Proposal for highly birefringent broadband dispersion compensating octagonal photonic crystal fiber

Optical Fiber Technology xxx (2013) xxx–xxx

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Optical Fiber Technology www.elsevier.com/locate/yofte

Proposal for highly birefringent broadband dispersion compensating octagonal photonic crystal fiber Md. Selim Habib a,⇑, Md. Samiul Habib a, S.M. Abdur Razzak a, Md. Anwar Hossain b a b

Department of Electrical & Electronic Engineering, Rajshahi University of Engineering & Technology, Rajshahi 6204, Bangladesh Graduate School of Engineering and Science, University of the Ryukyus, 1 Senbaru, Nishihara, Okinawa 903-0213, Japan

a r t i c l e

i n f o

Article history: Received 17 November 2012 Revised 23 May 2013 Available online xxxx Keywords: Dispersion compensating fiber Finite element method High birefringence Photonic crystal fiber Residual dispersion

a b s t r a c t In this paper, we propose and demonstrate a highly birefringent photonic crystal fiber based on a modified octagonal structure for broadband dispersion compensation covering the S, C, and L-communication bands i.e. wavelength ranging from 1460 to 1625 nm. It is shown theoretically that it is possible to obtain negative dispersion coefficient of about 400 to 725 ps/(nm km) over S and L-bands and a relative dispersion slope (RDS) close to that of single mode fiber (SMF) of about 0.0036 nm1. According to simulation, birefringence of the order 1.81  102 is obtained at 1.55 lm wavelength. Moreover, effective area, residual dispersion, effective dispersion, confinement loss, and nonlinear coefficient of the proposed modified octagonal photonic crystal fiber (M-OPCF) are also reported and discussed. Ó 2013 Elsevier Inc. All rights reserved.

1. Introduction Photonic crystal fibers (PCFs) or holey fibers (HFs) or microstructure optical fibers (MOFs) have a microscopic array of air channels running down their length that make a low index cladding around the undoped silica core [1]. Such holey claddings in PCFs help tuning dispersion slope and controlling confinement losses in a way that was not possible in conventional fibers [2]. PCFs offer flexibility in tuning dispersion [3,4] which is crucial in designing dispersion compensating fiber design. The dispersion must be compensated in the long-distance optical data transmission system to suppress the broadening of pulse. One way to realize this is to use the dispersion compensating fibers (DCFs) having large negative dispersion [5]. To minimize the insertion loss and reduce the cost, the DCFs should be as short as possible, and the magnitude of negative dispersion should be as large as possible. To efficiently compensate the dispersion at all the frequencies of dense wavelength division multiplexing (DWDM), the negative dispersion of DCFs should span a wide spectrum. Again, the dispersion and dispersion slope should be compensated at the same time [6]. Therefore, in designing DCFs, it is important to take into consideration dispersion, dispersion slope, relative dispersion slope, bandwidth, and mode property [7]. Highly birefringence photonic crystal fibers (HB-PCFs) on the other hand are suitable for various novel applications including sensing application. For such PCFs, high birefringence with high negative disper⇑ Corresponding author. Fax: +880 721750356. E-mail address: [email protected] (Md. Selim Habib).

sion coefficient is crucial. The idea of using PCF for dispersion compensation (DC) was first proposed by Birks et al. [8]. However, the design suffers from its small effective area. A similar approach was used whereby the designed PCF was optimized for broadband DC with a dispersion coefficient of approximately 475 ps/ (nm km) and a small effective area and resulted in a large coupling loss with SMF but no information about confinement loss was reported [9]. In addition, several attempts have been made by other groups with the aim of achieving a high negative dispersion as well as a suitable bandwidth for dispersion compensation. For example, Huttunen et al. [10] theoretically investigated a dual-core PCF with a highly doped internal core, resulting in a dispersion peak of 59,000 ps/(nm km) and a modal effective area of 10 lm2. Unfortunately, highly doped fibers, besides exhibiting high confinement losses, also make the design and fabrication process more difficult [11] and no attempt was made to match the relative dispersion slope (RDS) to that of the conventional SMF. Fujisawa et al. [12] employed a genetic algorithm procedure in a PCF for DC design to cover the entire S-band. The peak dispersion of 500 ps/ (nm km) was achieved at the expense of using a PCF structure with 14 air-hole rings. Recently, Matsui et al. have theoretically proposed a PCF capable of DC in all three telecommunications bands simultaneously [13]. The penalties for this type of design are a low dispersion parameter [approximately 100 ps/(nm km)], which requires a long fiber to compensate for the accumulated dispersion of the transmission fiber, and a more complicated arrangement of the internal air-holes in the inner cladding, than that used in previous cases. Recently, it has been reported that all glass (solid) DCFs can achieve a high negative dispersion of approximately

