Teaching the surprising part

Begin with crossed 0° and 90° ideal filters. The second receives a 0° state and transmits zero.

Insert a 45° filter between them. Take Iref = 100 intensity units immediately after the first filter. The middle passes 50 units and changes the transmitted field’s axis to 45°. The last filter now receives that new state and passes half again, leaving 25 units.

The relevant angle at the final stage is 45°, not the original 90° separation. The output rises relative to the crossed arrangement because the intermediate projection changes the state arriving at the last filter.

Every individual stage remains lossy. If an unpolarized source before the first filter has 100 units, the corresponding sequence is 50, 25 and 12.5 units. The reference must be stated.