  Nonlinearity induced nonreciprocity is studied in a system comprising two
resonators coupled to a one-dimensional waveguide when the linear system does
not exhibit nonreciprocity. The analysis is based on the Hamiltonian of the
coupled system and includes the dissipative coupling between the waveguide and
resonators, along with the input-output relations. We consider a large number
of scenarios which can lead to nonreciprocity. We pay special attention to the
case when the linear system does not exhibit nonreciprocal behavior. In this
case, we show how very significant nonreciprocal behavior can result from Kerr
nonlinearities. We find that the bistability of the nonlinear system can aid in
achieving large nonreciprocity. Additionally, We bring out nonreciprocity in
the excitation of each resonator, which can be monitored independently. Our
results highlight the profound influence of nonlinearity on nonreciprocal
behavior, offering a new avenue for controlling light propagation in integrated
photonic circuits. Nonlinearity induced nonreciprocity would lead to
significant nonreciprocity in quantum fluctuations when our system is treated
quantum mechanically.
