1. Introduction

Optical fibers are microscopic filaments of very pure glass or plastic, usually include a transparent core surrounded by cladding material of lower refractive index. The fiber acts as a waveguide because of the total internal reflection (TIR) technique utilized to keep the light in the core. An advanced optical fiber namely photonic crystal fiber (PCF) has a cladding consisting of a regular pattern of microscopic air holes around the core. Nowadays, PCFs are commonly used in optical fiber communication, nonlinear devices, fiber lasers, etc., because of their unique and exceptional optical properties [1–5]. Recent growing interest of PCFs are also observed for making optical devices including sensors (temperature sensor, biosensor, chemical sensors, etc.) [6,7], polarization filter [8,9], and polarization splitter [10–25]. Polarization splitters (PSs) are such type of optical devices which split light into two beams which are orthogonal in terms of polarization and found many applications. Conventional fiber-based PSs have long splitting length with small bandwidth. Hence, PCFs are used to achieve a compact and broadband splitter [10,11] because of their great flexibilities, extraordinary light controlling mechanisms and have received high attention from the researchers.

One of the common ways of controlling the polarization properties of PCFs is to fill or selectively coat the cladding air holes by metal [6,8–17]. This metal coating or filling enhances PCF’s optical properties due to the surface plasmon resonance (SPR). For example, Sun and co-workers presented a silver nanowire filled dual-core photonic crystal fiber (DC-PCF) to introduce a splitter having limited bandwidth of 146 nm [12]. Besides that, Lou et al. used a gold-plated film at the center with an octagonal structure, in 2019, for a shorter length of 47.26 µm but a narrow band of 104 nm at 1.55 µm [14]. An X-shaped splitter on DC-PCF platform, with a fiber length of 230 µm, was proposed in 2022 [24]. It uses two air holes-filled gold rods and has three different diameters air holes as well as two elliptical holes to obtain a bandwidth of 358 nm. Therefore, because of the surface plasmon resonance, the PCFs with metal wire infilling experience a dramatic rise in confinement losses and fabrication complexity. As a result, it has become increasingly common to create photonic functional devices in recent years using liquid crystals, which are sensitive to temperature and electric field [18–20,26,27]. For example, in [27] the authors discussed different interesting properties of a liquid crystal filled micro-structured optical fiber. Because, the anisotropic nematic liquid crystal (NLC) of E7 material works based on the two separate refractive indices changeable by temperature variation and can produce high birefringence [26,28]. Hence, tunable and ultra-short optical devices can be realized using NLC materials in PCF. For instance, Hameed et al. demonstrated a PS with NLC infiltration of all cladding holes to achieve 8.227 mm splitter length as well as 30 nm and 75 nm short bands, respectively, for two modes (quasi-TE and TM) [18]. Younis and co-authors have presented an asymmetric DC-PCF based PS of 5.678 mm length and a very narrow bandwidth (3 nm) where five air holes are filled with NLC material [19].

From the above survey, it is observed that some of the available splitters have wide bandwidth as desired but large splitting length [10,19,24], few designs have smaller length but limited bandwidth [14,23,25]. It is rarely found splitters have both wide bandwidth and smaller length but the structure is complex, use of expensive materials, and don’t have tunable capability [11]. Hence, it is desired to develop compact, broadband, low-loss, and tunable PS in a simpler structure. But it is always difficult to achieve all of the desired properties at a time and a tradeoff is needed among them.

In this research, an NLC of E7 filled silica glass PCF-based short length and wide band polarization splitter is presented. It has a short length of 71.35 µm and works over a wide bandwidth of 356 nm covering 1285 nm to 1641 nm wavelengths range. The properties are achieved by severing the structure's symmetry and boosting the difference of effective indices between the two modes having orthogonal polarization: we use two large air holes in the cladding area and an elliptical hole at center for this purpose which in turn results in a large birefringence. Additionally, the externally applied excitation (temperature in this case) changes the alignment of NLC molecule and so changes the refractive indices of NLC material which make the device externally tunable.

