Considering Moding Issues in High Speed PCB Design
You have slipped a digit.  Or three.  You have done your computation by plugging "0.2" into the formula while using m/s for \$c\$.  If you use consistent units then for the first mode you get

\$\omega_{cm}=\frac{1 \cdot \pi \cdot c}{(2.1)(0.2\cdot 10^{-3}\mathrm{m})} \simeq 2.2 \cdot 10^{12} \mathrm{\frac{rad}{s}} \simeq 360\,\mathrm{GHz}\$

This passes my personal sniff test, in that the cutoff happens at around 1/2 of a wavelength at the cutoff frequency.