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Please cite this article in press as: Md. Selim Habib et al., Proposal for highly birefringent broadband dispersion compensating octagonal photonic crystal fiber, Opt. Fiber Technol. (2013), http://dx.doi.org/10.1016/j.yofte.2013.05.014

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250 to 300 ps/(nm km) [14]. However, conventional solid optical fibers such as conventional DCFs, have some limitations related to their structure, for instance, materials of different thermal expansion coefficients (i.e., germanium-doped core and silica cladding regions). In addition, another drawback of germanium (or other index increasing dopants) doping in the core of conventional solid DCFs is increased fiber loss and a significant increase in nonlinearity owing to the high doping concentrations [15]. Besides these, several designs for single-material PCFs have been proposed to achieve a high negative dispersion coefficient or a wide compensation bandwidth [7]. Those PCFs possess air-holes arrayed in a triangular lattice with the same air-hole diameter or with a dual concentric core (with two different air-hole sizes), and they cannot simultaneously have a negative dispersion coefficient larger than 600 ps/(nm km) and a compensation bandwidth wider than C band. A honeycomb structure PCF with a Ge-doped central core has been proposed for a wide compensation bandwidth and a large dispersion coefficient which can reach 1350 ps/(nm km) [16] but the doped core will lead to fabrication difficulties. In a recent report, a PCF with the first ring of special ‘grapefruit’ holes is proposed and its potential as a broadband dispersion compensation fiber is shown [17]. However, the feasibility for practical fiber links has not been numerically studied and the structural variations analyzed are virtually not random in nature; therefore the model does not accurately represent influences from fabrication. In this paper, we propose a modified octagonal PCF (M-OPCF) that has both high negative dispersion coefficient of about 588 ps/(nm km) at 1.55 lm and high birefringence. We numerically investigate the dispersion compensation characteristics of the M-OPCF over the S, C and L-bands and show that the M-OPCF can be designed simply by introducing the defects into the core by omitting several air-holes from a conventional OPCF and using the elliptical air-holes adjacent to the OPCF core to produce high birefringence that has better polarization maintaining properties. In addition to this, the designed fiber has an effective dispersion range of ±0.20 ps/(nm km) in the entire S and L-bands. Undoubtedly, the proposed PCF architecture will be greatly applicable to optical communication systems.

2. Geometries of the proposed M-OPCF Fig. 1 shows the transverse cross section of the proposed PCF with optimized air-hole diameters d, d1, pitch K, and ellipticity, g. In contrast to conventional OPCF, the proposed structure has

two air-holes missing in the first ring (the dotted circle). Pitch K is related to K1 by the relation K1  0.765K. The designed octagonal PCFs have isosceles triangular unit lattices with a vertex angle of 45°. Due to such lattices, OPCFs contain more air-holes in the cladding region with the same numbers of rings than hexagonal PCFs (HPCFs). In the designed M-OPCFs, the total number of airholes for rings 1, 2, 3, 4, and 5 are respectively 6, 24, 48, 80, and 120, whereas in a regular triangular lattice, the number of air-holes is 6, 18, 36, 60, and 90, respectively. This results in a higher air-filling ratio and a lower refractive index around the core, thereby providing strong confinement ability. Air-holes adjacent to the core are transformed to elliptical air-holes (oval holes) by stretching them vertically. The minor axis and major axis lengths of the elliptical air-holes are defined as ds and df respectively. It is known that the size of the air-holes near the PCF core affects the dispersion characteristics [17]. This is also true when the circular air-holes are replaced with several elliptical air-holes near the core, as is carried out here to obtain better DC properties. It is also known that, when using a conventional PCF topology, it is difficult to engineer a high negative chromatic dispersion, and control dispersion slope, confinement loss, high nonlinear coefficient and polarization maintaining properties simultaneously. Consequently, we need to incorporate a structure with a higher degree of freedom regarding the total number of geometrical design parameters. Hence, by engineering the four design parameters, namely, pitch K, air-hole diameters d, d1, and ellipticity g, we can suitably design transmission properties such as chromatic dispersion, dispersion slope, and RDS, to simultaneously achieve a high negative dispersion coefficient, low confinement loss, and high birefringence over S and L-bands. In our simulations, we use the ratio g = ds/df for the ellipticity of the air-holes near the core, as shown in Fig. 1. 3. Numerical method The finite element method (FEM) with circular perfectly matched boundary layers (PML) is used to simulate properties of the proposed PCF. To model the leakage, an efficient boundary condition has to be used, which produces no reflection at the boundary. PMLs are the most efficient absorption boundary conditions for this purpose [18]. Using the FEM, the PCF cross-section is divided into homogeneous subspaces where Maxwell’s equations are solved by accounting for the adjacent subspaces. These subspaces are triangles that allow a good approximation of the circular structures. Using the PML, from Maxwell’s curl equations the following vectorial equation is obtained [19]

