There is two easy way to authenticate a user with Facebook JS SDK,

Using FB.UI,

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    FB.ui(
        {
            method: 'oauth',
            display:'iframe',
            perms:APP_EXT_PERMISSIONS
        },
        function(response) {
            if(response.session) {
                console.dir(response);
                if(redirectURL) location.href = redirectURL;
            }
        }
    );

Using FB.DIALOG,

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    FB.login(function(response) 
        {
            if (response.session) {
                if (response.perms) {
                    //Logged and Permission Granted
                    if(redirectURL) location.href = redirectURL;
                } else {
                    //Logged and Permisssion NOT Granted
                    if(redirectURL) location.href = redirectURL;
                }
            } else {
            alert("Only Authorized User can use this Application!");
                //Not Logged
            }
        }, 
        {
            perms: APP_EXT_PERMISSIONS
        }
    );

FB.UI dialog can use an iframe or a popup window, in an iframe, you need to set the cookie by your self to create a facebook session.

FB.dialog can only use a popup window, and cookie will be created automatically as your user granted the application.