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why can I see light from TEM00 laser in direction of propagation?

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In my lab I have a TEM00 laser, so there is no electric or magnetic field in the direction of propagation (call it z direction). However, I know that the intensity of the laser is greatest when my eye is along z direction...why? If there is no electric field along this direction, then what is exciting the molecules in my retina??

I know that the modern explanation is that the laser is actually a stream of photons, but I am trying to model laser light propagation using classical EM, so I am looking for the classical explanation

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