  Quadratic optical parametric processes form the foundation for a variety of
applications related to classical and quantum frequency conversion, which have
attracted significant interest recently in on-chip implementation. These
processes rely on phase matching among the interacting guided modes, and
refractive index engineering has been a primary approach for this purpose.
Unfortunately, the modal phase matching approaches developed so far only
produce parametric generation with fairly low efficiencies, due to the
intrinsic modal mismatch of spatial symmetries. Here we propose a universal
design and operation principle for highly efficient optical parametric
generation on integrated photonic platforms. By introducing spatial symmetry
breaking into the optical nonlinearity of the device, we are able to
dramatically enhance the nonlinear parametric interaction to realize an
extremely high efficiency. We employ this approach to design and fabricate a
heterogeneous titanium oxide/lithium niobate nanophotonic waveguide that is
able to offer second-harmonic generation with a theoretical conversion
efficiency as high as 2900% W$^{-1}$cm$^{-2}$, which enables us to
experimentally achieve a conversion efficiency of 36.0% W$^{-1}$ in a waveguide
only 2.35 mm long, corresponding to a recorded normalized efficiency of 650%
W$^{-1}$cm$^{-2}$ that is significantly beyond the reach of conventional modal
phase matching approaches. Unlike nonlinearity domain engineering that is
material selective, the proposed operation principle can be flexibly applied to
any other on-chip quadratic nonlinear platform to support ultra-highly
efficient optical parametric interactions, thus opening up a great avenue
towards extreme nonlinear and quantum optics with great potentials for broad
applications in energy efficient nonlinear and quantum photonic signal
processing.
