We present a simple method to fabricate concave surface at the optical fiber's end facet. Radii of etched surface curvature at the fiber tips can be controlled by the derived photothermal effects from a guided laser beam. The self-aligned concave surfaces are created by the temperature-dependent wet etching process at the end of the cleaved fiber facet. The fabricated concave shapes were verified by measuring the free space optical beam radiation divergence profiles using a beam profiler, which show good correlation with the applied optical power during the etching process.