Artificial Nonlinearity Generated from Electromagnetic Coupling Metamolecule

A purely artificial mechanism for optical nonlinearity is proposed based on a metamaterial route. The mechanism is derived from classical electromagnetic interaction in a metamolecule consisting of a cut-wire meta-atom nested within a split-ring meta-atom. Induced by the localized magnetic field in the split-ring meta-atom, the magnetic force drives an anharmonic oscillation of free electrons in the cut-wire meta-atom, generating an intrinsically nonlinear electromagnetic response. An explicit physical process of a second-order nonlinear behavior is adequately described, which is perfectly demonstrated with a series of numerical simulations. Instead of “borrowing” from natural nonlinear materials, this novel mechanism of optical nonlinearity is artificially dominated by the metamolecule geometry and possesses unprecedented design freedom, offering fascinating possibilities to the research and application of nonlinear optics.

Figure 1

Schematic of array (a) and unit cell (b) of the metamolecules. The local magnetic and electric fields, and the magnetic force, are marked. In the microwave regime, the geometric constants $l_1=3.4\mathrm{mm}$, $w_1=0.45\mathrm{mm}$, $g=0.1\mathrm{mm}$, $l_2=2.3\mathrm{mm}$, $w_2=0.5\mathrm{mm}$, $d=0.1\mathrm{mm}$, and $P=3.6\mathrm{mm}$.

Figure 2

Transmission, reflection, and absorption spectra of the metamolecule (a) with 10 GHz marked with a grey dashed line; the magnetic field distribution (b) with the scale normalized to the incident magnetic field amplitude and the orientation of the surface currents are marked with red arrows.

Figure 3

Original and high-pass filtered time-domain transmission spectra of the nonlinear metamolecule in $y$ polarization (a) and its frequency-domain spectrum (b); the inset is the frequency spectra of two meta-atoms.

Figure 4

Reflection frequency spectrum of the metamolecule in $y$ polarization; the inset is its original and high-pass filtered time-domain spectra.

Figure 5

Relation between the intensity of the transmitted SHG and the distance between two meta-atoms. Inset: the intensity of the SHG with different widths of the cut-wire meta-atom, and the linear fit of the data points.