Polarization

Concepts of Polarization

• Definition: Light is polarized when its electric fields oscillate in a single plane, rather than in any direction perpendicular to the direction of propagation.
  • basically, all light that propagates between a polarizer is all one orientation
    • 

Polarized Light and Polarizers

• Transmission: Polarized light will not be transmitted through a polarized film (polarizer or polarization filter) whose axis is perpendicular to the polarization direction.
• Outgoing Intensity:
  • When light passes through a polarizer, only the component parallel to the polarization axis is transmitted. If the incoming light is plane-polarized (linearly polarized), the outgoing intensity is proportional to the square of the cosine of the angle between the light’s polarization direction and the axis of the polarizer.

Behavior through Crossed Polarizers

• Crossed Polarizers: If initially unpolarized light passes through crossed polarizers (axes at 90°), no light will get through the second one.

Examples

• Two Polaroids at 60°: Unpolarized light passes through two Polaroids; the axis of one is vertical and that of the other is at 60° to the vertical. Describe the orientation and intensity of the transmitted light.
  • Intensity: $I_2=I_1{\cos }^{2}60°\approx \frac{1}{8}{I}_0$
• Three Polaroids: If a third Polaroid, with its axis at 45° to each of the other two (crossed at 90°), is placed between them, some light will pass through.
  • Intensity Pattern: $I=\frac{1}{8}{I}_0$.

Brewster’s Angle

• Brewster’s Angle: At the polarizing angle or Brewster’s angle, reflected light is 100% polarized perpendicular to the plane of incidence.i
  • we use: $\tan {\theta }_p=\frac{n_2}{n_1}$ to find angle
  • Example:
    • Given $n_1=1.00$ (air) and $n_2=1.33$ (water), calculate:
      • Polarizing angle: ${\theta }_P={\tan }^{-1}(1.33)=53.1°$
      • Refraction angle: ${\theta }_r={\sin }^{-1}\left(\frac{n_1\sin {\theta }_P}{n_2}\right)\approx 36.9°$

Circular Polarization

• Relative Phase Change: By changing the relative phase between $E_x$ and $E_y$ using a quarter wave plate (through birefringence), linear polarization can be converted to circular polarization.
• Right Circular Polarization (RCP): Use the right-hand rule to determine the direction.
• Behavior of Circular Light on a Linear Polarizer: When circularly polarized light is put through a polarizer along the y (or x) axis:
  • Answer: Intensity $I=\frac{1}{2}{I}_0$

Linear and Elliptical Polarization

• Phase Difference: Different phases between $E_x$ and $E_y$ produce elliptical or circular polarization.
• Example:
  • At ${\varphi }_x-{\varphi }_y=90°$, using $t=0$ \begin{align} E_x = \frac{E_0}{2} \cos (kz - \omega t) \\E_y=\frac{E_0}{2} \sin (kz - \omega t) \end{align} This configuration leads to circular polarization.

These notes have covered the main points presented in the lecture PDFs on polarization, including conceptual explanations, mathematical expressions, and examples.