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Abstract
In this paper, a dual-core liquid filled photonic crystal fiber coupler (PCFC) with rectangular (RPCFC) and hexagonal (HPCFC) geometry is presented from the 1200 to 1800 nm wavelength range. In the proposed design, super flint (SF10) glass is used as the background material and water, chloroform, and benzene are infiltrated in the dual-core, independently. The properties of the guided modes are studied by the finite difference time domain (FDTD) method with a perfectly matched layer (PML) boundary condition. Results reveal very small confinement loss with a low coupling length and birefringence for the wide wavelength range. At the 1.55 μm wavelength, RPCFC shows 0.000318, 0.000358, and 0.000379 m coupling lengths for the water, chloroform, and benzene filled dual-core, respectively. Additionally, the confinement loss of 1.57×10−7, 1.22×10−7, and 1.05×10−7 db/km is achieved through RPCFC. Moreover, both the PCFCs present a small polarization variation. Therefore, the proposed PCFC models can be used in optical communication systems, and polarization-independent and high temperature-sensitive applications areas.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Photonic crystal fibers (PCFs) have been shown significant amount of applications in the most recent decades because of their supple arrangement and numerous exclusive features like large effective mode area, high non-linearity, adjustable dispersion and birefringence, and continually single mode property [1,2]. Moreover, a number of essential concepts of PCFs with the structure, light guiding methods, categories, manufacture techniques, and a lot of curious and formerly unthinkable properties are important [3–5]. Since PCFs provide a enormous design suppleness, the design of PCFs coupler (PCFCs) with low coupling length with ultra low confinement loss and insensitive birefringence is a huge challenge for the researchers. Coupler based on optical fiber is an exceptionally significant part in appreciating optical fiber communication system. Optical couplers can implement by PCF applying exclusion of two adjacent air holes from the central region. PCFCs support a lot of guiding features compared to the conventional optical fiber like continual lone mode over broad wavelength spectrum, enriched non-linearity and nil dispersion wavelength, low coupling length, small bending loss, and lofty design suppleness used for the preferred purposes. Such favored properties can be accomplished through appropriate modeling of PCF construction parameters such as air hole diameter and separation, inter-core separation, and core radius [6–8].
Coupling distinctiveness play a most important part in wavelength division multiplexing (WDM), switching, coupling, and multiple frequency generation (MFG). In recent times, double-core PCFs examined comprehensively for their notable properties like small coupling length, wide-band characteristics, and polarization insensitive [9–11]. Introducing dual-core in PCF, there are four modes (odd and even for both polarization) propagating [12]. However, two basics modes propagating by the similar direction make mode coupling. This suggests a potential method of expanding directional couplers intended for optical systems [13, 14]. Mangan et al. proposed mode coupling first time of a dual-core PCFs [14]. Normally, the dual-core PCF couplers are sturdily wavelength dependent. As a result, optical systems bandwidth is partially decreased because inadequate bandwidth of the coupler [15]. As a result, to build up wide-band twin-core PCF couplers with wavelength autonomy is extremely vital. First dual-core PCF coupler with broadband behaviors is reported in 2004 which could not maintain the polarization state [10]. Another dual-core elliptical PCF is proposed as a directional coupler which shows wide-band and polarization-insensible properties from 900 to 1600 nm wavelength [11]. However, using elliptical air hole in the cladding region increases fabrication complexity.
Recently, different non silica-based glasses exhibit plentiful attractive openings for PCFs due to their considerably diverse material characteristics. Non silica glasses like chalcogenide, telluride and super flint (SF) provide superior linear and non-linear refractive indices, soaring simplicity in the mid infrared (MIR) region [16]. Traditionally, silica has been used widely as a background material of PCFs which show low refractive index and coefficient of thermal expansion. Coefficient of thermal expansion is a key parameter for designing opto-mechanical devices especially couplers operating in quick temperature differentiate location. The thermal steadiness of PCF is the major issue in near future. Different applications such as fiber optic gyros (FOG), phase sensitivity with temperature, recognized as the Shupe effect, which basis on the zero bias to drift, and also the Shupe constant is used to exemplify the phase difference [17]. As super flint glass (SF10) exhibits high refractive index and coefficient of thermal expansion with low abbe number then it can be used as background material in the proposed dual-core PCFC.
