Design and Characterization of Highly Birefringent ... - OSA Publishing

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JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 32, NO. 23, DECEMBER 1, 2014

Design and Characterization of Highly Birefringent Residual Dispersion Compensating Photonic Crystal Fiber Md. Imran Hasan, S. M. Abdur Razzak, Senior Member, IEEE, Student Member, OSA, and Md. Samiul Habib

Abstract—A residual dispersion compensating octagonal photonic crystal fiber (OPCF), with an elliptical array of circular airholes in the fiber core region, is proposed. The full-vector finiteelement method with perfectly matched layer boundary is used as the analysis tool. It is demonstrated that it is possible to obtain large average negative dispersion of –562.52 ps/(nm · km) over 240 nm and –369.10 ps/(nm · km) over 630 nm wavelength bands for the fast and the slow axis, respectively. In addition to large negative dispersion, ultra-high birefringence, high nonlinearity, and zero-dispersion wavelengths with low confinement loss are also warranted. The proposed OPCFs would be a promising candidate for residual dispersion compensation, supercontinuum generation, and other applications. Index Terms—Finite element method, highly birefringent fiber, negative flat dispersion, residual dispersion compensation.

I. INTRODUCTION N optical fiber communication systems, chromatic dispersion in single mode fibers (SMFs) induces temporal optical pulse broadening, resulting in serious restrictions in the transmission data rates. Currently, dispersion compensating fibers (DCFs) are extensively used to compensate the chromatic dispersion. It improves the transmission length without the need of using electronic regeneration of signals [1]. Regrettably, after dispersion compensation there remains some dispersion which is called the residual dispersion, thus requiring additional dispersion compensation [2]. This has made residual dispersion compensation techniques essential. A residual dispersion compensating fiber (RDCF) should provide large negative but flat dispersion and simultaneously cancel out the accumulated positive dispersion of standard SMFs. It is already known that a standard SMF has non zero flattened dispersion from 12 to 22 ps/(nm · km) in long-haul transmission system [3]. The photonic crystal fiber (PCF) has the potential to fulfill all requirements to be a good residual dispersion compensator in

I

Manuscript received June 17, 2014; accepted September 3, 2014. Date of publication September 21, 2014; date of current version October 24, 2014. M. I. Hasan is with the Department of Electronics & Telecommunication Engineering, Rajshahi University of Engineering & Technology, Rajshahi 6204, Bangladesh (e-mail: [email protected]). S. M. A. Razzak and M. S. Habib are with the Electrical & Electronic Engineering Department, Rajshahi University of Engineering & Technology, Rajshahi 6204, Bangladesh (e-mail: [email protected]; samiul.engieee@ gmail.com). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/JLT.2014.2359138

a smart way due to its novel propagation properties. Moreover, designing high nonlinear coefficient and high birefringence in addition to large negative dispersion is an ongoing challenge. This is because highly birefringent PCFs with nonlinear properties have received growing attention in telecommunication, supercontinuum (SC) applications and optical code division multiple access applications [4]. PCFs with zero-dispersion wavelengths (ZDWs) demonstrate stronger power spectral densities. Therefore PCFs with ZDW can be beneficial in SC applications. Various PCFs with negative flat dispersion properties [5]–[9] have been reported to date. Franco et al. [5] proposed a PCF with seven defected air-holes in the core region and Silva et al. in [6] and [7] proposed Ge doped core PCF having low average negative dispersion of –179 ps/(nm · km), –212 ps/(nm · km) and –203 ps/(nm · km) respectively. These PCFs although cover wide bandwidth, they have low average dispersion leading to long fiber requirement to compensate a standard SMF. It limits their application as potential residual dispersion compensators. The main drawback of the Refs. [6] and [7] is fabrication difficulty due to presence of a doped core. The fibers proposed by Islam et al. in [8] and [9] are based on equiangular spiral PCF. They cover E to U bands with a low average negative dispersion of –227 ps/(nm · km) and a high average negative dispersion of –393 ps/(nm · km) respectively. The main penalty of these two papers is the structure itself. The structural abstruse leads the design almost impractical by using conventional fabrication method. Recently, Tee et al. [2] has reported a RDCF with high average negative dispersion of –457.40 ps/(nm ·km) covering E to U bands. Although PCF in [2] is attractive with respect to negative flat dispersion, but its dispersion characteristic is more sensitive to the variation of air-hole diameter in the PCF core. Arrangement of very small air-hole in the PCF core requires extra care during the fabrication process. However, very recently, a large negative average dispersion of about −544.70 ps/(nm · km) over the wavelength range 1.46–1.70 μm has been reported by the authors for almost same structure with a dispersion variation of about 12.80 ps/(nm · km) [10]. In the PCFs mentioned above the ZDW issue and both axis flat for residual dispersion compensation was not achieved anywhere. Again, to minimize the insertion loss and cost, the RDCF should be as short as possible and this necessitates that the average of negative dispersion should be as large as possible. In this paper an OPCF structure is proposed to have large average negative dispersion, ultra-high birefringence and wide compensation bandwidth simultaneously. Besides, ZDW

