  Extended depth of focus (EDOF) lenses are important for various applications
in computational imaging and microscopy. In addition to enabling novel
functionalities, EDOF lenses can alleviate the need for stringent alignment
requirements for imaging systems. Existing EDOF lenses, however, are often
inefficient or produce an asymmetric point spread function (PSF) that blurs
images. Inverse design of nanophotonics, including metasurfaces, has generated
strong interest in recent years owing to its potential for generating exotic
and innovative optical elements, which are generally difficult to model
intuitively. Using adjoint optimization-based inverse electromagnetic design,
in this paper, we designed a cylindrical metasurface lens operating at ~ 625nm
with a depth of focus exceeding that of an ordinary lens. We validated our
design by nanofabrication and optical characterization of silicon nitride
metasurface lenses (with lateral dimension of 66.66 {\mu}m) with three
different focal lengths (66.66 {\mu}m,100 {\mu}m,133.33 {\mu}m). The focusing
efficiencies of the fabricated extended depth of focus metasurface lenses are
similar to those of traditional metalenses.