r  ð½s1 r  EÞ  k20 n2eff ½sE ¼ 0

ð1Þ

where E is the electric field vector, k0 is the wave number in the vacuum, neff is the refractive index of the domain, [s] is the PML matrix, [s]1 is the inverse matrix of [s]. The effective refractive index of the base mode is given as neff b = k0, where b is the propagation constant. Once the modal effective refractive index neff is obtained by solving an eigenvalue problem using FEM, the chromatic dispersion D(k), confinement loss Lc, and effective area Aeff can be calculated given by [20]. The chromatic dispersion D(k) of PCFs is calculated using the following 2

DðkÞ ¼ 

Fig. 1. Transverse cross section of the designed M-OPCF showing pitch K, air-hole channels with diameter d, and d1, ellipses with dimensions ds and df. For octagonal structure, K is related to K1 by K1  0.765K. The dotted circle in the first ring represents the missing air-hole.

k d Re½neff  c dk2

ð2Þ

in ps/(nm km), where Re[neff] is the real part of effective refractive index neff, k is the wavelength in vaccum, c is the velocity of light in vacuum. The material dispersion can be obtained from the three-term Sellmeier’s formula and it is directly included in the calculation. In PCFs, the chromatic dispersion D(k) is related to the

Please cite this article in press as: Md. Selim Habib et al., Proposal for highly birefringent broadband dispersion compensating octagonal photonic crystal fiber, Opt. Fiber Technol. (2013), http://dx.doi.org/10.1016/j.yofte.2013.05.014

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additional design parameters like geometry of the air-holes, pitch, and hole diameters. By optimizing these parameters, suitable guiding properties can be obtained. Because of the positive dispersion and dispersion slope of the SMF, the fundamental requirements of a DCF for WDM operation are a large negative dispersion and a dispersion slope over a broad range of wavelengths. Assuming that a fiber link consists of a transmission fiber SMF of length LSMF with the dispersion DSMF(k) and a DCF of length LDCF with the dispersion DDCF(k), the effective dispersion after compensation, De(k), on the fiber link in series can be written as [9]

De ðkÞ ¼ ðDSMF ðkÞLSMF þ DDCF ðkÞLDCF Þ=ðLSMF þ LDCF Þ

ð3Þ

To compensate for the accumulated dispersion of the SMF over a range of wavelengths, the following conditions must be satisfied [21]

RDS ¼ SSMF ðkÞ=DSMF ðkÞ ¼ SDCF ðkÞ=DDCF ðkÞ

ð4Þ

SSMF(k) and SDCF(k) are the dispersion slopes for the SMF and DCF, respectively. The unit of RDS is nm1. Once the RDS of the DCF is close to that of the single mode fiber, SMF, the design of the broadband DCF is accomplished. The RDS is used to judge DC satisfaction over a range of wavelengths. Confinement loss is the light confinement ability within the core region. By suitable choice of pitch, number of rings, position and diameter of air-holes, it is possible to control both dispersion and confinement loss. The confinement loss Lc is obtained from the imaginary part of neff as follows

Lc ¼ 8:686  k0 Im½neff 

ð5Þ

With the unit dB/m, where Im[neff] is the imaginary part of the refractive index. The complex refractive index of fundamental mode can be solved from Maxwell’s equations as an eigenvalue problem with the FEM. The effective area Aeff is calculated as follows

