How can we cause EM waves to travel through a tiny hole
in an infinite conducting plane?
I've always known one trivial answer to this question:
Place a 1/2-wave dipole antenna on one side of the
conducting plane, run wires from this antenna through
the tiny hole in the plane, then place a second 1/2-wave
dipole on the other side of the plane and connect the
wires to it. The first antenna acts as a receiver and
absorbs EM energy, which flows along the wires, through
the tiny hole, and drives the second antenna as a
transmitter. The two antennas have essentially "focused"
the Poynting-vector flux of the incoming EM waves so that
it passes through the tiny hole.
A naive description might read thus: "we turn the radio
waves into 'electricity' and then back into radio waves
again." This is wrong. Since electrical energy in
circuits is actually composed of e-fields and b-fields
surrounding the circuit, the EM energy in the above
description never actually "changes" into "electricity",
instead it becomes coupled to the mobile charges within
the conductors and so gains the ability to pass through
a very small hole in a conductive plate.
Note that there is no lower limit on how small the
hole can be in an ideal case, but of course there are
many practical limits in the real world case.
Also note: if we think in terms of photons, then
the antennas are somehow guiding photons to flow
THROUGH the hole rather than being reflected from
the conductive plane. With the wires installed
in the hole, MORE photons can get through. This seems
silly. However, when analyzed in terms of EM fields, it
makes perfect sense. The EM energy-flows surrounding
a 2-wire waveguide don't much care if the wires are
spaced closely or wide, or if they pass through a tiny
hole in a conductive plate. The photons which make up
those EM fields around the wires will happily seek out
the tiny hole and flow right through with no problem,
regardless of their frequency.
Here's a second answer to the original question. To allow EM waves to pass through the tiny hole in the infinite conductive plate, just place some molecules in the hole, but choose molecules which are resonant at the frequency of the EM waves. Suppose the EM waves are microwaves, and their frequency is at the ammonia resonance (think "ammonia maser"). If we place some ammonia molecules in that tiny hole, the molecules will strongly absorb the incoming radiation, then they will re-radiate it. Part will be scattered backwards, but part will move forwards through the hole. The presence of those ammonia molecules has allowed the EM radiation to pass through the hole.
The presence of the molecule can make a big difference.
Suppose we make our hole somewhat larger than a single
ammonia molecule. Without that molecule present, the
amount of EM wave energy which passes through such a
tiny hole will be vanishingly small. However, with the
molecule placed into the hole, relatively enormous
amounts of EM power suddenly can get through.
OK, here's a third option which doesn't involve molecules.
Place a very small lossless loop antenna in the hole,
and connect it to a capacitor. Tune the LC circuit to
resonate at the frequency of the incoming waves. The
loop antenna will build up a very large alternating
current at the resonant frequency. It will re-radiate
EM waves, with part of the energy scattering backwards
through the hole, but part being radiated out the other
side. The presence of the tuned circuit in the tiny
hole has allowed EM waves to pass through the hole.
Again note that there is no theoretical limit on how
small the hole can be. Obviously any PRACTICAL
applications will have many limits, but I'm not talking
about practical issues here, I'm talking "physics
homework questions" and "thought experiments."
Also note that the above LC circuit acts as a macroscopic
analogy for a molecular or an atomic oscillator.
If the "energy sucking" controversy is any guide, then one
or two people will read this and say "cool", while a huge
number of others will become enraged and launch personal
attacks. This message is aimed at those one or two people
who actually ENJOY thinking. Those who become angry and
descend into ridicule can fight with each other this time,
since I'm going treat their offensive behavior as it
deserves, and recoil in revulsion.
"I know that most men, including those at ease with problems of the greatest complexity, can seldom accept even the simplest and most obvious truth if it be such as would oblige them to admit the falsity of conclusions which they have delighted in explaining to colleagues, which they have proudly taught to others, and which they have woven, thread by thread, into the fabric of their lives." -Tolstoy
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