Response to Comment on “Nonreciprocal Light Propagation in a Silicon Photonic Circuit”

Fan et al. raised technical concerns about our study regarding the Lorentz reciprocity theorem, with which we completely agree. Unfortunately, we incorrectly used the term “nonreciprocal” to describe the behavior of electromagnetic propagation in our devices. In our paper, this term does not refer to Lorentz reciprocity but to the asymmetric mode conversion that is experimentally demonstrated. We recently demonstrated a silicon (Si)waveguide-based device that per-forms mode conversion in only one direction (1). We called this effect nonrecip-rocal, a term that could be misleading as it im-plies that our device avoids Lorentz reciprocity. Indeed, either a magnetic or a time-dependent response is needed to convert our device into an optical isolator. An analysis of reciprocity of our asymmetric optical mode converter, ob-tained by deriving the corresponding scatter-ing matrix, confirms that the mode conversion of our device is not sufficient for optical iso-lation on its own. Nevertheless, we believe, it may provide a useful element for on-chip op-tical isolation in Si photonics when combined with nonlinear optical wavemixing. Even though our device is not adequate to provide optical iso-lation, we have demonstrated spontaneous break-ing of parity-time symmetry. Our device uses a complex variation in the ef-fective dielectric constant to generate an asymmetric wave vector q. Reciprocity can be assessed by de-riving and analyzing the corresponding scattering matrix by solving the coupled mode equations in (1). It can be shown that at the two ends of the device in the z direction, z = 0 and z = L/2 (L = 2p/q is the period of modulations), the fields are as follows: A1ðL2Þ exp