Q: Cannot get AirPlay extended desktop to work

I have a late-2012 27" iMac running OS X Mavericks 10.9.1 and a 3rd Generation AppleTV on same network(both Ethernet hard-wired connections). I can turn on AirPlay "Mirror iMac" for AppleTV connection on iMac AirPlay Menu icon and it works fine showing whatever I do on the iMac, but if I select "Extend Desktop" it creates an "empty" desktop on the HDTV connected to the AppleTV(Menu Bar at top, but no Task Bar at bottom or application windows on the HDTV). No matter what I do I cannot seem to get the screen that appeared on the HDTV connected to Apple TV to display on my iMac for running an application on the AppleTV connection's screen and even though it appears that going between active sessions(using Command/Tab) on the iMac apperars to change the HDTV's "Menu Bar" nothing(Finder/Safari/App Store/etc. windows running on the iMac) that are displaying on the iMac for that selection in the iMac session appears on the HDTV screen. "Going to the edges of screens" on the iMac session screens, like the instructions for multiple displays recommends does nothing. Going to Mission Control, selecting the different desktop Displays(or clicking to the right and adding one) doesn't help and I simply cannot "run anything" that shows up on the HDTV screen's iMac display on AppleTV. Checked Firewall settings according to online Troubleshooting and all is OK. How do I get the "2nd Monitor" via AppleTV to work????

P.S.

What does "Gather Windows" do in Display Preferences?? Tried that but no joy:0)