  Frequency combs spanning over an octave have been successfully demonstrated
in Kerr nonlinear microresonators on-chip. These micro-combs rely on both
engineered dispersion, to enable generation of frequency components across the
octave, and on engineered coupling, to efficiently extract the generated light
into an access waveguide while maintaining a close to critically-coupled pump.
The latter is challenging as the spatial overlap between the access waveguide
and the ring modes decays with frequency. This leads to strong coupling
variation across the octave, with poor extraction at short wavelengths. Here,
we investigate how a waveguide wrapped around a portion of the resonator, in a
pulley scheme, can improve extraction of octave-spanning microcombs, in
particular at short wavelengths. We use coupled mode theory to predict the
performance of the pulley couplers, and demonstrate good agreement with
experimental measurements. Using an optimal pulley coupling design, we
demonstrate a 20~dB improvement in extraction at short wavelengths compared to
straight waveguide coupling.
