# Charge density in metal nanoparticles at plasmon resonance

It is important to know the magnitude and distribution of electric field near the metallic nanoparticles at plasmon resonance. One can look at the electric field and say whether the plasmon mode is dipolar or higher order mode such as qudrapolar mode. At many times one is also interested to know the surface charge density which makes easier to identify the plasmon mode. One can get the surface charge density by talking the divergence of electric field (near field) either calculated by DDA method or FDTD method [Reference paper]. Below I have calculated the electric field near nanoparticle at plasmon resonance using FDTD method and also calculated the corresponding surface charge density. One can see the dipolar nature of the electric field, and also the surface charge density maximum at one end of the particle and minimum at the other end. Surface Charge density plots become more useful when analyzing complex geometries with complex modes.

Electric field and charge density distribution

## 4 thoughts on “Charge density in metal nanoparticles at plasmon resonance”

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4. Shuyuan Xiao says:

Dear Bala,

I am a PhD student from China and now in my first year study.
I am doing research on LSPR, and I encounter a big dilemma that I don’t know how to calculate “Charge density in metal nanoparticles at plasmon resonance” with FDTD Solutions, which can directly reveal the resonance mode, such as dipole, quadrupole or higher.
The situation I face is a metamaterial, x, y periodic and z pml, with a planewave from z backward, and
I would like to calculate the charge density in the metamaterial at resonance, i.e., wavelength at transmittance dips or peaks, to find out whether it is a dipole or a quadrupole mode.
I have looked up to many references and they only provide the results, the charge density distribution rather how to calculate it with FDTD Solutions. The 2D example in Lumerical websites works well, but 3D example may be something wrong, as when I set the “field” monitor to a fixed wavelength it only give a blurred distribution.

Could you help me? With a simplest example that I described?

Sincerely,
Shuyuan Xiao (syxiao@hust.edu.cn)
From Hust, CHINA