  Superoscillations are a phenomenon where a band-limited wave may locally
oscillate faster than its highest Fourier component. They are a product of
destructive interference between the wave's constituent harmonics. In this
article, we demonstrate that superoscillations enable a new functionality in
linear optical sensing -- the 100-fold enhancement in the optical contrast of
the terahertz wave passing through two similar samples. To achieve this
enhancement, we optimize the optical contrast in the time domain in a short
observation window by varying the relative phases between the fundamental
harmonics that make up the input terahertz wave. We find that the contrast is
maximized when the wave intensity is minimized locally within the observation
window, which naturally leads to the emergence of the superoscillations. We
observe the 100-fold contrast enhancement both in our numerical simulations
with Gaussian time-domain harmonics and in our experimental realization with
narrow-band quasi-sinusoidal terahertz harmonics. Our results will have
profound influence on terahertz sensing and imaging applications in medicine,
pharmaceuticals, stand-off hazard detection, and nondestructive evaluation.
