# Surface plasmon coupling

1. Jun 22, 2010

### Singulani

Hi everyone,

I am trying to figure out what is the coupling of a surface plasmon with a photon for the generation of a surface plasmon polariton. In fact I don't understand what a coupling is in this context. Some texts say that for the coupling to happen is necessary that the dispersion curve for the photon touchs the dispersion curve of the surface plasmon and I don't know the reason. If anybody could enlight me what a coupling is and how is this connected with the dispersion curves encounters (momentum conservation) I would be very pleased. In the graph below is plotted the dispersion curves for the SP and a photon (Wikipedia), just for illustration.

Thanks for your attention an patience.

[PLAIN]http://upload.wikimedia.org/wikipedia/en/e/e8/Dispersion_Relationship.png [Broken]

Last edited by a moderator: May 4, 2017
2. Jun 23, 2010

### Cthugha

I am not sure I understand exactly where your problem is, but in your context coupling is just an interaction which connects two states of your system. In your case these are the following states:

1.: One photon present, no surface plasmon present
2.: No photon present, one surface plasmon present

In other words, it must be possible to optically excite the plasmon.

The dispersions shown give the photon/plasmon energy depending on their momentum. If you want photons and surface plasmons to couple efficiently, their dispersions must cross as you need conservation of energy and momentum. If they do not cross, you need additional particles (phonons for example) to carry away the remaining momentum, which decreases the efficiency of your coupling.

3. Jul 1, 2010

### josh_einsle

well there are a few things going on here. First the figure above only represents the dispersion relation for SPP on a smooth film. As mentioned by Cthugha the only way for coupling happens occurs when energy and momentum are matched. This means that with out any features on the film light can not couple to plasmons on the film since the SPP curve is to the right of the light line.

Now for many applications the easiest way to overcome this is to create a grating coupler. (ie a periodic structure) I will not go into this now as I need to get some dinner.

j

4. Aug 17, 2010

### hiyok

From a microscopic point of view, to get the SP-Photon coupling, one may start with a Hamiltonian supposed to describe a system of electrons and photons, and then make some transformations to arrive at the representation in which SP and photons are the direct entities, and as a result, the original electron-photon interaction is turned into the SP-photon interaction.

5. Aug 18, 2010

### cmos

Just to put it into other words, what (it seems, based on your question) you want to couple is a free space photon mode (i.e. a point on the blue line) with an SPP mode (i.e. a point on the red curve). Efficient coupling between two such modes means that you can excite a corresponding SPP with a corresponding photon.

As others have said above, the SPP modes carry more momentum than the free space photon modes (see: your plot), therefore you need some mechanism to give the additional momentum boost (e.g. a grating coupler).

6. Aug 24, 2010

### josh_einsle

You know I have understood this for a few years now, but this is one of the simplest statements of the coupling I have seen to date. thanks

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