Aeff ¼

ZZ

2

jEj dx dy

2 , ZZ

jEj4 dx dy

ð6Þ

in (lm2), where E is the electric field amplitude in the medium. In PCFs, the birefringence properties are imperative for polarization maintaining applications. PCFs with polarization maintaining (PM) properties are essential in applications such as in eliminating the effect of polarization mode dispersion (PMD) and in stabilizing the operation of optical devices, and can also be used in sensing applications. The birefringence is defined as [22]

B ¼ jnx  ny j

3

supermode, and the other is second order supermode. Guidance occurs in the inner and outer core. The propagation behavior of the PCF is the same as in [24]. At wavelengths shorter than the phase-matching wavelength k0, the propagation field is confined to the inner core. At wavelengths longer than k0 the mode field is confined to the outer core. Around k0, optical field coupling between the inner and outer core modes occurs. In the previously reported designs, the inner cladding usually had regular circular air-holes. This gave the inner core a strong guidance ability. At wavelengths shorter than the phase-matching wavelength, the mode field is well confined in the inner core. Therefore, the dispersion of the PCF is the waveguide dispersion of the inner core mode, which is usually small. Negative dispersion occurs only in a narrow wavelength range around the phase-matching wavelength when the mode field can redistribute from the inner core to the outer core. Such a fiber has only narrowband negative dispersion [25]. To broaden the bandwidth of the negative dispersion, we introduce elliptical with two missing air-holes in the inner cladding. By extending the air space of the inner cladding toward the inner core, the inner core is compressed. The diameter of inner core is 1.22 lm, which is at the level of the wavelength dimension. The guidance ability of the inner core is weakened. Thus, the mode field cannot be trapped tightly in the inner core, and part of the field leaks out and is coupled to the outer core in a wide wavelength range. It can be considered that part of the fundamental mode field exists in the inner core and part in the elliptical holes and the outer core. Therefore, the redistribution of the mode field occurs constantly when wavelength varies. This is unlike to the previously reported designs, where redistribution of the field occurs only in the narrow range of wavelength around the phase-matching wavelength. Therefore, the key reason of broadening of the bandwidth of negative dispersion in our proposed design is that elliptical with two missing air-holes in the first ring weaken the inner core’s guidance ability so that field distribution of the fundamental mode occurs whenever the wavelength varies. This redistribution is not limited to a narrow band of wavelength around the phase-matching wavelength. Fig. 2 shows wavelength response of chromatic dispersion of the proposed M-OPCF for optimum design parameters. Optimizing the parameters g, K, d1, and d, negative dispersion coefficient of 588 ps/(nm km) and 207 ps/(nm km) is obtained at 1.55 lm for x-polarized mode and y-polarized mode respectively. For optimization of the parameters, a simple technique is applied. First, the ellipticity, g is chosen 0.764, 0.787, 0.812, 0.838, and 0.896 while the rest of the geometrical parameters are kept constant to K = 0.90 lm, d/K = 0.70, and d1/K = 0.43. A larger value of air-hole

ð7Þ

where nx and ny are the mode indices of the two orthogonal polarization fundamental modes. As the holey cladding in PCFs makes the large difference of refractive index between the silica core and cladding, light concentrates more into a very small area of the core, resulting in enhanced effective nonlinearity. A small effective area provides the high optical power density necessary for nonlinear effects to be significant, and the nonlinear coefficient c calculated by using the following equation [23]

c¼

   2p n2 k Aeff

ð8Þ

in w1 km1, where n2 is the nonlinear refractive index. 4. Numerical results and discussion Due to the geometry of the proposed M-OPCF shown in Fig. 1, the fiber supports two supermodes. One is fundamental

Fig. 2. Wavelength response of chromatic dispersion of the proposed M-OPCF for both x- and y-polarization for the optimum design parameters: K = 0.90 lm, d/ K = 0.70, d1/K = 0.43 and g = 0.764.

