A unique hexagonal lattice structure of silica-based solid core photonic crystal fiber (PCF) surrounded by array of air holes is proposed. The cladding portion of the structure consists of five rings where core is made up of 11 small rings filled with methanol. Three different-shaped structures are used to analyze the effect on PCF parameters where the first structure uses circular air holes in cladding and core, the second structure consists of circular air holes in cladding and elliptical air holes in core, and the last structure was designed by using elliptical air holes in both cladding and core. Optical properties birefringence, confinement loss, and negative dispersion have been found theoretically and compared. A novel and relatively simple approach depicts the results that attain high birefringence, low confinement loss, and negative dispersion. It is found that the presence of elliptic air holes instead of circular air holes in the core region and the cladding brings higher birefringence, low confinement loss, and highly negative dispersion.