# Bulk plasmon: why can't they be excited by natural light?

Here is what I have understood from bulk plasmons.

We can show using an hydrodynamic model that they are are coupled to a longitudinal electric wave in a medium.

Thus we need to create a longitudinal electric wave in the metal to be able to have those bulk plasmons.

So, we can't excite them using light if the medium in which the metal is is the vacuum for example (bc in vacuum, the electric field is necesseraly transverse to the wavevector).

But, even if I get the global picture, it is not totally obvious for me that a transversal wave in vacuum can't convert into a longitudinal one when crossing the medium.

Indeed only the $E_{//}$ is continuous on the interface.

Why couldn't something like this happen :

We enlight the material at normal incidence.

When the light enters in it, the parallel part of the field is continuous. Thus we still have a transverse part of the electric field inside of the material. But the E_orthogonal could appear (because of surface charge appearing on the surface).

But at this point... we need the $E_{//}$ to vanish in the material to really have a longitudinal wave...

So in summary, we can't have longitudinal wave in the material using natural light because of the continuity of $E_{//}$ ?

We could imagine to have a longitudinal component inside of the material but we would need to "delete" the transverse part. And such a thing can't be done (excepted maybe in some very special material...?).

It is just to understand the link between : in vacuum with light, we have transverse E-wave then we can't have longitudinal E-wave in the bulk of a material if we enlighted it.

• Let's say the interface between metal and air is the x-y plane, and you have light traveling along z and with E-field along x. Presumably the light interacts with the bulk plasmon where the electrons move in the x direction. Is that what you're asking about? Or are you asking about the bulk plasmon where the electrons move in the z direction? – Steve Byrnes Dec 31 '17 at 19:46
• @SteveByrnes Well actually I know that in a general case, light can't excite bulk plasmons. Thus it should be true for any wavector direction of the light and any polarisation. But we can take an example of light travelling along z. As the wave must be longitudinal in the material I would rather expect a movment of the electron along z. With an appearing polarisation along the z direction at the interface (because E_orthogonal is not necesseraly continous). But such a thing can't occur and I would like to know why. I hope it is more clear – StarBucK Dec 31 '17 at 20:45
• Where did you learn that "in a general case, light can't excite bulk plasmons"? Because I am inclined to disagree with that statement. (Are you sure you're not confusing bulk plasmons with surface plasmons?) I think light traveling along z and with E-field along x, hitting a metal, can excite the bulk plasmons whose electrons move along x and whose wavevector is ≈0. – Steve Byrnes Dec 31 '17 at 21:09

I disagree with the premise. Light from free space is perfectly capable of exciting and interacting with bulk plasmons.

(You might be confusing bulk plasmons with surface plasmons? The latter indeed do not naturally interact with free-space light. They only interact if you coax them to, with gratings, prisms, etc.)

In fact, the strong interaction between light and bulk plasmons is essential for understanding the optical properties of materials, e.g. the fact that metals reflect visible light.

In detail: Say the metal has a surface normal to z, and light in air is traveling along z towards the metal, with electric field along x. That light will interact with the bulk plasmon in which the electrons move along x, and whose plasmon wavevector is ≈0.

I agree with Steve Byrnes, bulk plasmons definitely can be excited by light!

The dispersion relation for a bulk plasmon is $$\omega_{plasmon}(k)=\omega_0+\beta k^2$$

This curve will always have an intersection with the light cone.

$$\omega_{light}(k)=ck$$

So bulk plasmons can always be excited, provided you have the correct $$\omega$$ for the light, which is almost exactly $$\omega_0$$ because the $$\beta$$ term is irrelevant on optical length scales.

To make this even more concrete, below is the reflectivity of silver showing a plasmon absorption at roughly 330nm. This is known as the plasma edge. The drop in reflectivity is exactly caused by excitation of plasmons!