Numerical Modeling of the Fundamental Characteristics of ZBLAN Photonic Crystal Fiber for Communication in 2 3 m Midinfrared Region

Transcription

1 Numerical Modeling of the Fundamental Characteristics of ZBLAN Photonic Crystal Fiber for Communication in 2 3 m Midinfrared Region Volume 8, Number 2, April 2016 D. C. Tee N. Tamchek C. H. Raymond Ooi DOI: /JPHOT Ó 2016 IEEE

2 Numerical Modeling of the Fundamental Characteristics of ZBLAN Photonic Crystal Fiber for Communication in 2 3 m Midinfrared Region D. C. Tee, 1 N. Tamchek, 2 and C. H. Raymond Ooi 3 1 Photonics Lab, TM Innovation Centre, Telekom Research and Development Sdn. Bhd., Cyberjaya 63000, Malaysia 2 Department of Physics, Faculty of Science, Universiti Putra Malaysia, Serdang 43400, Malaysia 3 Department of Physics, Faculty of Science, University of Malaya, Kuala Lumpur 50603, Malaysia DOI: /JPHOT Ó 2016 IEEE. Translations and content mining are permitted for academic research only. Personal use is also permitted, but republication/redistribution requires IEEE permission. See for more information. Manuscript received February 7, 2016; accepted February 27, Date of publication March 3, 2016; date of current version March 11, C. H. Raymond Ooi was supported by the Ministry of Higher Education of Malaysia through the High Impact Research MoE Grant UM.C/625/1/ HIR/MoE/CHAN/04. Corresponding author: D. C. Tee ( tdchai@tmrnd.com.my). Abstract: We numerically studied ZrF 4 -BaF 2 -LaF 3 -AIF 3 -NaF (ZBLAN) photonic crystal fiber (PCF) for potential implementation in optical communication within a 2- to 3-m midinfrared wavelength region. We focused on solid-core uniform air-hole-size hexagonal lattice ZBLAN PCF. The fundamental characteristics such as normalized frequency, confinement loss, chromatic dispersion, effective mode area, and nonlinearity were simulated through a full-vectorial finite-element method with perfectly matched layer boundary condition. Two different structural design ZBLAN PCFs with nonuniform airhole size were designed with zero dispersion wavelength shifted to 2.5 m. In addition, a near-zero flattened chromatic dispersion ZBLAN PCF within a 2- to 3.5-m wavelength region was achieved. Furthermore, the sensitivity of the dispersion properties to a ±2% variation in the optimum parameters is studied for fabrication tolerance. Index Terms: Mid-infrared communication, ZrF 4 -BaF 2 -LaF 3 -AIF 3 -NaF (ZBLAN) photonic crystal fibers (PCFs), optical fiber dispersion, fiber properties, finite-element method (FEM). 1. Introduction Silica optical fiber is used to transmit light and information over long distances in optical communication from O to U band. Current optical communication focuses on 1.55 m wavelength due to fused silica material having the lowest intrinsic material attenuation loss of db/km at this particular wavelength [1]. Further reduction of the intrinsic loss for fused silica is impossible. Therefore, replacing the optical fiber with material that has a lower intrinsic material loss is an alternative method to reduce the attenuation loss and increase transmission distance in optical communication. Fluoride glasses especially ZrF 4 -BaF 2 -LaF 3 -AIF 3 -NaF (ZBLAN) is regarded as a promising replacement for fused silica in optical communication since its discovery in 1975 [2]. The intrinsic material loss for ZBLAN is less than 0.01 db/km at 2.5 m mid-infrared wavelength, suggesting the possibility of shifting the communication wavelength to longer wavelength with much lower loss [2], [3]. Moreover, the transmission window for ZBLAN covers

