# All-Optical Modulation and Ultrafast Switching in MWIR with Sub-Wavelength Structured Silicon
## 5 Demonstration of the Ultrafast Switching  
Using the optical model shown above, we optimised the condition for the demonstration of the ultrafast switching, which can be operated at a speed far faster than the natural or enhanced decay processes in semiconductors related to trap states, surface recombination and Auger decay [26; 29; 30; 31; 32; 33]. As an example of such a design, we show the reflective modulation of the signal at 4 \(\upmu\)m. This wavelength was also chosen because of its importance for the imaging and range-finding at MWIR [6]. The performance of the modulator, demonstrating the contrast reaching 30% and the response time (as defined by the FWHM) of 0.55 ps, is shown in Figure 3a. It surpassed an electro-optical reflective modulator based on a non-linear response of the surface plasmons [34]. We noted that small oscillations of \(\Delta R/R_{0}\) for \(\Delta t>1\) ps were due the experimental noise and cannot be routinely reproduced. Figure 3b shows the related temporal development of the real and complex parts of the effective dielectric function, \(\Re(\epsilon_{eff})\) and \(\Im(\epsilon_{eff})\), following the excitation by the pump pulse. Besides, in Figure 3c, we show the density of the carriers, \(N\), and their scattering rate, \(\gamma\), which transpired from the simulation of the experimentally-determined temporal evolution of \(\Delta R/R_{0}\). The simulation itself is shown in Figure 3a as the black dashed line. We measured the bulk silicon to compare its performance with that of the optical membrane. In the absence of the pumping, the optical membranes and bulk silicon had reflectances of 0.2 and 0.3,  
Figure 2: The change of the reflectance, \(\Delta R/R_{0}\), as a function of the arrival time difference, \(\Delta t\), between the pump and signal pulses, and the signal wavelength \(\lambda\) for the pump fluences of 3.8 mJ/cm\({}^{2}\) (**a**), 5.0 mJ/cm\({}^{2}\) (**b**), 6.3 mJ/cm\({}^{2}\) (**c**) and 8.8 mJ/cm\({}^{2}\) (**d**). The dashed box in (**d**) shows the region where the reflectance passes through the minimum. respectively. It was apparent that for identical optical pumping, the response \(\Delta R/R_{0}\) of the bulk silicon and optical membrane was quite different. The bulk material did not show a sharp negative peak, but rather dropped and remained constant. In addition, the modulation contrast was just above 5%. To explain the sharp peaked response and enhancement in the modulation contrast, it will be helpful to investigate the development of \(\Re(\epsilon_{eff})\), \(\Im(\epsilon_{eff})\), \(N\) and \(\gamma\) as a function of time shown in Figure 3b,c; Panel (b) also reproduces the reflectance response \(\Delta R/R_{0}(t)\) as the dashed line for the convenience of the discussion. It can be seen that following the pump pulse application, the carrier density increased, causing a decrease of \(\Re(\epsilon_{eff})\) and, alternatively, an increase of \(\Im(\epsilon_{eff})\). Yet at the earlier times, the main contribution to the reflectance change was from the variation of \(\Re(\epsilon_{eff})\), as \(\Im(\epsilon_{eff})\) was still too small. Around 0.5 ps, \(\Re(\epsilon_{eff})\to 1\), at which \(\Delta R/R_{0}\) reached the minimum, and its value was set by \(\Im(\epsilon_{eff})\) at this time. That is, higher \(\Im(\epsilon_{eff})\) resulted in lower contrast of \(\Delta R/R_{0}\). After 0.5 ps, the rate of \(\Delta R/R_{0}\) and its sign were determined by the the combined contribution of \(\Re(\epsilon_{eff})\) and \(\Im(\epsilon_{eff})\) as they have comparable absolute values. The steady state condition of \(\Delta R/R_{0}\) was reached after 1 ps when both the real and imaginary parts were saturated, on par with \(N\) and \(\gamma\). To summarise, initially, the rate of \(\Delta R/R_{0}\) drop was almost exclusively governed by the decrease of \(\Re(\epsilon_{eff})\); the minima was achieved when \(\Re(\epsilon_{eff})\to 1\); and the modulation contrast was determined by \(\Im(\epsilon_{eff})\).