Get php variable in functions.php & echo it in theme template inside JavaScript

I’m working in a WordPress template, and I try to echo the variable “citation_string_to_js” who is in function.php into the JavaScript in my theme footer.php… but it output it empty !

This is the code i use in function.php :

add_filter( 'citation_string_to_js', 'return_citation_string_to_js' );
function return_citation_string_to_js( $arg = '' ) {
return 'YOUR CONTENTS GOES HERE';
}

The JavaScript in Theme template (footer.php) :

<script type="text/javascript">
document.getElementById('grid-4').innerHTML = '<? echo apply_filters( 'citation_string_to_js', '' );?>';
</script>

what’s wrong ?

Thanks for helping.