You almost don't have to change anything. What I suggest you could do, would be to submit the form in the new window to a PHP-script which then could head(er) over to a "thankyou"-page if you want to.
As DKode writes, you need javascript to pop up the window and such. You just have to remember this :
"PHP is serverside - and can make whatever content you can do yourself in a HTML-page."
So PHP is not going to take care of opening windows with or without toolbars, alertboxes or whatever - that's all up to you by using to PHP to generate the ness. code.
Happy coding!