As coupling distinctiveness is foremost part in various applications, consequently this paper focuses mostly on the coupling characteristics of liquid-filled PCFCs. The dispersion results acquired for the dual-core PCF intimately is similar to the dispersion pattern of single-core PCFs obtainable formerly [18–20]. Also, at 1550 nm wavelength the confinement loss is observed very low. A new design is proposed in which the diameter of air holes, lattice pitch, and inter-core separation is slightly different from the conventional dual core PCF coupler which facilitates the use of PCFCs for wavelength selective uses. Moreover, the thermal steadiness of PCF is the major issue in near future research. For this reason we have decided to use SF10 as the background material which have high thermal expansion coefficient. The effect of structural parameters on the coupling characteristics of dual-core PCFCs are examined comprehensively using the finite difference time domain method (FDTD) with perfectly matched layer (PML) boundary condition. The proposed PCFC for both rectangular (RPCFC) and hexagonal (HPCFC) geometry demonstrate broadband and polarization-insensitive properties.
2. Fiber design and theory
In this report, a dual-core rectangular and hexagonal PCFC are proposed. SF10 glass (n = 1.72) is used as the background material. Also, the core region is filled by different liquids such as water (1.33), chloroform (1.445) and benzene (1.501), separately. The schematic of the planned double-core PCFC is presented in Fig. 1, wherever cores are documented through intentionally absent air-hole on the SF10 substrate. In the proposed design, four air-holes rings where each air-hole diameter, d=0.6 μm and lattice pitch Λ = 2.3 μm is chosen. Moreover, each hole diameter of dual core, dc = 0.4 μm is considered where inter-core separation is 4.6 μm (2Λ). The electric field confinement is shown for both rectangular and hexagonal PCFC in Fig. 2. Moreover, In Fig. 2, field confinement is shown for rectangular and hexagonal PCFC (a) RPCFC (even and odd mode) for x polarization, and (b) HPCFC (even and odd mode) for y polarization. Actually, there are four figures: RPCFC (even and odd mode) for both polarizations and HPCFC (even and odd mode) for both polarizations. RPCFC (even and odd mode) for y polarization and HPCFC (even and odd mode) for x polarization is not presented for simplicity. Usually, coupling length of x-polarized state almost overlaps that of the y-polarized state. Therefore, only the properties for x-polarized is presented [21–23].
Fig. 2 Electric field confinement of rectangular and hexagonal PCFC (a) RPCFC (even and odd mode, respectively), and (b) HPCFC (even and odd mode, respectively).
The different guiding properties of the proposed PCFCs are computed applying FDTD method. After simulating these proposed PCFCs model, the effective refractive index is obtained. The effective mode index is calculated using the eigenvalue problem taken by the Maxwell equation. Moreover, effective refractive index is derived by solving the Maxwell vector equations [24]
where s and s−1 are PML and inverse PML matrix accordingly, k0 is the free space wave number, λ is the free space wavelength, n is the refractive index and E is electric field vector. The propagation constant of an electromagnetic signal is the alternation of the amplitude propagating in a given direction. Therefore, the propagation constant of an electromagnetic wave is written by [3] where neff is the effective refractive index and λ is the operating wavelength of the input light.The dispersion can be calculated through [25]
where c is the speed of light. Also, confinement loss can be computed by [26] Here, Im(neff) is the unreal part of effective mode index. Coupling length provides the distance that supports the probability of permeable modes which shift the light starting from one guide to the further as evanescent waves. Coupling length is given by [3] neven and nodd are the effective refractive indexes of the two fundamental propagation modes, correspondingly. Moreover, birefringence is obtained by considering the real part of the effective mode index disparity of the two essential polarization modes and can be written as [27]3. Results and discussion
Figure 3 represents the effective refractive index (real) with respect to wavelength with two different PCFC geometry: RPCFC and HPCFC for x-polarization. Odd mode is not shown for simplification. As three different liquids like water, chloroform, and benzene are filled in the dual-core and benzene refractive index is maximum then it shows the highest effective index in the entire wavelength range. Generally, increasing wavelength the effective refractive index is decreased. Among the three materials, water shows small refractive index compared to other liquids. Moreover, rectangular PCFC shows the highest index for all the three liquids. However, increasing wavelength the rate of reduction of this index is higher for hexagonal geometry. Results imply this reduction rate for every 100 nm wavelength with water, chloroform, and benzene are 4.5%, 4.2%, and 4.0% for hexagonal PCFC and 3.67%, 3.5%, and 3.16% for rectangular PCFC, respectively. In addition, Fig. 4 presents the effective refractive index (real) with respect of wavelength for different PCFC geometry with y-polarization (even mode). As usual, increasing wavelength the effective index is decreased. However, at 1200 nm wavelength the effective index difference is very small which confirms the polarization insensitivity.
Fig. 3 Variations of effective refractive index (real) with respect to wavelength for rectangular and hexagonal geometry with x-polarization (even mode). Solid line presents rectangular where dashed line show hexagonal.
Fig. 4 Variations of effective refractive index (real) with respect to wavelength for rectangular and hexagonal geometry with y-polarization (even mode). Solid line presents rectangular where dashed line show hexagonal.