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HASAN et al.: DESIGN AND CHARACTERIZATION OF HIGHLY BIREFRINGENT RESIDUAL DISPERSION COMPENSATING PHOTONIC

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Fig. 2. The fundamental optical field distribution at 1.55 μm for (a) x-polarization (b) y-polarization.

Fig. 1. Transverse cross-section of five-ring OPCF with pitch and air-hole diameter. Here, y 1 = 0.8Λ, y 2 = 1.374Λ/2, y 3 = 0.375Λ, x1 = 1.15Λ, x2 = 1.3Λ/2.

nonlinear property and low confinement loss of the proposed fiber increase its potential in nonlinear optic applications. Due to superior optical properties; the proposed fiber will have important applications in residual dispersion compensation, maintaining single polarization and SC generation. II. DESIGN GUIDELINE OF THE PROPOSED PCF Fig. 1 shows the proposed design for RDCFs using OPCF geometry. Two types of air-hole diameter namely d, and d1 is used on the first ring to give elliptical shape to achieve high birefringence. While air-hole diameter on the second to five ring is d1 with the air-hole pitch between rings is Λ which is related to Λ1 (air-hole pitch on the same ring) by the relation Λ1 = 0.765Λ. We have proposed OPCF geometry for residual dispersion compensation because OPCF offers better dispersion accuracy, strong mode field confinement ability and lower confinement losses [11]. Octagonal cladding structure contains more air-holes on the same number of rings. This results in a higher air-filling ratio and a lower refractive index around the core, thereby providing strong confinement ability and less confinement loss. Moreover, the two air-holes of the first ring are relatively large, which results higher negative dispersion and better mode field confinement [12], at the same time others air-hole diameter on the first ring is scaled down to shape dispersion property [11] to obtain flattened negative dispersion. In Fig. 1 the background material is pure silica surrounding with air-holes. III. SIMULATION RESULTS The commercial full vector finite element method (FEM) software COMSOL of version 4.2 and about 13422 triangular vector edge elements with 1955 boundary elements have been used to represent the structure. The fundamental optical field distribution for x and y polarization modes at the operating wavelength of 1.55 μm is shown in Fig. 2. According to simulation, it is seen that x and y polarization modes are tightly bounded in the centre core region due to high-index contrast in the centre than the cladding.

From the structure it is evident that the effective indices of x-polarized mode will be larger than those of y-polarized mode due to smaller index difference between the core and cladding along x direction because air-holes are distributed more sparsely along x direction than along y direction. As the effective refractive index of the x-axis mode is higher therefore light travels slower along the x-axis than the y-axis. So, the x-polarization mode and the y-polarization mode act as slow axis mode and fast axis mode respectively. Once the modal complex effective index neff is obtained by solving an eigenvalue problem drawn from the Maxwell equations using the FEM, chromatic dispersion D, birefringent B, confinement loss Lc , and nonlinear coefficient γ can be given by following equations: λ d2 Re[neff ] D= − (1) c dλ2 (2) B = |nx − ny | Lc = 8.686 × k0 Im[neff ] 2π n2 γ= λ Aeff with

Aeff =

|E|2 dxdy

2 / |E|4 dxdy .

