Experimental demonstration of gauge confinement in point-wise shifted periodic potentials

Periodic structures along the propagation direction of light yields the very well known Bragg reflection. When the wavelength is away from any Bragg resonance, in first approximation optical beams perceive the average value of the refractive index. This idea is used, for example, in realizing the so called segmented or Bragg waveguides, once the refractive index is free to vary also across the transverse direction. Following this model, light should freely diffract if the average value of the refractive index is uniform across the wavefront, see Fig. 1(a). The above conclusion, even if quite appealing, is factually wrong due to the emergence of an additional phase contribution due to the Kapitza effect: the local transverse gradient induces a modulation of the transverse wave vector; when the longitudinal average of the effective kinetic energy (thus involving the square of the transverse wave vector) is computed, a longitudinally-independent effective potential emerges. In agreement with the physical origin of the Kapitza effect, the potential is proportional to the square of the modulation period and to the square of the transverse derivative of the refractive index. We already experimentally demonstrated the existence of the Kapitza guiding using synthetic lattice in fiber loops [1]. In this contribution we aim to extend the Kapitza confinement to the case of a point-dependent delay applied to the periodic potential, see Fig. 1(b). Physically speaking, a local gradient is now present even if the amplitude of the periodic oscillation does not vary on the transverse direction [2]. The new contribution to the delay can be interpreted as a gauge field [3,4] due to the local shifting of the propagation coordinate, providing in turn a new term in the Kapitza potential proportional to the square of the delay derivative. We confirmed the existence of this new way to manipulate waves using BPM numerical simulations and experiments in fiber loops using trains of pulses, see fig. 1(c,d). Experimental results are in good agreement with the theoretical predictions, see Fig. 1(e). In a broader perspective, we show that different symmetries in the index profile and delay allow the control of wave motion both on short and long scales.