  It has been shown recently that the optimal fluctuation method -- essentially
geometrical optics -- provides a valuable insight into large deviations of
Brownian motion. Here we extend the geometrical optics formalism to two-sided,
$-\infty<t<\infty$, fractional Brownian motion (fBM) on the line, which is
"pushed" to a large deviation regime by imposed constraints. We test the
formalism on three examples where exact solutions are available: the two- and
three-point probability distributions of the fBm and the distribution of the
area under the fBm on a specified time interval. Then we apply the formalism to
several previously unsolved problems by evaluating large-deviation tails of the
following distributions: (i) of the first-passage time, (ii) of the maximum of,
and (iii) of the area under, fractional Brownian bridge and fractional Brownian
excursion, and (iv) of the first-passage area distribution of the fBm. An
intrinsic part of a geometrical optics calculation is determination of the
optimal path -- the most likely realization of the process which dominates the
probability distribution of the conditioned process. Due to the non-Markovian
nature of the fBm, the optimal paths of a fBm, subject to constraints on a
finite interval $0<t\leq T$, involve both the past $-\infty<t<0$ and the future
$T<t<\infty$.
