We have studied the effects of interface on polarization dependence of waveguide and designed the polarization independent 2-dimensional waveguides on InP for arrayed waveguide grating. To figure out the effects of interface on polarization dependence, we have solved the 1-dimensional wave equation using a transfer matrix method. It is shown that the birefringence becomes stronger as the number of interfaces increases. In order to design polarization independent 2-dimensional waveguides, we have used effective index method. The structures considered are ridge type, raised strip type, and buried type waveguide. In the cases of ridge and raised strip type, conventional effective index method was used. In the case of buried type corrected effective index method was used. We have determined the height and width of waveguides such that the waveguides become polarization independent.