A novel Zeonex-based photonic crystal fiber (PCF) with a honeycomb-like cladding structure and a hexagonal slotted core is proposed. The finite-element method is used to numerically analyze the guiding characteristics of the proposed fiber. The investigations are carried out by optimizing various geometrical parameters of the fiber and varying the frequency, core diameter, and core porosity. The results indicate that the designed PCF demonstrates an ultrahigh birefringence of 0.083, extremely low confinement and effective material loss of 10 − 8 and 0.095 cm − 1, respectively, and a very high core power fraction of 52.2% at an operating frequency of 1.5 THz. In addition, other guiding properties such as numerical aperture, dispersion, and effective area are also analyzed and discussed in detail. The obtained results show that the proposed PCF is extremely suitable for use in numerous low-loss, polarization-maintaining applications in the terahertz frequency range. |
1.IntroductionIn recent years, there has been a massive surge in interest regarding applications in the terahertz (THz) frequency range, which extends from 0.1 to 10 THz and lies between the microwave and infrared frequency bands. The THz band provides a number of advantages for a wide variety of applications ranging from biotechnology,1 security screening,2 biomedical imaging,3 optical communication,4 sensing,5–8 and noninvasive medical procedures such as the detection of skin cancer.9 However, in order to utilize THz radiation effectively, it is necessary to guide THz waves in a manner that is suitable for long-distance transmission with minimal wavelength-dependent losses and near-flat dispersion at the desired wavelength. Conventional THz systems that rely on free-space propagation do not fulfill these criteria, namely due to high atmospheric losses and improper reception of THz waves due to the misalignment of transmitter and receiver. Numerous types of THz waveguides have been proposed in recent years for efficient and reliable THz signal transmission, such as metallic waveguides and bare metal wires,10 dielectric metal-coated tubes,11 plastic fibers,12 polymer tubes,13,14 and Bragg fiber.15 However, all of them suffer from very high losses. Metallic waveguides suffer from high bending and attenuation losses and undesirable interaction with complex environments, whereas dielectric waveguides suffer from high material absorption loss due to the dielectric material. Polymer tubes, while having high birefringence, suffer from high atmospheric losses. Recently, a new type of optical fiber called photonic crystal fiber (PCF) has been given a great deal of attention due to its beneficial properties such as high birefringence, low material and confinement losses, low dispersion, and flexibility in modifying the guiding properties by controlling geometrical parameters. Conventional solid core PCFs have high absorption losses.16 In order to mitigate that, a number of microstructured air holes are placed inside the solid core, to form a porous-core PCF. Since dry air does not absorb THz waves, it is essentially a considered a lossless medium for THz transmission.17 As a result, porous-core PCFs can guide THz waves with much lower effective material loss (EML)18 by confining most of the mode power inside the air holes. In addition to low absorption loss, modal birefringence is one of the most important properties of a PCF. Birefringence is defined as the absolute difference of the refractive indices of the and polarization modes. Typically, birefringence is induced in a porous-core PCF by breaking the symmetric characteristics of the core or cladding,19 causing the light to separate into two polarized components. High birefringence allows a PCF to maintain polarization characteristics for long-distance THz transmission. This is crucial for many polarization-sensitive applications such as time-domain spectroscopy,20,21 optical sensing,22 and polarized filtering of THz waves.23 Researchers have put forward various PCF structures in recent years with good birefringence properties. A square-lattice fiber implementing square air holes with round corners was proposed by Ren et al.24 This work achieved a high birefringence in the order of but did not report on the EML of the design. Atakaramians et al.25 investigated a rectangular air-hole porous fiber with a high birefringence value of 0.012 at 0.65 THz frequency. But this structure also exhibited an undesirably high EML of at the same frequency. Chen et al.26 proposed a polymer porous fiber with elliptical air-holes and attempted to enhance the birefringence by rotating the major-axis of the air holes. A birefringence as high as 0.045 was obtained using this method. Li et al.27 demonstrated a triangular lattice PCF with both circular and elliptical holes and achieved a birefringence up to in the frequency range of 0.1 to 5 THz but with the drawback of having a high confinement loss. A dual-hole unit-based hexagonal PCF was proposed28 in 2016 that yielded a birefringence of 0.033 but did not take into account the dispersion of the proposed waveguide. Later, Ahmed et al.29 proposed a hexagonal cladding PCF with a high birefringence of 0.019 at 1 THz frequency. However, this work neglected to mention the confinement loss property of the proposed PCF. Recently, a slotted cladding PCF30 and an oligoporous-core PCF31 were shown to have high birefringence of 0.063 and 0.079, respectively. A