Free-fall of photons in a planar optical cavity

We consider a planar optical cavity with its main axis oriented perpendicular to the earth's local gravity field. We examine the motion of a wavepacket of light trapped within the cavity spacer under the action of gravity. Within a relativistic framework, we find that the wavepacket initially at rest in terms of in-plane group velocity is accelerated by $g$ at early time in agreement the non-relativistic limit of free-fall. We show that this phenomenon is a manifestation of gravitational redshift, applied on photons at rest within the cavity.