Answer
$T = 2.09\times 10^{-14}~s$
Work Step by Step
We can find $\omega$:
$\omega = k~c = (1.00\times 10^6~m^{-1})(3.0\times 10^8~m/s) = 3.00\times 10^{14}~s^{-1}$
We can find the period:
$T = \frac{2\pi}{\omega} = \frac{2\pi}{3.00\times 10^{14}~s^{-1}} = 2.09\times 10^{-14}~s$
