  Controlling the flow of broadband electromagnetic energy at the nanoscale
remains a critical challenge in optoelectronics. Surface plasmon polaritons (or
plasmons) provide subwavelength localization of light, but are affected by
significant losses. On the contrary, dielectrics lack a sufficiently robust
response in the visible to trap photons similar to metallic structures.
Overcoming these limitations appears elusive, as it implies devising a path to
circumvent causality in the quantum-mechanical form of matter. Here we
demonstrate that addressing this problem is possible if we employ a novel
approach based on suitably deformed reflective metaphotonic structures. The
complex geometrical shape engineered in these reflectors emulates nondispersive
index responses, which can be inverse-designed following arbitrary form
factors. We discuss the realization of essential components such as resonators
with an ultra-high refractive index of $n=100$ in diverse profiles. These
structures support localization of light in the form of bound states in the
continuum (BIC), fully localized in air, in a platform in which all refractive
index regions are physically accessible. We discuss our approach to sensing
applications, designing a class of sensors where the analyte directly contacts
areas of ultra-high refractive index. Leveraging this feature, we report
differential sensitivities up to $350$~nm/RIU in structures with footprints of
approximately one micron. These performances are two times better than the
closest competitor with a similar form factor. Inversely designed reflective
metaphotonics offers a flexible technology for controlling broadband light,
supporting optoelectronics' integration with large bandwidths in circuitry with
miniaturized footprints.
