  Electron Cyclotron Emission (ECE) of different frequencies originates at
different locations in non-uniformly magnetized plasmas. For simultaneous
observation of multiple ECE frequencies from the outside edge of a toroidal
plasma confinement device (e.g. a tokamak), the focal length of the collecting
optics should increase with the frequency to maximize the resolution on a line
of sight along the magnetic field gradient. Here we present the design and
numerical study of a zoned metamaterial lens with such characteristics, for
possible deployment with the 83-130 GHz ECE radiometer in the DIII-D tokamak.
The lens consists of a concentric array of miniaturized element phase-shifters.
These were reverse-engineered starting from the desired Gaussian beam waist
locations and further optimized to account for diffraction and finite-aperture
effects that tend to displace the waist. At the same time we imposed high and
uniform transmittance, averaged over all phase-shifters. The focal length is
shown to increase from 1.37 m to 1.97 m over the frequency range of interest,
as desired for low-field DIII-D discharges (B = -1.57 T). Retracting the lens
to receded positions rigidly moves the waists accordingly, resulting in a good
match -within a fraction of the Rayleigh length- of the EC-emitting layer
positions at higher fields (up to B = -2.00 T). Further, it is shown how
varying the lens aperture might move the waists "non-rigidly" to better match
the non-rigid movement of the EC-emitting layers with the magnetic field. The
numerical method presented is very general and can be used to engineer any
dependence of the focal length on the frequency, including zero or minimal
chromatic aberration.
