  Nonlinear light-matter interactions and their applications are constrained by
properties of available materials. The use of metamaterials opens the way to
achieve precise control over electromagnetic properties at a microscopic level,
providing new tools for experimental studies of complex nonlinear phenomena in
photonics. Here a doubly resonant nonlinear meta-atom is proposed, analyzed and
characterized in the GHz spectral range. The underlying structure is composed
of a pair of split rings, resonant at both fundamental and nonlinear
frequencies. The rings share a varactor diode, which serves as a microscopic
source of nonlinearity. Flexible control over the coupling and near- and
far-field patterns are reported, favoring the doubly resonant structure over
other realizations. Relative efficiencies of the second and third harmonics,
generated by the diode, are tailored by dint of the double-ring geometry,
providing a guideline for selecting one frequency against another, using the
design of the auxiliary structures. The on-demand control over the microscopic
nonlinear properties enables developing a toolbox for experimental emulation of
complex nonlinear phenomena.
