Downloading file using php and ajax

Question

I'm trying to write a script to download a file. But when I click "Download" nothing happens. I'm using Laravel for my project. This is the function:

public function downloadUserFile(){
        $userid = Auth::id();
        $result = $_POST['filename'];
        $query = File::where('filename', $result)->where('userid', $userid)->get();
        foreach($query as $queryResult){
            $mimeType = $queryResult->mimetype;
            $filepath = $queryResult->filePath;
            $filesize = $queryResult->filesize;
            if (file_exists($filepath)) {
                header('Content-Description: File Transfer');
                header('Content-Type: ' . $mimeType);
                header('Content-Disposition: attachment; filename="'.basename($filepath).'"');
                header('Expires: 0');
                header('Cache-Control: must-revalidate');
                header('Pragma: public');
                header('Content-Length: ' . $filesize);
                ob_clean();
                flush();
                readfile($filepath);
                exit;
            }
        }       
    }

And the ajax:

           if(key === "download") {
                var classElements = document.querySelectorAll("tr.ui-selected td.filename");
                var csrf = $('input[name=_token]').val();
                for(var x = 0;x < classElements.length;x++){
                    var result;
                    result = classElements[x].innerHTML;
                    $.ajax({
                        async: true,  
                        method: 'POST',
                        url: '../public/downloadfile',
                        data: { filename: result, "_token": csrf  }   
                    });
                };
            }

The ajax response and the PHP don't give me errors and I can't understand why nothing actually happens. What could be the problem?