3 from 0.2 to 7.8 m, which is attractive for creating optical devices from deep-ultraviolet to the mid-infrared region [2]. ZBLAN step index fiber (SIF) is commercially available. However, it is not being used for longdistance communication purposes at the moment. The researches based on ZBLAN fiber are focused on the generation of supercontinuum in mid-infrared region [4] [6], fiber laser [7] [9], master oscillator power amplifier (MOPA) [10], and infrared spectrographs for extremely large future telescopes [11] as these devices are simply utilizing the SIF lightwave guiding properties. Since the beginning of optical fiber, the lightwave guiding characteristics of SIF depend on the host material and core dimension only. With these two parameters, it constrains the design of desired characteristics for applications based on SIF. For example, shifting the zero dispersion wavelength of ZBLAN SIF from around 1.65 m to its lowest material absorption loss at 2.5 m wavelength seems unlikely. Comparing SIF with photonic crystal fiber (PCF), PCF provides flexible controllability on the optical characteristics such as adjustable dispersion, zero dispersion wavelength, nonlinearity and transmission efficiency that enable tuning the characteristic of the optical fiber to fit the desired optical applications. Owing to the difficulty of eliminating impurities to draw high quality ZBLAN PCF, only two papers reporting experimental results on their fabricated ZBLAN PCF were found. The first one is about single air hole ring with large mode area ZBLAN microstructure fiber fabricated for mid-infrared transmission at 4 m wavelength [12]. The second one is a recent publication about the application of ZBLAN PCF for deep-ultraviolet to mid-infrared supercontinuum generation [2]. Furthermore, there have been numerical studies on ZBLAN PCF for high birefringent [13], [14] and mid-infrared femtosecond Raman soliton [15] applications reported recently. In this paper, we numerically study the fundamental characteristics of ZBLAN PCF for possible optical communication within the 2 3 m mid-infrared wavelength region. We concentrate on ZBLAN material because of its lower absorption loss compared to silica at this region which is an advantage for extremely low loss optical communication. In addition, we focus on PCF instead of SIF because of the ability to design and control the optical characteristics of the fiber. The aim of this work is to provide a general prescription for designing ZBLAN PCF based on its structural parameters. This manuscript is organized as follows. Section 2 describes the design of ZBLAN PCF and verification of the accuracy of our simulation. In Section 3, we analyze the simulated fundamental optical characteristics of uniform air holes ZBLAN PCF in terms of normalized frequency for single-mode operation, confinement loss, chromatic dispersion behavior, effective mode area, and nonlinearity of the fiber under different value of structural parameters. In Section 4, we show the design of non-uniform air holes ZBLAN PCFs with zero dispersion wavelength shifted to 2.5 m, the wavelength of lowest loss and also its fabrication tolerance on the optimum parameters. Moreover, a near-zero flattened dispersion ZBLAN PCF and the sensitivity of dispersion value to the variation in the optimum parameters are presented in Section 5. Finally, the conclusion of this work is presented in Section Design and Verification of ZBLAN Photonic Crystal Fiber Silica-based PCF has been widely studied around optical communication wavelengths (O to U band) due to the low loss material properties of silica at these wavelengths [16], [17]. In this study, we focus on ZBLAN-based PCF which has low material loss at wavelength within 2 3 m with lowest loss at 2.5 m wavelength. Fig. 1 shows the schematic drawing of the solid core ZBLAN PCF in hexagonal lattice structure for simulating its fundamental optical characteristics. The distance between air holes or pitch is denoted as and the air hole diameter is represented by d. From the work reported in [18], they showed that PCF with ten ðn ¼ 10Þ air hole rings is sufficient to reduce the confinement loss to negligible value. Therefore, in this study, we use the ZBLAN PCF with ten air hole rings for strong light confinement. Owing to the symmetric lattice structure of the ZBLAN PCF, only a quarter of the structure needs to be analyzed, as outlined by the red dashed lines. In this work, commercially available finite-element software is used to analyze and compute the optical properties of the proposed ZBLAN PCF. The computation region is truncated by

