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I just started to use Geant4 for a new project, where I need to simulate the response of a photocathode to optical photons. I am adding an entry to this post since I'd like to comment on the way Geant4 is currently implementing the reflectivity calculation for a dielectric_metal surface, when the user specifies the Real and the Imaginary part of the metal refractive index.
-> Geant4 is currently using only the metal refractive index to compute the reflectivity, i.e. the result does not depend on the refraction index of the material the metal is in contact with (that I assume to be purely real, since it is a dielectric).
-> The current implementation seems to follow the Fowlers 'Introduction to Modern Optics' approach, where only the complex refractive index of the metal is used.
I went to Fowlers calculation and, even if he doesn't say explicitely, he is using as first medium the vacuum (n=1). It is easy to see this:
-- In eq. 6.60 (and others), he is saying that the modulus of the wavevector for the incident and reflected waves is k0.
-- In eq. 6.66 he is "defining" k0 as w2/c2, i.e. as the modulus of the wavevector in the vacuum.
If, instead, the medium 1 (dielectric) has refractive index n1, then k0 has the same definition, but the incident and the reflected wave have wavevector modulus k1=n1*k0.
I went trough the full calculation, following Fowlers approach, but using n1 as the first material refractive index, and the main results are:
1) Define the "complex" refraction angle (eq. 71) as:
n1 * sin(theta_1) = n2 * sin (theta_2), where
theta_1 is the incident angle, n1 is the dielectric refractive index, n2 is the (complex) metal refractive index, and theta_2 is the (complex) refraction angle.
2A) The ratio of the electric fields amplitudes, for TE polarization (eq. 6.80) is:
r_s = (n1*cos(theta_1)-n2*cos(theta_2))/(n1*cos(theta_1)+n2*cos(theta_2))
2B) The ratio of the electric fields amplitudes, for TM polarization (eq. 6.81) is:
r_t = (n1*cos(theta_2)-n2*cos(theta_1))/(n1*cos(theta_2)+n2*cos(theta_1))
These are exactly the Fresnel's equations, but now n2 and theta_2 are complex numbers.
From this, the reflectivity is defined as R_s=|r_s|^2 and R_t=|r_t|^2