Gradient-index Alvarez lenses (GALs), a new,
to the best of our knowledge, type of freeform optical component, are
surveyed in this work for their unique properties in generating
variable optical power. GALs display similar behavior to conventional
surface Alvarez lenses (SALs) by means of a freeform refractive index
distribution that has only recently been achievable in fabrication. A
first-order framework is described for GALs including analytical
expressions for their refractive index distribution and power
variation. A useful feature of Alvarez lenses for introducing bias
power is also detailed and is helpful for both GALs and SALs. The
performance of GALs is studied and the value of three-dimensional
higher-order refractive index terms is demonstrated in an optimized
design. Last, a fabricated GAL is demonstrated along with power
measurements agreeing closely with the developed first-order
theory.