  We present ray tracing simulations combined with sets of large N-body
simulations. Experiments were performed to explore, for the first time,
statistical properties of fluctuations in angular separations of nearby light
ray pairs (the so-called lensing excursion angle) induced by weak lensing by
large-scale structures. We found that the probability distribution function
(PDF) of the lensing excursion angles is not simply Gaussian but has an
exponential tail. It is, however, found that the tail, or more generally
non-Gaussian nature in the PDF has no significant impact on the weak lensing of
the CMB. Moreover, we found that the variance in the lensing excursion angles
predicted by the power spectrum approach is in good agreement with our
numerical results. These results demonstrate a validity of using the power
spectrum approach to compute lensing effects on the CMB.
