In this paper, we optimize the geometries of some 2D photonic crystal waveguides to increase their single-mode bandwidths for TE and TM polarizations. Using the Plane Wave Expansion (PWE) method combined with optimization algorithm, we find the local maxima as well as the global maximum. A photonic crystal waveguide geometry is proposed which has a single-mode normalized bandwidth of 41% for TM polarization. This value is about 7% greater than the corresponding value for the commonly used square lattice of dielectric rods in which a row is removed. Also, some waveguide geometries are proposed for TE polarization and it is shown that one of these geometries can provide a single-mode bandwidth of 39%, while the widest bandwidth reported so far for the TE case is 21%. The dielectric material used for both cases is GaAs with a dielectric constant of 11.4.

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