  The light-matter interaction associated with a two-dimensional (2D) excitonic
transition coupled to a zero-dimensional (0D) photonic cavity is fundamentally
different from coupling localized excitations in quantum dots or color centers,
which have negligible spatial extent compared to the cavity-confined mode
profile. By calculating the radiation-matter coupling of the exciton transition
of a surface deposited 2D material and a 0D photonic crystal nanobeam mode, we
found that there is an optimal spatial extent of the monolayer material that
maximizes such an interaction strength due to the competition between
minimizing the excitonic envelope function area and maximizing the total
integrated field. This is counter to the intuition from the Dicke model, where
the oscillator strength is expected to monotonically grow with the number of
oscillators, which correlates to the monolayer area assuming the excitonic
wavefunction is delocalized over the entire quantum well. We also found that at
near zero exciton-cavity detuning, the direct transmission efficiency of a
waveguide-integrated cavity can be severely suppressed, which suggests
performing experiments by using a side-coupled cavity to get better
performances.
