  Tunable and multi-functional nanophotonic devices are used for applications
from beam steering to sensing. Yet little is understood about fundamental
limits to their functionality. The difficulty lies with the fact that it is a
single structure that must exhibit optimal response over multiple scenarios. In
this article, we present a general theoretical framework for understanding and
computing fundamental limits to multi-functional nanophotonic response.
Building from rapid recent advances in bounds to light-matter interactions, we
show that after rewriting the design problems in terms of polarization fields,
the introduction of suitable cross-correlation constraints imposes the crucial
"single-structure" criteria. We demonstrate the utility of this approach for
two applications: reflectivity contrast for optical sensing, and maximum
efficiency for optical beam switching. Our approach generalizes to any active
or multi-functional design in linear optics.
