var username = "ant1";
var password = "2015";

var url = 'https://test.ru/ajax.php';
$.ajax({
    type: "PROPFIND",
    url: url,
    success: function(json) {
        alert("Success", json);
    },
    error: function(XMLHttpRequest, textStatus, errorThrown) {
        alert(textStatus, errorThrown);
        console.log(XMLHttpRequest);
    },
    beforeSend: function (xhr) {
        xhr.withCredentials = true;
        xhr.setRequestHeader ("withCredentials", "true");
        xhr.setRequestHeader ("Authorization", "Basic " + btoa(username + ":" + password));
    }
});

var_dump($_SERVER['PHP_AUTH_USER'], $_SERVER['PHP_AUTH_PW']);

RewriteRule .* - [E=HTTP_AUTHORIZATION:%{HTTP:Authorization}]

curl --user username:password https://test.ru/ajax.php