slotted core design with uniquely shaped circular holes in the cladding by Monir et al.32 achieved excellent birefringence and ultralow EML and confinement loss. The core in this work was formed by rectangular air slots surrounded by circular air holes. However, despite its superior results, it also has a massive drawback with respect to its dispersion properties. The dispersion values are in the 100’s over the entire frequency range of 0.65 to 2 THz, which is around hundreds of times larger than our reported values. These results make this fiber undesirable for long distance transmission in comparison to our design. In addition, the large dispersion variation between and displayed by this fiber is highly unsuitable for simultaneous transmission of multiple signals in telecommunication applications. In this paper, we propose and numerically analyze a novel PCF structure with a slotted core and Zeonex as the background material. The asymmetric core consists of rectangular air slots inside a hexagonal shape. The cladding is made asymmetric by incorporating a unique honeycomb-like structure with hexagonal air holes. This design is named as such since it resembles the honeycomb formation in a beehive. The air holes are placed in an intricate manner to minimize the amount of background material and enable the ease of fabrication. The asymmetry of the core and cladding results in ultrahigh birefringence, which is the main aim of this design. In addition, the proposed design also shows low EML and confinement loss, along with excellent dispersion characteristics in the frequency range of 1.4 to 2 THz. This PCF waveguide shows great potential for use in low-loss polarization-maintaining THz region applications. 2.Design MethodologyThe cross-sectional view of the proposed PCF with honeycomb cladding is shown in Fig. 1, along with an enlarged view of the hexagonal core. The cladding consists of hexagonal air holes arranged in a honeycomb-like pattern. This design choice introduces a high level of asymmetry into the cladding, which facilitates ultrahigh birefringence. There are three rings of regular hexagonal air holes that follow an arithmetic sequence, with 12, 18, and 24 air holes in the first, second, and third ring, respectively. These air holes are equal in size and the distance between opposite vertices of each hole is represented by , with each side of the hexagons measuring . The distance between the centers of adjacent air holes in the cladding, called the cladding pitch, is given by and is maintained at . The strut width , which is the distance between adjacent hexagonal air holes, is equal to and is shown in Fig. 1. These distances are chosen in a manner so as to maximize the confinement of light within the core. The hexagonal slotted core consists of seven rectangular air slots with decreasing lengths away from the center of the core. The core diameter has been varied in order to analyze its effects on the different guiding properties, and the variations of the core for different values are displayed in Fig. 2. The lengths of the rectangular slots can be expressed in terms of the core diameter. The middle slot has length , its two adjacent slots are equal to , the two outermost slots have length and the two remaining slots are long. Although these lengths could be increased further to enhance birefringence, they are optimized in order to minimize difficulties in the fabrication process. In our investigation, we have also observed the effects of varying the porosity of the core, which is given by the ratio of the total area of rectangular air slots to the total area of the core. The porosity is varied by varying the width of the rectangular slots while keeping the diameter of the core fixed. The center to center distance between adjacent rectangular slots is called the core pitch and is denoted by . For the background material of our proposed fiber, we have used Zeonex, the commercial name for Cyclo-olefin polymer. Zeonex provides a number of useful advantages over other materials, namely its low bulk material absorption loss of and the fact that it maintains a constant refractive index of in the frequency range 0.1 to 1.5 THz.33 In addition, it has very low material dispersion, is not affected by humidity and water vapor in the atmosphere due to having low hygroscopicity30 and is highly suitable for biosensing applications.31 A humidity insensitive fiber Bragg grating temperature sensor was fabricated by Woyessa et al.34 with Zeonex as the cladding material. Utilizing the high glass transition temperature of Zeonex, the same author also characterized a Zeonex/PMMA-based microstructured polymer Bragg grating sensor for simultaneous monitoring of temperature and humidity,35 and an endlessly single-mode polymer optical fiber temperature and strain sensor using Zeonex grade 480R.36 3.Results and DiscussionThe commercially available COMSOL Multiphysics version 5.3 software based on the finite-element method has been used to design and simulate the proposed PCF waveguide. In order to accurately analyze the guiding properties of the fiber and calculate the losses, a circular perfectly matched layer (PML) boundary has been applied around the outside of the cladding. The PML acts as an antireflective layer37 and absorbs electromagnetic waves propagating toward the cladding surface. The optimum thickness of the PML was determined by performing a convergence test, and it was found that a