Circular dichroism of four-wave mixing in nonlinear metamaterials

Metamaterial engineering offers a route to combine unusual and interesting optical phenomena in ways that are rare or nonexistent in nature. As an exploration of this wide parameter space, we experimentally demonstrate strong cross-phase modulation and four-wave mixing in a chiral metamaterial, highlighting the interplay of nonlinearity and circular dichroism. Furthermore, we show that the magnitude of the nonlinear parametric interaction follows certain selection rules regarding the circular polarizations of the various interacting waves. Using a coupled-mode analysis and finite element simulations, we relate these selection rules to the metamaterial's internal symmetries as well as its circular dichroism in the linear regime.

Figure 1

(a) Metamaterial unit cells, each consisting of two nonlinear particles. (b) Details of one side of the nonlinear particle. (c) and (d) Photographs of the two sides of the fabricated sample.

Figure 2

Modes of the structure excited by (a) right-handed and (b) left-handed circularly polarized waves. Arrows represent the direction of the surface currents while the magnitude is given in false color.

Figure 3

(a) Simulated refractive indices of the varactor loaded spirals, optimized to exhibit strong circular dichroism around 3.54 GHz. (b) Comparison of simulated and experimental transmission coefficients for both circular polarizations.

Figure 4

Schematics of the experimental setups used for studying (a) cross-phase modulation and (b) four-wave mixing in the varactor loaded metamaterials.

Figure 5

Experimental results for the cross-phase modulation effect. (a) Difference in transmission spectra for RCP and LCP waves as a function of the power of an additional pump wave, $P_p$, with ${\omega }_p=2\pi \times 3.536$ GHz. (b) Maximum circular dichroism magnitude and frequency as a function of $P_p$.

Figure 6

Coefficients of the four-wave mixing interactions $\eta$ (m${}^4$/W${}^2$) calculated from experiment (left) and simulation (right) for different combinations of circularly polarized waves.