I have a mongodb collection named students, where there are 3 documents:

{
  _id: ObjectId('66880dd88517a33fd8141e08'),
  name: 'Mark',
  courses: [
    {course_id: ObjectId('6684e9c8122ef4d77a9dfd1a'), active: true},
    {course_id: ObjectId('6684e9c8122ef4d77a9dfd1b'), active: false}
  ]
}

{
  _id: ObjectId('668626f11b64d2e86632e7cb'),
  name: 'John',
  courses: [
    {course_id: ObjectId('6684e9c8122ef4d77a9dfd1a'), active: false},
    {course_id: ObjectId('6684e9c8122ef4d77a9dfd1b'), active: true}
  ]
}

{
  _id: ObjectId('6684e3b628fcee8f24ead736'),
  name: 'Doe',
  courses: [
    {course_id: ObjectId('6684e9c8122ef4d77a9dfd1a'), active: true},
    {course_id: ObjectId('6684e9c8122ef4d77a9dfd1b'), active: true}
  ]
}

I have another collection named courses, where there are 2 documents:

{
  _id: ObjectId('6684e9c8122ef4d77a9dfd1a'),
  note: 'Course on mongodb.'
}

{
  _id: ObjectId('6684e9c8122ef4d77a9dfd1b'),
  note: 'Advanced mongodb course.'
}

I want to query on courses collection and get desired document matched by given _id. This document should contain an array named students. In this array each student should contain a courses array where only those courses should reside which have matching course_id with given _id and active: true.

Suppose, given _id is 6684e9c8122ef4d77a9dfd1b. So, my desired output should look like this:

{
  _id: ObjectId('6684e9c8122ef4d77a9dfd1b'),
  note: 'Advanced mongodb course.',
  students: [
    {
      _id: ObjectId('668626f11b64d2e86632e7cb'),
      name: 'John',
      courses: [
        {course_id: ObjectId('6684e9c8122ef4d77a9dfd1b'), active: true}
      ]
    },
    {
      _id: ObjectId('6684e3b628fcee8f24ead736'),
      name: 'Doe',
      courses: [
        {course_id: ObjectId('6684e9c8122ef4d77a9dfd1b'), active: true}
      ]
    }
  ]
}

I am using express, mongodb and mongoose. I tried this query:

app.get('/:id', async function (req, res) {
    try {
        const batch = await Course.aggregate([
            {"$match": {"_id": req.params.id}},
            {"$lookup": {
                    "from": "students",
                    "localField": "_id",
                    "foreignField": "courses.course_id",
                    "as": "students"
                }
            }
        ])

        res.send(batch)
    } catch (error) {
        res.json({
            error: error
        })
    }
})

This query doesn’t provide me my desired output. How to get my desired output?