  We report a new type of symmetry-breaking bifurcation of solitons in optical
systems with parity-time-symmetric potentials. In this bifurcation, the two
bifurcated branches of asymmetric solitons exhibit opposite stability, which
contrasts all previous symmetry-breaking bifurcations in conservative and
non-conservative systems. We show that this novel symmetry-breaking bifurcation
can be exploited to achieve unidirectional propagation of high-intensity light
beams in parity-time-symmetric potentials.