2. Structure and basic theory

Figure 1 is the claimed DC-PCF based polarization splitter with hexagonal structure. The structure consists of four air holes ring. Dual cores, namely A and B, are created by avoiding two air holes from both sides, and the central elliptical hole separates the two cores. Triangular lattice is considered to arrange all the air holes and the lattice constant is Λ. The diameters of small air holes and two large air holes are denoted by d ₁ and d ₂, respectively. The diameters (along major and minor axes) of the central elliptical hole are denoted by d _x and d _y, respectively. Pure silica is the fiber material in this case and its material dispersion is characterized by the Sellmeier dispersion relation [20] as

 

Fig. 1. 2D layout of our DC-PCF PS. Here in cladding region, d ₁ and d ₂ are the small and large air hole’s diameters, respectively, and at the center, d _x and d _y are diameters of elliptical hole along major and minor axis, respectively. The pitch of the triangular lattice is denoted by Λ and the two cores are symbolized by A and B. Besides, Ψ is the rotational angle of anisotropic NLC material.

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Dual-core modes coupling theory is used to evaluate the performance of our splitter. The odd mode birefringence (B _o) and even mode birefringence (B _e) can be defined as [29]

3. Numerical results and analysis

The proposed DC-PCF based PS is modelled and analyzed with COMSOL Multiphysics software. The perfectly matched layer boundary is used to fix the computational area and absorb the inside radiation. The use of mesh and boundary layer is carefully optimized for our computation which has been justified by regenerating the results of related existing splitters [10,19,20] thus achieved good agreement. The relationship between the refractive indices of both (x and y) polarized odd and even modes and the wavelength are shown in Fig. 2(a). From here, it is seen that the index difference increases between the x-odd and x-even modes with the wavelength, which decreases the x-polarized coupling length considerably. Figure 2(b) shows the mode birefringence variation as a function of wavelength when the central elliptical hole is filled with air and then NLC of E7. The mode birefringence keeps a very low value with the wavelength variation when NLC is not used but the NLC infiltration increases the even mode birefringence. Although, the odd mode birefringence keeps very low value, the even mode birefringence increases largely from 0.007498 to 0.015863 for the corresponding wavelengths range of 1.2 µm to 1.7 µm (Fig. 2(b)).

 

Fig. 2. (a) Effective refractive index as a function of wavelength for NLC infiltrated DC-PCF polarization splitter, and (b) the effect of NLC of E7 infiltration on odd and even modes birefringence.

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The distribution of field for four super-modes (x-odd, x-even, y-odd, and y-even) are given in Fig. 3(a). The arrow indicates the electric field orientation. A little amount of power is transferred in NLC core which is negligible compared to the power in both cores. Figure 3(b) summarizes the confinement losses of the above four super modes. Due to small energy transferring in E7 material, the confinement loss increases with wavelength. Among the four super modes, only x-even mode has larger confinement loss than others which also keeps a very low value. It can be seen that energy confinement in the cores becomes weaker with the increase in wavelength. Also, the energy transfer in the NLC of E7 elliptical hole increases with increasing wavelength. The confinement losses for x-odd, y-odd, and y-even are almost zero for different wavelengths between 1.2 µm to 1.7 µm. The confinement loss for x-even mode is also closer to zero value upto about 1.5 µm and then with the further increase in wavelength increases the energy transfer in the E7 elliptical hole which results in somewhat higher loss, as shown in Fig. 3(b). The proposed splitter is a passive device having short length and need to be connected with standard single mode fiber (SMF) from both ends. Hence, in order to couple the source to the device SMF is needed to connect and there will be some coupling or splice loss (L_s) which can be calculated by following procedures given in [16] with the help of Petermann II formula [30]. Since the proposed fiber is a polarization splitter and its performance analysis is a major issue, the splicing loss calculation is avoided here.

 

Fig. 3. (a) Electric field profiles of (i) x-odd, (ii) x-even, (iii) y-odd, and (iv) y-even supermodes at 1.55 µm. The field profiles are taken at the optimized structural parameters. The arrows indicate the orientation of electric field; (b) Confinement loss spectra at the optimized structural parameters of Λ = 1.813 µm, d ₁= 1.0 µm, d ₂= 1.8 µm, d _x= 1.0 µm, d _y= 0.8 µm, and Ψ = 90° at 25°C temperature.

