When Feynman describes scatterers

[WiFO215]

I was reading the Feynman lectures, on the parts that deal with optics, and he explains diffraction in a very interesting way. He imagines a diffraction grating to be made up of a long line of infinitesimal dipole oscillators, all oscillating in phase. What I don't understand is, in which direction are all these oscillators aligned? If you consider the grating as a line of oscillators, are the oscillators aligned such that they oscillate in and out of the paper or such that they oscillate along the line?

I have understood thus far in this fashion: that a dipole oscillator is simply a wire along which charges (electrons) move up and down. So then in my case, I thought a diffraction grating would be charges oscillating about infinitesimal wires aligned perpendicular to the plane along which I have assumed the line of oscillators to be on.

 

[Born2bwire]

The dipoles would be oscillating along the lines of the grating.

If I have a plane wave that is linearly polarized along the z-axis and strikes a conducting sheet, then it will induce currents along the z-direction. If I replace the plate, parallel to the x-z plane, with a grating that has sub-wavelength spacing and runs along the z-axis, then the grating will behave almost the same as the original sheet. That is, currents will still be produced along the z-axis. This is how they are able to use these as polarizers since it restricts the movement of currents along the z-axis. Hence, if a plane wave that is linearly polarized along the x-axis strikes the plate then it will pass through more or less unimpeded since it is unable to excite any first-order eddy currents along the x-axis.

Basically, the grating restricts the excitation of currents that move along the length of the wires. We could make the grating of different materials but as long as it is made of thin scatterers this is a good approximation for a lot of behavior.

 

[WiFO215]

So if I had a rod like this --------------, and say each of the hyphens represent a dipole oscillator, then each charge is constrained to move along its own hyphen?

If that is correct, then when he takes the case of the number of dipole oscillators tending to infinity, and the phase between each dipole tending to zero, he just means he's allowing the charges to oscillate along the wire, right? So basically in a continuous distribution, the charges are allowed to move along the full length of wire.

 

[Born2bwire]

So if I had a rod like this --------------, and say each of the hyphens represent a dipole oscillator, then each charge is constrained to move along its own hyphen?

If that is correct, then when he takes the case of the number of dipole oscillators tending to infinity, and the phase between each dipole tending to zero, he just means he's allowing the charges to oscillate along the wire, right? So basically in a continuous distribution, the charges are allowed to move along the full length of wire.

Yes, except any electromagnetic field has oscillating electric and magnetic fields. So the charges will not move the full length of the wire (well, ok I'm sure you can come up with a strong enough field and short enough wire where that is true) but they will oscillate about a fixed point.

His description though is more useful because I feel that it applies to arbitrary media. If we talk about perfect conductors, then we are talking about surface currents. But in a penetrable medium we have conduction and displacement currents. The displacement current arises from the polarization of the molecules due to the electric field in the dielectric. In this case, the oscillation of the polarization of the molecules gives rise to a set of currents that is physically different from the conduction currents that are induced due to the conductivity of the media.

So if I have a grating made of say glass rods, then there will be little conduction currents, glass is a good electrical insulator so few electrons are available in the conduction band. However, the molecules in the glass' lattice will oscillate due to the incident electric field. In that sense we can think of dipole oscillators. So I like his description because it covers more than just a perfect electrical conductor case (which you can probably model as dipoles again because of the constraint of the currents and the oscillation of the currents about fixed points).

 

[WiFO215]

Yeah. I like this description also because he seems to avoid those Huygens' wavelets. Every other book seems to start with "Huygens-Fresnel principle is wrong, but it gives the right answers" and this is annoying. Needless to say, I liked this description better, as I can understand electrons oscillating and creating their own fields better than these other shenanigans.

Thanks B2bw!