Magnonic Frequency Comb in the Magnomechanical Resonator

An optical frequency comb is a spectrum of optical radiation which consists of evenly spaced and phase-coherent narrow spectral lines and is initially invented in a laser for frequency metrology purposes. A direct analog of frequency combs in the magnonic systems has not been demonstrated to date. In our experiment, we generate a new magnonic frequency comb in the resonator with giant mechanical oscillations through the magnomechanical interaction. We observe the magnonic frequency comb contains up to 20 comb lines, which are separated by the mechanical frequency of 10.08 MHz. The thermal effect based on the strong pump power induces the cyclic oscillation of the magnon frequency shift, which leads to a periodic oscillation of the magnonic frequency comb. Moreover, we demonstrate the stabilization and control of the frequency spacing of the magnonic frequency comb via injection locking. Our Letter lays the groundwork for magnonic frequency combs in the fields of sensing and metrology.

Figure 1

(a) Illustration of the coupling between magnon and phonon with single magnon-phonon coupling strength $g$. (b) The magnonic frequency comb is generated via a two-magnon process. Two magnons with frequency ${\omega }_m+n{\omega }_b$ are annihilated to create two magnons with frequency ${\omega }_m+(n-1){\omega }_b$ and ${\omega }_m+(n+1){\omega }_b$, where the ${\omega }_m$ and ${\omega }_b$ are the frequency of the magnon and mechanical modes, respectively. (c) A cascaded two-magnon process is initiated to form a frequency comb separated with a mechanical frequency of ${\omega }_b$. (d) Schematic of the experimental setup for the magnonic frequency comb. SRC: microwave source; VNA: vector network analyzer; ESA: electrical spectrum analyzer. (e) Measured microwave reflection spectrum around 4.725 GHz. (f) The detailed spectrum showing the mechanical mode in (e). The red lines are the results of theoretical calculations discussed in the main text with the parameters of $g/2\pi =2.36\mathrm{mHz}$, ${\kappa }_m/2\pi =12\mathrm{MHz}$, ${\kappa }_b/2\pi =220\mathrm{Hz}$, and ${\kappa }_{\mathrm{in}}/2\pi =6.1\mathrm{MHz}$.

Figure 2

(a) Evolution of the magnonic frequency comb along increased pump power from 16 to 24 dBm with the frequency of ${\omega }_p=4.725\mathrm{GHz}$. Inset: evolution of the spectrum over a period of 7 s at a power of 23.1 dBm and frequency ${\omega }_p-{\omega }_b=4.714\mathrm{GHz}$ component. (b) Snapshots with different evolution stages in (a). (c) Simulated spectra of the magnonic frequency combs with the same conditions in (b).

Figure 3

(a) Evolution of the $S_{21}$ spectrum along time (within 7 s) with the pump power of 23.1 dBm and frequency of ${\omega }_p=4.725\mathrm{GHz}$. (b),(c) The typical $S_{21}$ spectrum under $t=2\mathrm{s}$ and 3 s in (a). (d) Threshold curve for phonon amplitude and detuning at the pump power of 23.1 dBm. (e),(f) The oscillation period and the frequency shift versus pump power from 21.85 to 23.1 dBm. The solid line is the theoretical curve.

Figure 4

(a) Evolution of one comb tooth when the external source is on and off. The initial comb tooth is unstable (I). The comb tooth is synchronized to the external source (II). The comb tooth returns to the initial state after turning off the external source (III). (b) Evolution of the rf spectrum with varied injected frequency. The injected power is $-6.4\mathrm{dBm}$, and the comb is synchronized to the external source when the frequency difference is less than 400 Hz. (c) Locking ranges with varied pump power.