JQuery Ajax Post cannot send data (json) to express.js server

I am a newbie on Node.js. What I want to do here is to send some data in json format, from client side javascript to express.js server. Once I can do this, I will use those parameters that have been sent to the server to further retrieve information from MongoDB. The client side code is really simple, with a click event:

 $.ajax({
                url: 'http://localhost:8020/1',
                type: 'post',
                dataType: 'jsonp',
                data: JSON.stringify({name: "test"}),
                contentType: 'application/json',
                success: function(data){
                alert("success");
                alert(data);
            }
    });

At the server side, the code looks like this:

    var express = require('express');
    var app = express();
    var cons = require('consolidate'),
        MongoClient = require('mongodb').MongoClient,
        Server = require('mongodb').Server; 

    var mongoclient = new MongoClient (new Server('localhost', 27017,
                            {'native_parser' : true}));
    var db=mongoclient.db('test');

    var bodyParser = require('body-parser');

    app.use(bodyParser.json());
    app.use(bodyParser.urlencoded({extended: true}));


    app.all('/*', function(req, res, next) {
      res.header("Access-Control-Allow-Origin", "*");
      res.header("Access-Control-Allow-Headers", "X-Requested-With");
      next();
     });

    app.get('/1', function (req, res) {
        db.collection('test').findOne({}, function (err, doc){
           console.log(doc);
        });
        console.log(JSON.stringify(req.body));
        var x = req.body.name;
        console.log(x);
        res.send({});
    });


    app.post('/1', function (req, res){

           db.collection('test').findOne({}, function (err, doc){
               console.log(doc);
            });

           console.log(req.body);
    });

    mongoclient.open(function (err, mongoclient) {

        if (err) throw err;
        app.listen(8020);
        console.log("listening on port 8020");
    });

When I make the client side ajax call, it seems that the server-side code successfully returns an item in my mongoDB database, but it fails to capture the data, which is {name : "test"} in this case.

Any one has any idea on this? Is this something related to cross domain issue? Thank you very much!