  Interacting resonators can lead to strong non-linearities but the details can
be complicated to predict. In this work, we study the non-linearities
introduced by two nested microcavities that interact with nitrogen vacancy
centers in a diamond waveguide. Each cavity has differently designed resonance;
one in the green and one in the infrared. The magnetic-field dependence of the
nitrogen vacancy center absorption rates on the green and the recently observed
infrared transitions allows us to propose a scalable on-chip magnetometer that
combines high magnetic-field sensitivity and micrometer spatial resolution. By
investigating the system behaviors over several intrinsic and extrinsic
parameters, we explain the main non-linearities induced by the NV centers and
enhanced by the cavities. We finally show that the cavities can improve the
magnetic-field sensitivity by up to two orders of magnitudes.
