Phrase proximity with simple_query_string and NEST

I'm using the simple_query_string with the tilde ~ operator to specify proximity between words in a phrase, and it works. The simple query has other functions that match doesn't provide.

     {
               "simple_query_string":{

                  "query":"\"small demonstration\"~10",
                  "fields":[
                     "data"
                  ]
               }
    }

But, using "small demonstration"~10 or "\"small demonstration\"~10" in an equivalent NEST query doesn't add proximity search.

    m => m
		.SimpleQueryString(s => s
						.Query("small demonstration"~10)
						.Fields(f => f
						.Fields(emptyFieldArray))
						)

There can be multiple phrases using double-quotes, "phrase-1" other words "phrase-2". Can I add the tilde character to single or multiple phrases with NEST using the simple_query_string?

In the Fields method, at least one field needs to be specified.

.Fields(f => f
.Fields(specifyAtLeastOneFieldArray))

When the field array is empty, Elastic searches through all the fields, but it seems that it doesn't make use of the proximity character.