HomerReid / scuff-em

A comprehensive and full-featured computational physics suite for boundary-element analysis of electromagnetic scattering, fluctuation-induced phenomena (Casimir forces and radiative heat transfer), nanophotonics, RF device engineering, electrostatics, and more. Includes a core library with C++ and python APIs as well as many command-line applications.
http://www.homerreid.com/scuff-em
GNU General Public License v2.0
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Scattering Green's function units in SCUFF-SCATTER #125

Closed psv2 closed 7 years ago

psv2 commented 7 years ago

I'm trying to compute the scattering Green's function defined as G^sca = G - G^vac, where G^vac is the homogeneous (vacuum) Green's function and G solves the equation ((\nabla \times (\nabla \times) + (\xi/c)^2 * (1 + \chi))G)_{ij} = -(\xi/c)^2 \delta_{ij} \delta^3 (x - x') in imaginary frequency \omega = i\xi, where \chi is the susceptibility (and coordinates x & x' are 3-dimensional vectors). In particular, the Green's functions G^vac and G^sca should have units of [length]^-3. If I compute the scattered fields from a point dipole source (in each of the 3 dipole orientations) in SCUFF-SCATTER, what factors of 4\pi, \epsilon_0, \xi, and c do I need to multiply by in order to get a scattering Green's function consistent with the definitions and units above?

psv2 commented 7 years ago

I figured out the solution to this: to go from the scattered fields (with units of volt*micron^-1) to my definition of the scattering Green's function (with units of meter^-3), simply multiply the numerical value of the scattered electric field by 10^18 (and divide by the numerical value of the norm of the dipole vector, if it is not unity). With this, I am closing the issue.