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.
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