In a manner relating to or by means of the interaction between electrical fields and light.
Formed from 'electrooptical' plus the adverb suffix '-ly' (from Old English -lice). This adverb allows description of how electrooptical processes occur or can be measured.
When scientists describe something happening 'electrooptically,' they're describing processes that are so fast and intricate that they operate at the intersection of electricity and light—two of physics' most fundamental phenomena.
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