# Ultrafast Optical Heating Induced Polarization-Dependent Optical Switching in Gold Nanowires
## 3 Ultrafast Optical Switching Performance
### Pump Fluence Dependence of the Ultrafast Optical Switching Effect  
Figure 4a,b shows the measurement results on the pump fluence dependence of the transient spectrum for TE and TM polarization, respectively, where the pump fluence was increased from 1.8 to 23.1 \(\upmu\)J/cm\({}^{2}\). To demonstrate the large difference in the optical switching effect between TE and TM polarization, we have scaled the vertical axis using the same range of \(\Delta\)A. We can observe a much larger amplitude of the TA spectrum for TE than for TM polarization in the spectral range from 625 to 725 nm, verifying our proposed mechanisms in this work. Narrow-band TA spectra with negative features on the left and positive on the right for TE polarization imply a red-shift of the resonance spectrum. However, for TM polarization, we observe a negative dip centered at about 690 nm with relatively broad-band positive spectra on both sides, indicating complicated transient processes involved in the excitation of the Fano resonance mode.  
For both TE and TM polarization, we observed increased amplitude of the TA spectrum with increasing pump fluence, which is convincing evidence that higher pump fluence induced larger spectral shift of the plasmon resonance. For clearer observation of the red-shifted plasmon resonance, we rebuilt the spectra of the optically excited plasmon resonance by including the TA spectra into the steady-state optical extinction spectrum. Assuming that the optical extinction spectrum of the gold nanowires is described by A(\(\lambda\)) for TE polarization with A(\(\lambda\)) = -log\({}_{10}\)T(\(\lambda\)) and the TA spectrum by \(\Delta\)A(\(\lambda\)) in \(mOD\), where T(\(\lambda\)) is the transmission spectrum through the gold nanowires, the optical  
Figure 3: Calculated optical extinction spectrum at different gap width of the dimer system consisting of two identical gold nanoparticles with a diameter of 100 nm. Inset: schematic illustration of a dimer system consisting of two gold nanoparticles with a gap width of 2 and 15 nm, showing the calculated optical electric field distribution.  
extinction spectrum of the optically excited plasmon can be written as: A\({}_{\mathrm{E}}(\lambda)\) = A(\(\lambda\)) + \(\Delta\)A(\(\lambda\))/1000. Figure 4c shows the plots of A\({}_{\mathrm{E}}(\lambda)\) at pump fluence of 1.8, 5.3, 10.7, 17.8, and 23.1 \(\upmu\)/cm\({}^{2}\). A(\(\lambda\)) was also plotted in Figure 4c by the dotted curve for comparison. We can observe a red-shift of more than 2 nm when the pump fluence was increased from 0 to 23.1 \(\upmu\)/cm\({}^{2}\). Thus, the results in Figure 4 verified different plasmonic response for different polarizations, where the scheme of TM-pump/TE-probe has much higher efficiency than TM-pump/TM-probe, and higher pump fluence resulted in larger spectral shift of the cross-plasmon for TE polarization.  
We may verify the agreement between our proposed mechanisms and the TA measurements by a comparison between the simulation results in Section 3.2 and the experimental results in Section 3.3. If we assume an approximately linear red-shift of the resonance spectrum with the reduction in the gap width, we can estimate a spectral shift of about (633 \(-\) 565)/(15 \(-\) 2) \(\times\) 0.35 \(\approx\) 1.8 nm, where we have used the thermal expansion amount of the gold nanostructures as large as 0.35 nm under optical excitation. The measured spectral shift using the rebuilt spectra in Figure 4c is about 2.2 nm at the peaks and at the falling edges. However, such a difference justifies a rough agreement between the simulation and the measurement. The reasons for the deviation may be understood by considering the deviation of the dimmer spheres in the modeling from the practical plasmonic nano-segments in the sample.