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diameter, d is chosen for better field confinement, while the airhole diameter, d1 is chosen smaller to shape the dispersion slope. From Fig. 3, it can be seen that chromatic dispersion of the fast axis mode decreases as the ellipticity, g decreases, for example, at k = 1.55 lm, the dispersion figures are about 351, 427, 473, 526, 588 ps/(nm km) for g = 0.896, 0.838, 0.812, 0.787, and 0.764 respectively. From these results, it is clear that for g = 0.764, a large negative dispersion [400 to 725 ps/(nm km)] is obtained, which monotonically decreases over the S, and Lwavelength bands and, furthermore, possesses a negative dispersion slope, providing good dispersion compensation. The dispersion value of the proposed PCF at k = 1.55 lm is about 588 ps/(nm km), far exceeding the dispersion values of conventional dispersion compensating fibers [15] [typically 100 ps/ (nm km)]. Fig. 4 reveals the effect of pitch, K on chromatic dispersion when other parameters are kept constant. At k = 1.55 lm, it is observed that dispersion value decreases (increase in absolute dispersion value) when scaling down the parameter K. It can be clearly seen that the design parameter K = 0.90 lm possesses a larger negative dispersion value than the other design parameters. After shaping the dispersion curve to the desired level (Fig. 2) 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 [26] during the fabrication process. Therefore, roughly an accuracy of ±2% may require ensuring dispersion tolerance [27]. To account for this structural variation, air-hole diameter, d1 is varied up to ±5% from their optimum values. Corresponding dispersion curve is shown in Fig. 5. Solid lines indicate dispersion curves due to increment in parameters and dashed lines for decrement. Fig. 5 depicts the dispersion accuracy of the proposed fiber for air-hole diameter, d1 along with the optimum dispersion curve. It is found that the M-OPCF maintains dispersion within a ±50 ps/ (nm km) for variations of and up to ±1% at 1.55 lm. Fig. 6 shows dispersion accuracy of the proposed fiber for pitch, K along with the optimum dispersion curve. This figure ensures that design accuracy of the fiber up to ±1% change in the pitch is within ±68 ps/(nm km) maintaining desired dispersion characteristics. Fig. 7 shows dispersion accuracy of the proposed fiber for airhole diameter, d along with the optimum dispersion curve. This figure ensures that design accuracy of the fiber up to ±1% change in the pitch is within ±44 ps/(nm km) maintaining desired dispersion characteristics. According to Eq. (6), Fig. 8 shows effective areas of the fiber for optimum design parameters and for global diameter variations of order ±1–5%. The effective area of the fiber at 1.55 lm is 3.43 lm2. It changes about ±0.14 lm2 for ±2% change in parame-

Fig. 4. Dispersion properties of M-OPCF for d/K = 0.70, d1/K = 0.43 and g = 0.764, and K = 0.90 to 1.00 lm.

Fig. 5. Dispersion properties of M-OPCF: optimum dispersion and effects of changing d1.

Fig. 6. Dispersion properties of M-OPCF: optimum dispersion and effects of changing pitch K.

Fig. 3. Dispersion properties of M-OPCF showing the effect of air-hole ellipticity, g when other geometrical parameters are kept constant.

ters. At this point, we would like to address possible limitations of our proposed PCF design associated with a small effective area. First, its small effective area presents potential difficulties in the input coupling and output coupling of light. Nevertheless, it has been reported that PCFs can be interfaced to conventional SMFs using a tapered intermediate PCF (reported 0.1 dB measured taper loss) mode matched to each fiber at each end [28]. Another possible solution to the splicing problem is to splice the PCFs to

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5

(a)

Fig. 7. Dispersion properties of M-OPCF: optimum dispersion and effects of air-hole diameter d.

(b)

Fig. 9. Confinement loss of the proposed M-OPCF for (a) x-polarization mode (b) ypolarization mode for the optimum design parameters and also for fiber’s global diameter variations of order ±1–5% around the optimum value. Fig. 8. Effective area of the proposed M-OPCF for optimum design parameters and also for fiber’s global diameter variations of order ±1–5% around the optimum value.

conventional SMFs in a specially constructed manner [29]. The splice-free interface of PCFs with the SMF technique is versatile enough to interface with any type of index guiding silica PCF [29]. We believe that our proposed PCF can be interfaced with existing technology without major complications. One important point worthy of consideration is the fabrication issue. The OPCF can be drawn from individual stackable units of suitable size and shape [30]. Moreover, PCFs with elliptical air-holes can be fabricated [31]. Therefore, we believe that the M-OPCF could be fabricated without any major complication. Fig. 9 shows wavelength dependence of fiber’s confinement losses of x-polarized mode and y-polarized mode according to Eq. (5) for optimum design parameters and also for fiber’s global diameter variations of order ±1–5%. Note that the loss is increasing smoothly with the wavelength and there is no evidence of abrupt change in leakage. Again increasing losses due to corresponding decrease in air-hole diameters are also consistent. Confinement loss at 1.55 lm is less than 10 dB/m and 1 dB/m for x-polarized mode and y-polarized mode respectively considering five air-hole rings. It is also evident from Fig. 9 that changes in design parameters up to ±2% have an insignificant effect on the confinement losses. Fig. 10a shows the calculated residual dispersion obtained after the dispersion compensation by a 1.17 km long optimized M-OPCF for the dispersion accumulated in one span (40 km long) of the transmission fiber, SMF. It can be observed that the residual dispersion ranges from 7 to 4 ps/nm in the entire S and L-bands,

