  Integrated photonics has enabled signal synthesis, modulation and conversion
using photonic integrated circuits (PIC). Many materials have been developed,
among which silicon nitride (Si$_3$N$_4$) has emerged as a leading platform
particularly for nonlinear photonics. Low-loss Si$_3$N$_4$ PIC has been widely
used for frequency comb generation, narrow-linewidth lasers, microwave
photonics, photonic computing networks, and even surface-electrode ion traps.
Yet, among all demonstrated functionalities for Si$_3$N$_4$ integrated
photonics, optical non-reciprocal devices, such as isolators and circulators,
have not been achieved. Conventionally, they are realized based on Faraday
effect of magneto-optic materials under external magnetic field. However, it
has been challenging to integrate magneto-optic materials that are not
CMOS-compatible and that require bulky external magnet. Here, we demonstrate a
magnetic-free optical isolator based on aluminum nitride (AlN) piezoelectric
modulators monolithically integrated on ultralow-loss Si$_3$N$_4$ PIC. The
transmission reciprocity is broken by spatio-temporal modulation of a
Si$_3$N$_4$ microring resonator with three AlN bulk acoustic wave resonators
that are driven with a rotational phase. This design creates an effective
rotating acoustic wave that allows indirect interband transition in only one
direction among a pair of strongly coupled optical modes. Maximum of 10 dB
isolation is achieved under 100 mW RF power applied to each actuator, with
minimum insertion loss of 0.1 dB. The isolation remains constant over nearly 30
dB dynamic range of optical input power, showing excellent optical linearity.
Our integrated, linear, magnetic-free, electrically driven optical isolator
could become key building blocks for integrated lasers, chip-scale LiDAR
engines, as well as optical interfaces for superconducting circuits.
