  New equations are derived which describe the evolution in curved spacetime of
null geodesics with non-zero (complex) shear $\sigma$ and twist $\omega$ rates
resembling Grishchuk's squeezed states evolution equations from inflationary
cosmology. A ``squeeze" angle $\phi$ (obtained from the direction of the major
axis of the elliptical cross section of the congruence and the direction of the
shear rate), an ellipse axis ratio parameter $w$ and a rotation angle $v$ are
the primary variables. Interpreting $\phi$ as a polar angle and $w$ as a radial
distance, we obtain a mapping to points on the upper sheet, $H_{2}^{+}\,,$ of a
two-sheet hyperboloid, establishing the connection between gravitational optics
and hyperbolic geometry. Points on $H_{2}^{+}$ trace out paths evolving
according to hyperbolic Bloch equations, similar to the optical Bloch
equations, which can also be represented as a Schr\"{o}dinger-like equation
with a non-Hermitian Hamiltonian. A single vector equation on $H_{2}^{+}$
describes the precession of hyperbolic Bloch vectors about a rotation or
birefringence vector on $H_{2}^{+}\,,$ analogous to the precession of Bloch
vectors on the Bloch sphere or Stokes vectors on the Poincar\'{e} sphere. Tidal
gravitational effects and a non-zero twist $\omega$ contribute to the
precession of hyperbolic Bloch vectors.
