Surface plasmon, Fresnel's equations

[_Andreas]

I'm writing a school paper on surface plasmons (as I said in another post), and among other things, I'm supposed to deduce Fresnel's equations for p-polarized light (that is, the ratios $$\frac{E_{0r}}{E_{0i}}=\frac{a}{b}$$ and $$\frac{E_0t}{E_0i}=\frac{c}{b}$$). Now, apparently, when a surface plasmon is induced, the denominator, $$b$$, is approximately zero. I find this very odd, since it seems to imply that the amplitude of the reflected light, $$E_{0r}$$, is infinite, which woud mean that the reflected light has an infinite intensity. Could someone explain where my thinking goes wrong?

 

[Jhero]

Dear writer,

Thank you for your interest in surface plasmons and Fresnel's equations for p-polarized light. It is a complex and fascinating topic, and I am happy to help clarify some of your doubts.

First of all, let me explain the concept of Fresnel's equations. These equations describe the behavior of light when it hits a boundary between two media with different refractive indices. They give us the ratios of the reflected and transmitted electric field amplitudes to the incident electric field amplitude. These ratios are denoted as \frac{E_{0r}}{E_{0i}} and \frac{E_{0t}}{E_{0i}} for the reflected and transmitted light, respectively.

Now, when it comes to surface plasmons, the denominator, b, in these equations becomes very small, approaching zero. This is because surface plasmons are collective oscillations of electrons at the interface of a metal and a dielectric material. These oscillations are highly confined to the surface and have a very short decay length. This means that the electric field amplitude of the surface plasmon is much larger than that of the incident light, resulting in a very small denominator in the equations.

However, this does not mean that the amplitude of the reflected light, E_{0r}, is infinite. In fact, as the denominator approaches zero, the reflected light also becomes very small. This is known as the Goos-Hänchen effect, where the reflected light is shifted parallel to the interface due to the surface plasmon resonance. Therefore, the intensity of the reflected light remains finite and does not become infinite.

I hope this explanation has cleared up your confusion. If you have any further questions, please feel free to ask. I wish you all the best with your school paper on surface plasmons.