Applying plane wave expansion method to one dimensional multilayer system formed from alternating layers of GaAs and air, a defect mode was artificially introduced by removing a GaAs layer at the centre of a supercell and the band structures and mode field distributions were obtained. The defect mode normalized frequency was 0.28. The parameters for developing a Febry-Perot filter in the visible frequencies are given. The point defects in a two dimensional square lattice formed from GaAs rods of radius 0.16a in air was created by removing one GaAs rod at the centre of a supercell and also by increasing the centre GaAs rod radius to 0.5a. The removal of the rod folded the band structure 25 times creating a localized evanescent defect mode. The increment of the centre GaAs rod radius led to five defect bands inside the band gap with one degenerate state creating a monopole, two quadrupoles and two hexapoles. Evolution of the defect modes with the variation of the radius of GaAs rod is also presented.