Full Idea
On the possible world's account, x's being essentially F is nothing more nor less than x's being F in every world in which it appears.
Gist of Idea
An x is essentially F if it is F in every possible world in which it appears
Source
Frank Jackson (Possible Worlds and Necessary A Posteriori [2010], 6)
Book Reference
'Modality', ed/tr. Hale,B/Hoffman,A [OUP 2010], p.261
A Reaction
There you go - 'true in every possible world' is the definition of metaphysical necessity, not the definition of essence. Either get back to Aristotle, or stop (forever!) talking about 'essence'!