Limitations of nonlinear optical isolators due to dynamic reciprocity

Researchers show that optical isolators based on nonlinearity cannot provide complete isolation for arbitrary backwards propagating noise, revealing limitations for their practical application. Motivated by the demands of integrated and silicon photonics, there is significant interest in optical isolators in on-chip integrated systems. Recent works have therefore explored nonlinear optical isolators and demonstrated non-reciprocal transmission contrast when waves are injected in forward or backward directions 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 . However, whether such nonlinear isolators can provide complete isolation under practical operating conditions remains an open question. Here, we analytically prove and numerically demonstrate a dynamic reciprocity in nonlinear optical isolators based on Kerr or Kerr-like nonlinearity. We show that, when a signal is transmitting through, such isolators are constrained by a reciprocity relation for a class of small-amplitude additional waves and, as a result, cannot provide isolation for arbitrary backward-propagating noise. This result points to an important limitation on the use of nonlinear optical isolators for signal processing and for laser protection.