Surface Plasmon Study notes

I am currently studying the physics of surface plasmons.
Starting with the wave equations and boundary conditions, I have discussed the very basics  in the Surface plasmon notes(constantly updating), which is mainly about the conditions for the existence of such surface waves at the interface of 2 different medium.

Interface between two medium

In order to fulfill the wave equation and boundary conditions, if there exists a TE polarized surface wave, it should have a real wavevector as follows:

,

 if there exists a TM polarized surface wave, it should have a real wavevector as follows:

.

For non-magnetic metals like gold/silver, their relative permeability u1=u2=1, and they normally have Re(epsilon)<<0, hence they are quite good materials for supporting surface plasmons in the visible range and normally the surface plasmons on the metal surface is TM polarized.

Let's consider the permittivity of metal can be approximated as the simplified Drude model, where dissipation term is not considered:

then the wavevector-frequency relationship can be expressed as:

where k~=k/kp, w~=w/wp, kp=wp/c, where wp is the plasma frequency.

A typical configuration for SPR sensing is given in the following image:

Kretschmann confi guration

To excite the surface plasmons, we need to match the wavevectors  components which is parallel to the interface.

 In the above configuration, we are only able to excite surface plasmons on the gold-sensing area interface. When the permittivity of the sensing area changes, the k-w relation for the surface plasmon also changes, as a result, we will excite surface plasmons at different wavevector and frequency. The figure below serves as an example:

Surface plasmon excitation condition when the permittivity of the

sensing area varies

In a recent publication, Z.F. Yu, S.H. Fan [2011] argue from a theoretical point of view that "The extraordinary spectral sensitivity of surface plasmon resonance sensors is commonly attributed to the modal overlap or unique dispersion of surface plasmons.In contrast to this belief, we show that such high sensitivity is due to the multimode nature of the sensing scheme."

The main results of their publication is given as follows:
the spectral sensitivity S can be written as