4 Fig. 1. Schematic drawing of the hexagonal lattice 10 air hole rings ZBLAN photonic crystal fiber. Red dashed lines indicate quarter transverse structure used for modeling. Fig. 2. Quarter structure for finite-element method (FEM) modeling and verification of the accuracy of anisotropy PML setting to the work reported in [21]. (Left) Quarter analysis for single air hole ring PCF with anisotropy PML. Vertical blue lines indicate the PMC boundary condition, whereas horizontal red lines are the PEC boundary condition. (Right) Constant Re(Neff) value and convergence of Im(Neff) value simulated with respect to the changes in a max parameter. applying anisotropy perfectly matched layer (PML) as absorbing boundary layer [19]. The wavelength-dependent refractive index of the ZBLAN material is included in the simulation by considering the following equation [19]: n 2 1 ¼ f 1 2 ð Þ þ f 2 2 ð Þ where 1 and 2 are the resonant absorption wavelengths in the UV and IR regions, respectively, and f 1 and f 2 are the corresponding oscillator strengths. For ZBLAN fiber, 1 ¼ 0:08969 m, 2 ¼ 21:3825 m, f 1 ¼ 1:22514, and f 2 ¼ 1:52898 are used in obtaining the wavelengthdependent refractive index [20]. The symmetry of the hexagonal lattice PCF allows quarter structure analysis with proper boundary conditions as indicated in Fig. 2. Perfect electric conductor (PEC) and perfect magnetic conductor (PMC) boundary conditions are applied at bottom-top and left-right or vice versa to simulate the fundamental degenerate modes. The anisotropy PML is applied according to the formulation proposed by Saitoh et al. [19] as indicated in 2 s i ¼ 1 ja max ; i ¼ 1; 2 t i

5 Fig. 3. Relative cutoff wavelength = as a function of relative hole diameter d=. Black solid-line indicates V-parameter equals to and corresponding to the boundary between single-mode and multimode regions. where s i is the complex PML parameter, is the distance from the beginning of PML, t i is the thickness of the PML, and a max is the maximum attenuation parameter of the PML. In order to verify that the anisotropy PML is accurately implemented in our simulation, we simulated a single air hole ring solid-core PCF with d ¼ 5 m, ¼ 6:75 m, and background material refractive index of 1.45 at wavelength of 1.45 m as indicated in Fig. 2, which is the same as that reported in [22]. The computed fundamental mode has a constant real effective index (Re(Neff)) and imaginary effective index (Im(Neff)) converges as the value of PML attenuation parameter, a max is increased. The computed effective index 1: þ j3: is in good agreement with the reported value [21], [22]. Therefore, we ensure the accuracy and reliability of our simulation results presented in the following sections. 3. Fundamental Optical Characteristics of ZBLAN PCF In this section, we study the basic properties of hexagonal lattice ZBLAN PCF within 2 3 m wavelength in the mid-infrared region. We show the V-parameter for single-mode operation and simulated confinement loss at different structural parameters at low loss 2.5 m wavelength. In addition, we present the effect of number of air hole rings to the confinement loss within 2 3 m wavelength. Following that, we also calculate the chromatic dispersion, effective mode area and nonlinearity of the proposed ZBLAN PCF which are important considerations for optical communication Normalized Frequency for Single-Mode Operation The V-parameter (normalized frequency) equation for step index fiber (SIF) is applicable for this ZBLAN PCF with some modifications [18]: V eff ¼ 2 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi a eff nco 2 n2 FSM where V eff is the effective V-parameter, and a eff is the effective core radius. The fundamental space filling mode n FSM is calculated by taking the effective mode index of the lowest-order fundamental mode propagating in the periodically repeated hole-zblan structure without any p defects. The value of a eff is taken to be = ffiffiffi 3 [24]. To design fiber with single-mode operation, the V-parameter value must be less than Fig. 3 shows the relative cutoff wavelength = as a function of relative hole diameter d= for V eff. The black solid-line indicates V eff ¼ 2:405, where it means that fiber with design parameters that falls below this region is multimode. From the work reported in [18], it confirmed that for d= G 0:43 (left side region of blue

