How to search multiple collections in mongoDB

Question

I have 2 collections in mongoDB namely product and author . Now the product collection has an object called the detail which has the title and other details whereas the author table has details regarding the author . Now i am trying to make a search that finds both title and author .. For eg: if the title is matched the details of that product should be listed and if the author is matched then again the details of that product should be shown. The author_id is a foreign_key in the product collection and the _id is a primary key in the author collection.

Below is my collection

The Product Collection

{
    "_id" : ObjectId("5af2bd44a003533a8abf4e56"),
    "product_type_id" : "5ae834807ae0d9538e45ab45",
    "date_added" : "2018-03-12 12-3-54",
    "status" : 1,
    "detail" : {
        "title" : "The random title",
        "author_id" : "5af2c401a003533a8abf4e57",
        "test_id" : 12345,
        "description" : "I have a mongoDB collection with f rows",
        "mrp" : 200,
        "binding" : "sd",
        "language" : "English",
        "isbn" : NumberLong("9788700631625"),
        "isbn_10" : 747532745,
        "ean" : 897655,
        "pages" : 200
    }
}

This is the author collection

{
    "_id" : ObjectId("5af2c401a003533a8abf4e57"),
    "name" : "Dan Brown",
    "test_id" : 12345
}

So far i have to search on the collections independently . But not together

For author search

db.author.aggregate
([{
    "$match":   
            {
              "name":"Dan Brown"
             }
   },
   {
   "$lookup": 
            {
              "from": "product",
              "localField": "test_id",
              "foreignField": "detail.test_id",
              "as": "users"
             }
   }
  ]
 ).pretty();

And title has been accessed using the normal find() method EDIT 1:

So this is what i have tried so far. Is this the right approach . Btw it's still not working though

  db.product.aggregate
  (

    [

      {

         "$match":
            { 
                 detail.title : 'The random title'
             }
      },
      {
         "$lookup":
           {
            "from": "author",
            "localField": "test_id",
            "foreignField": "detail.test_id",
            "as": "tb2"
            }
      },
      {
         "$unwind": "$tb2" 
      },

      {
         "$match":
             {
                 "tb2.name": "agent" 
              }
       }
    ]
  );