How to use Elasticsearch's Completion suggester with Javascript and typeahead.js?

I am trying since many day to build a simple demo autocomplete search form. I'm using javascript and typeahead.js library.

I have a probleme to get all of them working together. I am using Elasticsearch service from amazon web services.

When i type the first letter of the word am searching, the form doesn't suggest a list of words indexed in my cluster which start with the letter entered.

I read the Completion suggester documentation but i don't understand how i can query completion suggester by using javascript.

Here is my code :

$('#remote .typeahead').typeahead({
    highlight: true,
  },
  {
    source: function(query, process){
       $.ajax({
        url:'https://xxxxxxxxxxxxxxx.es.amazonaws.com/xxxxxxxxx/_search',
        type:'GET',
        data:'q=' + query,
        dataType:'JSON',
        async:true,
        success: function(data){
          console.log(data);
        }

       })
    }
  })

When i type the "g" in the search file i get this result in the browser console log:

{"took":1,"timed_out":false,"_shards":{"total":5,"successful":5,"failed":0},"hits":{"total":0,"max_score":null,"hits":[]}}

Whereas there are several words starting with a "g" in my cluster.

What am i doing wrong ?

Thanks for helping.