  Two-dimensional (2D) heterostructures integrated into nanophotonic cavities
have emerged as a promising approach towards novel photonic and opto-electronic
devices. However, the thickness of the 2D heterostructure has a strong
influence on the resonance frequency of the nanocavity. For a single cavity,
the resonance frequency shifts approximately linearly with the thickness. Here,
we propose to use the inherent non-linearity of the mode coupling to render the
cavity mode insensitive to the thickness of the 2D heterostructure. Based on
the coupled mode theory, we reveal that this goal can be achieved using either
a homoatomic molecule with a filtered coupling or heteroatomic molecules. We
perform numerical simulations to further demonstrate the robustness of the
eigenfrequency in the proposed photonic molecules. Our results render
nanophotonic structures insensitive to the thickness of 2D materials, thus
owing appealing potential in energy- or detuning-sensitive applications such as
cavity quantum electrodynamics.