thickness of 5% of the total fiber radius shows the best results, which is the value we have chosen for this simulation. For the simulation, the bulk material absorption loss of Zeonex has been taken as , as mentioned previously. Since dry air is considered to be a completely transparent medium for waves in the THz range,38 its absorption loss has been assumed to be zero for this investigation. Figure 3 shows the mode field distributions of the proposed PCF for both and polarizations at different core porosities. It is clearly evident from this figure that the mode power is tightly confined within the porous core, which is essential for the transmission of THz waves. As the porosity is increased, the difference in refractive index between the core and the cladding reduces. As a result, the mode field starts to spread out toward the cladding region, which can be observed from this figure. The variations of the effective refractive index of the proposed fiber with frequency and core diameter for both orthogonal polarization components at different core porosities are shown in Figs. 4 and 5, respectively. It can be seen from these figures that the effective index increases gradually both with increasing frequency and core diameter. At higher frequencies, some of the mode power starts to spread away from the core to the cladding, resulting in higher refractive index. When the core diameter is increased, the amount of solid Zeonex inside the core increases, which enhances the refractive index. The polarization mode has higher effective index at all porosities compared to the polarization mode, which indicates that light is more tightly confined inside the core for polarization. Hence, we have chosen polarization as the optimum mode for our design. The birefringence of a PCF is defined as the difference in refractive index of the polarization and the polarization mode and is mathematically given by where is the refractive index of the polarization mode and is the refractive index of the polarization mode. The birefringence as a function of frequency at different core porosities is shown in Fig. 6. It is observed that the birefringence increases very slowly with frequency up to 1.5 THz, and then remains almost flat from 1.5 to 2 THz. The increase occurs due to the enhancement of index contrast between the core and cladding at higher frequencies, which can also be seen from Fig. 4. On the other hand, the birefringence increases gradually with increasing , which can be visualized from Fig. 7. When the core diameter is increased, the air slots become larger, which increases the asymmetry between the two polarization modes. Consequently, the index difference and thus the birefringence increases. From Figs. 6 and 7, it can be observed that the birefringence decreases with increase in core porosity. This is because at higher porosities, some of the mode power escapes from the slotted core into the cladding, reducing the refractive index difference between them. A birefringence value as high as 0.093 is obtained at 30% core porosity, and , which is one of the highest reported birefringences in the THz range to the best of our knowledge. However, in order to balance a high birefringence with lower losses, we choose 50% porosity, and as the optimum design parameters, which yields an ultrahigh birefringence of 0.083. Since birefringence is the most important property of a PCF waveguide for polarization maintaining applications, our proposed fiber shows excellent potential in this regard. It is very suitable for use in long-distance transmission and other applications requiring a high birefringence such as polarized filtering and optical sensing.One of the biggest limiting factors in the propagation of THz waves along a PCF waveguide is the material absorption loss encountered by the waves due to the solid core material. This EML can be expressed by39 where and represent the bulk material absorption loss and the effective refractive index of Zeonex, respectively, is the relative permittivity, is the relative permeability of free space, and is the component of the Poynting vector given by, , where and are the electric field component and complex conjugate of the magnetic field component, respectively. The integration in the numerator of Eq. (2) is performed only over the solid material, whereas the integration in the denominator is performed over the entire region. Figures 8 and 9 show the variation of EML of the fiber with frequency and core diameter, respectively, at different values of core porosity for the polarization mode. EML increases gradually with both frequency40 and core diameter, and increasing the core porosity results in lower EML. At higher core porosity, the amount of solid material is reduced and the mode power flows mostly through the rectangular air slots, resulting in lower EML. Conversely, increasing the core diameter causes the propagating electromagnetic field to encounter more of the solid material, which increases the EML. At the optimum design parameters of , and 50% porosity, an extremely low EML of is obtained, which is comparable to the previously reported fibers in Refs. 28, 29, 31, and 4142.43.44.45.