# Ultrafast Optical Heating Induced Polarization-Dependent Optical Switching in Gold Nanowires
## 3 Ultrafast Optical Switching Performance
### Mechanisms for the Ultrafast-Heating Enhancement  
Although the temperature dependence of dielectric permittivity of the host matrix may also contribute to the redshift of plasmon resonance [17], such mechanisms should not have polarization dependence. In this work, we observed strong redshift of the spectrum for TE polarization in the direction of the grating lines. This is the basis for us to attribute the TA spectroscopic response to a cross-plasmon at the gaps between the gold nanostructures along the grating lines. Actually, thermal expansion effects for gold nanoparticles have been investigated [18]. We made an evaluation of the thermal expansion amount of the gold nanostructures using parameters of gold: thermal expansion coefficient (\(\alpha_{L}\)): 14 \(\times\) 10\({}^{-6}\)/\({}^{\circ}\)C; heat capacity (\(C_{T}\)): 128 J/kg.\({}^{\circ}\)C; and density (\(\rho\)): 19.3 g/cm\({}^{3}\). We also use the following parameters of the gold nanostructures in our pump-probe measurements: average volume of gold nanostructures along the grating lines (\(V\)): 3.9 \(\times\) 10\({}^{-15}\) cm\({}^{3}\); average length of the gold nano-segments (\(L\)): 300 nm; and estimated average optical pulse energy absorbed by such a gold nanostructure (\(\Delta E_{O}\)): 8 \(\times\) 10\({}^{-13}\) J. Thus, if we assume homogeneous and linear thermal expansion of the gold nanostructures under optical-excitation heating, the expansion amount can be evaluated roughly by \(\Delta\)L = \(\alpha_{L}\frac{\Delta E_{O}}{C_{T}\cdot\rho\cdot\rho}\cdot L\). As a result, the thermal expansion of the gold nanostructures after excitation can be estimated to be 0.35 nm.  
As has been reported, a kind of cross-plasmon may be induced if the gap between the plasmonic nanostructures is smaller than 20 nm [19]. The resonance spectrum of such plasmons shifts to the red with reducing gap width. Figure 3 shows a series of simulation results of optical extinction spectra of the gold nanoparticles when changing the separation distance or the gap width between them. In the simulation, we used finite-difference time-domain (FDTD) method, where the parameters of the gold nanoparticles were adopted from the Palik database and the calculation was performed in the spectral range from 400 to 700 nm. The light beam was assumed to be polarized along the co-axis of the two gold nanoparticles, and the gold nanoparticles were assumed to be immersed in air with an ITO glass substrate. The gold nanoparticles have the same diameter of 100 nm. The optical extinction spectrum was calculated at different separation distances (_d_). As shown in Figure 3, the optical extinction spectrum shifted from about 633 to 565 nm when \(d\) was increased from 2 to 15 nm. Furthermore, the amplitude of the optical extinction spectrum was also reduced with increasing separation distances, corresponding to the reduction in the cross coupling between the gold nanoparticles. It can be understood that a sufficiently large separation between the gold nanoparticles corresponds to a system consisting of isolated gold nanoparticles, where the spectrum of plasmon resonance is a response of a single gold nanoparticle.  
Excitation using femtosecond pulses has heated the electrons in the gold nanowires. Such a heating process led to thermal expansion of the nanostructures along the gold nanowires. However, red-shift of the resonance spectrum has verified a reduction process of the gap width between the gold nanostructures appearing as particles or segments.