Notes:

Although most lenses are created with glass or plastic that has uniform refractive index and a curved shape, some lenses are made with perfectly flat surfaces but have non-uniform refractive index. Such lenses can still shape light wavefronts because they retard the light more in some places than in others.

For example, if the refractive index is highest in the middle of a lens but then declines gradually towards the edge of the lens, then light will be retarded in the center more than at the edge. Consequently, the plane wave will become curved, just like in the conventional lens, and so focus the light down to a point.

This basic principle of using variable refractive index instead of curved surfaces to make lenses is how a liquid crystal lens works.