6 Fig. 4. Confinement loss of hexagonal lattice uniform air hole sizes ZBLAN PCF. (a) For 10 air hole rings at different and d= at 2.5 m wavelength. (b) For different number of air hole rings (N ¼ 5, 7, 9) and different ratio of d= (0.4, 0.6, 0.8) at ¼ 3 m within2 3 m wavelengths. dash-line), the PCF will be endlessly single-mode. From Fig. 3, when the value of d= is known, we can calculate the cutoff wavelength for single-mode operation by scaling the fiber structure Confinement Loss The loss in PCF mainly comes from confinement loss due to single material for PCF. Since the core and the cladding are of the same material, the light confinement in the PCF is determined by the size of the air hole and the number of air hole rings surrounding the core. Having a bigger air hole or increasing the number of air hole rings reduces the confinement loss of the PCF. The following equation is used to calculate the confinement loss ðl c Þ of the ZBLAN PCF: L c ¼ 8:686 imðþ where is the propagation constant of the leaky mode. We computed the confinement loss for 10 air hole rings ZBLAN PCF at different pitch and air holesizeat2.5m wavelength, as shown in Fig. 4(a). We focused on ¼ 2:5 m because at this wavelength the ZBLAN material has the lowest attenuation loss. For very small hole and pitch size, the confinement loss is much greater than 1 db/m due to the effective cladding index being similar to the core refractive index. This low index contrast causes light to leak out from the core. Furthermore, as shown from the red region in Fig. 4(a), higher confinement loss occurs when the air hole diameter is approximately less than 1 m (when d= 0:45 at ¼ 2 m and d= ¼ 0:2 at G 5 m), which is much smaller compared to the operating wavelength of 2.5 m. This suggests that when the air hole diameter is smaller than 1 m, the ZBLAN PCF with uniform air hole rings more than 10 is needed to reduce the loss for practical use in optical communication. Another alternative to overcome the aforementioned loss issue while maintaining the number of air hole rings is by enlarging few number of outer air hole rings, as will be presented in Section 4. On the other hand, with a large air hole size (see the blue region in Fig. 4(a)), the confinement loss is much lower than db/m for N ¼ 10. This shows that 10 air hole rings ZBLAN PCF with large air hole diameter can be free from confinement loss when utilize in optical communication. Fig. 4(b) shows an example of the effect of number of air hole rings and ratio of d= at ¼ 3 m to the normalized confinement loss within 2 3 m wavelengths. In general, the confinement loss is significantly reduced when the number of air hole rings increases or when the ratio of d= is larger which is expected due to the guided mode becomes more confined to the core region. Noticed also from Fig. 4(b), the number of air hole rings requires to minimize the confinement loss for practical implementation in optical communication depends to the signal wavelength, pitch and air hole size. The number of air hole rings requires for ZBLAN PCF to have low loss optical communication can be reduced when the ratio of d= is larger and operate at shorter signal wavelength. As a result, we have to select a different number of air hole

7 Fig. 5. Chromatic dispersion of the 10 air hole rings ZBLAN PCF at 2 3 m wavelength for different hole size at pitch size of (a) ¼ 3 m, (b) ¼ 5 m, (c) ¼ 7 m, and (d) ¼ 9 m. rings for ZBLAN PCF with different design parameters to reduce the confinement loss for a practical fabrication process Chromatic Dispersion Chromatic dispersion in optical fiber is an undesired effect for optical communication. Minimizing the chromatic dispersion reduces cross talk and also maintains the communication signal quality. One of the attractive properties of PCF is its ability to control the chromatic dispersion by altering the pitch and air hole size of the fiber structure. By selecting suitable structural parameters, we can minimize, control, and obtain a desired chromatic dispersion value. The chromatic dispersion is calculated from the guided mode effective refractive index at its corresponding wavelength by the following equation: D ¼ d 2 n eff c d 2 where c is the velocity of light in a vacuum. Fig. 5 depicts the calculated chromatic dispersion within 2 3 m wavelength region for d= ranging from 0.2 to 0.8 in steps of 0.1 at ¼ 3 m (seefig.5(a)),at ¼ 5 m (see Fig. 5(b)), at ¼ 7 m (see Fig. 5(c)), and at ¼ 9 m (see Fig. 5(d)). In general, reducing the ratio of d= will lower the chromatic dispersion. When the ratio of d= is small and is large, the chromatic dispersion curve approximates to the material dispersion of pure ZBLAN material. This is due to the air hole diameter being small where the waveguide dispersion is minimum. On the other hand, as the air hole diameter increases (large d =), the influence of waveguide dispersion becomes stronger. Generally, increasing the size at constant ratio of d= reduces the chromatic dispersion as indicated in Fig. 5. Notice that the zero dispersion wavelength ZDW happens at small d= and values, as shown in Fig. 5(a), but it suffers from undesired high