which enables the proposed PCF to be a suitable candidate for high-bit-rate transmission systems [32]. Fig. 10b shows the effective dispersion of the SMF + M-OPCF for the optimum design parameters. The length ratio of the compensated fiber (SMF) to the compensating fiber M-OPCF, which is the variation in the effective dispersion over a considered wavelength range (S and L-bands), is the smallest one. The effective dispersion should be lower than ±0.8 ps/(nm km) to compensate for a 40 Gbps system [12]. As shown in Fig. 8b, with an effective dispersion within a ±0.2 ps/(nm km) range, it is clearly proved that our proposed M-OPCF (with optimized parameters) is suitable for systems with high bit rates, particularly in the S and L-bands. Fig. 11a shows effective refractive indices for the orthogonal axis of the optimum proposed M-OPCF design with their respective fundamental electric field properties at k = 1.55 lm. It is found that the effective refractive index of the slow-axis direction is higher than that of the fast-axis direction, and that their differences provide a high birefringence on the order of 102. The asymmetrical design of the core of the proposed M-OPCF causes a considerable increase in linear birefringence properties, which is suitable for polarization maintaining (PM) applications. PCFs with PM properties are enviable in many applications [32]. However, conventional PM fibers show a modal birefringence of about 5  104. In our design, the realized beat length is far smaller than that of conventional PM fibers. Fig. 11b shows the wavelength dependence of birefringence achieved for the M-OPCF. The results shown here are those for the optimized geometrical parameters and it can be seen that the M-OPCF exhibits a high birefringence of about 1.81  102, which is approximately 35 times larger than that of conventional PM fibers [33] and a beat length of about

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(a)

(a)

(b)

(b)

Fig. 10. (a and b) The wavelength dependence of residual dispersion and effective dispersion of SMF and M-OPCF for the optimum design parameters: K = 0.90 lm, d/ K = 0.70, d1/K = 0.43 and g = 0.764. Here, corresponding residual dispersion curve after compensating for 40 km SMFs.

0.085 mm, both at k = 1.55 lm. The realized beat length is smaller than that of Ref. [22]. This shows that the proposed M-OPCF is highly birefringent and for that reason should show a high polarization extinction ratio, and can be used to eliminate the effect of PMD in transmission systems and many other areas where PM properties are required, such as sensing applications. There is an advantage of having both high birefringence and high negative dispersion, particularly in optical amplification applications. Typical long conventional optical fiber links do not maintain linear polarization; the Raman gain assumes an average value, which is approximately half of the corresponding polarized gain. Thus, with a maintained linear polarization, gain efficiency may be improved by approximately a factor of 2 [34]. The proposed M-OPCF is such that it offers a high birefringence as well as a high negative dispersion, which leads to a relatively small fiber length required to achieve dispersion compensation. Hence, we expect that the MOPCF will be able to maintain linear polarization. As we considered a simple condition for designing broadband dispersion compensation phenomena, it is worth noting that, at k = 1.55 lm, the RDS for the dispersion curve with g = 0.764 is close to that of the SMF (for the SMF; RDS  0.0036 nm1) [35] as shown in Table 1. From the results shown in Table 1, it can be clearly seen that hole ellipticity, g can be used to tune the desirable RDS so that it can match that of the SMF. The RDS of proposed M-OPCF is close to 0.0036 nm1 for the optimum design parameters K = 0.90 lm, d/K = 0.70, d1/K = 0.43 and g = 0.764. Fig. 12 shows the wavelength dependence of the nonlinear coefficient for the optimum design parameters. The nonlinear coefficient is found 31.85 W1 Km1 at 1.55 lm, which may be

Fig. 11. (a) Variation in the effective refractive index for the slow and fast axis of the optimized M-OPCF. (The insets are electric field distributions at k = 1.55 lm for each polarization.) (b) Birefringence property for the optimum design parameters: K = 0.90 lm, d/K = 0.70, d1/K = 0.43 and g = 0.764.

