  The engineering of light confinement is a topic with a long history in optics
and with significant implications for the control of light-matter interaction.
In inhomogeneous and disordered media, however, multiple scattering prevents
the application of conventional approaches for the design of light fields with
desired properties. This is because any local change to such a medium typically
affects these fields in a non-local and complicated fashion. Here, we present a
theoretical methodology for tailoring an inhomogeneous one-dimensional (1D)
Hermitian dielectric index distribution, such that the intensity profile of an
incoming light field can be controlled purely locally, i.e., with little or no
influence on the field profile outside of a designated region of interest.
Strongly increasing or decreasing the light's intensity at arbitrary positions
inside the medium thereby becomes possible without, in fact, changing the
external reflectance or transmittance of the medium. These local modifications
of the medium can thus be made undetectable to unidirectional far field
measurements. We apply our approach to locally control the confinement of light
inside 1D materials with inhomogeneous continuous refractive index profiles and
extend it to multilayer films as well as to chains of coupled micro-resonators.
