JQuery :: How To Supply XHR Exception Object To Ajax Function

I've been using $.get() and $.post() extensively, but then noticed the more functional $.ajax, which lets you handle server-side errors using the "error" option. The parameters to the callback function for the error option are:
(xhr, status, exception), where in the documentation it says "exception" is the Exception object if it's supplied.

My server-side is PHP, and when I perform a:
throw new Exception("You can't do that!")
or
trigger_error("You can't do that!", E_USER_ERROR)
It does run my error callback, but it puts 'undefined' in the "exception" object, and my custom error message is nowhere to be found. How do I populate that Exception object on the server side, so that the error callback can then access it?