In this paper, we propose a novel design of a photonic crystal fiber (PCF) with tellurite-cladding, three rings of air-holes and elliptical concentration of As2S3 in the fiber core. The combined effect of tight mode confinement (an effective mode area of nearly 0.6 µm2), large non-linear refractive index of As2S3 and significant variation between the effective modal index values of the two orthogonal states of the fundamental guided mode leads to extreme non-linear coefficient and birefringence values, all achieved at the zero dispersion wavelength (ZDW) of 1550 nm. The corresponding birefringence and non-linear coefficient (7 × 10−3 and 28 W−1 m−1, respectively) are more than three orders of magnitude larger than that of the regular silica-based highly non-linear PCFs. In addition, we numerically demonstrate that by modifying the core and air-hole dimensions one can easily control the dispersion curve and tune the ZDW of the proposed fiber to any excitation wavelength ranging from near-infrared to short-wave-infrared, including optical telecommunication windows close to 1550 nm. The superior characteristics of the proposed elliptical-core composite PCF including extreme non-linearity, nearly-zero confinement loss (2.47 × 10−12 dB/cm), the ability to maintain polarization of light, and tunable ZDW can open the door to new possibilities in non-linear optics, optical telecommunications, optical signal processing, and sensing devices.