We propose a long period grating (LPG) characterized by specially designed refractive index (RI) profile in which each grating plane is tilted at increasing angles, as moving away from the center of symmetry of the structure towards its both edges. This internally manufactured geometric structure, which basically simulates the bending of an optical fiber, increases the RI sensitivity of an LPG to the external medium. We experimentally demonstrate a three-fold improvement in the RI sensitivity, thus providing the basis for another step forward in the field of RI sensors based on optical fiber gratings. (C) 2013 AIP Publishing LLC.