What you want is default Laravel authentication behavior..
return $this->authenticated($request, $this->guard()->user())
?: redirect()->intended($this->redirectPath());
If a user visits /privatepage and that page is protected by the auth middleware then the user is redirected to the login page and /privatepage is saved to session as url.intended. Then after a successful authentication Laravel checks if the session has the url.intended key, and if does, it will redirect to the URL saved in the session. If not, it will redirect to whatever page you have defined, default is /home.
If you would like to manually handle what happens when a user is authenticated, then you can create a function called authenticated() which will be called instead.