  In the extreme near-field, when the spatial extension of the atomic
wavefunction is no longer negligible compared to the atom-surface distance, the
dipole approximation is no longer sufficient to describe Casimir-Polder
interactions. Here we calculate the higher-order, quadrupole and octupole,
contributions to Casimir-Polder energy shifts of Rydberg atoms close to a
dielectric surface. We subsequently investigate the effects of these
higher-order terms in thin-cell and selective reflection spectroscopy. Beyond
its fundamental interest, this new regime of extremely small atom surface
separations is relevant for quantum technology applications with Rydberg or
surface-bound atoms interfacing with photonic platforms.
