嵌套文档MongoDB查询的PHP语法

Question

Document Sample:

stdClass Object
(
    [_id] => MongoDB\BSON\ObjectId Object
        (
            [oid] => xxxxxxxxxxx
        )

    [sent_date_time_stamp] => MongoDB\BSON\UTCDateTime Object
        (
            [milliseconds] => xxxxxxxxxxxxxxx
        )


    [sent_data] => {"switchId":"db_sw_001","isQuery":true,"command":"6541"}

    [device_identifier] => stdClass Object
        (
            [$ref] => device
            [$id] => db_sw_001
        )

)

PHP Code:

$manager = new MongoDB\Driver\Manager("mongodb://$username:$p@$hostPort");
$filter = array("sent_data.switchId"=>"db_sw_001");
$filter = array();
$options = array(
                    'limit'=>10,
                    'sort'=>array("_id"=>-1)

    );
$query = new MongoDB\Driver\Query($filter, $options);

The Above Query returns NULL

Please help