We report on a simple experimental scheme based on a pair of cylindrical lenses (convex and concave) of the same focal length and common optical elements, producing high power optical beams in 1D and/or 2D Airy intensity profiles with laser polarization as the control parameter. Using an ultrafast Yb-fiber laser at 1064 nm of average power of 5 W in a Gaussian spatial profile and pulse width of ∼180 fs, we have generated 1D and 2D Airy beams at an efficiency of 80% and 70%, respectively, and a pulse width of ∼188 and ∼190 fs, respectively. We have measured the transverse deflection rate of 1D and 2D beams to be ∼5.0×10-5 1/mm and ∼2.0×10-5 1/mm, respectively. Simply rotating the polarization state of the 1D cubic phase modulated beam in the experiment, we can produce 1D and 2D Airy beams on demand. Using a 5 mm long bismuth borate (BiB3O6), we have also studied frequency-doubling characteristics of both 1D and 2D Airy beams. Like the 2D Airy beam, the 1D Airy beam also produces a frequency-doubled 1D Airy and an additional 1D spatial cubic structure. Like the Gaussian beams, we have observed the focusing dependence of conversion efficiency for both 1D and 2D Airy beams, producing green 1D and 2D Airy beams of output powers in excess of 110 and 150 mW for 3.4 and 2.8 W of fundamental power, respectively.