Transient Second-Order Nonlinear Media: Breaking the Spatial Symmetry in the Time Domain via Hot-Electron Transfer

Second-order optical effects are essential to the active control of light and the generation of new spectral components. The inversion symmetry, however, prevents achieving a bulk ${\chi }^{(2)}$ response, limiting the portfolio of the second-order nonlinear materials. Here, we demonstrate subpicosecond conversion of a statically passive dielectric to a transient second-order nonlinear medium upon the ultrafast transfer of hot electrons. Induced by an optical switching signal, the amorphous dielectric with vanishing intrinsic ${\chi }^{(2)}$ develops dynamically tunable second-order nonlinear responses. By taking the second-harmonic generation as an example, we show that breaking the inversion symmetry through hot-electron dynamics can be leveraged to address the critical need for all-optical control of second-order nonlinearities in nanophotonics. Our approach can be generically adopted in a variety of material and device platforms, offering a new class of complex nonlinear media with promising potentials for all-optical information processing.

Figure 1

Breaking the inversion symmetry via hot-electron transfer. A suitable plasmonic platform for the demonstration of the proposed idea comprises a centrosymmetric dielectric (e.g., ${\mathrm{TiO}}_2$), serving as the host material, and a plasmonic system capable of the spatial confinement of the plasmon field in an asymmetric manner (e.g., Au triangles). The on-resonance excitation of the plasmonic structure using a control beam initiates the generation and subsequent injection of hot electrons. The transferred high-energy electrons project the asymmetricity of the plasmonic array into the host material, in an ultrafast timescale (top row). In addition, the separation of the positive and negative charges across the Schottky junction induces a transient electric field $E_{\mathrm{tr}}$ along the host medium, facilitating the conversion of its ${\chi }^{(3)}$ response to an effective second-order nonlinear susceptibility, ${\chi }^{(2)}\propto E_{\mathrm{tr}}{\chi }^{(3)}$ (blue arrows, middle row). The combination of asymmetric electron transfer and a transient electric field breaks the crystal symmetry of the host dielectric material and enables the ultrafast all-optical control of second-order nonlinear processes such as SHG (bottom row).

Figure 2

Static and transient second-order nonlinear characterizations of the plasmonic platform. (a) Schematic of the sample and the simplified measurement setup. (b) Static reflection spectra of the plasmonic structure for the two eigenpolarizations. The definition of polarization states (left), the simulated field profile at 700 nm (middle), and the field profile at 800 nm (right) are presented above the reflection spectra. (c) Measured static $I_{2\omega }$ spectra when the structure is excited with a $U$-polarized fundamental light of varying ${\lambda }_{\omega }$. (d) Dependence of the $I_{2\omega }$ signal on the input polarization state of the fundamental wave for ${\lambda }_{\omega }=800\mathrm{nm}$. (e) Temporal response of the normalized $\mathrm{\Delta }{I}_{2\omega }$ and the transient reflection change $\mathrm{\Delta }R$ upon the illumination of the structure with a $V$-polarized 700 nm control beam. (f) The static $I_{2\omega }$ as a function of the intensity of the fundamental wave at 800 nm (red squares) and the $\mathrm{\Delta }{I}_{2\omega }$ as a function of the control beam intensity (green hexagons), monitored at ${\tau }_d=300\mathrm{fs}$.

Figure 3

Dynamic of the second-order nonlinear response without the involvement of the hot-electron transfer. (a) Polarized static optical reflection spectra of the control sample. The control device provides two orthogonally polarized resonances at 696 and 839 nm. (b) Two-dimensional transient reflection map acquired using a $U$-polarized broadband probe light upon the excitation of the structure with a 700 nm $V$-polarized control light. The intensity of the control light is set to provide an absolute reflection change equal to that of the ${\mathrm{TiO}}_2$-incorporated sample. The black and blue arrows indicate the spectral location of the fundamental light and the center of the $U$-polarized plasmonic resonance, respectively. (c) Dynamics of the normalized second-harmonic change $\mathrm{\Delta }{I}_{2\omega }$ and the induced linear reflection change $\mathrm{\Delta }R$ in the control sample in the absence of the hot-electron transport.

Figure 4

Transient linear and nonlinear polarization responses. (a) Effect of the refractive index change of gold on the spectral line shape of resonance modes, illustrated schematically. (b) Polar diagrams of the absolute reflection change at 700 and 800 nm, as a function of the polarization angle, induced using a control light intensity identical to what we used for acquiring the transient SHG response in Fig. 2. (c) Polar diagrams revealing the polarization state of the emitted frequency-doubled light before (${\tau }_d=-5\mathrm{ps}$) and after (${\tau }_d=300\mathrm{fs}$) the hot-electron transfer into the ${\mathrm{TiO}}_2$ film, with the fundamental beam being polarized along the $U$ direction.