Why can wire mesh reflect radio waves for telescope dishes?

[aster79]

I’ve heard that the reason radio telescope dishes can be made out of wire mesh is because, so long as the size of the holes is less than (I believe) 1/10 the wavelength of the radio wave, the wave be reflected (it will see the dish as being solid). I was wondering what the physical reason was that this should be true, as I haven’t seemed to have found an adequate answer for this anywhere.

 

[Born2bwire]

Any solid sheet of conductor will reflect a radio wave. This is done because electromagnetic waves induce currents on the surface of a perfect conductor. These currents will generate their own electromagnetic waves. The secondary waves will cancel out the incident wave inside the PEC (thus there are no waves inside the PEC) and will represent the scattered wave outside of the PEC. In the case of a large flat surface this scattered wave will be a nice reflection of the incident wave.

If we look at the results for a plane wave, we know that a plane wave is generated by an infinite sheet of current that runs along the direction of polarization for a linearly polarized wave. Via reciprocity, we know that if this wave struck an infinite PEC sheet that the induced currents would be the same as the source currents and would run in the direction of the electric field's polarization. This means that the induced currents on a very large sheet that is illuminated over a small section of the sheet will approximately flow along one direction. Thus, we can cut strips in this sheet so that we now have a bunch of wires that run along the direction of the incident wave's polarization. Since the induced current will flow largely along, say, the x direction, if were we replace our solid sheet with insulated wires that run in the x direction then we can achieve the same reflection of the wave since the induced currents can be the same. This only works along the polarization of the wave. But, for linear polarization we can decompose any arbitrarily linearly polarized wave into the summation of two orthogonally linearly polarized waves. Thus, if we run another set of wires orthogonally to our first set (say now in the x and y directions) then the induced currents from the decomposed wave (which we now decompose into x and y polarized waves) can run the lengths of the wires without being impeded. So this is why we can replace the solid sheet with lengths of wires running crosswise. Finally, we can extend this to any kind of incident signal since we can decompose any electromagnetic wave into a superposition of plane waves.

Now if we allow gaps between the wires, we find that we can still achieve very good reflection if the gaps are on the order of subwavelength in size. This is because the resulting currents can still approximate a good representation of the reflected wave. This is similar to how we can sample an audio signal at 10 KHz and be able to reproduce perfectly any signal with frequency of 5 KHz or less.

 

[aster79]

Thank you for the post; it helped to clear things up for me. :)