laravel orm where条件查询怎么写？

Question

如代码所示，如果只是没有pay_time的话，数据正常取出，但是加了pay_time大于的判断就没有数据了，肯定是写法不对，请问这种情况下，要怎么写？
$where['pay_time'] = array('gt',"2017-11-03");
$where['shop_id'] = $shop_id;
$where['pay_status'] = 1;
$orders = order::where($where)->orderBy('order_id', 'desc')->orderBy('pay_time', 'desc')->paginate(50);