## 1 Introduction  
The design and development of compact non-linear devices based on highly non-linear photonic crystal fibers (HNL-PCFs) have attracted much attention in both academia and industry over the last decade [1]. HNL-PCFs can be used as a non-linear medium to realize all-optical wavelength conversion [2], supercontinuum generation [3], pulse compression [4], and parametric amplification [5]. According to [PERSON]'s rule [6], third-order optical non-linearity of the glass strongly depends on the linear refractive index. As silica glass does not exhibit large linear and non-linear refractive indices (nearly 1.45 and 2.9 \(\times\) 10\({}^{-20}\) m\({}^{2}\)/W, respectively, at optical communication wavelengths near 1550 nm), a long fiber length and/or huge power levels are usually required to utilize non-linear effects [7]. These requirements render the silica-based HNL-PCFs limited in most of the non-linear applications, especially in terms of costs and practicality. To realize non-linear processes with low powers and in short interaction lengths, non-silica photonic crystal fibers (PCFs) made of high-index glasses such as tellurite [8], bismuth-oxide [9], and chalcogenide glasses [10] as well as PCFs filled with high-index liquids such as carbon-disulfide [11; 12] are designed, studied and fabricated. Among different materials, chalcogenide glasses with a large refractive index of around 3, ultra-high non-linear refractive index of 3 \(\times\) 10\({}^{-18}\) m\({}^{2}\)/W, and a high transmission window from 0.6 to 15 \(\upmu\)m, open up new possibilitiesto design and develop compact non-linear devices [13]. However, this great potential of chalcogenide fibers is limited in real-world applications due to the relatively large material dispersion of chalcogenide glasses in visible and near-infrared regions. Chalcogenide nano-fibers or nano-wires [13] can solve the problem by shifting the zero dispersion wavelength (ZDW) of chalcogenide from mid-IR to near optical telecommunication bands [14]. Unfortunately, nano-wires are fragile and the degradation in their surface is a crucial challenge that has not been resolved yet. For example, in the environment of a conventional optics laboratory the air cladding nano-wires fail completely within a few weeks [13; 14]. PCFs can solve the dispersion problem of chalcogenide glasses by shifting the ZDW from mid-IR to a near-IR band using an appropriate material selection and array of air-holes in the cladding. The composite PCF with As\({}_{2}\)S\({}_{3}\) core and tellurite cladding, with a ZDW in near-IR and stable optical properties has been fabricated successfully before [13; 14]. The use of tellurite glass in the cladding region can protect the core glass from the degradation over time and also can minimizes toxicity concerns about As\({}_{2}\)S\({}_{3}\). Furthermore, highly birefringent PCFs have been developed during the last few years for applications in temperature, pressure and refractive-index sensing [15; 16], single-polarization-single-mode communications [17], polarization-sensitive optical modulators [18], and polarization-maintaining linear and non-linear devices [19]. Birefringence appears due to the asymmetry in fiber structure, which causes a huge difference between the effective refractive index of x-axis and y-axis polarized modes [19]. If this difference is greater than \(1\times 10^{-4}\), the modes are quite separated and the fiber is considered to be highly birefringent. In this paper, we design extremely non-linear composite tellurite-chalcogenide PCFs with circular holes and study the optical properties of PCF (nonlinear coefficient, dispersion, loss, and birefringence) in detail. To achieve polarization maintaining, we introduce an asymmetry in the PCF structure by using an elliptical core to induce a large birefringence in the fiber. We then compare all of the optical characteristics of the proposed elliptical-core PCF with a regular circular-core PCF to highlight the differences between two designs.