Add Search Bar at bottom of Menu

It would be nice to have an option to show a search bar underneath the popped up left or right menu at the bottom, below the menu choices. So if you hit the hamburger menu, you get your menu choices, and a search bar somewhere on the screen (bottom?). I use the menu minimally and only show the hamburger menu, nothing else on the screen. So a search bar inside the menu and it unfurls would be most useful.