(3) (4)

(5)

where Re[neff ], Im[neff ] is the real part and imaginary part of the effective refractive index neff , λ is the wavelength, and c is the velocity of light in vacuum, k0 = 2π/λ is free space wave number, n2 is Kerr constant, Aeff is effective area, E is the electric field amplitude in the medium, nx and ny are the mode indices of two orthogonal polarization fundamental mode. The material dispersion given by the Sellmeier formula is directly included in the calculation. Therefore, D in (1) corresponds to the total dispersion of the PCF. At first the dispersion properties of the proposed OPCF with different structural parameters have been investigated. As shown in Fig. 1, there are three degrees of freedom (d, d1 and Λ) in the design procedure; those three parameters are adjusted separately and their influence on the dispersion curve is investigated. Fig. 3 shows the effect of the air-hole diameter of d/Λ on the dispersion behavior with Λ = 0.882 μm and d1 /Λ = 0.70, where d/Λ is chosen as 0.46, 0.48 and 0.50. In the figure dotted line indicates slow axis and solid line indicates fast axis. For slow axis the corresponding dispersion varies between (−331.55

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Fig. 3. Effect of d/Λ on the dispersion behavior for both slow axis (dotted line) and fast axis (solid line).

Fig. 5. Effect of Λ on the dispersion behavior for both slow axis (dotted line) and fast axis (solid line).

Fig. 4. Effect of d1 /Λ on the dispersion behavior for both slow axis (dotted line) and fast axis (solid line).

to −337.65) ps/(nm · km), (−364.48 to −372.92) ps/(nm · km) and (−397.20 to −411.26) ps/(nm · km) respectively covering 1.58 to 1.70 μm wavelength bands. The dispersion variation (ΔD) for slow axis is 6.10, 8.44 and 14.10 ps/(nm · km) respectively and corresponding average dispersion (Da ) of slow axis is −335.30, −369.10 and −405.30 ps/(nm · km) respectively. For the fast axis the corresponding dispersion varies between (−487.50 to −507.75) ps/(nm · km), (−555.704 to −567.80) ps/(nm · km) and (−613.10 to −641.10) ps/(nm · km) respectively covering 1.46 to 1.70 μm wavelength bands. The ΔD for fast axis is 20.25, 12.10, and 28 ps/(nm · km) respectively and corresponding Da of fast axis is −501.10, −562.52 and −633.90 ps/(nm · km) respectively. It is apparent that increasing values of the d/Λ, negative dispersion is increased but ΔD is increased gradually for slow axis and on the other hand, ΔD is very high for fast axis when d/Λ is 0.46 or 0.50 except 0.48. So, d/Λ = 0.46 or d/Λ = 0.50 cannot be optimum for fast axis due to high value of ΔD. Considering ΔD and Da of both axis the optimal value of d/Λ is selected as 0.48 while the other parameter remain constant at which ΔD for slow axis and fast axis is 8.44 ps/(nm · km) and 12.10 ps/(nm · km) respectively. Fig. 4 shows the effect of d1 /Λ on the dispersion behavior with Λ = 0.882 μm and d/Λ = 0.48, where d1 /Λ is chosen as 0.68, 0.70 and 0.72. In the figure dotted line indicates slow axis and solid line indicates fast axis. For slow axis the corresponding

