  Optical-field emission from nanostructured solids such as subwavelength
nanoantennas can be leveraged to create sub-femtosecond, PHz-scale electronics
for optical-field detection. One application that is of particular interest is
the detection of an incident optical pulse's carrier-envelope phase. Such
carrier-envelope-phase detection requires few-cycle, broadband optical
excitation where the resonant properties of the nanoantenna can strongly alter
the response of the near field in time. Little quantitative investigation has
been performed to understand how the geometry and resonant properties of the
antennae should be tuned to enhance the carrier-envelope phase sensitivity and
signal to noise ratio. Here we examine how the geometry and resonance frequency
of planar plasmonic nanoantennas can be engineered for enhancing the emitted
carrier-envelope-phase-sensitive photocurrent when driven by a few-cycle
optical pulse. We find that with the simple addition of curved sidewalls
leading to the apex, and proper tuning of the resonance wavelength, the net
CEP-sensitive current per nanoantenna can be improved by $5$-$10\times$, and
the signal-to-noise-ratio by $50$-$100\times$ relative to simple triangular
antennas operated on resonance. Our findings will inform the next generation of
nanoantenna designs for emerging applications in ultrafast photoelectron
metrology and petahertz electronics.
