Focus is lost when menu is closed

[huygaa11]

Bug, feature request, or proposal:

Menu should return focus to the host element when closed.

What is the expected behavior?

When a menu is closed, focus should go back to the host element that called the menu.

What is the current behavior?

The focus is being lost and sent to body element.

What are the steps to reproduce?

1. Open the first menu in https://material.angular.io/components/menu/overview
2. Close it by pressing ESC or choosing one of the options.
3. check document.activeElement using the developer console. Or, press TAB to see that the focus is set on the first element of the DOM.

What is the use-case or motivation for changing an existing behavior?

Losing focus in a middle of a workflow is really bad for a11y.

Which versions of Angular, Material, OS, TypeScript, browsers are affected?

My set up: Angular 2, Material 2, TS, Mac, Chrome

Is there anything else we should know?

buganizer: b/64452100

[crisbeto]

Currently we only return focus if the menu was opened by keyboard. Should we expand the behavior to when the menu is opened by mouse as well @jelbourn?

[jelbourn]

The only reason I could see not to would be if you open the menu, scroll a bunch, and then close it- your viewport would jump back to the focused element (on certain platforms). That seems like more of an edge case.