  We propose a mechanism to achieve the group velocity control of bifurcation
light via an imaginary coupling effect in the non-reciprocal lattice. The
physical model is composed of two-layer photonic lattices with non-reciprocal
coupling in each unit cell, which can support a real energy spectrum with a
pair of Dirac points in the first Brillouin zone due to the Hermicity.
Furthermore, we show that the systems experience topological phase transition
at the Dirac points by tuning the coupling strength, allowing the existence of
topological edge states on the left or right boundaries of respective lattice
layers. By adjusting the imaginary coupling and the wave number, the group
velocity of the light wave can be manipulated, and bifurcation light
transmission can be achieved both at the Dirac points and the condition without
the group velocity dispersion. Our work might guide the design of photonic
directional couplers with group velocity control functions.
