Polarizer chain Malus law intensity calculator

What this calculation answers

A sequence of linear polarizers changes both beam power and polarization direction. Each stage projects the incoming linear state onto a new axis, so the difference between adjacent axes matters more than each angle measured alone.

This page follows power stage by stage and allows a separate pass-axis power transmission for each element. The initial beam can be unpolarized or already linearly polarized.

The Normal incidence Fresnel interface power balance calculator balances power across a dielectric boundary. An ideal polarizer instead projects a polarization state, so its loss cannot be inferred from that interface relation.

Use the right input conventions

All axes use degrees from one common reference. For unpolarized input, the first ideal projection passes one half before applying its entered pass-axis transmission. The initial axis field is relevant only for linearly polarized input.

Transmission percentages describe loss along the passing axis; they are not extinction ratios. Use values from zero to one hundred percent. The stage table makes each angular factor and resulting power visible.

Interpret the result

Two crossed ideal polarizers block a linear beam, but inserting a forty-five-degree stage between them can leave nonzero output. That stage changes the polarization before the final projection; it is not adding optical energy.

For zero incident power the output power is zero, while a transmitted fraction relative to zero is undefined and is labelled accordingly. Very small numerical residuals near a crossed angle should be interpreted as the ideal zero limit.

Work through the example

One watt of unpolarized light passes through axes zero, forty-five and ninety degrees with ideal pass-axis transmission. The successive powers are 0.5 W, 0.25 W and 0.125 W.

Removing the middle stage leaves crossed first and last axes, giving the ideal zero-output result. Changing one stage’s pass-axis transmission to eighty percent multiplies the downstream power by 0.8.

Where the model stops

Only ideal linear projections and entered pass-axis losses are represented. Real extinction leakage, partial polarization, retarders and depolarization are excluded.

The calculation follows optical power rather than coherent field phase. It is not a model of an arbitrary interferometer or an exposure-safety limit. Use the stage order actually present in the beam path.