Surface-Enhanced Nonlinear Four-Wave Mixing

We report on a particularly strong third-order nonlinear response from nanostructured gold surfaces. Two incident laser beams with frequencies ${\omega }_1$ and ${\omega }_2$ give rise to four-wave mixing (4WM) fields with frequencies $2{\omega }_1-{\omega }_2$ and $2{\omega }_2-{\omega }_1$. We demonstrate that the nonlinear response can be purely evanescent and that nanostructured surfaces convert the evanescent energy into propagating radiation, thereby increasing the efficiency of frequency conversion. The emitted 4WM radiation is found to be directional, polarized, coherent, and both frequency and angle tunable. The ability to perform efficient frequency conversion in reduced dimensions provides new opportunities for nanophotonics and active plasmonics.

Figure 1

Nonlinear four-wave mixing at a nanostructured gold surface. Two incident laser beams with frequencies ${\omega }_1$ and ${\omega }_2$ give rise to reflected beams with frequencies ${\omega }_{4{\mathrm{wm}}_1}=2{\omega }_1-{\omega }_2$ and ${\omega }_{4{\mathrm{wm}}_2}=2{\omega }_2-{\omega }_1$, respectively.

Figure 2

(a) Efficiency of four-wave mixing ($|{\mathbf{E}}_{4\mathrm{wm}}{|}^2$) at ${\lambda }_{4{\mathrm{wm}}_1}=633\mathrm{nm}$ as a function of excitation angles ${\theta }_1$ and ${\theta }_2$. The solid line indicates the boundary between propagating and evanescent 4WM waves. (b) Line cut along the dashed line. The shaded area corresponds to the evanescent region. The intensity at the surface plasmon peak is more than 3 orders of magnitude larger than the intensity in the propagating region.

Figure 3

Angular dependence of 4WM emission. (a) Calculated emission angles (${\theta }_{4{\mathrm{wm}}_1}$, ${\theta }_{4{\mathrm{wm}}_2}$) as a function of excitation angle ${\theta }_1$. The angle of ${\theta }_2$ is ${\theta }_1+60°$. ${\lambda }_1=707\mathrm{nm}$, ${\lambda }_2=800\mathrm{nm}$, ${\lambda }_{4{\mathrm{wm}}_1}=633\mathrm{nm}$, and ${\lambda }_{4{\mathrm{wm}}_2}=921\mathrm{nm}$. (b), (c) Measured 4WM intensity as a function of excitation angle ${\theta }_1$. The four resonance curves correspond to the angles marked by triangles and squares in (a).

Figure 4

Enhanced 4WM from nanostructured surfaces. (a) The 4WM intensity at ${\lambda }_{4{\mathrm{wm}}_1}=633\mathrm{nm}$ as a function of excitation angle ${\theta }_1$. A grating with period $a=300\mathrm{nm}$ is used to couple out evanescent 4WM fields with in-plane wavelength of $365\mathrm{nm}$. (b) The 4WM intensity at ${\lambda }_{4{\mathrm{wm}}_2}=921\mathrm{nm}$ as a function of excitation angle ${\theta }_1$. A grating with period $a=371\mathrm{nm}$ is used to couple out evanescent 4WM fields with in-plane wavelength of 461 nm. Dots are data points, and the solid curves are a Gaussian fit. Data normalized with the 4WM intensity measured for a flat gold surface.