  We discuss a general method for constructing nonreciprocal, cavity-based
photonic devices, based on matching a given coherent interaction with its
corresponding dissipative counterpart; our method generalizes the basic
structure used in the theory of cascaded quantum systems, and can render an
extremely wide class of interactions directional. In contrast to standard
interference-based schemes, our approach allows directional behavior over a
wide bandwidth. We show how it can be used to devise isolators and directional,
quantum-limited amplifiers. We discuss in detail how this general method allows
the construction of a directional, noise-free phase-sensitive amplifier that is
not limited by any fundamental gain-bandwidth constraint. Our approach is
particularly well-suited to implementations using superconducting microwave
circuits and optomechanical systems.