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All the device dimensions are optimized to get the desired CLR of 2 at 1.55 µm. A very little decrease in the coupling lengths (L _x and L _y) is observed as the smaller cladding air holes diameter d ₁ is varied from 0.95 µm to 1.1 µm (Fig. 4(a)). Also, Fig. 4(b) illustrates the effects of changing the diameter of the big cladding air holes (d ₂) from 1.7 µm to 1.9 µm on coupling lengths, L _x and L _y. The desired CLR = 2.0 is reached at the optimized values of d ₁= 1.0 µm, and d ₂= 1.8 µm. It is clear to say that increase in air holes diameter cause a drop in the cladding region's ERI which results in drops of the ERIs of the two polarized modes. More specifically, increasing d ₁ and d ₂ increase the structure's air-filled area, which increases the difference of ERIs between the even and odd modes polarized along x- and y- directions. However, the rise in effective index difference is very tiny in both scenarios, which causes a slight reduction in coupling lengths.

 

Fig. 4. Variation of coupling lengths (CL) and coupling length ratio (CLR) at 1.55 µm wavelength and 25°C temperature with different (a) small air hole diameter d ₁, and (b) large air hole diameter d ₂. Optimized dimensions are considered for each case, and Ψ = 90°.

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Now, the impact of deforming the NLC-infiltrated central elliptical hole is investigated. The variation of L _x, L _y, and CLR at different d _x values is illustrated in Fig. 5(a) while rest of the parameters are same as Λ = 1.813 µm, d ₁= 1.0 µm, d ₂= 1.8 µm, d _y= 0.8 µm, Ψ = 90° at the temperature and wavelength of 25°C and 1.55 µm, respectively. The coupling lengths L _x and L _y are increased and decreased, respectively, as ${d_x}$ is increased from 0.8 µm to 1.2 µm. Figure 5(b) shows the effect of d _y variation on L _x, L _y, and CLR keeping other parameters fixed. In case of d _y variation, the y-polarized coupling length is slightly increased first and then continues to decrease. At Ψ = 90°, E7 material has diagonal permittivity tensor of [n _o ², n _e ², n _o ²]. Here, n _o ² is less than n _e ²; therefore, the ERI of the y-polarized core modes is greater than that the x-polarized core modes. Consequently, the y-polarized modes have greater effective index than that of the x-polarized modes. Hence, the vertical (y) polarization state is more influenced by the alteration of d _x and d _y than the horizontal one (x-polarization state). At ${d_x} = 1.0$µm and ${d_y} = 0.8$ µm, the CLR reaches to the desired value of 2.0. Figure 5(c) explains the variation of both polarized coupling lengths (L _x and L _y) and CLR as the pitch, Λ varies from 1.75 µm to 1.9 µm while other dimensions are unchanged. Now, increasing lattice constant leads to a smaller birefringence since the defect areas are increased and the core mode confinement reduces. So, the difference in effective indices decreases which results in an increase in coupling length and CLR reaches to 2.0 at Λ value of 1.813 µm (Fig. 5(c)).

 

Fig. 5. Coupling lengths and CLR, at 1.55 µm wavelength and 25°C temperature, with the (a) major axis diameter d _x, and (b) minor axis diameter d _y, (c) the lattice constant Λ. In each case, the rest of parameters are considered at optimized level.

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A large birefringence has been obtained by infilling the central elliptical hole with anisotropic NLC of E7 material. Without the NLC infiltration of the central hole, the coupling lengths are L _x = 209.17 µm and L _y= 279.66 µm at 1.55 µm which is very high. Also, the variation of CLR is 1.363 at 1.2 µm to 1.322 at 1.7 µm without NLC infilling, which is very low. From Fig. 6(a), it is evident that CLR values are far away from the desired value of either 0.5 or 2.0 which makes it difficult to separate the two polarized light. Infiltration of the central elliptical hole with anisotropic NLC of E7 improves the condition, hence, leads to smaller coupling lengths of L _x= 35.67 µm and L _y= 71.35 µm at 1.55 µm and CLR increases gradually over the wavelengths. However, NLC infiltration makes it easy to achieve CLR = 2.0 (Fig. 6(b)), hence, two orthogonally polarized lights can be separated into the two different cores A and B.

 

Fig. 6. Coupling length and CLR as a function of wavelength (a) without the infiltration of NLC of E7, and (b) with the infiltration of NLC of E7 into the central elliptical hole at the optimized conditions with Ψ = 90° at 25°C temperature.

