Discussion Forum

Posted: 5 years ago 22 ott 2019, 02:48 GMT-4

Updated: 5 years ago 22 ott 2019, 05:49 GMT-4

Hi, as far as I know, when calculating cross-sections from Poynting vector, one should integrate over a sphere that is furthest away from the source (as long as this sphere is between PML and the scatterer). When calculating *scattering* cross-section from Efar, one should use a sphere that lies the closest to the scatterer (that would be a sphere of far-field transform) since such a sphere usually has the best-resolved mesh (and the built-in Efar variable has an intrinsic error - refer to the definition in the manual). These I have learned on COMSOL conference of late. Btw, where did you find the equations for cross-sections? I don't get why there is this division by geometrical cross-section? S_in = E0^2/(2Z0const) has unit of W/m^2 and thus (intop_surf(nrelPoav)/S_in)/sigma_geom gives you units of [1], which is not the proper unit for cross-section (rather the efficiency). intopvol(emw.Qh)/sigma_geom gives units of W/m^2, which again is not the proper unit for cross-section (rather the power flow). For sure I can tell you that the proper way to define absorption cross-section is intopvol(emw.Qh)/S_in. This yields proper values and units when the integration is over the near-field. When talking about scattering - this is another story. I have some doubts, too, because I obtain electronic-resonance-like curve instead of plasmonic one - when calculating from Poynting vector (or the values are too small by 15 orders of magnitude when with proper plasmonic curve - when calculating from Efar). EDIT: Now, I have found in my notes that for the scattering cross-section you need to use emw.nPoav, as this is time-average power outflow (which is what scattered light is, see Stratton's "Electromagnetic Theory" quote below): > The second term obviously measures the outward flow of the secondary or scattered energy from the diffracting sphere, and the total scattered energy is > > (20) W_s=\frac{1}{2} Re \int_{0}^{\pi}\int_{0}^{2\pi} \left(E_{r\theta}\tilde{H}_{r\phi}-E_{r\phi}\tilde{H}_{r\theta}\right) R^2 \sin\theta d\theta d\phi > Therefore sigma_sca = intop_surf(emw.nPoav)/S_in where integration is over boundary between far-field and PML. Now I also got rid of the problems with such a solution. EDIT2: Just to mention: In my case the Far-field to PML boundary has wavelength-dependent size (radius = lambda/2), so (whether I'm right or not) I had to add geometry part as: \oint\frac{emw.nPoav\left(\pi\, r_{eff}^2\right)}{S_{in}\left(\pi\,\left(\frac{\lambda}{2}\right)^2\right)}, where r_eff is effective radius of all scatterers volume. Cheers, Radek