A multifocal IOL (M-IOL) has a phase-altering characteristic that can control the diffraction and interference of light propagating there through to effect multifocality and extended depth of focus (EDOF). The embodied IOLs include engineered, discrete phase profiles on one or both of the anterior and posterior surfaces of the lens to intentionally manipulate the light in a designated manner. A design method for defining the discrete phase profile on the lens surface. The engineered phase profile is constructed by concentric annular zones having an abrupt step jump at the trailing circumferential edge of each zone. An optical modeling method to simulate the optical performance of the embodied IOLs in an optical ray tracing environment.