8 Fig. 6. Effective mode area of the 10 air hole rings ZBLAN PCF at 2 3 m wavelength region for different hole size at pitch size of (a) ¼ 3 m, (b) ¼ 5 m, (c) ¼ 7 m, and (d) ¼ 9 m. confinement loss (1 db/m), as predicted by the confinement loss map in Fig. 4(a). From the confinement loss map, we can reduce the confinement loss by using larger. However, at larger as depicted in Fig. 5(b) (d), there is no ZDW within 2 3 m wavelength region. From Fig. 4(b), we knew that we can further reduce the confinement loss by increasing the number of air hole rings from the current N ¼ 10 fiber. However, higher number of air hole rings increases the difficulty of capillary stacking and fiber fabrication since there are more variables to be controlled and hence prompt for higher fabrication error. This implies that if we cannot increase the number of air hole rings, then the transverse structure of 10 air hole rings ZBLAN PCF other than uniform air hole diameter distribution is needed to attain negligible confinement loss at ZDW ¼ 2:5 m for small and d. Thus, specially designed 10 air hole rings ZBLAN PCF with two different air hole diameters distribution at ZDW ¼ 2:5 m will be discussed in Section Effective Mode Area and Nonlinearity Effective mode area, A eff is a qualitative measurement of the cross section area covered by guided mode of the fiber and is calculated by following equation: A eff ¼ RR je 2 2 jdx dy RR jej 4 dx dy where E is the transverse electric field vector. It is well known that the A eff depends on the wavelength of the guided mode. As the wavelength becomes larger, the width of the guided mode becomes wider which leads to wider area covered by mode and hence larger A eff.inaddition, A eff becomes smaller as we enlarge the air hole diameter due to the guided light being better confined into the core region of the fiber. Furthermore, we expect the A eff to increase with increasing since the core diameter is becoming larger and the effective cladding is relatively far away from the core center. Fig. 6 shows the effective mode area of ZBLAN PCF as a

9 Fig. 7. Nonlinear coefficient of the 10 air hole rings ZBLAN PCF at 2 3 m wavelength region for different hole size at pitch size of (a) ¼ 3 m, (b) ¼ 5 m, (c) ¼ 7 m, and (d) ¼ 9 m. function of wavelength at different and different ratio of d=. Moreover, Fig. 6 also serves as a guideline to design ZBLAN PCF with different A eff. For example, large mode area ZBLAN PCF for high power devices can be designed by fabricating fiber with larger and smaller d, suchas ¼ 9 m and d= ¼ 0:3. Based on the effective mode area, we can obtain another important parameter for optical communication which is the nonlinearity of the fiber. The nonlinear coefficient is calculated with the following equation: ¼ 2 n 2 A eff where n 2 is the material-related nonlinear Kerr coefficient and is equal to 5: cm 2 W 1 for ZBLAN material [2]. Fig. 7 shows the nonlinear coefficient for ZBLAN PCF within the 2 3 m wavelength region for various d= at ¼ 3 m [seefig.7(a)], ¼ 5 m [seefig.7(b)], ¼ 7 m [seefig.7(c)], and ¼ 9 m [see Fig. 7(d)]. Fiber with high nonlinearity favors the occurrence of nonlinear effects which will deteriorate the transmitted signal quality for optical communication. Therefore, for optical communication purposes, fiber with low nonlinearity is preferred. From our simulation, ZBLAN PCF with nonlinear coefficient as low as ¼ 0:5 W 1 km 1 at low loss 2.5 m wavelength can be realized when the is large (9 m) and when d= is small (0.2). 4. Zero Dispersion of ZBLAN PCF As discussed in Section 3.3, ZDW ¼ 2:5 m does not exist when the is large. This can be explained by considering that with large, the core diameter is proportionally large where the guided mode electromagnetic field is totally within the core region with overlapping of the air

