Producing polarized light

Figure 16.2: A linear polarizer producing a polarized light along the $y$ direction

There are devices called polarizers which produce linearly polarized light. Figure 16.2 shows a polarizer placed in the path of light travelling along the $z$ axis. The electric field $\vec{E}$ of the incident light can oscillate in any direction in the $x-y$ plane. The polarizer permits only the $\vec{E}$ component parallel to the transmission axis of the polarizer to pass through. Here we consider a polarizer whose transmission axis is along the $y$ direction. So the light that emerges from the polarizer is linearly polarized along the $y$ axis.

Figure 16.3: Consecutive polarizers

We next consider two polarizers whose transmission axes have an angle $\theta$ between them as shown in Figure 16.3. The light is linearly polarized after the first polarizer with

$$\vec{E}(z,t)=E_0 \, \cos(\omega t - k z) \hat{j}$$ (16.1)

and intensity $I_0=E_0^2/2$. The second polarizer allows only the $\vec{E}$ component along its transmission axis to pass through. The light that emerges is linearly polarized along the transmission axis of the second polarizer. The transmitted wave is

$$\vec{E}(z,t)=E_0 \,\cos \theta \, \cos(\omega t - k z) \hat{e}$$ (16.2)

The amplitude of the wave goes down by $\cos \theta$ and the intensity is $I=E_0^2 \, \cos^2 \theta /2 =\cos^2 \theta \, I_0$. We see that linearly polarized light of intensity $I_0$ has intensity $I_0 \, \cos^2 \theta$ after it passes through a polarizer. Here $\theta$ is the angle between the transmission axis of the polarizer and the polarization direction of the incident light. This is known as Malus's Law.

There are essentially four methods to produce polarized light from unpolarized light: [a.] Dichroism [b] Scattering [c.] Reflection [d.] Birefringence.