical communication purpose.

Fig. 2(b) Birefringence relation. PCF with higher birefringence have various applications in fiber optic sensors interferometric system and optical devices. The investigated fiber reports a birefringence of the order of

10−3 at the first optical window.

A full vector method finite element method has been used to simulate the design fiber. We have employed optiPDTD software for simulation proposes. The smallest circular air hole has a diameter of 0.6 μ m . Circular air holes of largest area

1.4 μ m whereas the other 1μ m . The refractive index of wafer taken is 1.46. The pitch factor, center to center spacing of 2 circular air holes, is considered to be 2 μ m . The mess size for used in the fiber have diameter of

air holes are of diameter

International Conference on Applied and Theoretical Computing and Communication Technology (iCATccT)

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It is to be noted that the mode field distribution of the simulated fiber shows that the maximum power propagates in the core of the fiber. IV. CONCLUSION Thus we have investigated a new PCF structure with variation in the area of circular air holes. The arrangement of circular air holes is made such that the three outermost ring of the hexagonal structure consists of circular air holes of largest area and the innermost ring has the circular air holes of smallest area. Besides, these circular air holes, all the circular air holes are smaller in size. However the designed fiber reports a very low dispersion at the first optical window. The −3

Fig. 2(c) The confinement loss at different wavelength .

The low value of confinement loss assures the ability of confinement light in PCF is stronger. The result of the simulated design PCF reports a very low confinement loss. The −6

reported loss is of order of 10 . The decrease in the value of normalized frequency or V number along with increase in wavelength, shows a proper design which can be fabricated easily. The reported V number is less than 4.1 proves the PCF to be single mode fiber.

Fig. 2(d) The normalised frequency vrs wavelength.

birefringence is very high and is of the order of 10 . Thus we can conclude that the designed fiber is supposed to be eligible for high data rate transfer, fiber optic sensor and optical devices. REFERENCES [1] E. Yablonovitch, “Inhibited spontaneous emission in solid state physice and electronics”, Phys. Rev. Lett. 58, pp. 2059-2062, 1987 [2] J. C. Knight, T. A. Birks, P. St. J. Russell, D. M. Atkin, “All silica single mode optical fiber with photonic crystal cladding”, Opt. Lett. 21, pp. 1547-1549, 1996. [3] T. P. Hansen, J. Broeng, E. B. Libori, E. Knudsen, A. Bjarklev, J. R. Jensen, H. Simonsen, “Highly birefringent index guiding photonic crystal fibers”, IEEE Photon. Technol. Lett., 13, pp. 588-590, 2001. [4] Saitoh, K., Koshiba. M., “Chromatic dispersion control in photonic crystal fibers: application to ultra flattened dispersion”, Opt. Express, 2003, 11, pp. 843-852. [5] T. A. Birks, J. C. Knight, P. St. J. Russell, “Endlessly single mode photonic crystal fiber”, Opt. Lett., 21, pp. 1547-1549, 1997. [6] Large. M. C. J, Lwin. R, Manos S., et al, “Experimental studies of bandwidth behavior in graded index microstructured polymer optical fibers”, ECOC, Berlin, 2007. [7] R. F. Cregan, B. J. Magnan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, D. C. Allan, “Single mode photonic bandgap guidance of light in air”, Science, 285, pp. 1537-1549, 1999. [8] T. Hasegawa, E. Sasaoka, M. Onishi, M. Nishimura, Y. Tsuji, M. Koshiba, “Hole assisted lightguide fiber for large anamolous dispersion and low optical loss,” Opt. Express, 9, pp. 681-686, 2001. [9] J. C. Knight, J. Arriaga, T. A. Birks, A. Ortgosa- Blanch, J. W. Wadsworth, P. St. J. Russsell, “Anamolous dispersion in photonic crystal fiber”, IEEE Photon. Technol. Lett., 12, pp. 807-809, 2000. [10] N. Nakazawa, H. Kubota, K. Tamura, “Random evolution and coherence degradation of a high order optical soliton train in the presence of noise”, Opt. Lett., 24, pp. 318-320, 1999. [11] F. Duron, N. Sanner, G. Lucas-Leclin, P. Georges, R. Guame, B. Viana, K. P. Hansen, A. Peterson, “Self-compression of 1um femtosecond pulses in a photonic crystal fiber,” CLEO, 2012. [12] J. E. Sharping, M. Fiorentino, P. Kumar, R. S. Windeler, “All optical switching based on cross phase modulation in

Fig. 2(e) The mode field distribution.

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