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After analysis of Figs. 4 –6, the optimized dimensions are finalized as Λ = 1.813 µm, d ₁= 1.0 µm, d ₂= 1.8 µm, d _x= 1.0 µm, and d _y= 0.8 µm. At 25°C temperature, and Ψ = 90°, the CLR reaches to 2.0001 with L _x= 35.67 µm and L _y= 71.35 µm at 1.55 µm.

If the injected input power P_in is applied into core A, the output power P_out for the both polarized (x- and y-polarized) states can be defined as [10]

Figure 7(a) shows the normalized output power spectra with propagation distance for both polarized (x and y) modes in core A at 1.55 µm. It is assumed that the hybrid polarized light is launched into core A and the normalized power difference continues to increase with propagation distance and reaches its maximum at a distance of 71.35 µm. The x-polarized power of the initially launched hybrid light reaches at its supreme in core A. Meanwhile, y-polarized light is almost transmitted into core B at the short splitter length of 71.35 µm (Fig. 7(a)). It is also noted that leakage loss is very low and not included in the power curve because the device length is very short (71.35 µm).

 

Fig. 7. (a) Variation of normalized output power along the propagation distance in core A, and (b) extinction ratio (ER) spectra for the final optimized parameters of Λ = 1.813 µm, d ₁= 1.0 µm, d ₂= 1.8 µm, d _x= 1.0 µm, d _y= 0.8 µm, and Ψ = 90° at 25°C temperature at 1.55 µm. The dotted line indicates the standard -20 dB reference line.

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Extinction ratio (ER) is an important term which determines the working bandwidth of a PS and is defined as [20]

Fabrication tolerances of the proposed splitter parameters have been examined by varying the parameter values up to ±1% of their optimized values, because modern fabrication technology is capable of controlling the fabrication accuracy within ±1% [31]. Figure 8(a) includes the ER spectra for different fabrication tolerances of d ₁. It is seen that the bandwidth increases slightly with the decrease in d ₁ by 1% and decreases a little with the increase in d ₁ by 1%. Because in both cases, the y-polarized index difference increases first and then decreases after a certain point to obtain L _y ≈ L for almost at the same wavelength range. Although the minimum ER increases in both cases the working bandwidth remains close to the optimized value. Hence, the proposed splitter performed well within ±1% fabrication tolerances of d ₁.

 

Fig. 8. ER spectra for different fabrication tolerances (±1%) of (a) small air hole diameter d ₁, and (b) large air hole diameter d ₂; by keeping other structural parameters constant at their optimized values. The dotted straight line indicates the standard -20 dB reference line.

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The ER spectra versus d ₂ is justified for different fabrication tolerances (±1%) in Fig. 8(b). The available bandwidth increases to 380 nm (1280 nm to 1660 nm) with 1% decrease of d ₂. But the bandwidth remains almost same as the optimized value when it is increased by 1%. Figures 9(a) and 9(b) show the impacts of different tolerances of d _x and d _y on the ER variation, respectively. The bandwidth becomes broadened to around 390 nm (1270 nm to 1660 nm) with a decrease of d _x by 1% while ER is kept -20 dB or better over this bandwidth (Fig. 9(a)). This is due to the fact that the y-polarized index difference decreases rapidly for lower and higher wavelength regions of interest compared to the mid-band, hence, L _y attains value close to L for a wide wavelength range. But the minimum ER is also shifted to 1.57 µm of wavelength having a value of -48.01 dB and secondary minimum value having -44.02 dB is shifted to 1.3 µm wavelength. Again, the bandwidth becomes narrower to 320 nm (1310 nm - 1630 nm) when d _x is increased by 1%. On contrary, the bandwidth remains nearly constant as d _y is either increased or decreased by 1% from optimized value (Fig. 9(b)) because in both cases L _y ≈ L for almost the same wavelength range. Also, the wavelength of minimum ER remains same at 1.55 µm although decreases to a value of -67.18 dB and -61.98 dB, respectively, for d _y variation of -1% and +1%.

 

Fig. 9. ER spectra for different (a) major axis diameter d _x; and (b) minor axis diameter d _y of the central elliptical hole, showing the fabrication tolerances of the design. The other structural parameters are kept constant at their optimized values. The dotted straight line indicates the standard -20 dB reference line.

