The universal dispersion graph and mode field profile of different transverse electric (TE)/transverse magnetic (TM) modes are evaluated of the α-power refractive index (RI) profile curved optical waveguide. To maintain the high-power confinement in the core high refractive index contrast guiding approximation condition is applied. The finite difference method in conjunction with the conformal transformation technique has been devised to extract the TE/TM modes of a bent optical waveguide. A very efficient Eigenvalue/Eigenvector solver algorithm based on MATLAB software has been devised to extract allowed TE/TM modes of a bent optical waveguide. It has been found that upon bending of optical waveguide multimode nature emerges with good mode conversion capability. To avoid the radiation mode generation perfectly absorbing boundary has been applied in our numerical technique so the modes remain guided throughout of computational window. The objective is then to study the TE/TM mode cut-off conditions of curved waveguides irrespective of their RI profile parameters and curvature. The effect of waveguide bending on mode field profile and power confinement factor is also discussed.