dispersion varies between (−350.50 to −361.50) ps/(nm · km), (−364.48 to −372.92) ps/(nm · km) and (−377.11 to −385.01) ps/(nm · km) respectively covering 1.58 to 1.70 μm wavelength bands; ΔD is 11, 8.44 and 7.90 ps/(nm · km) respectively and Da is −356.80, −369.10 and −381.90 ps/(nm · km) respectively. Besides, for fast axis the corresponding dispersion varies between (−548.34 to −563.50) ps/(nm · km), (−555.704 to −567.80) ps/(nm · km) and (−560.63 to −574.21) ps/(nm · km) respectively covering 1.46 to 1.70 μm wavelength bands; ΔD is 15.16, 12.10 and 13.58 ps/(nm · km) respectively and Da is −557.50, −562.52 and −568.90 ps/(nm · km) respectively. When d1 /Λ is 0.68, ΔD is high for both fast and slow axis. Again, ΔD is low of 7.90 for slow axis when d1 /Λ is 0.72, but ΔD of fast axis is high. So considering the value d1 /Λ = 0.70 as optimal value because in this case ΔD of fast axis is very low and ΔD of slow axis is moderate while the other parameters remain constant. All of the above investigations are performed with a fixed pitch Λ = 0.882 μm. We then vary the pitch 0.875, 0.882 and 0.90 μm with normalized air-hole diameters being fixed as d/Λ = 0.48, and d1 /Λ = 0.70. The results are shown in Fig. 5. While the pitch of the PCF shrinks, the negative dispersion increases because core area is reduced and that reduced the effective refractive index. For slow axis the corresponding dispersion varies between (−368.60 to −377.22) ps/(nm · km), (−364.48 to −372.92) ps/(nm · km) and (−350.20 to −362.80) ps/(nm · km) respectively covering 1.58 to 1.70 μm wavelength bands; ΔD is 8.62, 8.44 and 12.60 ps/(nm · km) respectively and Da is −373.70, −369.10 and −357.40 ps/(nm · km) respectively. Besides, for fast axis the corresponding dispersion varies between (−566.70 to −582.70) ps/(nm ·km), (−555.704 to −567.80) ps/(nm · km) and (−534.20 to −553.80) ps/(nm · km) respectively covering 1.46 to 1.70 μm wavelength bands; ΔD is 16, 12.10 and 19.60 ps/(nm · km) respectively and Da is −577.80, −562.52 and −546.90 ps/(nm · km) respectively. When pitch Λ = 0.882 μm the value of ΔD is lowest for both slow axis and fast axis. Thus Λ = 0.882 is chosen as optimum value while the others parameter remain constant. Based on the above results, to compensate the residual dispersion of standard SMF the design parameters of the proposed OPCF can be selected as Λ = 0.882 μm, d/Λ = 0.48


Fig. 6. Wavelength dependence CR curve for both axis when the optimum geometric parameters are Λ = 0.882 μm, d/Λ = 0.48 and d1 /Λ = 0.70.

Fig. 7. Wavelength dependence optimum dispersion curve for both axis when the optimum geometric parameters are Λ = 0.882 μm, d/Λ = 0.48 and d1 /Λ = 0.70.

and d1 /Λ = 0.70, the corresponding compensation ratio (CR) of the proposed fiber for both axis is shown in Fig. 6 within the wavelength range is 1.46 to 1.70 μm. The calculation shows that the proposed OPCF can compensate residual dispersion of the SMF and it can do this within ±48% deviation of the dispersion compensation ratio (DCR) over the entire (1.46–1.70 μm) 240 nm band centered at 1.55 μm for fast axis and ±40% deviation of the DCR over the entire (1.46–1.70 μm) 240 nm band centered at 1.55 μm for slow axis. Now the corresponding optimum dispersion curve for both axes is shown in Fig. 7. Here the wavelength range is taken from 0.80 to 2.24 μm to see how long flat dispersion curve is achievable for Λ = 0.882 μm, d/Λ = 0.48 and d1 /Λ = 0.70. From Fig. 7 it reveals that ZDW at 0.908 μm and 0.88 μm is obtained for fast axis and slow axis respectively which is near infrared region. The dispersion for fast axis is relatively flat and varies between −555.704 to −567.80 ps/(nm · km) from 1.46 to 1.70 μm (solid red line). It means that the proposed OPCF presents flat negative dispersion over S + C + L+ U wavelength bands and an average dispersion, Da near to −562.52 ps/(nm · km) with a dispersion variation, ΔD = 12.10 ps/(nm · km) for fast axis. To the best of our knowledge this is the highest average negative dispersion than all previously published paper. Simultaneously, the dispersion for slow axis also relatively flat and varies between −364.48 to

