If you want to generate a Popup Child Window inside the Silverlight application, you can use the Silverlight Toolkit to create the Child Window. And if you want to create a browser window instance to create the Popup Window then you can write the following code within Silverlight:
HtmlPage.PopupWindow(new Uri("http://google.com", UriKind.Absolute), "_blank", new HtmlPopupWindowOptions() { Height = 300, Width = 300, Resizeable = false });
This will ensure to open up a Popup Window. You can add more HtmlPopupWindowOptions properties as per your need.