  Today's best optical lattice clocks are based on the spectroscopy of trapped
alkaline-earth-like atoms such as ytterbium and strontium atoms. The
development towards mobile or even space-borne clocks necessitates concepts for
the compact laser-cooling and trapping of these atoms with reduced laser
requirements. Here we present two compact and robust achromatic mirror
structures for single-beam magneto-optical trapping of alkaline-earth-like
atoms using two widely separated optical cooling frequencies. We have compared
the trapping and cooling performance of a monolithic aluminium structure that
generates a conventional trap geometry to a quasi-planar platform based on a
periodic mirror structure for different isotopes of Yb. Compared to prior work
with strontium in non-conventional traps, where only bosons were trapped on a
narrow line transition, we demonstrate two-stage cooling and trapping of a
fermionic alkaline-earth-like isotope in a single-beam quasi-planar structure.
