  Asymmetric mode transformation in waveguide is of great significance for
on-chip integrated devices with one-way effect, while it is challenging to
achieve asymmetric nonlinear-mode-conversion (NMC) due to the limitations
imposed by phase-matching. In this letter, we theoretically proposed a new
scheme for realizing asymmetric NMC by combining frequency-doubling process and
periodic PT symmetric modulation in an optical waveguide. By engineering the
one-way momentum from PT symmetric modulation, we have demonstrated the
unidirectional conversion from pump to second harmonic with desired guided
modes. Our findings offer new opportunities for manipulating nonlinear optical
fields with PT symmetry, which could further boost more exploration on on-chip
nonlinear devices assisted by non-Hermitian optics.