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Figure 10(a) shows the extinction ratio behavior over wavelengths for different Λ. It clearly shows that the bandwidth gets narrower (260 nm) ranging from 1320 nm to 1580 nm with 1% decrease in adjacent air hole distance and reaches a single minimum value of -47.05 dB at 1.43 µm. On the contrary, the bandwidth increases when Λ increases because when Λ increases the y-polarized index difference decreases first and hence, L _y increases to reach L. In addition, after a certain point, the y-polarized index difference starts increasing and again, L _y approaches to L. When L _y ≈ L, the ER decreases beyond -20 dB and hence, the bandwidth increases. An 1% increase in Λ leads to a wider bandwidth of around 430 nm (1260 nm to 1690 nm), but the ER exceeds -20 dB at some points and maintains an ER better than -10 dB over this bandwidth (Fig. 10(a)). The 1^st minimum ER dip is also shifted to 1.61 µm and 2^nd one is moved to 1.29 µm. Figure 10(b) shows the extinction ratio spectra for different fabrication tolerance of the proposed splitter length. The bandwidth increases with the decrease in fiber length as L _y ≈ L for a wide wavelength range, but this range decreases with the increase in fiber length which results in reduced bandwidth. When the length decreases by 1%, the bandwidth gets wider (around 370 nm), hence, enables to work over 1280 nm to 1650 nm with ER better than -20 dB, and the minimum ER attaining a value of -52.32 dB is shifted to the wavelength of 1.57 µm. Again, the bandwidth gets shortened to 335 nm (close to the optimized value), when the length increases by 1% and at this length, the ER maintains better than -20 dB from 1290 nm to 1625 nm.

 

Fig. 10. ER spectra for different (a) lattice constant Λ, and (b) splitter length L showing the fabrication tolerances of the proposed design. The other structural parameters are kept constant at their optimized values. The dotted straight line indicates the standard -20 dB reference line.

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One of the important properties of using anisotropic NLC of E7 is its temperature based tunability. The temperature dependence of ordinary and extraordinary refractive indices of E7 material is shown by Li et al. in 2005 [28]. To control the applied temperature with an accuracy of 0.1°C, the system can be placed in a thermostat [28] and hence, the alignment of the NLC molecule can be controlled as desired. The extraordinary index n _e decreases gradually, and the ordinary index n_o decreases initially and then increases slowly at 1.55 µm as the temperature is varied from 15°C to 50°C. The average refractive index of E7 decreases linearly with the increase in temperature at 1.55 µm [28]. The bandwidth of our PS is actually the wavelength region through which the ER is better than -20 dB and this criterion can be achieved at the wavelength where L _x ≈ L/2 and L _y ≈ L. The refractive index difference between two polarized (x and y) modes can be written as

 

Fig. 11. (a) Refractive index difference and coupling lengths (x and y polarized modes) with temperature at 1.55 µm; (b) ER spectra with different temperatures ranging from 15°C to 50°C showing the temperature-based tuning of our polarization splitter. For different temperatures, the device can be operated between different specific wavelength ranges. The dotted straight line indicates the standard -20 dB reference line.

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Figure 11(b) presents the ER spectra for different temperatures ranges from 15°C to 50°C with 5°C of incremental step. It is clear that the ER retains better than -20 dB at 1.55 µm while the temperature raises from 15°C to 50°C. Hence, the bandwidth increases to 365 nm (1260 nm to 1625 nm) maintaining the ER better than -20 dB when the temperature rises to 30°C. At 35°C temperature, the bandwidth increases to 370 nm (1240 nm to 1610 nm) but the ER exceeds -20 dB and maintains a value better than -10 dB at the entire bandwidth. This is happening because the L _y approaches to L at lower wavelength areas, then exceeds L and again starts decreasing to approach L at higher wavelength areas of our interest. Similarly, further increase in temperature broadens the bandwidth and working wavelength range but the extinction ratio exceeds -20 dB. The working spectral regions with different temperatures, for ER < 20 dB, have been summarized in Table 1. From Table 1 and Fig. 11(b), it is believed that by varying the temperature, the proposed polarization splitter can be tuned to work within 1200 nm to 1650 nm, meaning that it could covers O to U optical telecommunication bands, as desired by different applications. So, the working bandwidth can be increased to 450 nm by using the temperature sensitivity of NLC of E7 material.

