Design of low loss photonic crystal fiber based on

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Design of low loss photonic crystal fiber based on porous-core with elliptical holes in THz regime Erick Reyes-Vera J. Úsuga-Restrepo J. Zuñiga-Bedoya Juan F. Botero-Cadavid

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Design of low loss photonic crystal fiber based on porous-core with elliptical holes in THz regime Erick Reyes-Vera*,a,b, J. Úsuga-Restrepoa, J. Zuñiga-Bedoyaa, and Juan F. Botero-Cadavidc a Department of Electronic and Telecommunications Engineering, Instituto Tecnológico Metropolitano, Medellin, Colombia; b Department of Electrical and Electronic Engineering, Universidad Nacional de Colombia, Bogota, Colombia. c Escuela de Física, Universidad Nacional de Colombia, Medellín, Colombia. ABSTRACT In this work, we present a new design of a low loss and high birefringence THz Photonic Crystal Fiber (PCF) made of TOPAS material, featuring a porous core with elliptical holes. The full-vector finite element method was employed to analyze the optical properties such as birefringence, confinement losses, and effective material losses; as well as to study how these parameters are dependent on the geometry of the structure. The simulation results showed confinement losses ≈ 0.06 dB/m when a configuration with high grade of porosity in the core was implemented. At the same time, birefringence values close to 3×10-2 there were obtained. The proposed design can be fabricated easily using standard stack and draw technique and be used in several applications in the THz region to propagate the radiation. Keywords: Photonic crystal fibers; Fiber optics devices; Terahertz wave; Terahertz polymer fiber; High birefringence.

1. INTRODUCTION Electromagnetic (EM) radiation in the Terahertz (THz) portion of the spectrum has gained great interest in the last decade. Researchers turned heads towards this range in the EM spectrum because these wavelengths exhibit strong interactions in systems with short lifetimes (picoseconds) and energies in the range of meV. These type of systems are common in complex biological, solid-state, and other physical phenomena1. Making the signals in the range of 0.1 to 10 THz suitable for fields such as new sensing applications. Free space propagation of the waves reduces the possible uses that they can provide, in particular because it is not easy to limit the area where the interaction with the systems happens. For this reason, it has also become of cumbersome importance the development of THz waveguiding components. Metal devices have been proposed and used in the past as waveguides for THz signals. However, the metal finite conductivity limits their applications2. On the other hand, dry air is the most transparent medium for THz EM waves. Polymers, vitreous materials, and water (even the present as humidity in the air), absorb the radiation of the THz wavelengths, and loss will occur when the signals propagate in these materials. In order to reduce the propagation loss, there have been reports of approaches that are focused on maximizing the confinement of the signals either in materials with structures that are surrounded by air, in Bragg-stack claddings, or in hollow-core waveguides that rely on bandgap phenomena. Examples of the first approach include suspended core waveguides3, and the micro-structured waveguides with periodic concentric rings of holes1,4 that are inspired in the extensively studied Photonic Crystal optical fibers (PCFs) for the near infrared and visible range of the EM spectrum5–8; the Bragg-stack claddings that consists of layers of materials with different refractive index; and finally, the hollow-core waveguides where the signal travels in a core made of air that is surrounded by material arranged in concentric structures and surrounded by arrays of holes or other empty-like regions2. The state of the art for the fabrication techniques reported for these THz waveguides includes stacking of polymer rods that are held in place tightly9, stacking of polymer or vitreous materials fused together by heat, the drilling and drawing of a preform4,10,11, and lately, rapid prototyping techniques such as 3D-printing have become readily available and make possible the design of more intricate geometries2,12.

Third International Conference on Applications of Optics and Photonics, edited by Manuel F. M. Costa, Proc. of SPIE Vol. 10453, 1045337 · © 2017 SPIE · CCC code: 0277-786X/17/$18 · doi: 10.1117/12.2276427

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Within the micro-structured PCFs, the modal propagation can be controlled and tailored to specific regions of the THz range of the spectrum. The geometries of both the waveguide and the microstructure array play a crucial role in the modal propagation7,13,14. The size of the holes, and the pitch at which the array is organized determined whether the waveguide is guiding a single or multiple modes1. Even the geometry of the holes can be used to alter propagation conditions such as polarization of the fiber. This is particularly helpful since there is no need during the fabrication of inserting Stress Applying Parts that create induced birefringence due to elasto-optic effect like in PANDA fibers15, but rather controlling the polarization maintaining properties only with the hole geometry. This work presents a study of a novel design of a PCF fiber for the THz region of the EM spectrum. In order to reduce the propagation loss, a polymer known as TOPAS with a reduced absorption at these wavelengths and a very stable refractive index was used as material of the waveguide. The core of this waveguide is formed by a hexagonal array of elliptical holes. This core is surrounded by concentric rings of holes acting as cladding. Propagation properties such as reduced loss and polarization control are the main advantages of this proposed design.

