How do you calculate extinction ratio?

Calculation of Extinction Ratio

The extinction ratio is a parameter that quantifies the effectiveness with which a polarizer eliminates light polarization. It is particularly relevant in fields such as telecommunications, where polarization-dependent devices are common. The extinction ratio is computed by taking the ratio of the transmitted light intensity of the preferred polarization to the transmitted light intensity of the blocked polarization.

The Extinction Ratio (ER) is mathematically expressed as:

ER = I_max / I_min

Where:

• I_max: The maximum intensity of the light transmitted through the polarizer (in the desired polarization state).
• I_min: The minimum intensity of the light that is also transmitted through the polarizer but in the orthogonal polarization state (meant to be blocked).

Steps to Calculate Extinction Ratio:

1. Set up the optical experiment with a known polarized light source directed towards the polarizer.
2. Align the polarizer to pass the desired polarization state (this usually corresponds to the maximum transmitted intensity I_max).
3. Measure the transmitted light intensity using a photodetector or power meter. This measurement is I_max.
4. Rotate the polarizer or adjust the experiment such that the orthogonally polarized light is being passed (corresponding to the minimum transmitted intensity I_min).
5. Again, measure the transmitted light intensity, which is now I_min.
6. Calculate the ratio of I_max to I_min to obtain the Extinction Ratio (ER).

Additional Notes:

• The extinction ratio is often expressed in decibels (dB), where:
  ER(dB) = 10 log₁₀(ER).
• An ideal polarizer would have an infinite extinction ratio, while practical polarizers have finite, but typically high, extinction ratios.
• A higher extinction ratio indicates better polarization purity and a better quality polarizer.

Example Table of Extinction Ratios for Different Polarizers

Knowing the extinction ratio of a polarizer provides insight into its performance in applications where the control of light polarization is critical. Accurate measurements and calculations of this ratio allow for better design and optimization of optical systems.