Table 1. Working Spectral Regions for Different Temperatures

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A comparative study between our splitter and some of the recent PBS is summarized in Table 2 based on structural complexity, splitter length, working bandwidth, spectral region, and tunability. Some of the reported splitters have smaller length but lower working bandwidth. For example, the device [14] has smaller length of 47.26 µm with a very narrow bandwidth (104 nm) and the splitter [25] has a short length of 109.5 µm but the bandwidth is only 280 nm. Again, some have considerably wide bandwidth but larger in device length. For example, Qu and colleagues presented a splitter [24] in 2022, has a broad bandwidth of 358 nm with a comparatively larger splitter length (230 µm). Some other splitters are also introduced in literatures which have both larger bandwidth and smaller length [11,22]. For example, Rahman et al. proposed a square structure gold filled broadband splitter with bandwidth of 530 nm having short device length of 56.33 µm [11] but plasmonic creates fabrication complexity. The splitter proposed in [22] has short length (94 µm) and broad bandwidth (349 nm) but misses O band of communication wavelength. In 2014, Chen et al. proposed another PS which has a length of 175 µm with a bandwidth of 250 nm, but the structure uses three different diameter circular holes and is not regular hexagonal [20]. Moreover, neither of them has important tunability property. Although, the splitter [19] is tunable but the length is very large (5678 µm) and the bandwidth is also very narrow (3 nm). Our proposed polarization splitter has a compact length of 71.35 µm, reasonably large bandwidth of 356 nm, and temperature tunablity in a simpler structure which allows to tune the device externally without changing structural parameters.

Table 2. Comparative Performance of the Proposed and Existing Polarization Splitters

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It is necessary to discuss the fabrication feasibility of our proposed fiber for practical implementation. There have been many recent developments in fabrication techniques. Sol-gel, stack and drilling, and capillary stacking techniques can only fabricate circular air holes. There are few literatures having realization of using elliptical holes [10,11,23,24] and our central elliptical hole dimensions (d_x= 1 µm, d_y= 0.8 µm) are comparatively larger as well as more practical which increases the fabrication possibility of the design. Moreover, it is hoped that with the rapid development of modern fabrication technology, more complex and irregular shape in fiber structure could be fabricated easily. Different fabrication processes for NLC filled PCF have been proposed in the literatures [32–35]. One of the processes is heating the fiber along with liquid crystal to about 100°C and filling the liquid crystal material by capillary action [32]. Another method is to apply insertion pressure of several atmospheres at room temperature [32]. Famous stack and draw technique can also be employed to fabricate NLC-PCF, since, the structure depends on the well-known triangular lattice [33]. Also, two photon direct laser writing process has been used to demonstrate full flexibility of individual closing of holes as well as subsequent filling of PCFs with nonlinear liquids [35]. They have used capillary forces for liquids filling to the fiber. To infiltrate the central hole of our fiber selectively, other air holes have to be blocked individually to prevent liquid crystal infiltration [35]. Wolinski et al. successfully infiltrate the NLC in a hole of 1.0 µm or less (0.7-1.0 µm) diameter and a distance between holes (pitch) of 2 µm [36] which is in the range close to our structural parameters. So, this method may also be used for liquid crystal infiltration in our designed fiber. A similar filling method that solely fills core holes has also been proposed in [37]. Additionally, the infiltration of the central defect core has been successfully accomplished using arc-fusion procedure [38]. Also, utilizing the extrusion method, micro structured optical fibers (MOFs) with various sized air holes in the cladding and core have previously been fabricated [39]. Since, our proposed fiber consists of circular air holes and an elliptical NLC filled hole, the aforementioned existing fabrication techniques prove its fabrication feasibility.

4. Conclusions

A compact, tunable, and wideband polarization splitter has been proposed on a PCF platform. The appropriate optimization of the structural dimesions and infilling NLC of E7 material leads to a short device length of 71.35 µm and a large bandwidth of 356 nm, from 1285 nm to 1641 nm, able to work over the O-E-S-C-L-U communication bands. The results also show that the minimum value of ER is achieved as -83.34 dB at 1.55 µm and maintain < -20 dB over the entire bandwidth. Moreover, it also has excellent fabrication tolerance and the temperature sensitivity of NLC of E7 makes the splitter tunable and the resulting total operating bandwidth increasable to 450 nm (1200 nm to 1650 nm). Therefore, the proposed fiber, has excellent performances compared to the recent related works, can be used as polarization splitter in optical communication and sensing systems.