According to Facebook\'s Graph API documentation (here), you can access various sizes of a user\'s profile picture through URLs such as:
https://graph.facebo
You must request the API with the field_expansion syntax
These api requests works :
$results = $facebook->api('/me', array('fields' => 'picture.height(300).width(300)'));
$results = $facebook->api('/me', array('fields' => 'picture.type(large)'));