Nachdichtung combines the preposition nach ("after", "according to") with Dichtung ("poetry"). The word denotes a piece of poetry that tries to re-create the spirit in which another piece of poetry was written and its effect on the reader without being literal about it—what's more important is that the new piece is a successful piece of poetry in its own right while staying "true" to the original in a deeper sense.
The term is particularly useful in discussions about translations, and the discussions we had on this blog about translations (from the German) motivated me to introduce the term, for which I cannot find an English equivalent. I'll give examples and a note on pronunciation in my comments.
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