  We demonstrate the design, fabrication and characterization of nanobeam
photonic crystal cavities in (111)-GaAs with multiple high quality factor
modes, with large frequency separations (up to 740 nm in experiment, i.e., a
factor of 1.5 and up to an octave in theory). Such structures are crucial for
efficient implementation of nonlinear frequency conversion. Here, we employ
them to demonstrate sum frequency generation from 1300 nm and 1950 nm to 780
nm. These wavelengths are particularly interesting for quantum frequency
conversion between Si vacancy centers in diamond and the fiber optic network.
