Visualization of solution
Absorption cross section
This time I have chosen to show you absorption cross-section, because of two reasons. First is that there is no problem as in the case of far-field calculations of scattering-cross sections with Straton-Chu formula. Second, when solving scattering cross-section of big objects, Rayliegh scattering might dominate the weakly excited modes, especially with high-order numbers m=3,4,etc.
Fresnel formulas are incorporated, with possibility to chose angle of incidence before running solving loop. Two loops are solved, one for normal incidence and one for oblique incidence.
Plot of absorption cross-section is shown in Figure 1. It is clear that there is a big difference, especially, peak at around 1um is not present for normal incidence. This mode can be excited only if symmetry is broken. To identify modes by modal numbers, where modes are characterized according to expression L=m*Lambda/2, we should check near-field response (or charge distribution).
Figures 2. and 3. show near-field response of 500x50x50nm gold nanobar on glass substrate under normal (Fig.2) and oblique incidence (Figure 3.) for plane wave illumination of free-space wavelength of 750nm. This correspond to absorption peaks at the same wavelength in Figure 1. It is obvious that response under normal incidence is stronger, which is the case. Figure 2. shows symmetrical near-field distribution, stronger that Fig.3. It displays four lobes, reveling that modal number is m=3 (3/2*Lambda mode). Figure 3 shows non-uniform, and weaker response. One is the consequence of smaller component of electric field in the x-direction, because there is z-component that excites transverse modes at 550-600nm. Due to oblique incidence, distribution is not uniform, but four lobes can be identify.
Figure 4. shows distribution for 1000nm under oblique illumination. Clearly, this corresponds to modes that is not allowed for non-symmetric braking case. Displays 3 lobes, modal number 2, for Lambda mode.