Because Vader does not want to give Luke the advantage he won't enter the darkened alcove. In the novelization luke throws away his lightsaber, hands it over to vader who clips it to his belt and steps into the darkness to confront Luke.

When Vader senses Luke Thoughts about his sister leia He Roars "twins!!". "Obi Wan was wise to hide her from me if you will not turn to the darkside then perhaps your sister will"

Then Luke uses the force to make his saber fly to his hands and unclip form vaders belt, shouting "Neverrrrrrr!" in Fury and is one step away from completely going over to the darkside. All he has to do is murder his own father in anger.