Specify that web scoped (request, session, application) beans are injectable in async servlets

@WebServlet(urlPatterns="/test2", asyncSupported=true)
public class TestAsyncMESServlet extends HttpServlet {
    @Resource
    private ManagedExecutorService managedExecutorService;

    @Inject
    MyRunnableImpl myRunnableImpl;

    @Override
    protected void doGet(HttpServletRequest req, HttpServletResponse res)
            throws ServletException, IOException {

        final AsyncContext asyncContext = req.startAsync();
        final PrintWriter writer = res.getWriter();

        managedExecutorService.submit(myRunnableImpl);
    }

    public static class MyRunnableImpl implements Runnable {

      @Inject
      Bean bean; // Bean is @RequestScoped

      @Override
      public void run() {
	  writer.println("Done");
	  asyncContext.complete();
      }

    }
}