Empty Zip file downloaded in custom plugin

Hi !

I created a custom plugin very simple with just a button that create a ZIP file of a folder when is clicked.
Here is my code when the button is clicked :

if(isset($_POST['Submit'])) {
        $rootPath = realpath('../wp-content/uploads/users/photo');
        $zip = new ZipArchive();
        $zip->open('Utilisateurs.zip', ZipArchive::CREATE | ZipArchive::OVERWRITE);

        $files = new RecursiveIteratorIterator(
            new RecursiveDirectoryIterator($rootPath),
            RecursiveIteratorIterator::LEAVES_ONLY
        );

        foreach ($files as $name => $file)
        {

            if (!$file->isDir())
            {
                $filePath = $file->getRealPath();
                $relativePath = substr($filePath, strlen($rootPath) + 1);
                $zip->addFile($filePath, $relativePath);
            }
        }

        header("Pragma: public");
        header("Expires: 0");
        header("Cache-Control: must-revalidate, post-check=0, pre-check=0");
        header("Cache-Control: public");
        header("Content-Description: File Transfer");
        header("Content-type: application/octet-stream");
        header("Content-Disposition: attachment; filename=\"Utilisateurs.zip\"");
        header("Content-Transfer-Encoding: binary");
        header("Content-Length: ".filesize("Utilisateurs.zip"));
        ob_end_flush();
        readfile("Utilisateurs.zip");
    }

My problem is : the ZIP file is created correctly and I download it automatically but the downloaded version is empty. This problem appears only when I execute the code from the plugin, when I try to execute it from an other place it works perfectly the ZIP file contains all elements. Someone knows why or how to fix this problem?

Thank you !