10 holes. In this situation, the fiber dispersion is solely due to the material dispersion of the fiber. As reported by X. Li et al. [25], the material dispersion for ZBLAN is zero at wavelength of 1.65 m, therefore, we cannot get ZDW within 2 3 m wavelength region for large. Onthe other hand, ZDW ¼ 2:5 m exists when the and d aresmall,asindicatedinfig.5(a),but with drawback of >1 db/m confinement loss, even N ¼ 10 is considered. For small, the guided mode can interact with the air holes, altering the waveguide dispersion and, hence, the chromatic dispersion of the fiber to be affected by the air holes. This makes it possible to shift the ZDW to 2.5 m wavelength at smaller value. Based on the above considerations, we can obtain low dispersion value ZBLAN PCF at small by tuning the waveguide dispersion to significantly alter the chromatic dispersion of the fiber. The general strategies adopted to design ZDW ¼ 2:5 m or low dispersion value ZBLAN PCF are either by enhancing the guided mode electromagnetic field interaction with the inner air hole rings or by inserting extra air hole in the core region so that the added air hole changes the waveguide dispersion of the designed fiber. After that, we run some simulations on different combination of the structural parameters and observe at which combination of the parameters produces dispersion value closer to the targeted dispersion value. Finally, we further optimize the parameters to exactly match the simulated and targeted dispersion value. It is worth noting that the alternative method applicable to obtain optimum parameters in a more systematic approach can be based on common optimization technique such as the genetic algorithm method. As mentioned previously, the confinement loss of the N ¼ 10 ZBLAN PCF is >1 db/m when the and d are small. Nevertheless, the loss can be reduced by only enlarging the air hole size at the outer air hole rings without further increasing the number of air hole rings. Thus, we designed a 10 air hole rings ZBLAN PCF with two different air hole diameters as depicted in Fig. 8. This non-uniform air holes ZBLAN PCF has d= ¼ 0:2 for the first five inner air hole rings and d= ¼ 0:6 for the five outer air hole rings at ¼ 2 m. The enlarged air holes ðd ¼ 1:2 mþ at 5 outer air hole rings are for the purpose of providing stronger light confinement in the fiber. As shown from the dispersion graph in Fig. 8(a), the ZDW is successfully shifted to coincide with the wavelength of lowest loss, 2.5 m from1.65m of material zero dispersion wavelength. From the fundamental mode field profile in Fig. 8(b), the electric field confined within the first five air hole rings indicates minimum leakage loss. In addition, simulation shows that the confinement loss is predicted to be as low as db/km at ZDW ¼ 2:5 m which is attractive for low loss mid-infrared optical communication. Such negligible confinement loss is solely due to the enlarged outer air holes. Moreover, this non-uniform air hole sizes ZBLAN PCF has a large effective mode area of 131 m 2 at 2.5 m wavelength and, hence, effectively lower the nonlinearity. The large effective mode area arises from the distribution of guided mode field throughout the first five air hole rings. Since the presented work is pure simulation, we investigate the tolerance analysis of the optimum parameters for fabrication error. Experimental results for PCF fabrication show that fabrication tolerances in the structural parameters can occur up to ±2% [26]. Therefore, the impact of the changes in the structural parameters to the dispersion properties of the proposed zero dispersion ZBLAN PCF is studied by variation of ±2% in the structural parameters. We consider the most significant structural parameter as the parameter that causes highest dispersion deviation from zero dispersion at 2.5 m wavelength. Fig. 8(c) depicts the sensitivity of the dispersion when a ±2% variation is applied on, d 1 5 and d From the figure, the air hole diameter for the first five air hole rings, d 1 5 is the most significant parameter affecting the ZDW ¼ 2:5 m. Therefore, precisely controlling the air hole size of d 1 5 during fabrication is crucial for this proposed ZBLAN PCF. Low confinement loss ZBLAN PCF with ZDW ¼ 2:5 m is not limited to single transverse cross section design only as presented in Fig. 8. It also can be achieved with other transverse cross section designs. Here, we designed another non-uniform air hole sizes ZBLAN PCF with a sub-micron center air hole of diameter d c ¼ 0:5 m surrounded by 10 air hole rings, as shown in Fig. 9. The first air hole ring has d 1 = ¼ 0:3, while the remaining nine air hole rings are with

