  We discuss the semi-classical transverse trapping of waves by means of an
inhomogeneous gauge field. In the proposed scheme a temporally-periodic
perturbation is shifted in time, the imparted delay being dependent on the
transverse direction. We show that, due to the Kapitza effect, an effective
potential proportional to the square of the transverse derivative of the delay
arises. On a more physical ground, the delay induces a transversely-varying
periodic force acting on the wave, in turn providing a phase delay owing to the
local modulation of the kinetic energy. Our results are quite generic and can
find application in several fields, ranging from cold atoms to optics:
accordingly, an experimental proof-of-principle is provided using an optical
set-up based upon fiber loops.

Optics;Quantum Physics