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−373.69 ps/(nm · km) from 1.58 to 2.21 μm (dotted green line). It indicates the proposed OPCF presents flat negative dispersion over 630 nm wavelength ranges and an average dispersion, Da near to –369.20 ps/(nm · km) with a dispersion variation, ΔD = 9.21 ps/(nm · km) for slow axis. This is, to our knowledge, the highest flattened range than all previously published RDCF papers. Although the total flatness of slow axis is not in communication bands but this large average negative dispersion is enough to compensate standard SMF and can be useful in the wavelength division multiplexing optical communication systems in future applications. To be a good residual dispersion compensator small dispersion slope value is needed. For the proposed structure, the calculated dispersion slope varies between −0.31 to 0.01 ps/(nm2 · km) for fast axis over 1.46 to 1.70 μm wavelength at optimum parameters and dispersion slope varies between −0.15 to 0.025 ps/(nm2 · km) for slow axis over 1.58 to 2.21 μm wavelength at optimum parameters. After shaping the dispersion curve to the desired level (see Fig. 7) in the way just described, we then have checked the dispersion accuracy of the design. It is known that in a standard fiber draw, 1% variations in fiber global diameter may occur unavoidably [11] during the fabrication process. Therefore, roughly an accuracy of 2% may require ensuring dispersion flatness [13] and the corresponding dispersion curves are also shown in Fig. 8. In the figure global parameter varied up to ±2% from their optimum values. Solid lines indicate dispersion curves due to increment in parameters and dashed lines (blue) indicate for decrement. For fast axis in Fig. 8(a) reveals that, ±1% variation in the global parameter causes ±1.53% changes in the average dispersion from the optimum dispersion value. Also, it can be seen that that, ±2% variation in the global parameter causes ±2.72% changes in the average dispersion from the optimum dispersion value. Fig. 8(b) depicts the effect on slow axis optimum dispersion curve by varying global parameters. From the curve it is seen that variation of ±1% causes ±2.60% change and variation of ±2% causes ±6.90% change in the average dispersion from the optimum dispersion value within the range 1.58 to 2.21 μm wavelength bands. The air-holes of the first ring are placed in such a way that leads to obtain flat negative dispersion with high birefringence. From Fig. 9 it is seen that at 1.55 μm the birefringence is of the order 2.1 × 10−2 . Again birefringence of 0.97 × 10−2 and 1.04 × 10−2 are obtained for ZDW at 0.88 μm and 0.908 μm respectively on slow axis and fast axis respectively. Birefringent properties in a fiber can be used to eliminate the effect of polarization mode dispersion in transmission systems and many other areas where polarization maintaining property is required, such as sensing applications, maintaining single polarization. Besides, highly birefringent fibers are extensively used in fiber loop mirrors as a major component for optical fiber sensing applications; the additional property of high negative dispersion would provide better performance for the fiber sensor design and also in long distance data transmission system [14]. Fig. 10 shows that the nonlinear coefficient of the fiber are 48.70 and 38.90 W−1 · km−1 at 1.55 μm for fast axis and slow

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Fig. 10. Nonlinearity for both axis as a function of wavelength for optimum design parameters.

Fig. 8 (a) Sensitivity of the dispersion up to ±2% variation in global parameter for fast axis. (b) Sensitivity of the dispersion up to ±2% variation in global parameter for slow axis.

Fig. 9. eters.

Birefringence as a function of wavelength for optimum design param-

axis respectively and the corresponding calculated effective area (Aeff ) is 1.91 and 2.40 μm2 respectively. Due to the small effective mode area; the proposed RDCF is expected to be insensitive to bending losses [4]. Also it is known that, low effective mode area has a positive effect on bending loss [4]. Moreover, PCF with higher nonlinear coefficient are found to be suitable for dispersion compensation, where four-wave mixing is prone to appearing [15]. The obtained nonlinear coefficient at ZDW on fast axis is 130.20 W−1 km−1 and on slow axis is 125.90 W−1 km−1 . The ZDW with high nonlinear property and high birefringence

