Did Plato have an affair with Socrates' wife Xanthippe?

I dont think it is ether confirmed but I remember reading in a book Plato writing a poen to a Xanthippe. But, it does not state whether the Xanthippe is Socrates wife or not. I believe the book I saw it in was called 'Ribaldry of Greece' but the author escapes me.

Unfortunately, this neither answers the question but it proves he was in love with a women called Xanthippe. Unfortunately, I do not know if Xanthippe was a popualr name in Ancient Athens or read any confirmation either way.

Hope this helps.

Steve Black