Past exam of the laser science and quantum information processing course of the University of Oxford / 2015 / 3 / d / Solution

The raised-index region has $n_1=1.01(1.50)=1.515$, whereas $n_2=1.50$. Therefore its numerical aperture factor is $\sqrt{n_1^2-n_2^2}=0.212662$. With the printed rounded cutoff,ThusSlower scanning increases the written radius and makes the guide multimode; faster scanning makes it single-spatial-mode in this idealization, provided a physically meaningful positive core radius remains. Using $j_{0,1}=2.404825\dots$ gives $s_c\simeq 586.2\mathrm{mm}{\mathrm{s}}^{-1}$. This numerical threshold extrapolates the supplied empirical radius law; its experimental range is not given.