I am just guessing, but does "dhiaidh" translate to 'wake'... as in "in my wake" -wake being the wave that a boat makes as it travels through water.
It doesn’t literally translate as “wake”, but it’s used as a translation of that English metaphor. There isn’t a precise definition given in either the FGB or in Dinneen. The eDIL identifies it as coming from the Old Irish word dead (“end”) — one of its more voluminous entries. It notes that its use as an independent word ended at the beginning of the Middle Irish period, but that its use in prepositional phrases has survived to the present day.