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Limitations of nonlinear optical isolators due to dynamic reciprocity


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 directions1,2,3,4,5,6,7,8. 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.

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Figure 1: Operating principle for a nonlinear optical isolator.
Figure 2: Frequency spectra of various input waves for a nonlinear optical isolator.
Figure 3: Simulation of a nonlinear optical isolator.
Figure 4: Numerical demonstration of dynamic reciprocity.


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This work was supported in part by the US Air Force Office of Scientific Research (grant no. FA9550-09-1-0704) and the US National Science Foundation (grant no. ECCS-1201914). Y.S. also acknowledges the support of a Stanford Graduate Fellowship.

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Authors and Affiliations



Y.S., Z.Y. and S.F. designed the study and contributed to the analytic derivation. Y.S. wrote the numerical code and performed the simulation. Y.S. and S.F. wrote the manuscript with input from Z.Y., and S.F. supervised the project.

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Correspondence to Shanhui Fan.

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The authors declare no competing financial interests.

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Shi, Y., Yu, Z. & Fan, S. Limitations of nonlinear optical isolators due to dynamic reciprocity. Nature Photon 9, 388–392 (2015).

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