  Nonlinear frequency conversion plays a crucial role in advancing the
functionality of next-generation optical systems. Portable metrology references
and quantum networks will demand highly efficient second-order nonlinear
devices, and the intense nonlinear interactions of nanophotonic waveguides can
be leveraged to meet these requirements. Here we demonstrate second harmonic
generation (SHG) in GaAs-on-insulator waveguides with unprecedented efficiency
of 40 W$^{-1}$ for a single-pass device. This result is achieved by minimizing
the propagation loss and optimizing phase-matching. We investigate
surface-state absorption and design the waveguide geometry for modal
phase-matching with tolerance to fabrication variation. A 2.0 $\mu$m pump is
converted to a 1.0 $\mu$m signal in a length of 2.9 mm with a wide signal
bandwidth of 148 GHz. Tunable and efficient operation is demonstrated over a
temperature range of 45 $^{\circ}$C with a slope of 0.24 nm/$^{\circ}$C.
Wafer-bonding between GaAs and SiO$_2$ is optimized to minimize waveguide loss,
and the devices are fabricated on 76 mm wafers with high uniformity. We expect
this device to enable fully integrated self-referenced frequency combs and
high-rate entangled photon pair generation.
