Effect of local field enhancement on the nonlinear terahertz response of a silicon-based metamaterial

We demonstrate the strong effect of the local field enhancement on the nonlinear terahertz response of a hybrid photoexcited silicon/double concentric ring metamaterial structure. The ring resonators enhance the local terahertz electric field by more than a factor of ten, pushing the terahertz-semiconductor interaction into the high-field regime even for moderate-strength incident terahertz pulses. In this regime, terahertz field-induced intervalley scattering in the photoexcited silicon substrate dynamically alters the substrate conductivity, which in turn strongly modifies the pulse transmission. The spatial distribution of the local field enhancement within the resonator structure results in a modified bandwidth, amplitude, and central frequency of the transmission resonance occurring on a subcycle time scale. These results demonstrate an enhancement of the nonlinear terahertz response of silicon-based metamaterials that must be accounted for in the design of terahertz nonlinear devices.

Figure 1

(a) A photograph of the unit cell of the CRR with the relevant dimensions: a lattice constant of $p=125$ μm, an outer resonator radius of $r=30$ μm, a resonator width of $w=5$ μm, and a gap of $g=10$ μm. The axes on the figure indicate the orientation of the exciting THz field. (b) Simulated spatial electric field at the resonance. (c) The measured transmission of photoexcited silicon with the Drude fit. (d) The measured and simulated transmission response for the unpumped metamaterial sample as well as for the pumped sample. As the pump fluence is increased, the resonance frequency is blue-shifted and the transmission at resonance is reduced due to the change in the imaginary and real parts of the conductivity of the silicon, respectively.

Figure 2

Schematic of the optical-pump terahertz-probe realized with a LiNbO${}_3$ high-power THz source based on the tilted-pulse-front technique.

Figure 3

(a) Schematic diagram showing the photoexcited layer on the silicon wafer and the penetration depth of $d=10$ microns at 800-nm wavelength, (b) transmission amplitude for the photoexcited bare silicon wafer at different THz levels, (c) real and (d) imaginary parts of the extracted conductivity for the pumped bare silicon wafer at different THz levels. High electric field enables intervalley scattering in the conduction band and leads to increase in transmission due to the reduction in conductivity.

Figure 4

The ratio of transmission of the four levels of 11, 41, 70, and 90 kV/cm $\{$T(E)$\}$ and the transmission of the 0.4 kV/cm case $\{$(T(0)$\}$.

Figure 5

Experimental transmission amplitude measured (a) using the unpumped silicon wafer as a reference and (b) considering the photoexcited silicon as a reference at five different THz levels. Simulated transmission amplitude using the unpumped (c) and pumped (d) silicon wafer as a reference, without considering any enhancement from the metamaterial resonators. Simulated transmission amplitude using the unpumped (e) and pumped (f) silicon wafer as a reference, respectively, when considering the field-enhancement from the metamaterial resonators. The two insets in (c) and (e) show nonenhanced and enhanced field areas. As the THz field increases, the transmission amplitude is most strongly modulated at resonance, where the field enhancement reaches its peak.

Figure 6

(a) Schematic for the resonator with two designated colors: red denotes the enhanced regions, where the conductivity is taken to be an unknown complex function that is determined by matching the simulated transmission spectra to the measured spectra and blue denotes the nonenhanced regions, where the parameters from Fig. 3 are employed to model the silicon conductivity. (b) Cross section of the unit cell along the dashed line in (a). (c) Absolute conductivity of the red-colored area extracted from the transmission response. (d) The difference in absolute conductivity between the red and blue (enhanced and nonenhanced field, respectively) colored areas of the part (a).