# Lens for an electric field

1. Jan 2, 2009

### thinktank1985

Hii all..

Is it possible to design a lens(using magnetic fields, dielectric media etc) so as to focus an existing electric field on to a localized region on a electrode. I hope the following picture illustrates what I am trying to do.
What I need is a electric field which is considerably high on a small region at the center compared to that on the outside. The electric field need not be static but could be pulsating too. Since I am thinking of length scales of around 1 μm, I cannot use very sharp objects, hence I cannot use a pointed electrode.

The figure above shows a simple version of the configuration I am interested in. Figure A shows the configuration and the electric field variation on the bottom electrode when no "lens" is placed within. Figure B shows the configuration and the graph with the lens within the plates. The graph in figure B shows the desired electric field variation over the surface of the bottom electrode.

Last edited by a moderator: May 3, 2017
2. Jan 5, 2009

### Antenna Guy

I can't say anything authoritative, but I suspect that a (quasi?) parabolic discontinuity in dielectric constants between the plates might do something like that.

Regards,

Bill

3. Jan 6, 2009

4. Jan 6, 2009

### Antenna Guy

I don't know why you think cavity resonators focus fields.

Regards,

Bill

5. Jan 7, 2009

### thinktank1985

Hii all,

thanks a lot for your reply. I know that a sharp pointed needle like structure might be able to produce a high electric field in the surrounding geometry, but as I said earlier, I am thinking of a dimension close to 1 micrometer, so in order to produce a sharp needle, I would have to have fabricate electrodes with minimum dimension of 10 nm or so. This is a very difficult task, possible by only very advance fabrication techniques. For conducting media, you just have to introduce masks with low conductivity, while material with higher conductivity is located in the gaps of the mask. The equations and boundary conditions for electrostatic fields are similar so, for the same relevant parameters (i.e. conductivity=dielectric constant), the solution would be the same.

The figure above shows the geometry: the blue region is essentially a region of high conductivity, while the red region is a region of low conductivity. The figure on the left shows the electric field produced on the bottom electrode. However here too, the size of the gaps plays an important role, and would be difficult to fabricate. I had read that electric fields and magnetic fields are inherently related, so I was hoping that it might be possible to use an external magnetic field to simulate the effect of the mask, albeit without fabricating the mask.

You must have heard of electrostatic lenses/magnetic lenses used to orient electrons/ions for bombardment in electron beam lithography/ion beam lithography. Similar lenses are used in cyclotrons to focus electron/neutrons, however here a plasma column is used. In a similar way, the mask can be considered to be a lens which focuses the electric field on the bottom electrode. By lens I essentially mean a device or object which concentrates a given field or beam at a given point or surface.

Last edited by a moderator: May 3, 2017
6. Jan 7, 2009

### thinktank1985

@Naty1: I am indeed interested in the flow of particles, not a static electric field. The reason I said an electrostatic field is because I thought if it is possible to concentrate the field locally in the electrostatic case, it would be possible too in cases where there are moving ions/electrons.

Essentially ions move up from the bottom electrode towards the top surface. But I want to localize the region where the ions originate from. In order to localize the generation and movement of ions to a particular region on the bottom electrode, I have to have a concentrated electric field in a small region.