$facet \ $bucket date manipulation - mongodb

Question

I am using $facet aggregation for e-commerce style platform.
for this case I have an products collections, and the product schema contain many fields.
I am using same aggregation process to get all the required facets.
the question is, if I am able to use the same $facet \ $bucket aggrigation to group documents by manipulation of specific field -
for example - in product schema I have releaseDate field which is Date (type) field.
currently the aggregation query is looking like this:
let facetsBodyExample = {
'facetName': [
{ $unwind: `$${fieldData.key}` },
{ $sortByCount: `$${fieldData.key}` }
],
'facetName2': [
{ $unwind: `$${fieldData.key}` },
{ $sortByCount: `$${fieldData.key}` }
],
...,
...
};
let results = await Product.aggregate({
$facet: facetsBodyExample
});
the documents looks like
{
_id : 'as5d16as1d65sa65d165as1d',
name : 'product name',
releaseDate: '2015-07-01T00:00:00.000Z',
field1:13,
field2:[1,2,3],
field3:'abx',
...
}
I want to create custom facets (groups) by quarter + year in format like 'QQ/YYY', without defining any boundaries.
now, I am getting groups of exact match of date, and I want to group them into quarter + year groups, if possible in the same $facet aggregation.
Query result of the date field I want to customize:
CURRENT:
{
relaseDate: [
{ "_id": "2017-01-01T00:00:00.000Z", "count": 26 },
{ "_id": "2013-04-01T00:00:00.000Z", "count": 25 },
{ "_id": "2013-07-01T00:00:00.000Z", "count": 23 },
...
]
}
DESIRED:
{
relaseDate: [
{ "_id": "Q1/2014", "count": 100 },
{ "_id": "Q2/2014", "count": 200 },
{ "_id": "Q3/2016", "count": 300 },
...
]
}
Thanks !!