Abstract
Nonlinear response of dielectric polarization to electric field in certain media is the foundation of nonlinear optics. Optically, such nonlinearities are observed at high light intensities, achievable by laser, where atomic-scale field strengths exceeding 106–108 V/m can be realized. Nonlinear optics includes a host of fascinating phenomena such as higher harmonic frequency generation, sum and difference frequency generation, four-wave mixing, self-focusing, optical phase conjugation, and optical rectification. Even though nonlinear optics has been studied for more than five decades, such studies in analogous acoustic or microwave frequency ranges are yet to be realized. Here, we demonstrate a nonlinear dielectric resonator composed of a silicon micromechanical resonator with an aluminum nitride piezoelectric layer, a material known to have a nonlinear optical susceptibility. Using a novel multiport approach, we demonstrate second and third-harmonic generation, sum and difference frequency generation, and four-wave mixing. Our demonstration of a nonlinear dielectric resonator opens up unprecedented possibilities for exploring nonlinear dielectric effects in engineered structures with an equally broad range of effects such as those observed in nonlinear optics. Furthermore, integration of a nonlinear dielectric layer on a chip-scale silicon micromechanical resonator offers tantalizing prospects for novel applications, such as ultra high harmonic generation, frequency multipliers, microwave frequency-comb generators, and nonlinear microwave signal processing.
Highlights
The nonlinear relation between electric field and polarization response is at the heart of nonlinear optics[1,2,3,4]
We use a micron-sized piezoelectric resonator, shown in Fig. 1a, consisting of an aluminum nitride (AlN) piezoelectric layer sandwiched between two layers of metallic electrodes which are deposited on a suspended silicon resonator
AlN has a non-centrosymmetric crystalline structure, enabling both second and third-harmonic generation, whereas the underlying silicon layer with centrosymmetric crystal structure may contribute to only third-harmonic generation
Summary
The nonlinear relation between electric field and polarization response is at the heart of nonlinear optics[1,2,3,4]. Second harmonic generation (SHG) combines two identical photons of frequency ω1 to form a single photon with twice the frequency (ω2 = 2ω1). The order nonlinear effect, third-harmonic generation (THG), can take an input of three dissimilar frequencies and generate various algebraic combinations of sums and differences from the inputs, in addition to frequency tripling. Other SHG-related fundamental effects include optical rectification, Pockel’s effect, and parametric amplification, and THG-related effects include Kerr nonlinearity and nonlinear Raman scattering[3, 4]
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