How to navigate to a page in my application after external php file?

I can understand your problem. Even i have several solutions for you.

Solutions-1
When user is pressing the submit button on "contactForm.html", then just don't fire the form submit. Rather in-place of submit button use "html buttons only" and after pressing that button call the angular ajax i.e $http to post all your to your page, and after a response in $http success callback you can use $state.go('app.home'); to redirect to particular page.

Solution-2
Create a iframe in your ionic html page. So your contactForm.html should be placed on server rather than ionic resources. So that contactForm.html should post to your php page and things can be handled. Even from the ionic itself you can check the iframe state and src base on that you can redirect your page.