AVRO optional nullable field

Question

Is that possible to have nullable optional values in AVRO. E.g.:

Avro schema:

{
  "type": "record",
  "name": "test",
  "fields": [
      {
        "type": [
          "null",
          "string"
        ],
       "name": "elem"
      }
  ]
}

So that all following data would be possible to encode/decode:

1. { }
2. { "elem" : null }
3. { "elem" : "some-value" }

I've already "fixed" the problem with the 2 and 3 data, since avro would require having { "elem" : { "string": "some-value" } }, so that's not a problem anymore, but at the same time - trying to encode the 1 will produce 2 in the output, because there is no way to say if the value was present or was null initially.

Create schema with/without fields is not an option, because then I will need to create schema for each combination of fields.