11 Fig. 8. (a) Zero dispersion wavelength at 2.5 m for non-uniform air hole sizes ZBLAN PCF at optimum parameters. (b) Corresponding fundamental mode field profile for 10 air hole rings (d ¼ 0:4 m for first five air hole rings and d ¼ 1:2 m for the remaining air hole rings). (c) Tolerance analysis on structural parameters for fabrication error at optimum parameters. d= ¼ 0:405. The optimization of this ZBLAN PCF starts with adding a sub-micron air hole into the core center. Preliminary simulation results indicate desired dispersion value not achievable if only tuning the sub-micron air hole. Therefore, nearest air holes (air holes for first air hole ring) is included and varied together with the sub-micron air hole which finally leads to achieve ZDW ¼ 2:5 m as shown in Fig. 9(a). Fig. 9(b) indicates that the fundamental guide mode field profile interacts within the first two air hole rings, suggesting a strong waveguide dispersion effect within the first two air hole rings. The function of the outer eight air hole rings is basically to provide better light confinement to obtain a negligible loss level. At optimum parameters, the simulated confinement loss for this sub-micron center air hole ZBLAN PCF is as low as db/km. Compared to the ZBLAN PCF in Fig. 8, this structure yields a smaller effective mode area of 41 m 2 as can be observed from the mode field confinement in Fig. 9(b). Fabrication tolerances are also investigated for this ZBLAN PCF design. Fig. 9(c) and (d) show the sensitivity of zero dispersion at 2.5 m wavelength for ±2% variation in, d, d 1,and d c. A ±2% variation in any of the structural parameters causes non-zero dispersion value at 2.5 m wavelength. Among the structural parameters, the air hole pitch, is the most significant parameter in causing largest dispersion deviation from zero. The dispersion value becomes 1.6 ps/nm/km from zero when a ±2% variation in happens. In addition, a ±2% variation in d 1 and d c produce similar dispersion deviation of 0.46 ps/nm/km at 2.5 m wavelength. 5. Near-Zero Flattened Dispersion of ZBLAN PCF Long-haul optical transmission requires small but nonzero chromatic dispersion to prevent nonlinear interaction to occur [27]. Optical communication is not limited to single wavelength, but different wavelengths can be used for uplink, downlink, or in wavelength division multiplexing