are key issues for SC generation. However, PCF with ZDW can make strong power SC spectral in the near infrared band. In addition, the ZDW for both slow and fast axis is located in the working wave band of the Ti:sapphire oscillator (0.70–0.98 μm) used to frequency conversion of Ti:sapphire femtosecond laser [16]. On the other hand, if a fiber is highly birefringent then short fiber length would be enough (fiber length) in most polarization related applications and high negative dispersion is necessary (which reduce the fiber length) to suppress the nonlinear parametric process in fibers [17]. As our proposed fiber has high negative dispersion, a small length the proposed fiber will suppress the nonlinear effect. A good RDCF design should have low confinement losses and the ability of the structure to guide light with minimum losses. It is seen from Fig. 11(a) that the confinement loss for fast axis exhibits low confinement loss as 11 × 103 and 0.091 dB/km for ring number, Nr = 5 and 8 respectively at 1.55 μm. Low confinement loss for Nr = 5 at ZDW on fast axis is obtained 12.3 × 10−6 dB/km. Fig. 11(b) reveals that confinement loss for the slow axis is 5.2 × 102 to 5.4 × 105 dB/km for Nr = 5 and 4.6 × 10−3 to 1.4 × 103 dB/km for Nr = 8 within 1.58 to 2.21 μm wavelength bands. Again, the confinement loss at ZDW for slow axis is 4.8 × 10−7 dB/km for Nr = 5. Moreover, this confinement loss can be further reduced by increasing air-hole rings in the cladding. It is to be mentioned that the fiber supports weak higher order modes with loss 2.82 × 106 dB/km around 1.55 μm wavelengths. The calculated confinement loss of the second order modes were found more 20 times higher than that of the fundamental modes. Therefore, the fiber effectively operates in the single mode because the higher order modes will not be guided due to high confinement losses in comparison to the fundamental modes [18]. At this point, we would like to address possible limitations of our proposed PCF architecture associated with a high nonlinear coefficient. High nonlinearity provides small mode field diameter which presents potential difficulties in the input coupling and output coupling of light. Nevertheless, it has been reported that PCFs can be interfaced to standard SMFs using a tapered intermediate PCF (reported 0.10 dB measured taper


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TABLE I COMPARISON BETWEEN PROPERTIES OF THE OPCF AND OTHER RESIDUAL DISPERSION COMPENSATION DESIGNS PCFs Ref. [5] Ref. [6] Ref. [7] Ref. [8] Ref. [9] Ref. [2] Ref. [23]

OPCF

Da (Δ D)

B×10−2

Aeff

L c (N r )

ZDW

−179 (2.1) −212 (11) −203 (10) −227 (11.9) −393 (10.4) −115 (14) −457.4 (12.7) −491.5 (10.5) Fast axis –562.52 (12.1) Slow axis –369.2 (9.21)

10−4 — — Around 1.75 0.65 2.78 10−5 2.68

6 — 3.8 5 3.55 3.92 9 2.36 Fast axis 1.91 Slow axis 2.40

0.1 (8) — — 0.1 (10) 4 (16) 2 (16) 0.09 (10) 0.035 (9) Fast axis 0.091(8) Slow axis 0.0016 (8)

No No No No

2.1

No No No Yes Yes

B, A e f f , L c measured at 1.55 μm

Fig. 11 (a) Confinement loss for fast axis as a function of wavelength (b) Confinement loss for slow axis as a function of wavelength.

loss) mode matched to each fiber at each end [19]. Another possible solution to the splicing problem is to splice the PCFs with the standards SMFs using the splice free interconnection technique [20]. The splice-free interface of PCFs with the SMF technique is versatile to interface with any type of index guiding silica PCF. We believe that our proposed PCF can be interfaced with existing technology without major complications. While designing an RDCF, fabrication is the challenging issue. The OPCF can be drawn from individual stackable units of suitable size and shape [21]. Theoretical and experimental investigations by Suzuki et al. [22] have shown that it is possible to fabricate even complex PCF structures by adapting conventional stack and draw methods. Again, Ref. [23] proposed almost same type of structure that can be fabricated using the standard stackand-draw technique. Therefore, we believe that our proposed RDCF could be fabricated without any major complications. Finally, a comparison is made in Table I between properties of the OPCF and some other fiber designed for residual dispersion compensation applications. Table I compares those fibers taking into account average negative dispersion = Da ps/(nm · km), dispersion variation = ΔD ps/(nm · km), birefringent = B, effective area = Aeff μm2 , confinement loss = Lc dB/km and number of ring = Nr . It should be pointed out that the PCF in Ref. [23] and the proposed one in this paper both have almost same design, but different core ellipticity ratio. The proposed fiber has three degree of freedoms (d, d1 and Λ) where Ref. [23] has four degree of freedoms (d, d1 , d2 and Λ) used in the design procedure. The proposed fiber has large negative dispersion than that of the PCF

