  We predict that a liquid crystal/silver nanoparticles mixture can be designed
so that, in a frequency range, its effective ordinary and extraordinary
permittivities have real parts of different signs. We exploit this result to
design a nano-photonic device obtained by sandwiching a few hundred nanometer
thick slab of the proposed mixture between two silica layers. By resorting to
full-wave simulations, we show that, by varying the direction of an externally
applied electric field, the device can be used as an optical modulator since
its transmissivity can be switched between 0.02 and 0.4 at a wavelength close
to the frequency range where the medium is indefinite. The device functionality
physically stems from the fact the orientation of the hyperbola characterizing
extraordinary waves within the indefinite medium follows the applied electric
field direction and therefore, if the hyperbola asymptote is nearly normal to
the slab, full switch between evanescent and homogeneous propagating waves can
be achieved within the medium.