–46.The core power fraction is defined as the amount of power that flows through the core air and represents how much useful power is propagating through the porous core. A high core power fraction is essential for obtaining ultrahigh birefringence and maintaining efficient transmission of THz waves.47 It is given by the following equation:48 where denotes the core power fraction. The region of interest in the numerator is the core area and the integration in the denominator is performed over the enter area of the fiber. The core power fraction of the polarization mode as a function of frequency and core diameter is shown in Figs. 10 and 11. At 50% and 70% core porosity, the core power fraction increases with both frequency and core diameter but remains almost flat for 30% porosity. By increasing the core diameter, the total volume of air compared to the solid material in the core is increased, which increases the power fraction. At fixed diameter and frequency, the power fraction increases with core porosity. This can be explained by the fact that increasing the core porosity increases the amount of air inside the core, resulting in a higher amount of mode power flowing through the core air slots. However, it is observed that at very low frequencies of around 1 THz, the core power fraction is almost similar for 50% and 70% porosity. This is because, under low-frequency conditions, the confinement of light in the core is very low, and thus there is negligible difference between the core power fractions at these two porosities. Moreover, the core power fraction for 50% porosity is slightly higher than that for 70% porosity when the core diameter is very low. This shows that when the core diameter is very small, it has a much greater effect on the core power fraction than the porosity. At the optimum design parameters of 50% porosity, and , a core power fraction of 52.2% is achieved, which ensures that the majority of the core power is concentrated within the air slots for efficient THz wave transmission. Although a higher porosity and core diameter could be used to enhance the power fraction, they also reduce the birefringence and increase the EML, respectively. Hence, our chosen parameters are retained.In THz transmission, confinement loss is another important parameter to consider when designing a PCF. Confinement loss is defined as the amount of light that spreads out of the core into the cladding region and is mainly dependent on the lattice structure of the cladding. The confinement loss is calculated from the imaginary part of the effective mode index by the following equation:38 where is the velocity of light equal to , is the frequency of operation, and is the imaginary component of the effective refractive index. Figure 12 shows that the confinement loss decreases steadily with increasing frequency for both and polarization modes. This is because, at higher frequencies, light is more tightly confined inside the slotted core region. The confinement loss for polarization mode is observed to be lower compared to the polarization mode since for polarization mode, the index difference between the core and cladding is larger, which results in tighter confinement of light inside the core. Increasing the core porosity results in a corresponding increase in confinement loss. At high core porosity, there is a greater volume of air inside the porous core, which reduces the refractive index of the core. As a result, the index contrast between the cladding and the core is lower, and more light spreads out into the cladding region, which increases the confinement loss. At our chosen design parameters of , and 50% porosity, a good balance is maintained between the EML and confinement loss. Under these conditions, an ultralow confinement loss of around is achieved, which is almost negligible when compared with our obtained EML. This low value is made possible by the highly asymmetric honeycomb-like structure of the cladding.Dispersion plays an important part in the long-distance transmission of THz waves since it indicates the extent to which spreading of pulses occur. In order to efficiently transmit signals over wide frequency ranges, the dispersion should be very small.41 The dispersion should also show very little variation over wide ranges of frequency for simultaneous transmission of multiple signals. The induced material dispersion due to Zeonex is negligible since it has a constant refractive index in the range 0.1 to 1.5 THz. So we only need to consider the waveguide dispersion, which can be expressed by49 where is the dispersion parameter, indicates the angular frequency, represents the speed of light in vacuum, and indicates the effective refractive index of the proposed PCF structure. The variation of dispersion with frequency of the fiber is demonstrated in Fig. 13 for both polarization modes at different core porosity values. It can be seen from this figure that at low porosities and low frequencies up to 1.4 THz, the dispersion variation for both and polarization modes is quite high. But from 1.4 to 2 THz, the proposed fiber displays flattened dispersion for both modes, which enables multiple signals to be transmitted simultaneously over this frequency range. Increasing the porosity causes the dispersion parameter to decrease in value and become more flat. For the polarization mode, the dispersion is at the optimum design conditions.We have considered two final parameters for our proposed fiber, which are the effective area and numerical aperture (NA). The effective area is given by the following relation:50 where is intensity distribution of the transverse electric field and is given by . On the other hand, the NA is given by the following equation:51The