# Combination of three polarizing filters which (in any order) completely block transmission, such that no two filters do so

A pair of ideal linear polarizing filters, oriented perpendicular to each other, will be opaque despite the fact that each filter individually only blocks 50% of the light. I would like to extend this to three filters. Obviously this is impossible if we are restricted to linear polarizers, but I cannot determine if it can be done when circular polarizers are included.

Is there a combination of three ideal polarizing filters such that all arrangements of the three completely block transmission of light, while no two of the filters can do so?

Notes:

• These filters may be complex e.g. if one of the filters is a linear polarizer followed by a quarter-wave plate, that is fine.
• Assume each filter retains the orientation and direction you specify i.e. if you specify 'a vertical polarizer followed by a quarter-wave plate' the linear polarizer will stay vertical and the light is guaranteed to pass through it first and the quarter-wave plate second.
• If desired, you can assume a specific polarization of the incident light.
• How do you define a circular polarizer? Commented Feb 2, 2022 at 21:14
• I see no possibility of having 3 ideal linear polarizers, because no pair can be orthogonal and the last pair in the optical path would have to be orthogonal in order for the 3 polarizer train to block the light. I will fire up my optical calculus simulation software, used here, and see what happens with circular polarizers and such, but my gut feeling is your task has no solution. But I am upvoting because it piqued my interest! I will post an answer if I find one.
– Ed V
Commented Feb 3, 2022 at 1:00