Longitudinal plasmon oscillation

In summary, according to Kittel's solid state physics book (chapter 14), if the dielectric permittivity is zero, there is a possibility of a longitudinal polarization wave existing. This may be difficult to imagine, but it is explained by the fact that at higher frequencies there are solutions to the Maxwell equations which are not bound to external sources and have a zero permittivity. This means that the electric field can exist without an associated displacement field, resulting in a longitudinal solution. The longitudinal dielectric constant is dependent on both the frequency and wavevector, and if it is equal to zero, the longitudinal electric field will be a solution to the free wave equation.
  • #1
scivet
12
0
Kittel solid state physics book ( chapter 14)says when dielectric permittivity is zero, then longitudinal polarization wave possibly exists. It is hard to imagine how this is possible. Can anybody explain this?
If the permittivity is zero, then there shouldn'n be any response, right? How come the longitudinal mode-are generated?
 
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  • #2
Given that [itex] D=\epsilon E[/itex], [itex]\epsilon=0[/itex] means that you can have an electric field E without an associated displacement field. If you take the full Maxwell equations you can see that for slightly higher frequencies there exist free longitudinal solutions of these equations which are not bound to external sources.
 
  • #3
The epsilon is positive at the higher frequency than plasma, which means the transverse propagating wave. Right? So, epsilon is zero, then the electromagnetic wave equation says del^2 E is zero. How does this say the solution is longitudinal? It only says K, the wave vector must be also zero?
 
  • #4
The longitudinal dielectric constant is a function of both omega and wavevector k.
If [itex]D_L(\omega,k)=0[/itex] due to [itex] \epsilon_L(\omega,k)=0[/itex]then clearly [itex] E_L(\omega, k) [/itex] is a longitudinal solution of the free wave equation.
 

1. What is longitudinal plasmon oscillation?

Longitudinal plasmon oscillation is a type of collective electronic oscillation that occurs in metallic nanoparticles. It involves the oscillation of the electrons in the longitudinal direction, parallel to the direction of the incident light.

2. How is longitudinal plasmon oscillation different from transverse plasmon oscillation?

Unlike longitudinal plasmon oscillation, transverse plasmon oscillation involves the oscillation of electrons in the transverse direction, perpendicular to the direction of the incident light. Additionally, longitudinal plasmon oscillation is typically observed in smaller nanoparticles, while transverse plasmon oscillation is more common in larger nanoparticles.

3. What factors affect the frequency of longitudinal plasmon oscillation?

The frequency of longitudinal plasmon oscillation is primarily affected by the size and shape of the nanoparticle, as well as the dielectric properties of the surrounding medium. Additionally, the type of metal used in the nanoparticle can also influence the frequency of the oscillation.

4. How is longitudinal plasmon oscillation relevant in nanotechnology?

Longitudinal plasmon oscillation plays a crucial role in various nanotechnological applications, such as surface-enhanced Raman scattering, sensing, and photothermal therapy. Its ability to concentrate and amplify light at the nanoscale makes it a valuable tool for manipulating and controlling light-matter interactions in nanosystems.

5. Can longitudinal plasmon oscillation be controlled or tuned?

Yes, longitudinal plasmon oscillation can be controlled and tuned by altering the size, shape, and composition of the nanoparticle, as well as the dielectric properties of the surrounding medium. This allows for precise control of the plasmonic properties, making it a versatile tool in nanotechnology and other fields.

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