  Dispersion problem has always constrained the development of see-through
near-eye displays with diffractive waveguide. Here, we propose a design method
and optical systems for achromatic surface microstructure composed with a
triple-carved-sub-grating. The triple-carved-sub-grating with specified period
is designed based on rigorous coupled wave theory, corresponding to Red, Green
and Blue (RGB) wavelengths, respectively, with diffraction efficiencies of
1st(-1st) orders reach 47.5% under TE polarization. The surface microstructure
with period of 18.9um is realized by integrating the three sub-gratings
together, and it is verified numerically that the diffractive angle of RGB
wavelengths is 35{\deg} and the crosstalk is less than 4.5% under the normal
incidence of TE polarization, which imply the surface microstructure diffracts
the certain RGB wavelengths achromatically. Via proper duplication it could be
utilized as the combining optics of diffractive-waveguide near-eye display and
head-up display because of its light and compact features.
