  We report on the demonstration of an effective, nonlinearity-induced
non-reciprocal behavior in a single non-magnetic multi-mode Taiji resonator.
Non-reciprocity is achieved by a combination of an intensity-dependent
refractive index and of a broken spatial reflection symmetry. Continuous wave
power dependent transmission experiments show non-reciprocity and a
direction-dependent optical bistability loop. These can be explained in terms
of the unidirectional mode coupling that causes an asymmetric power enhancement
in the resonator. The observations are quantitatively reproduced by a numerical
finite-element theory and physically explained by an analytical coupled-mode
theory. This nonlinear Taiji resonator has the potential of being the building
block of large arrays where to study topological and/or non-Hermitian physics.
This represents an important step towards the miniaturization of nonreciprocal
elements for photonic integrated networks.
