There are many applets on the internet which demonstrate Huygens Principle or reflection/refraction geometrically. This is one such example: https://www.olympus-lifescience.com/zh/microscope-resource/primer/java/reflection/huygens/
In all of these applets it appears that the wave is polarized so that the E field is going "out of the screen". This seems crucial to the argument as this guarantees that the surface is 'activated' by the wave crest (or any other part of the wave ) in a staggered way to get the desired effect.
Does Huygens Principle of reflection take polarization into account, or must one assume that the wave is polarized so that the E field points out of the screen? Lastly if it does take it into account, how?