In the sentence "The street lights are shining brightly at my window" there is no participle, only verb, "shinning". The word "brightly" is acting as an adverb, modifying the verb, "shinning" in the sentence. Remember, adverbs modify verbs, nouns, adjectives, or pronouns. It describes the manner, degree, extent, such as brightly describes in what manner or degree to which the light shines.
My mistress' eyes are nothing like the sun; Coral is far more red than her lips' red; If snow be white, why then her breasts are dun; If hairs be wires, black wires grow on her head.
