Here we have consider an air-silica honeycomb lattice and demonstrate a new approach to the formation of a core defect. The honeycomb lattice has recently been suggested for the formation of a photonic band-gap guiding silica-core. Here we discuss how a core defect can be formed by manipulating the cladding region rather than the core region itself. There are so many difficulties occur during the design process. Because when parameters are being changed the designing varies accordingly. For this purpose we have use HPCF in scalar effective index method (SEIM) and consider chromatic dispersion of HPCF for having air hole diameter 1.0 micro.m, and pitch 2.0 micro.m. The maximum pitch can be consider as 5.0 micro.m and air hole diameter is 9.0 micro.m. Transparent boundary condition (TBC) is proposed here for the calculation of Refractive index of HPCF