I figured it out for myself. Solution is as follows:
## at first populate the main menu
var mainMenu = PopupMenu.new()
var mainMenu_items = [item_a, item_b]
for i in range(0, mainMenu_items.size()):
var subMenu_items = [sub_item_a, sub_item_b]
var subMenu = PopupMenu.new()
for j in range(0, subMenu_items.size()):
subMenu.add_item(subMenu_items[j])
mainMenu.add_child(subMenu) ## it is important to add that node as a child node, otherwise it won't work
mainMenu.add_submenu_item(mainMenu_items[i], subMenu.get_name())