  Nonreciprocal devices that allow the light propagation in only one direction
are indispensable in photonic circuits and emerging quantum technologies.
Contemporary optical isolators and circulators, however, require large size or
strong magnetic fields because of the general weakness of magnetic light-matter
interactions, which hinders their integration into photonic circuits. Aiming at
stronger magneto-optical couplings, a promising approach is to utilize
nonlinear optical processes. Here, we demonstrate nonreciprocal magnetoelectric
second harmonic generation (SHG) in CuB2O4. SHG transmission changes by almost
100% in a magnetic-field reversal of just 10 mT. The observed nonreciprocity
results from an interference between the magnetic-dipole- and
electric-dipole-type SHG. Even though the former is usually notoriously smaller
than the latter, it is found that a resonantly enhanced
magnetic-dipole-transition has a comparable amplitude as non-resonant
electric-dipole-transition, leading to the near-perfect nonreciprocity. This
mechanism could form one of the fundamental bases of nonreciprocity in
multiferroics, which is transferable to a plethora of magnetoelectric systems
to realize future nonreciprocal and nonlinear-optical devices.
