  Theoretical bounds are commonly used to assess the limitations of photonic
design. Here we introduce a more active way to use theoretical bounds,
integrating them into part of the design process and identifying optimal system
parameters that maximize the efficiency limit itself. As an example, we
consider wide-field-of-view high-numerical-aperture metalenses, which can be
used for high-resolution imaging in microscopy and endoscopy, but no existing
design has achieved a high efficiency. By choosing aperture sizes to maximize
an efficiency bound, setting the thickness according to a thickness bound, and
then performing inverse design, we come up with high-numerical-aperture (NA =
0.9) metalens designs with record-high 98% transmission efficiency and 92%
Strehl ratio across all incident angles within a 60-deg field of view, reaching
the maximized bound. This maximizing-efficiency-limit approach applies to any
multi-channel system and can help a wide range of optical devices reach their
highest possible performance.
