Figure 3
In frame (a), the exact extinction efficiency is shown for a cylinder in the case where the E-field is parallel to the cylinder axis (blue line). The radius of the cylinder is 10 \(\upmu\)m and the refractive index is 1.3. The red dashed line shows the approximation of \(Q_{ext}\) given in Eq. (3). The yellow line is the extinction efficiency the stadium shaped scatterer will approach according to Eq. (4) when \(d>>a\) in the case where the thickness of the straight part is 20 \(\upmu \rm m\) and the refractive index of the scatterer is 1.3. Frame (b) shows \(Q_{ext}\) of a stadium with a refractive index of 1.3 and a radius of the circular end caps equal to 10 \(\upmu \rm m\). The length of the straight sections is 0 \(\upmu\)m (blue lines), 5 \(\upmu\)m (red lines), 10 \(\upmu\)m (yellow lines) and 15 \(\upmu\)m (purple lines). The figure shows that the wiggles are shifted to the right both according to the COMSOL Multiphysics simulations of the electromagnetic field (solid thick lines) and according to the approximation of \(Q_{ext}\) (thin lines with circles) given by Eq. (4). For the frames (c)–(f), the radius of the circular end caps is 10 \({\upmu \rm m}\) and the refractive index of the scatterer is 1.3. Frames (c)–(f) show the norm of the E-field in the case where a plane wave is incident from the left with wavenumber \({\tilde{\nu }} = 2600\) \(\mathrm {cm}^{-1}\). Frame (g) shows \(Q_{ext}\) as a function of wavenumber. The change in \(Q_{ext}\) is illustrated as a function of the length d of the straight sections of the stadium as we change d from 0.001 (dark blue), which is close to a disk, to a stadium with \(d=50\,\upmu\)m (dark red). The radius of each of the endcaps is 10 \(\upmu\)m and the refractive index of the stadium is 1.8. The simulations are done by COMSOL Multiphysics.
