Inadequate Cext for Gaussian beams

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Currently, ADDA uses the same simplest formula to calculate Cext for any beam 
type. The problem is that for Gaussian beams it is inadequate, i.e. it doesn't 
describe the total energy removed from the beam. In other words, for 
non-absorbing particles in Gaussian beam calculated Cext is not equal to Csca 
(the latter is calculated correctly by integrating the scattered field). So 
ADDA calculates exactly the quantity, that is described in the manual, but it 
is not a physically-meaningful Cext for Gaussian beams.

The main problem in this issue is to derive the correct general expression for 
Cext. Most likely they would involve some kind of integration over the solid 
angle, similarly as is done now for Csca. Here, angular-spectrum representation 
of the Gaussian beam may help.

Original issue reported on code.google.com by yurkin on 2 Nov 2011 at 9:51

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As a workaround, the physically meaningful Cext can be calculated as Cabs + 
Csca (the latter is produced by -Csca command line option).

Original comment by yurkin on 2 Nov 2011 at 4:09

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I have studied this issue in more details and concluded that this is false 
alarm. Cext was (and is) calculated correctly for Gaussian (or any other) beams.

1) The formula used is valid for any incident plane wave, and is linear in 
incident field. Hence, it is valid for any combination of plane waves, that is 
for any beam.

2) Numerical tests do show that significant (say, 0.1%) difference between Csca 
and Cext are possible when using Gaussian beams with default ADDA parameters. 
But this issue is no different from the one described in the Section 10.3 
"Integral scattering quantities". In particular, I was able to make Csca and 
Cext agree in all shown digits using '-eps 12' and increasing both Jmax in 
alldir_params.dat by 2 over the default values.

P.S. The reasoning in (1) does not apply to "extinction" radiation forces, 
because there the expression for each (constituent) plane wave is additionally 
multiplied by the propagation direction of this wave. Thus issue 135 is valid.

Original comment by yurkin on 23 May 2012 at 4:22

• Changed state: Invalid