  Deep-subwavelength all-dielectric composite materials are believed to tightly
obey the Maxwell Garnett effective medium theory. Here, we demonstrate that the
Maxwell Garnett theory could break down due to evanescent fields in
deep-subwavelength dielectric structures. By utilizing two- and
three-dimensional dielectric composite materials with inhomogeneities at the
scale of {\lambda}/100, we show that local evanescent fields generally occur
nearby the dielectric inhomogeneities. When tiny absorptive constituents are
placed there, the absorption and transmission of the whole composite will show
strong dependence on the positions of the absorptive constituents. The Maxwell
Garnett theory fails to predict such position-dependent characteristics,
because it averages out the evanescent fields. By taking the distribution of
the evanescent fields into consideration, we made a correction to the Maxwell
Garnett theory, such that the position-dependent characteristics become
predictable. We reveal not only the breakdown of the Maxwell Garnett theory,
but also a unique phenomenon of "invisible" loss induced by the prohibition of
electric fields at deep-subwavelength scales. Our work promises a route to
control the macroscopic properties of composite materials without changing
their composition, which is beyond the traditional Maxwell Garnett theory.
