  All-optical photonic devices are crucial for many important photonic
technology and applications, ranging from optical communication to quantum
information processing. Conventional design of all-optical devices is based on
photon propagation and interference in real space, which may reply on large
numbers of optical elements and are challenging for precise control. Here we
propose a new route for engineering all-optical devices using photon internal
degrees of freedom, which form photonic crystals in such synthetic dimensions
for photon propagation and interference. We demonstrate this new design concept
by showing how important optical devices such as quantum memory and optical
filter can be realized using synthetic orbital angular momentum (OAM) lattices
in a single main degenerate cavity. The new designing route utilizing synthetic
photonic lattices may significantly reduce the requirement for numerous optical
elements and their fine tuning in conventional design, paving the way for
realistic all-optical photonic devices with novel functionalities.
