import javafx.application.Application;
import javafx.scene.Scene;
import javafx.scene.control.Alert;
import javafx.scene.control.Alert.AlertType;
import javafx.scene.control.Button;
import javafx.scene.control.ButtonType;
import javafx.scene.control.Dialog;
import javafx.scene.layout.StackPane;
import javafx.stage.Modality;
import javafx.stage.Stage;
import javafx.stage.Window;

public class FullscreenTest2 extends Application {

    @Override
    public void start(Stage primaryStage) {
        final Button button = new Button("Open Dialog");
        button.setOnAction(e -> showDialog(primaryStage));

        final Scene scene = new Scene(new StackPane(button), 600, 400);
        primaryStage.setTitle("Main Stage");
        primaryStage.setScene(scene);
        primaryStage.setFullScreen(true);
        primaryStage.show();
    }

    private void showDialog(final Window owner) {
        final Dialog<ButtonType> dialog = new Alert(AlertType.INFORMATION);
        dialog.setTitle("Dialog");
        dialog.initModality(Modality.APPLICATION_MODAL);
        dialog.initOwner(owner);
        dialog.setContentText("Press OK");

        dialog.show();
    }

}