Populating Mongoose objects from id to new field

I was working with mongoose to populate field of ids with their respective documents to a new field.my question is assuming my cart model is -

let CartSchema = new mongoose.Schema({
    userId: {
        type: mongoose.Schema.Types.ObjectId,
        ref: 'User'
    },
    productIds: [
        {
            type: mongoose.Schema.Types.ObjectId,
            ref: 'Product'
        }
    ]
});

i want to populate the products so i used

Cart.find({}).populate("products").exec(function (err, cart) {
    console.log(cart)
}

but this populates the documents in the same field name productIds and i want to populate those fields in a new field name called "products" so i tried this

let CartSchema = new mongoose.Schema({
        userId: {
            type: mongoose.Schema.Types.ObjectId,
            ref: 'User'
        },
        productIds: [
            {
                type: String
            }
        ]
    }, { toJSON: { virtuals: true } });

CartSchema.virtual('products', {
    ref: 'Product',
    localField: 'productIds',
    foreignField: '_id',
});

Cart.find({}).populate("products").exec(function (err, cart) {
    console.log(cart)
}

but returned empty array named products.so how can i populate the productIds array to a new field name products with their respective document array.

Thanks.

the approch is correct you should see your data poulated in the products field. make sure you have the correct data and model n