Figure 5 represents the dissimilarity of propagation constant with respect to wavelength for both rectangular and hexagonal PCFC geometry. Propagation constant decreases with the increases of wavelength for both structures and for all the three liquids filled in the core region. For smaller wavelength, the propagation constant is linearly relative to the effective mode index and created to be utmost. Increasing wavelength, the propagation constant reduces with function of the effective mode index. For both structures, propagation constant is observed high for benzene comparatively. Moreover, rectangular PCFC presents higher propagation constant from the entire wavelength range. At 1550 nm wavelength, propagation constant is varied between 7.068 to 7.015 (rad/m×106) for both the PCFC with three liquids. Changing the structure from rectangular to hexagonal, propagation constant is reduce to approximately 4.93% at 1550 nm wavelength for benzene. Water and chloroform exhibit the same tendency. However, at 1800 nm wavelength these constant is reduced to almost 6.125 (rad/m×106) for both the models and the three liquids, respectively. The rate of reduction of the propagation constant is around 4.70% for every 100 nm wavelength for all the three liquids.
Fig. 5 Variations of propagation constant (x-polarization) with respect to wavelength for rectangular and hexagonal geometry. Solid line presents rectangular where dashed line show hexagonal.
Figure 6 demonstrates the variations of coupling length with respect to wavelength for both models. Coupling length is found lower at the larger wavelength for both PCFCs structures. Coupling length increases by increasing of the effective core area, due to increase the inter-core separation [28]. Usually, increasing wavelength the field confinement is reduced. As a result, the effective core area is increased which confirms small coupling length. However, the shorter coupling lengths should be due to the low filed confinement and the corresponding enhanced coupling coefficients. When core is filled with water then coupling length is comparatively small for both the structures at shorter wavelength. However, higher wavelength RPCFC with chloroform filled dual-core gives small coupling length. It is noted that for small wavelength (1200 to 1500 nm) HPCFC exhibits low coupling length whereas higher wavelength (1500 to 1800 nm) RPCFC shows the similar behavior for all the three liquids. Among the three liquid benzene shows the maximum coupling length due to higher refractive index.
Fig. 6 Variations of coupling length (x-polarization) with respect to wavelength for rectangular and hexagonal geometry. Solid line presents rectangular where dashed line show hexagonal.
Moreover, at 1.55 μm wavelength RPCFC with water filled dual-core shows the lowest coupling length (0.000318 m). Furthermore, RPCFC presents the lowest coupling length 0.000318, 0.000358, and 0.000379 m for water, chloroform, and benzene at 1.55 μm compared to the existing literature [3] as shown in Table 2. In addition, using RPCFC instead of HPCFC the coupling length is reduced to 12%, 10.33%, and 12.13% at the same wavelength for water, chloroform, and benzene, correspondingly. It is also observed that increasing wavelength chloroform and benzene maintain this reduction rate. Nevertheless, water does not maintain this reduction rate at higher wavelength and shows almost similar coupling length for both the PCFC models. Another significant observation is that increasing every 100 nm wavelength the coupling length with three different liquids (benzene, chloroform, and water) is reduced to 0.000057, 0.000055, and 0.000048 m for RPCFC and 0.000038, 0.000036, and 0.000032 m for HPCFC, respectively.
Figure 7 demonstrates the variations of confinement loss with respect to wavelength for rectangular and hexagonal PCFC geometry. It is noted that confinement loss raises with the increases of wavelength. High confinement loss is seen when core region is filled with water and low confinement loss is observed when core is filled with benzene for both the geometry. Increasing wavelength the confinement loss is increased though the rate of increment is high for HPCFC compared to RPCFC. In Table 1, the comparison of confinement loss is presented at 1.55 μm wavelength. Among the different PCFC models and liquids filled in the dual-core, benzene with RPCFC shows the lowest confinement loss of 1.05×10−7 dB/km. Also, low confinement loss is observed at RPCFC compared to HPCFC. Moreover, changing the PCFC model from hexagonal to rectangular geometry the confinement loss is reduced to 43.72%, 37.11%, and 33.12% at 1.55 μm wavelength for water, chloroform, and benzene, respectively. Generally, rectangular PCFC model exhibits the lower confinement loss than hexagonal PCFC. In addition, RPCFC shows raising the confinement loss of 6.32×10−7, 4.92×10−7, and 4.36×10−7 dB/km for increasing every 100 nm wavelength with water, chloroform, and benzene. On the same condition, HPCFC shows this increment rate 10.96×10−7, 7.71×10−7, and 6.26×10−7 dB/km.
