How to measure the polarization density

[netheril96]

All I know is that polarization density satisfies two equations
$$\[ \begin{array}{l} \rho _{bound} = - \nabla \cdot \vec P \\ \sigma _{bound} = \vec n_{out} \cdot \vec P \\ \end{array} \]$$
This is the divergence and boundary conditions of P.But to determine a vector field uniquely,one need more than those;at least we should know the curl.

So how can we directly measure or calculate from other quantities the polarization density?
Don't tell me that for homogeneous dielectrics,P is proportional to E.That must have been tested by experiments,too.The question is HOW to prove this by experiment.

 

[eljose79]

Thank you for your post. You are correct that polarization density satisfies two equations, the divergence and boundary conditions. However, to determine a vector field uniquely, we do indeed need more information, such as the curl. The curl of the polarization density is related to the electric field through the Maxwell's equations.

To directly measure or calculate the polarization density, we can use various experimental techniques such as polarimetry, dielectric spectroscopy, and ellipsometry. These techniques involve measuring the electric field and its components at different points and using mathematical models to calculate the polarization density.

Additionally, the proportionality between P and E in homogeneous dielectrics has been proven through experiments. For example, one can perform a dielectric constant measurement by applying an electric field and measuring the resulting polarization. This can be repeated at different electric field strengths to determine the relationship between P and E.

I hope this helps to answer your question. Thank you for your interest in polarization density and its measurement.