  We consider the coupling of light, via an optical cavity, to two-dimensional
atomic arrays whose lattice spacing exceeds the wavelength of the light. Such
'superwavelength' spacing is typical of optical tweezer arrays. While
subwavelength arrays exhibit strong atom-photon coupling, characterized by high
optical reflectivity in free space, the coupling efficiency of superwavelength
arrays is reduced due to collective scattering losses to high diffraction
orders. We show that a moderate-finesse cavity overcomes these losses. As the
scattering losses peak at certain discrete values of the lattice spacing, the
spacing can be optimized to achieve efficient atom-photon coupling in the
cavity. Our cavity-QED theory properly accounts for collective dipolar
interactions mediated by the lossy, non-cavity-confined photon modes and for
finite-size effects of both the array and the light field. These findings pave
the way to harnessing the versatility of tweezer arrays for efficient
atom-photon interfaces in applications of quantum computing, networking, and
nonlinear optics.
