  The effect of a Kerr nonlinearity on dynamical tunneling is studied, using
coupled whispering gallery modes in an optical microcavity. The model system
that we have chosen is the 'add-drop filter', which comprises an optical
microcavity and two waveguide coupled to the cavity. Due to the evanescent
field's scattering on the waveguide, the whispering gallery modes in the
microcavity form doublets, which manifest themselves as splittings in the
spectrum. As these doublets can be regarded as a spectral feature of dynamical
tunneling between two different dynamical states with a spatial overlap, the
effect of a Kerr nonlinearity on the doublets is numerically investigated in
the more general context of the relationship between cubic nonlinearity and
dynamical tunneling. Within the numerical realization of the model system, it
is observed that the doublets shows a bistable transition in its transmission
curve as the Kerr-nonlinearity in the cavity is increased. At the same time,
one rotational mode gets dominant over the other one in the transmission, since
the two states in the doublet have uneven linewidths. By using coupled mode
theory, the underlying mode dynamics of the phenomena is theoretically modelled
and clarified.
