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

TL;DR

This paper demonstrates stable microwave frequency conversion in a sapphire resonator caused by paramagnetic nonlinearity, producing a frequency comb and third harmonic generation through four-wave mixing and threshold suppression.

Contribution

It reveals a novel nonlinear frequency conversion mechanism in sapphire using paramagnetic spins, expanding microwave nonlinear optics.

Findings

High stability microwave frequency comb generated

Third harmonic generation achieved in sapphire WG modes

Cascaded four-wave mixing with 7.7 MHz repetition rate

Abstract

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