lens for an electric field.

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.

 
**broken link removed**

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.

When designing electrostatic lenses respectively a specific field geometry, you have to consider general electrostatic properties. It's not clear to me, if you already did. One property is, that the line integral of field strength must be equal the potentential difference between the two electrodes for any possible path.

Furthermore, the field strength is a vectorial quantity, I can't see from your sketched function, what's the intended field geometry.

As another point, electrostatic lenses can be formed by electrodes only (plates, wires). So they considerably affect the field outside the target region. Arbitrary field geometries may be impossible in many cases.

What you actually want is to increase the local gradient.
One way to do it is to use a sharp end on one side which you do not want. The other way is to introduce a piece of dielectric which essentially increases the gradient by dielectric polarisation, P = k.E where k is the permittivity.
The easiest way to increase gradient locally is to bend the other electrode so its distance to the other will diminish.
There is no device like a lens for electric fields: with magnetic fields, shaping magnet body helps to "focus" magnetization. In an electrostatic field, the intensity is proportional to the voltage between the electrodes and inversely proportional to distance between them. Adding a dielectric layer or body can work.