Coupling of cavities: the way to impose control over their modes

In this work, we demonstrate that the compound mode properties of coupled photonic-crystal cavities can depend critically on the interplay of distance between cavities and their longitudinal shifts. Thus the robust control over the cavity modes can be imposed. The simple coupled-mode theory employed for such systems predicts a peculiar behavior of band dispersion in the slow light regime at the photonic band-edge. In particular, it reveals an interesting effect that the frequency detuning of the fundamental supermodes in the coupled cavities can be reduced down to zero. We anticipate that this property will be generic for side-coupled cavity systems irrespectively of the individual cavity design, e.g. point-defect cavities in a photonic crystal or linear cavities in one-dimensional arrays of elements (rods or holes). We report here about the finite-difference frequency-domain method (FDFD) developed by us to analyze nanocavities with a very high Q-factor. The method is utilized to confirm by simulations the coupled-mode theory predictions. As an example we choose coupled cavities in one-dimensional periodic arrays of holes in dielectric nanowires known also as nanobeams.