Table 1 Effect of ellipticity, g on M-OPCF’s RDS when the other geometrical parameters (d, d1 and K) are kept constant at 1.55 lm. Ellipticity, g

RDS (nm1)

0.764 0.787 0.812 0.838 0.896

0.0036 0.0034 0.0033 0.0031 0.0028

Fig. 12. Nonlinear coefficient c of the proposed M-OPCF for the optimum design parameters: K = 0.90 lm, d/K = 0.70, d1/K = 0.43 and g = 0.764.

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Md. Selim Habib et al. / Optical Fiber Technology xxx (2013) xxx–xxx Table 2 Comparison between properties of the proposed M-OPCF and other various PCFs for DC applications at 1.55 lm. PCFs

D(k) Ps/(nm km)

B(|nx  ny|)

Aeff (lm2)

NDP (Nr, NK, Nd)

Ref. [9] Ref. [22] M-OPCF

474.5 239.5 588.0

– 1.67  102 1.81  102

1.60 2.60 3.43

– 6, 1, 1 5, 1, 2

suitable for nonlinear applications. Finally, a comparison is made between properties of the M-OPCF and some other fibers designed for dispersion compensation. Table 2 compares those fibers taking into account the dispersion coefficient, birefringence, and effective area. Nr, NK, and Nd correspond to the number of rings, pitches, and different sized air-hole diameters used in PCF design, respectively. It clearly indicates that the designed fiber is better for dispersion compensation and sensing applications. 5. Conclusions A relatively simple highly birefringent broadband dispersion compensating M-OPCF has been reported. It is shown through numerical results that the proposed broadband dispersion compensating M-OPCF can be designed to provide high negative dispersion coefficients of about 400 to 725 ps/(nm km) over the S, and L-bands and an RDS close to that of a conventional singlemode fiber simultaneously. We also successfully achieved an effective dispersion of ±0.20 ps/(nm km), which allows the designed fiber suitable for systems with high bit rates within the S, C and L-communication bands. The proposed fiber exhibits birefringence as high as 1.81  102. Hence, the fiber is a promising candidate for PM and sensing applications. We expect that the proposed M-OPCF will be useful for a number of future applications such as broadband dispersion compensation in high-bit-rate transmission networks, PM devices, and sensing systems. References [1] J.C. knight, Photonic crystal fibers, Nature 424 (2003) 847–851. [2] J.C. Knight, T.A. Birks, P.S.J. Russell, D.M. Atkin, All-silica single-mode optical fiber with photonic crystal cladding, Opt. Lett. 21 (1996) 1547–1549. [3] S.M.A. Razzak, Y. Namihira, Proposal for highly nonlinear dispersion-flattened octagonal photonic crystal fibers, IEEE Photon. Technol. Lett. 20 (2008) 249– 251. [4] K. Saitoh, M. Koshiba, T. Hasegawa, E. Sasaoka, Chromatic dispersion control in photonic crystal fibers: application to ultra-flattened dispersion, Opt. Express 11 (2003) 843–852. [5] M. Koshiba, K. Saitoh, Structural dependence of effective area and mode field diameter for holey fibers, Opt. Express 11 (2003) 1746–1756. [6] S.G. Li, X.D. Liu, L.T. Hou, Numerical study on dispersion compensating property in photonic crystal fibers, Acta Phys. Sin. 53 (2004) 1880–1886. [7] B. Zsigri, J. Laegsgaard, A. Bjarklev, A novel photonic crystal fibre design for dispersion compensation, J. Opt. A Pure Appl. Opt. 6 (2004) 717–720. [8] T.A. Birks, D. Mogilevtsev, J.C. Knight, P.St.J Russell, Dispersion compensation using single-material fibers, IEEE Photon. Technol. Lett. 11 (1999) 674–676. [9] L.P. Shen, W.P. Huang, G.X. Chen, S.S. Jian, Design and optimization of photonic crystal fibers for broad-band dispersion compensation, IEEE Photon. Technol. Lett. 15 (2003) 540–542. [10] A. Huttunen, P. Torma, Optimization of dual-core and microstructure fiber geometries for dispersion compensation and large mode area, Opt. Express 13 (2005) 627–635.

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Please cite this article in press as: Md. Selim Habib et al., Proposal for highly birefringent broadband dispersion compensating octagonal photonic crystal fiber, Opt. Fiber Technol. (2013), http://dx.doi.org/10.1016/j.yofte.2013.05.014