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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
and thus (intop_surf(nrelPoav)/S_in)/sigma_geom gives you units of
, which is not the proper unit for cross-section (rather the efficiency).
intopvol(emw.Qh)/sigma_geom gives units of
, 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) ![](data:image/png;base64,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)
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:
, where r_eff is effective radius of all scatterers volume.
Cheers,
Radek
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