Electron beams interfere in ways that light beams don't, though. If they cross in vacuum, they deflect each other due to the electric charge carried by electron

Electron beams interfere in ways that light beams don't, though. If they cross in vacuum, they deflect each other due to the electric charge carried by electrons. Light beams can only deflect each other in media with non-linear response to electromagnetic fields, i.e. the response to one beam modifies the response to the other beam.