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Nonlinear frequency conversion is a well known and widely exploited family ofeffects in optics, often arising from a Kerr nonlinearity in a crystal medium.Here, we report high stability frequency conversion in the microwave regime dueto a $\chi^{(3)}$ nonlinearity in sapphire introduced by a dilute concentrationof paramagnetic spins. First, we produce a high stability comb from twomicrowave fields at 12.029 and 12.037 GHz corresponding to two high $Q$-factorWhispering Gallery (WG) modes within the Electron Spin Resonance (ESR)bandwidth of the Fe$^{3+}$ ion. The resulting comb is generated by a cascadedfour-wave mixing effect with a 7.7 MHz repetition rate. Then, by suppressingfour-wave mixing by increasing the threshold power, third harmonic generationis achieved in a variety of WG modes coupled to various species of paramagneticion within the sapphire.

Frequency Conversion in a High Q-factor Sapphire Whispering Gallery Mode Resonator due to Paramagnetic Nonlinearity