2. SIMULATIONS AND RESULTS Figure 1 shows the cross section of the proposed THz photonic crystal fiber (PCF). The core of the PCF is comprised of elliptical holes in an array with hexagonal distribution. Geometrical parameter of the ellipses in this array can be defined by its two axis = 125.7 μm and = 19.2 μm. The major axis of all the ellipses that form the core of the PCF are oriented with an angle = 0°. This array of holes are separated a distance pitch ( = 42.4 μm) in all directions. On the proposed design, the cladding is formed by five concentric rings of circular air-holes, also arranged in a hexagonal distribution. For the cladding the diameter of holes , = 271.4 μm , and the pitch, = 285.7 μm . Hereinafter a parameter known as porosity is defined. Porosity is the relationship between the area of the holes and the area covered by the material in the cross section of the PCF. To obtain better results, TOPAS material was used in the design of this THz-PCF. This material have a refractive index of 1.53 and material losses of 1 dB/cm as shown in 1. The total diameter of this THz-PCF is 3200 µm (3.2 mm). TOPAS

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a

Figure 1. Cross-section view of the proposed design for a photonic crystal fiber with elliptical holes

The influence of the porosity on the birefringence for different sizes of Dcore was evaluated, as it is shown in Figure 2a. In this case it is clear that, as expected, the porosity has a great influence on the birefringence values of the PCF. This behavior owing to the fact that the more the amount of holes, the higher the anisotropy of the structure. In addition, it can be observed that the birefringence for all porosities studied remains nearly constant after Dcore=350 µm. The highest value of birefringence obtained for this design of THz-PCF was ≈ 1.3×10-2, which is at least one order of magnitude higher than the birefringence previously reported in the literature 16. Since one of the main issues with waveguides in the THz range of the electromagnetic spectrum is the propagation loss, the losses due to absorption of the material and the


confinement losses were analyzed a in thhis proposed PCF P design. Determining D t absorptionn loss in the proposed the p PCF F requires emplloying the exppression givenn by 17: ∬

=

,

∬

(1)

where andd are the peermittivity annd permeabilitty in the vacu uum respectivvely, is the refractivee index of thee material, and is the bulk’s b material absorption loss, which deepends on the operating frequency1. The results of thiss first analysis are shown inn Figure 2b. From F the resuults obtained it is possiblee to infer thatt the effectivee material losss (EML) can be b reduced through t increasing the corre’s porosity.. Waveguidess with lowerr losses will allow greaterr transmission distances to be b achieved. Also, A it is cleear that for th he y-polarization the EML is lower than that of the xpolarization. The reason for fo this being that in this case the analy ysis was perfoormed with = 0°, and at this conditionn there is an allignment withh the major axis of the elliiptical holes as a it was illustrated in Figgure 1. These results are of potential advaantage, since increasing thee amount of holes h makes po ossible to tunee the behaviorr of the propo osed polymericc PCF in the TH Hz region.

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Figure 3. (a) Confinemennt losses as a fuunction of Dcore for different porosity p cases at a 1 THz., (b) C Confinement lossses as a funnction of Dcore for f different oriientation angless of elliptical ho oles at 1 THz


Finally, the confinement losses of proposed waveguides were studied. To perform this analysis in the proposed design of the THz-PCF, different values of Dcore and porosities were considered, while remaining constant the ellipses orientation ( = 0°) and the operating frequency (1 THz). The results are illustrated in Figure 3(a). The influence of the core’s porosity was evaluated and small values were obtained in all cases. From these results, two regions can be identified, Region I, where Dcore values are smaller than 200 µm. In this first region, the confinement losses are greater due to the fact that there is more material. Region II (Dcore ≥ 200 μm), on the other hand, shows confinement losses smaller than 0.06 dB/m, and essentially constant. In Figure 3(b) the effect of the orientation of the elliptical holes on the confinement losses is shown. In this case, the porosity of the PCF was maintained constant at 60%. Here for small values of Dcore; the confinement losses are smaller when the angle of orientation of the elliptical holes = 90°. In addition, the difference is not representative for Dcore values greater than 200 µm.

3. CONCLUSION A novel design of PCF with porous core operating in the THz band was proposed and analyzed using the full vector Finite Element Method. The obtained simulation results demonstrate that this fiber can used as waveguide owing to it have smaller losses than other proposed configurations. It was found that the porosity and other structural parameters have an important role to increase the birefringence, in addition to minimize the EML and confinement losses. The proposed fiber could be use in THz sensing, telecommunications, imaging, and spectroscopy applications. Further work on this proposed design includes to study the impact of the rotation of the elliptical holes on the optical parameters such as the polarization, dispersion, propagations, among others.

ACKNOWLEDGMENTS This work was supported by Instituto Tecnológico Metropolitano (project P15108). The Instituto Tecnológico Metropolitano through the program Young Researchers 2017 supported the author J. Úsuga-Restrepo.

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