Intensity gates are found all throughout the world of Kid Icarus: Uprising. These gates are found in every level except for chapters 21, 22,and 25. In these rooms you'll have some enemies, but in chapter 5 its a puzzle. Theses gates range from level 4 to level 9 intensity and carry rare and powerful weapons, powers, and lots of hearts.
The earliest you'll find is in chapter 1 to the right of the fountain (bring one grenade into that room to make it easier to kill the crawler and the 2 gyrazers). After killing these a chest will appear and the room will unlock. Food will appear for any loss of health. The treasure can vary greatly from from a twinbellows cannon to a fortune bow, or even a Palutena blade. After that you won't find any more in chapter 1.