Optical waveguides based upon a gauge field

Photons are neutral particles, thus they are not affected by magnetic fields. Nonetheless, light propagation under the action of an effective magnetic field has been demonstrated [1] , [2] . This counter-intuitive result can be grasped by thinking in terms of gauge fields, that is, a point-wise change of the framework. Synthetic magnetic fields have been generated by introducing phase shifts in coupled resonators [1] or by longitudinal modulation of arrays of coupled waveguides [2] . Intuitively, an inhomogeneous gauge field can induce a transverse gradient in the optical phase such that it compensates the spreading by diffraction, eventually forming an optical waveguide. As a matter of fact, in discrete systems this type of light trapping has been first theoretically predicted in coupled resonators [3] , and very recently experimentally demonstrated in femtosecond-written waveguides [4] . Here, we propose a new method to realize gauge-based continuous waveguides using a longitudinally periodic modulation of the refractive index [5] featuring a point-wise shift; specifically, the phase of the periodic modulation varies along the cross-section of the waveguide and represents the gauge field in our proposal.