[Physics] About partially polarized light and the degree of polariztion

homework-and-exercisesopticspolarization

When I was taking Optics course, I found there were several questions about polarization of light. I use the textbook of Hecht.

  1. It seems that the definition of degree of polarization may be not so well-defined if $V=\frac{I_{max}-I_{min}}{I_{max}+I_{min}}$. For a elliptical polarized light, there is no natural polarized part, but still $V\neq 0$.

  2. I found it hard to deal with partially polarized light. First the definition. What is the definition of partially polarized light? Light with $0<V<1$?

  3. Is all partially polarized light can be presented by the superposition of a plane polarized light and a natural light? I suppose it is true but why? Is there any formal explanation?

  4. Consider a real problem. Suppose there is a beam of light incident on an air-glass interface with $n_{ti}=1.5$ at a certain degree, say $30°$. Then how to characterize the reflected light or the transmitted light since they are all partially polarized. What is $V$ for these lights? I gauss the answer may be $V=\frac{|r_p|^2-|r_s|^2}{|r_p|^2+|r_s|^2}$. But I can't convince my self why this correspondes to the definition above. (This is essentially a problem in Hecht.)

Thanks a lot! I am really confused with that.

Best Answer

Here is some possibly useful information from Goodman's "Statistical Optics." (Sorry about the lack of symbol quality -- so much for cut/paste from a PDF)

Light from a thermal source is regarded as unpolarized if two conditions are met. First, we require that the intensity of the light passed by a polarization analyzer, situated in a plane perpendicular to the direction of propagatof the wave, be independent of the rotational orientation of the analyzer. Second, we require that any two orthogonal field components $u_x( P, t) $ and $u_y(P, t)$ have the property that $(u_x(t + T)u_t(t))$ is identically zero for all rotational orientations of the $X- Y$ coordinate axes and for all delays $T$.

Later, in section 4.3.3,

We define the degree of polarization of the wave as the ratio of the intensity of the polarized component to the total intensity,

I'd recommend reading section 4.3 in its entirety.

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