In this work, three double-focal configurations are obtained by considering different phase and/or amplitude modulations. First, we study a bifocal lens with only a single mixed-phase profile. Second, we define an ophthalmic lens achieved by dividing of the metasurface into two sub-sections. Each section has its own phase profile. Finally, for the third step, an amplitude mask is implemented by the ophthalmic lens. In the latter double-focal lens, called an engineered ophthalmic lens, the amplitude mask and phase profiles should simultaneously be introduced by the patterning of metatoms.

For the first case, to design a bifocal metalens, the phase profile of \(\varphi_1(r)\) should be imparted by the metasurface.