Any suggestion for a non-Apple monitor to connect to MBA (mid-2011)? The display has to reach the same resolution without flickering. Does a non-Apple Thunderbolt display exist?
It's not advertised all that well, but Apple still sells the non-Thunderbolt 27" LED Display (Apple Store US Link).
As CajunLuke points out, there are other good 27" displays out there, notably by Dell and HP, just be careful that you're getting one that isn't low resolution (1920x1080 on a 27" won't look great - the good ones are 2560x1440), and has a native Displayport input - as you may be aware, the miniDisplayport to dual-link DVI adapters have some issues.
Asus allegedly demoed a 27" thunderbolt display at computex, but the disappointing thing is that the review says it's only 1920 x 1080. There is no mention of the display on Asus' website.
According to the Thunderbolt Technology Community, Apple is, as of May 14, 2012, the only manufacturer to offer a display with Thunderbolt connectivity.