  A dynamically-modulated ring system with frequency as a synthetic dimension
has been shown to be a powerful platform to do quantum simulation and explore
novel optical phenomena. Here we propose synthetic honeycomb lattice in a
one-dimensional ring array under dynamic modulations, with the extra dimension
being the frequency of light. Such system is highly re-configurable with
modulation. Various physical phenomena associated with graphene including Klein
tunneling, valley-dependent edge states, effective magnetic field, as well as
valley-dependent Lorentz force can be simulated in this lattice, which exhibits
important potentials for manipulating photons in different ways. Our work
unveils a new platform for constructing the honeycomb lattice in a synthetic
space, which holds complex functionalities and could be important for optical
signal processing as well as quantum computing.
