The fabrication of internal diffraction gratings with photoinduced refractive index modification in transparent materials was demonstrated using low-density plasma formation excited by a femtosecond (130 fs) Ti: sapphire laser (${lambda}_p$=800 nm). The refractive index modifications with diameters ranging from $1{mu}m$ to $3{mu}m$ were photoinduced after plasma formation occurred upon irradiation with peak intensities of more than $2.0{ imes}10^{13}W/cm^2$. The graded refractive index profile was fabricated to be a symmetric around from the center of the point at which low-density plasma occurred.