Frequency conversion in periodically driven systems lies at the heart of nonlinear physics. While the second harmonic generation (SHG), sum- and different frequency mixing in the optical frequency range originate from the chi(2)-nonlinearities, in acoustics and magnetism they are often dominated by parametric resonances, where system parameters are modulated at frequencies comparable to the natural oscillation frequencies, typically in the MHz-GHz range.
Keeping in mind the intrinsic differences in the physical nature and frequency range of these phenomena, here we discuss, in a comparative manner, two examples of frequency mixing in magneto-plasmonics [1,2] and magneto-acoustics [3,4]. The ability to experimentally tune both systems through Surface Plasmon Resonance (SPR) and Ferromagnetic Resonance (FMR) as well as to theoretically describe these resonant interactions within the framework of phenomenological models based on the Lorentz oscillator, represent the key idea behind this presentation.
In nonlinear magneto-plasmonic experiments, the Kretschmann configuration SPR resonances for different optical wavelengths occur at different angles (Fig. 1a,b), offering the unique possibility to match the fundamental and SHG resonances. In magneto-plasmonic Au/Co/Ag/glass samples, the plasmonically assisted SHG also depends on the direction of magnetization M in ferromagnetic cobalt, which can be reversed with a weak external magnetic field. A simple model utilizing the resonant plasmonic enhancement of the chi(2)-susceptibility confirms the experimental observation that magnetization-induced effects are most pronounced between the SHG and fundamental SPR resonances [1,2].
In the second experiment [3,4], the magnetization in a Ni/glass sample is excited by two distinct transient surface acoustic waves (SAW and SSLW). Magnetic tuning the FMR frequency in resonance to the their SHG, sum- and difference frequencies demonstrates the full variety of frequency mixing phenomena (Fig. 1c). In contrast to nonlinear optics, the frequency mixing is dominated by the parametric effect in the externally driven FMR oscillator. An analytical model based on the resonant enhancement of frequency-mixed signals explains the experimental observations [4].
References:
[1] I. Razdolski et al., ACS Photonics 3, 179 (2016)
[2] V.V. Temnov et al., J. Opt. 18, 093002 (2016)
[3] J. Janusonis et al., Phys. Rev. B 94, 024415(2016)
[4] C.L. Chang et al., arxiv1610.02926 (2016)