in Ref. [23]. As a result small fiber length is required than Ref. [23] to compensate dispersion of a standard SMF. The proposed fiber also provides flat dispersion for both the polarization axes. Table I reported previously published papers on the residual dispersion compensation. None of them have any ZDW. The ZDW with high nonlinear property and high birefringence are key factors for the SC generation [24]. However, PCF with ZDW can make strong power SC spectral in the near infrared band. Again, ZDW of the proposed fiber is located in the working wave band of the Ti:sapphire oscillator (0.70–0.98 μm) which is suitable for frequency conversion of Ti:sapphire femtosecond laser [16]. IV. CONCLUSION A novel OPCF design is proposed to obtain very large average negative dispersion for both the fast and the slow axis with a ZDW for compensating the residual dispersion of SMFs. The proposed design simultaneously ensures ultra-high birefringence, high nonlinear coefficient and low confinement loss in the entire telecom bands. The tolerance of designed guiding properties to variation in fiber dimension due to fabrication imperfection has also been analyzed. The proposed PCF would be a smart candidate in many emerging applications such as residual dispersion compensation, SC generation, ultra-short soliton pulse transmission, and frequency conversion of Ti:sapphire femtosecond laser as its guiding properties should suit those applications. REFERENCES [1] L. G. Nielsen, S. N. Knudsen, B. Edvold, T. Veng, D. Rasmussen, C. C. Larsen, and H. Damsgaard, “Dispersion compensating fibers,” Opt. Fiber Technol., vol. 6, no. 2, pp. 164–180, 2000. [2] D. C. Tee, M. H. A. Bakar, N. Tamchek, and F. R. M. Adikan, “Photonic crystal fiber in photonic crystal fiber for residual dispersion compensation over E + S + C + L + U wavelength bands,” IEEE Photon. J., vol. 5, no. 3, art. ID 7200607, Jun. 2013. [3] G. P. Agrawal, Fiber-Optic Communication Systems, 3rd ed. New York, NY, USA: Wiley, 2002, pp. 15–64. [4] H. Ademgil, S. Haxha, and F. AbdelMalek, “Highly nonlinear bendinginsensitive birefringent photonic crystal fibres,” Engineering, vol. 2, no. 8, pp. 608–616, 2010.

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Md. Imran Hasan was born in Bangladesh in 1989. He received the B.Sc. Eng. degree in electronics & telecommunication engineering from the Rajshahi University of Engineering & Technology (RUET), Rajshahi, Bangladesh, in 2011. He is currently a Lecturer with the same department of RUET. His current research interests include photonic crystal fibers (PCFs), THz transmission in PCFs and photonic devices.

S. M. Abdur Razzak (S’07) was born in Natore, Bangladesh, on December 31, 1974. He received the B.Sc. degree from the Rajshahi University of Engineering & Technology (B.I.T. Rajshahi), Rajshahi, Bangladesh, in 1998, and the M.Eng. and Ph.D. degrees in electrical and electronic engineering from the University of the Ryukyus, Okinawa, Japan, in 2007 and 2010, respectively. Dr. Razzak received the President’s Honorary Award from the University of the Ryukyus in 2007 and the Board of Governors’ Gold Medal from B.I.T. Rajshahi in 2000. He is a Member of Institution of Engineers, Bangladesh, and a Student Member of the Institute of Electronics, Information and Communication Engineers of Japan and the Optical Society of America.

Md. Samiul Habib was born in Thakurgaon, Bangladesh, on March, 1986. He received the B.Sc. Eng. M.Sc. Eng. degrees in electrical & electronic engineering from the Rajshahi University of Engineering & Technology, Rajshahi, Bangladesh, in 2008 and 2012, respectively. He is currently an Assistant Professor at the Rajshahi University of Engineering & Technology. His current research interests include photonics, optimization of photonic crystal fibers, and photonic devices. Mr. Samiul is a Member of the Institution of Engineers, Bangladesh.