Real materials may also be Anisotropic, not the same in all directions,

and that would be codified by the dielectric response of the material.

Being a second rank or three by three tensor, such that when you

push on a material in an electric field, the displacement current, and

the displacement field may not be in exactly the same direction.

So quartz crystals, and things like that we do use in optics need this

form of Anisotropic dielectric response.

Most of the time in this course, we'll make the Isotropic assumption.

We'll turn this tensor into a scalar, and it becomes a simple multiplication.

Magnetic fields are described by the same relationship, but

almost always the relative permeability of the material can be taken as one.

Materials generally don't respond to magnetic fields at these frequencies, and

so we can ignore that term.

And though we do have materials that have absorption or

loss, in many cases we'll assume there's absolutely no loss, and

therefore the conductivity is zero, and the current is zero.

We don't normally deal with terms in the time domain here,

of course we Fourier transform.

And so, there's the Fourier transform integral.

It says that we can represent these functions of time as a function of

frequency, and of course this transform goes back both ways.

That should be a two-pi right there.

The key thing is we can transform between domains.

If you're not intimately familiar with the Fourier transform,

that would be a quick thing to go review as well.

And that's essentially equivalent to saying that we have only monochromatic

fields, and so we're only dealing with one frequency component at a time anyway.

So in many cases in optics, we do have lasers,

or something that are pretty good approximations of monochromatic.

And so the physical version of this is you're only dealing with one

temporal frequency, or one wavelength at a time.