# A circularly polarized EM wave is perfectly absorbed by any interface?

According to the Fresnel equations, the effective reflectivity of an arbitrarily polarized electromagnetic wave is given as:

$$\Gamma = \frac{\Gamma_p + \Gamma_s}{2} ,$$

where $$\\Gamma_p\$$ and $$\\Gamma_s\$$ are the reflectivities for p and s polarization, respectively.

I assume the common scenario of an electromagnetic wave traveling through empty space ($$\n_1=1; \epsilon_1=\epsilon_0, \mu_1=\mu_0\$$) hitting a non-magnetic surface ($$\\mu_2=\mu_0\$$) with dielectric $$\\epsilon_2=\epsilon_0 \epsilon_2'\$$ ($$\n_2=\sqrt{\epsilon_2'}\$$) at a straight angle.

If I plug these into the Fresnel equations with an angle of incidence $$\\theta_i=0\$$, I obtain:

$$\Gamma_p = \frac{\epsilon_2'-\sqrt{\epsilon_2'}}{\epsilon_2'+\sqrt{\epsilon_2'}} , \\ \Gamma_s = \frac{1-\sqrt{\epsilon_2'}}{1+\sqrt{\epsilon_2'}} .$$

Then it is easy to see that $$\\Gamma=(\Gamma_p+\Gamma_s)/2=0\$$ ! This suggests that any circularly polarized wave hitting a surface at a perpendicular angle would be perfectly aborbed. That must be nonsense.

Where is the mistake?

• THis is easy to answer: what do the p and s in your polarization names stand for? – Marcus Müller Jan 7 at 8:23
• senkrecht und parallel ;-) How does this answer? (I see how the wave-fronts are reaching the surface for both cases: de.wikipedia.org/wiki/Fresnelsche_Formeln#/media/… and de.wikipedia.org/wiki/Fresnelsche_Formeln#/media/…) – divB Jan 7 at 17:46
• senkrcht means "normal to the surface"; and your wave is hitting the surface in a straight angle, and since there's no longitudinal field components in electromagnetic waves in free space... – Marcus Müller Jan 7 at 19:36
• Sorry, I really don't understand. Both, $\Gamma_p \neq 0$ and $\Gamma_s \neq 0$! For example, for $\epsilon_2'=9$, $\Gamma_p = 0.5$ and $\Gamma_s = -0.5$. This makes sense. In both cases things are reflected. My question is why does in the circularly polarized case nothing seem to be reflected? – divB Jan 7 at 19:45
• maybe I'm misinterpreting what "in a straight angle" means – Marcus Müller Jan 7 at 19:51