variation of both these parameters with frequency for the polarization mode of the proposed fiber is shown in Fig. 14. It is observed that the effective area decreases steadily with increase in frequency. At higher frequencies, the mode field is strongly localized within the core air slots,52 decreasing the effective area covered by the mode. In addition, increasing the porosity causes the effective area to increase. Since the index contrast between the cladding and the core is reduced with increasing porosity, the mode field starts to spread out from the core, which increases the effective area. At , and 50% porosity, a very high effective area of is achieved for polarization mode. From Fig. 14, we can observe that the NA decreases almost linearly with frequency and is higher at lower core porosity. At the optimum design conditions, the calculated NA is 0.36. In order to implement our proposed fiber practically, we must consider whether its fabrication is possible using existing technologies. Numerous fabrication methods have been developed over the years, which include drilling,53 stack and draw,54 the sol–gel technique,55 and among others. All these methods are suitable for fabricating microstructured circular air holes. However, our designed PCF has complex asymmetric structures in both the core and the cladding, with different shaped air holes. Kiang et al.56 employed the extrusion technique for fabricating fibers with highly asymmetric structures. In addition, the 3-D printing method57 has also been shown to be able to fabricate any complex PCF structure. Both of these methods are extremely feasible for fabricating our proposed fiber. Furthermore, the similarly shaped hexagonal air holes in the cladding reduce the complexity of fabrication of both these techniques. The characteristics of our proposed slotted core fiber are compared with some recently reported PCFs in Table 1. In addition to superior birefringence, our proposed PCF shows excellent characteristics, which make it highly suited for polarization-maintaining applications in the THz regime. Table 1Comparison of proposed fiber with some recently reported PCF. 4.ConclusionA slotted core PCF based on Zeonex is proposed and numerically analyzed. High asymmetry is introduced in the cladding using a novel honeycomb-like structure with three rings of hexagonal air holes. The various guiding properties of the proposed fiber are investigated with respect to frequency, core diameter, and core porosity. From the simulation results, an ultrahigh birefringence of 0.083 is obtained at 1.5 THz frequency, with minimal confinement loss and EML of and , respectively. In addition, the proposed fiber shows nearly zero flattened dispersion of in the frequency range 1.4 to 2 THz, along with a very high core power fraction of 52.2% and an effective area of at the optimum design parameters. Practical implementation of the PCF structure using existing fabrication technologies has also been discussed thoroughly. The ultrahigh birefringence along with the excellent guiding properties makes the proposed fiber an excellent candidate for use in low-loss, polarization-preserving applications, and efficient transmission of THz waves. ReferencesM. Nagel et al.,
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BiographyMohammad Rakibul Islam received his BScEngg and MScEngg degrees in electrical and electronic engineering from Bangladesh University of Engineering and Technology (BUET), Bangladesh, in 1998 and 2004, respectively, his MBA degree in marketing from the Institute of Business Administration (IBA) under the University of Dhaka in 2006, and his PhD from the Department of Electronics and Radio Engineering, Kyung Hee University, South Korea, in 2010. He joined the Department of Electrical and Electronic Engineering at Islamic University of Technology (IUT) as a faculty in 1999 and is serving as a professor there. He is currently the dean of Faculty of Science and Technical Education. His research interests include optical waveguide design, optical sensing, surface plasmon resonance, cooperative technique for wireless sensor networks, LDPC and QC-LDPC codes, secrecy capacity, and other wireless applications. Md. Faiyaz Kabir received his BSc Eng degree in electrical and electronic engineering from Islamic University of Technology, Bangladesh, in 2017. He is currently working as a lecturer in the Department of Electrical and Electronic Engineering. His research interests include photonics, nanoplasmonics, silicon photonics, and fiber optics. Khandoker Md. Abu Talha received his BSc degree in electrical and electronic engineering from IUT, Bangladesh, in 2018. Currently, he is working as a support engineer at Wipro Technologies Ltd. His research interests include optical sensing, photonic crystal fiber, biomedical sensing, surface plasmon, and supercontinuum generation. Md. Shamsul Arefin received his bachelor’s degree in electrical and electronic engineering from BUET in 2012, and is continuing his MSc degree at BUET currently. He did his thesis during BSc degree in biometric identification based on fingerprint recognition. He also published two IEEE conference papers in secrecy capacity for MIMO communication. He is currently working as a lecturer at Green University Bangladesh. His research interests include wireless communication, signal processing, wireless sensor networks, photonics, and their application in communication arena. |