  Nonlinear Kerr micro-resonators have enabled fundamental breakthroughs in the
understanding of dissipative solitons, as well as in their application to
optical frequency comb generation. However, the conversion efficiency of the
pump power into a soliton frequency comb typically remains below a few percent.
We introduce a hybrid Mach-Zehnder ring resonator geometry, consisting of a
micro-ring resonator embedded in an additional cavity with twice the optical
path length of the ring. The resulting interferometric back coupling enables to
achieve an unprecedented control of the pump depletion: pump-to-frequency comb
conversion efficiencies of up to 98\% of the usable power is experimentally
demonstrated with a soliton crystal comb. We assess the robustness of the
proposed on-chip geometry by generating a large variety of dissipative Kerr
soliton combs, which require a lower amount of pump power to be accessed, when
compared with an isolated micro-ring resonator with identical parameters.
Micro-resonators with feedback enable accessing new regimes of coherent soliton
comb generation, and are well suited for comb applications in astronomy,
spectroscopy and telecommunications.
