PHP 文件未获取使用 POST 通过 AJAX 发送的变量

我正在尝试将jquery变量发送到php脚本，作为我为网站构建的搜索功能的一部分。我希望使用 AJAX 来执行对 php 文件的请求，到目前为止，我已经将其作为我的new-search.js脚本：

$('#bt_search').click(function(){
        $keyword = $('#keyword').val();//get the keyword from the input box
        $contentArray = []; //Hold checked "content" filters
        $typeArray = []; //Hold checked "type" filters
        $locationArray = []; //Hold checked "location" filters
        //Content Filter - cycle through each filter and add value of checked ones to array
        $('.content-filter :checked').each(function(){
            $contentArray.push(this.value);
        })
        //Type Filter
        $('.type-filter :checked').each(function(){
            $typeArray.push(this.value);
        })
        //Location Filter
        $('.location-filter :checked').each(function(){
            $locationArray.push(this.value);
        })
        //Testing 
        console.log("Keyword: " + $keyword);
        console.log("Content Filters: " + $contentArray);
        console.log("Type Filters: " + $typeArray);
        console.log("Location Filters: " + $locationArray);

        /*
         * Make AJAX Request to "new-search-get-results.php", passing 
         * keyword and filter arrays to the requested file.
         * 
         */ 
        $.ajax({
            url: "../pages/ajax/new-search-get-results.php",
            data: JSON.stringify({keyword: $keyword}),
            type: "POST",
            success: function(response){
                console.log(response);
            }
        });

以上方法有效，但是我从new-search-get-results.php文件中返回的响应遇到了麻烦。这是错误：

( ! ) Notice: Undefined index: keyword in C:'wamp'www'mysite.tld'pages'ajax'new-search-get-results.php on line 6

它在php文件中相关的行是：$keyword = $_POST['keyword'];

有谁知道我哪里出了问题，以便我可以修复此错误？这是我new-search-get-results.php文件：

$keyword = $_POST['keyword'];
echo $keyword;