# A Difference between polarization and the dielectric constant?

#### epsilonita

Hi everyone,

When an electromagnetic wave passes through a material, then depending upon the atomic structure of that material it polarizes that material. There is another definition of polarization in physics which says that polarization is the direction of oscillating electric field in EM wave. My question is that are these polarization same or they have different formulas?

Can anyone please clear this confusion.

bests

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#### sophiecentaur

Gold Member
Dielectric Constant is a complex quantity, involving Power Loss during transmission through a medium so that could be one thing to distinguish it from Polarisation. Have you actually looked these terms up in more than one source?
Also, "Polarisation" of a molecule is not the same use of the word as when its used to describe E field direction.

#### Cryo

You are talking about completely different things here.

Effect of polarizing the material is described by the polarization (density) $\mathbf{P}$, which literally is the density of induced electric dipoles per volume. Depending on the material $\mathbf{P}$ is related to refractive index, susceptibility coefficients (linear and non-linear), conductivity, dielectric constant etc. etc. The units of $\mathbf{P}$ are Coulomb.meter/Volume = Coulomb/meter^2. Note that induced $\mathbf{P}$, in general, can depend on the applied electric field in arbitrary way (local, nonlocal, linear, non-linear, scalar, tensorial).

Polarization of the electrmagnetic wave on the other hand is loosely defined as the direction in which the electric field points as the wave propagates. I intentionally keep the definition vague since, one can have linear polarization, circular/elliptic polarization, azimuthal polarization, radial polarization, and probably many more. This kind of polarization has no units, it is simply the direction in space.

It is unfortunate that there are two completely different things called 'polarization' in electromagnetism, but there is nothing deep here - simply a quirk of history.

#### epsilonita

Yes that is exactly my point as well. When we say that an em wave is polarized, we mean the way how its electric field oscillates. Then we can describe this in detail using Jones matrix etc. But when we talk about Lorentz model which is used to extract several properties of a material when it is in contact with em wave. In that model, we also say that material polarization is directly proportional to its linear optical susceptibility.

Now we have several methods in optics to measure the phase of polarized em wave. But when it comes to the phase difference between polarization vector and incident electric field on the material, do we have any methods?

#### Cryo

Can I suggest you use 'polarization' or $\hat{\mathbf{E}}$ for the direction in space and 'polarization density' or $\mathbf{P}$ for the density of induced electric dipoles. Otherwise it will get too confusing.

Now... Are you asking about the phase of $\mathbf{P}$?

#### epsilonita

Yes exactly I am referring to polarization density P here.

#### Cryo

As I mentioned before there is an extemely broad range of ways the induced polarization density can depend on electric field. There is no point trying to cover all the cases, so we can limit our-selves to linear dependence, ignore spatial dispersion as well as any tensorial effects.

Phase only makes sence in time-harmonic picture, so let us stick to that. In this case $\mathbf{P}=\epsilon_0 \left(\tilde{n}^2 -1\right)\mathbf{E}$, where $\tilde{n}$ is the complex refractive index, so measuring the phase of polarization density becomes equivalent to measuring the refractive index. Is this what you were after?

I have not seen many papers that reported measuring the polarization density. Usually one has a model of how the polarization depends on electric (and possibly magnetic) field. That model includes coefficients (e.g. refractive index). People then measure the coefficients, and report their findings within the framework of the chosen model

#### epsilonita

As I mentioned before there is an extemely broad range of ways the induced polarization density can depend on electric field. There is no point trying to cover all the cases, so we can limit our-selves to linear dependence, ignore spatial dispersion as well as any tensorial effects.

Phase only makes sence in time-harmonic picture, so let us stick to that. In this case $\mathbf{P}=\epsilon_0 \left(\tilde{n}^2 -1\right)\mathbf{E}$, where $\tilde{n}$ is the complex refractive index, so measuring the phase of polarization density becomes equivalent to measuring the refractive index. Is this what you were after?

I have not seen many papers that reported measuring the polarization density. Usually one has a model of how the polarization depends on electric (and possibly magnetic) field. That model includes coefficients (e.g. refractive index). People then measure the coefficients, and report their findings within the framework of the chosen model
thank you, that is almost what I was looking for. :)

#### Cryo

I think you changed your post since I last saw it. In your last version you were saying something to the effect is there a way to measure polarization without measuring the susceptibility (that's my recollection of the question). Since you are working with plasma (my recollection), I presume the frequencies are low. So perhaps there could be a way to use light to actually track the displacement of particles and then to re-interpret this as the polarization. But this sound very complicated to do. :-)

#### epsilonita

I think you changed your post since I last saw it. In your last version you were saying something to the effect is there a way to measure polarization without measuring the susceptibility (that's my recollection of the question). Since you are working with plasma (my recollection), I presume the frequencies are low. So perhaps there could be a way to use light to actually track the displacement of particles and then to re-interpret this as the polarization. But this sound very complicated to do. :-)
:) yes I did change it and your recollection is almost correct :) What I want to do is to verify some modifications that I made in theory for calculating plasma and damping frequency. Idea was to measure the phase difference of P (polarization density) and original electric field. But as you said, its complicated. So I am figuring out some other ways, like measuring nonlinear refractive index. lets see how it works! Thanks anyway, this small discussion cleared up some confusions :)

"Difference between polarization and the dielectric constant?"

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