Fig. 7 Variations of confinement loss (x-polarization) with respect to wavelength for rectangular and hexagonal geometry. Solid line presents rectangular where dashed line show hexagonal.
Table 1. Comparison of Different Guiding Properties of the Proposed RPCFC and HPCFC at 1.55 μm Wavelength
Table 2. Coupling Length Comparison of the Proposed PCFCs with the Existing Literature at 1.55 μm Wavelength
Figure 8 shows the birefringence with respect to wavelength for both the PCFCs. As shown in the figure, birefringence increases with the raises of wavelength. It has been shown that the birefringence varies by changing the core area and pitch of the lattice. This is because, when the air holes are close to each other, the light will interact more with air-holes and thus reduces the effective index. It is observed that birefringence becomes high for constant air hole size at a larger wavelength, but decreases as the wavelength and air-hole size decreases. For rectangular PCFC as the core area is increased then effective index is reduced which provide lower birefringence [29]. Water shows large birefringence for both these PCFC models. The minimum birefringence is observed for benzene at lower wavelength with RPCFC model whereas higher wavelength HPCFC shows the minimum value. In Table 1, the comparison of birefringence is showed at 1.55 μm wavelength. Generally, at 1.55 μm wavelength rectangular PCFC presents higher birefringence than hexagonal. RPCFC shows birefringence of 0.000220, 0.000218, and 0.000204 for water, chloroform, and benzene where HPCFC this value is 0.000216, 0.000196, 0.000182. These value is very small compared to the existing literature [3]. Changing the PCFC structure from hexagonal to rectangular the polarization is altered to 1.81%, 10.09%, and 10.78% for water, chloroform, and benzene liquids, respectively. Therefore, it is clear that water exhibits the maximum polarization insensitivity than the other two liquids filled in the dual-core. Moreover, RPCFC shows increment of birefringence for every 100 nm wavelength is of 0.000032, 0.000033, and 0.000031 for water, chloroform and benzene, correspondingly. On the other hand, HPCFC presents 0.000027, 0.000025, and 0.000023 for water, chloroform and benzene, respectively. As raise every 100 nm wavelength, the change of birefringence is very small for both the PCFC model. However, HPCFC model is more polarization independent than RPCFC.
Fig. 8 Variations of birefringence with respect to wavelength for rectangular and hexagonal geometry. Solid line presents rectangular where dashed line show hexagonal.
Figure 9 illustrates the dispersion relation with respect to wavelength for x-polarization. Generally, increasing wavelength the dispersion is decreased. However, both the models with three different liquids show positive dispersion. This is due to the very minute change of the effective refractive index (real part) as shown in Fig. 3. The group index of effective mode can be calculated by where nph is the phase index. Usually, ng >nph which suggests the positive involvement of dispersion (maximum power is confined to the high-index region). RPCFC model shows higher dispersion than HPCFC at this specific wavelength. Moreover, changing the PCFC structure the dispersion variation is very low at this particular wavelength. In addition, dispersion is observed almost constant from broad wavelength range. In Fig. 10, dispersion is plotted from 1500 to 1600 nm wavelength for both the PCFC models with water, chloroform, and benzene liquids, respectively. Results imply RPCFC with benzene liquid demonstrates the lowest variation of dispersion at this particular wavelength range. Thus, these PCFC models can be also used in dispersion compensation fiber (DCF). In Table 1, the comparison is made for three different liquids with both PCFC models at 1.55 μm wavelength. Also, compared the coupling length to the existing literature which is shown in Table 2.
Fig. 9 Variations of dispersion (x-polarization) with respect to wavelength for rectangular and hexagonal geometry. Solid line presents rectangular where dashed line show hexagonal.
Fig. 10 Variations of dispersion (x-polarization) with respect to wavelength (1500 nm to 1600 nm) for rectangular and hexagonal geometry. Solid line presents rectangular where dashed line show hexagonal.
4. Conclusion
In this report, four rings dual-core PCFC for both rectangular and hexagonal geometry is proposed. Also, SF10 is used first time as a background material with three different liquids (filled in dual-core). Various guiding properties like propagation constant, confinement loss, birefringence, dispersion, and coupling length are investigated and compared. The proposed PCFCs based on SF10 background material show ultra small confinement loss and coupling length at 1.55 μm wavelength. Moreover, at this particular wavelength the birefringence value is significantly small. It is concluded that the dual-core SF10 based RPCFC and HPCFC exhibit lowest coupling length than the existing literature. However, it is required to optimize the structure parameters to further decrease the coupling length and offset the birefringence. The planned PCFCs will hopeful potential in wide-band optical data transmission, polarization maintaining, and temperature related coupling applications.
Disclosures
The authors declare that there are no conflicts of interest related to this article.
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