12 Fig. 9. Chromatic dispersion of ZBLAN PCF with 0.5 m sub-micron air hole added in the core center. (a) Optimum value for parameters where zero dispersion wavelength is designed to happen at 2.5 m wavelength. (b) Corresponding fundamental mode field profile for 10 air hole rings (d 1 = ¼ 0:3 for first air hole ring and d= ¼ 0:405 for remaining air hole rings). (c) Sensitivity of thezerodispersionat2.5m wavelength for ±2% variation in and d. (d) Sensitivity of the zero dispersion at 2.5 m wavelength for ±2% variation in d 1 and d c. technique to increase the data bandwidth. Optical fibers with near zero flattened dispersion over large wavelength region satisfy aforementioned practical implementation considerations. We designed a ZBLAN PCF with near-zero flattened dispersion over m wavelength range as depicted in Fig. 10. The transverse cross section of this flattened zero dispersion ZBLAN PCF is same as the one shown in Fig. 9 but with different values of structural parameters. As shown in Fig. 10(a), at optimized structural parameters of ¼ 3:04 m, d= ¼ 0:4, d 1 = ¼ 0:295 and d c ¼ 0:5 m, the flattened dispersion is between ps/nm/km at maximum and 0.4 ps/nm/km at minimum (absolute dispersion variation, D 0:81 ps/nm/km) over a 1140 nm bandwidth from 2.36 m to3.5m wavelength region. However, when considering 2 m to3m wavelength region, the D is larger and approximately 1.7 ps/nm/km. Fig. 10(b) depicts the fundamental mode profile at 2.5 m wavelength with the inset showing the zoom out of the core region. In addition, numerical simulation shows that the confinement loss is as low as db/m at 2.5 m wavelength with 10 air hole rings. Within the 2 3 m wavelength region, the simulated confinement loss is less than db/m. Moreover, the effective mode area increases from 36 m 2 to 50 m 2 due to longer wavelength. Finally, we study which structural parameter is most significant for fabrication tolerance. Sensitivity of the near-zero flattened dispersion for ±2% variation in and d is presented in Fig. 10(c). From Fig. 10(c), a ±2% variation in shifts the dispersion curve upwards or downwards without affecting the slope of the dispersion curve. However, variation of d causes the dispersion curve to shift upwards or downwards together with the changes in the slope of the dispersion curve. Fig. 10(d) shows the sensitivity of the near-zero flattened dispersion for ±2% variation in d c and d 1. A ±2% variation in d c has a less-significant effect on the slope of

13 Fig. 10. Near-zero flattened dispersion ZBLAN PCF at m wavelength region. (a) Near-zero flattened dispersion curve at optimum parameters. (b) Corresponding fundamental mode profile for 10 air hole rings (d 1 = ¼ 0:295 for first air hole ring and d= ¼ 0:4 for remaining air hole rings) with a0.5m sub-micron air hole in the core center. (c) Sensitivity of the near-zero flattened dispersion for ±2% variation in and d. (d) Sensitivity of the near-zero flattened dispersion for ±2% variation in d 1 and d c. dispersion curve and only varied the absolute dispersion D by less than 0.05 ps/nm/km compared with the optimum design. The most significant parameter affecting the flatness and low dispersion value of the proposed near-zero flattened dispersion ZBLAN PCF is the air hole size of the first air hole ring, d 1. The absolute dispersion variation becomes 2.9 ps/nm/km when a +2% increases in d 1 and a highest dispersion value of 1.9 ps/nm/km when a 2% decreases in d Conclusion We have presented the numerical modeling on ZBLAN PCF within 2 3 m wavelength for extremely low loss optical communication in mid-infrared region. We studied the fundamental characteristics of uniform hexagonal lattice structure ZBLAN PCF such as normalized frequency, confinement loss, chromatic dispersion, effective mode area, and nonlinear coefficient, which served as a reference to design ZBLAN PCF with different functions. Furthermore, two nonuniform air hole hexagonal lattice ZBLAN PCFs with 10 air hole rings were proposed to achieve low loss zero dispersion wavelength at 2.5 m,whichwasnotachievablewith10airholerings uniform air hole ZBLAN PCF. We have shown the effect of the hole size closed to the core layer capable to control and shift the zero dispersion wavelength, dispersion value and slope polarity of ZBLAN PCF. In addition, we showed a ZBLAN PCF with near-zero flattened chromatic dispersion from m wavelengths where the absolute dispersion variation is as small as 0.81 ps/nm/km from m wavelength region. Finally, tolerance analyses for fabrication error were discussed for both zero dispersion ZBLAN PCFs and near-zero flattened dispersion ZBLAN PCF in order to investigate the most significant structural parameter affecting the wanted dispersion value.

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