EM Shielding Dilemma: Understanding Transverse Wavelengths

[invisigo]

In the classical picture of an electromagnetic wave, the wavelength is specified along the direction of travel. However, with EM shielding that is using a grid (microwave, chicken wire), I've heard that so long as the spaces are less than the wavelength, you will achieve electromagnetic shielding. This description implies that there is a transverse wavelength to a EM wave that is "blocked", but in our classical picture, we never defined a transverse wavelength.

Can anyone explain this dilemma or propose a physical picture that works?

 

[Born2bwire]

The fields are transverse to the direction of propagation. The tangential electric field and the normal magnetic field are canceled out along the surface of a perfect conductor. If we have a screen of vertical wires (not a grid, but just along one direction), then what will happen is that the component of the electric field along the wires and the magnetic field perpendicular to the wires will not propagate through the screen as they will be canceled out. However, the component of the electric field normal to the wire and the magnetic field tangent will transmit through. Hence, you have a polarizer. So a mesh are two polarizers at right angles, each one will remove one of the two polarizations that the field can be decomposed into (the wave can be polarized in any direction in the plane perpendicular to the direction of propagation but it can always be decomposed into the summation of two polarizations) and thus it will prevent the transmission of an arbitrary field.

 

[invisigo]

The idea I'm more confused about is the relationship between wavelength and the grid hole size. One idea I just thought about is maybe it has to do with the minimum spot size of the radiation. If this is the case, then the rule of thumb for hole size does not hold exactly. I can get a beam with wavelength 1m into shielding with holes of 1m just by increasing my aperture.

Since spot size d = focal length*wavelength*3.83 / pi*aperture diameter

Then a focal length of 50meters and a aperture diameter of 100meters would allow me to get through your EM shielding designed to block 1m waves.

 

[Born2bwire]

It has to do with the boundary conditions. The grid spacing is indicative of the lowest mode (and wavelength) that can be supported in the grid. The grid will always have a finite amount of depth, and so you can do a very crude analysis by treating a single grid element as a rectangular waveguide. In this case, we know that the tangential electric field and the normal magnetic field must go to zero on the surface of the conductor (assuming PEC). All of the fields must be zero inside the conductor, past the surface. So the boundary conditions are the zeroing of certain components on the surface for wave solutions. The result is that the components of the wave in the plane parallel to the grid must be sinusoidal and thus the lowest mode is going to be of a wavelength twice the distance between the edges of the grid.

If the electromagnetic wave has a wavelength lower than around twice the grid spacing (normally we choose 1/4 wavelength spacing), then there will not be a supported propagating mode through the grid. The radiation will still transmit through because it will travel as an evanescent mode, but it will be severely weakened. The degree of this attenuation will be dependent upon the thickness of the grid's wire and the spacing of the grid in comparison to the incident wave.

 

[invisigo]

Ah! Yes, thank you for the clear explanation! I never thought to think of shielding as a waveguide, but it makes perfect sense now! I am indebted to you for this insight.