  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, the multiple scattering of
light prevents the application of conventional approaches for the design of
modes with desired properties. This is because any local change to such a
medium typically affects the entire modal structure 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 methodology
to locally control light's confinement inside 1D materials with disordered
continuous refractive index profiles and extend it to discrete 1D stacks of
dielectric slabs and chains of coupled micro-resonators.
