Unravelling real and complex parts of material parameters

swooshfactory

Hi,

I'm writing a term paper and am having a lot of trouble understanding what is meant by the real and imaginary parts of various quantities. It seems a lot of textbooks have their own conventions and it's hard to understand whether they've redefined some symbol when they "complexify" them.

I do understand certain things, like how in the Drude model a complex electric field implies a complex magnitude of velocity for the oscillating electrons, which in turn means that they pick up some offset phase from the electric field.

An example of my discomfort is captured by the following excerpt from Wooten's Optical Properties of Solids, available (with his consent) online.

"Although D-hat can be written in complex notation, the values for the physical quantities that D-hat represents are not ovtained by taking the real part of D-hat. The quantity D-hat is truly a complex quantity and represents two real quantities D and J. The true values from D-hat must be obtained from the right-hand side of D-hat = D + i 4 pi J/ omega by taking the real parts of D and J, i.e., D-hat(true) = Re(D-hat) + i (4 pi / omega) Re (J). Having recognized that there is a truly complex D-hat, we shall from here on generally follow convention and simply write D."

He says "two real quantities D and J" then takes Re(J).

It's difficult to capture my confusion, because I now mistrust all of this complex stuff and never know what's supposed to be real and what's complex and what either of those mean.

Help, please!