  Grating magneto-optical traps are an enabling quantum technology for portable
metrological devices with ultracold atoms. However, beam diffraction efficiency
and angle are affected by wavelength, creating a single-optic design challenge
for laser cooling in two stages at two distinct wavelengths - as commonly used
for loading e.g. Sr or Yb atoms into optical lattice or tweezer clocks. Here,
we optically characterize a wide variety of binary gratings at different
wavelengths to find a simple empirical fit to experimental grating diffraction
efficiency data in terms of dimensionless etch depth and period for various
duty cycles. The model avoids complex 3D light-grating surface calculations,
yet still yields results accurate to a few percent across a broad range of
parameters. Gratings optimized for two (or more) wavelengths can now be
designed in an informed manner suitable for a wide class of atomic species
enabling advanced quantum technologies.
