  The optical properties of BAlN and BGaN ternary alloys are investigated using
first-principle calculation. Hybrid density functional theory is applied to
determine the refractive indices of different alloys. A peculiar non-linear
behavior of the static refractive index as a function of boron composition is
found. The results of this calculation are interpolated to generate a three
dimensional dataset, which could be used for designing a myriad of strained and
strain-free optoelectronic and photonic devices. This is then used to find a
lattice-matched heterostructure optimized for DBR applications
(B0.108Ga0.892N/AlN). A DBR design with 25 pairs at a wavelength of 375 nm is
found to have peak reflectivity of 99.8% and a bandwidth of 26 nm.
