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Broadband passive isolators based on coupled nonlinear resonances


Isolators are devices that transmit waves only in one direction, and are widely used to protect sensitive equipment from reflections and interference. These devices inherently require the breaking of Lorentz reciprocity, which can be achieved with an external bias, such as a magnetic field, that breaks time-reversal symmetry. Alternatively, nonlinear effects can be used, which offer a route to fully passive devices that do not require any form of external bias. However, the nonlinear isolators developed so far have limitations in terms of insertion loss, isolation, bandwidth and isolation intensity range. Here, we show that any isolator formed from one nonlinear resonator suffers from these limitations, and that they can be overcome by combining multiple nonlinear resonators with suitable intensity dispersion. We theoretically show, and then experimentally demonstrate using a microwave circuit, that the combination of one Fano and one Lorentzian nonlinear resonator, and a suitable delay line between them, can provide unitary transmission, infinite isolation, broad bandwidth and broad isolation intensity range. We also show that a larger number of resonators can be used to further increase the isolation intensity range without diminishing the other metrics of the device.

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Fig. 1: Nonlinear isolator based on a single nonlinear resonator.
Fig. 2: Nonlinear isolator based on a nonlinear Lorentzian resonator and a nonlinear Fano resonator.
Fig. 3: Nonlinear isolator based on multiple nonlinear resonators.
Fig. 4: Microwave realization of a Lorentzian–Fano nonlinear isolator.


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This work was supported by the Air Force Office of Scientific Research with grant No. FA9550-17-1-0002, the Simons Foundation and the National Science Foundation.

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All authors contributed equally to this work, including development of the concept, design and execution of the experiment, and manuscript preparation.

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Correspondence to Andrea Alù.

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The authors declare no competing financial interests.

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Supplementary Figure 1 and Supplementary Tables 1–3.

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Sounas, D.L., Soric, J. & Alù, A. Broadband passive isolators based on coupled nonlinear resonances. Nat Electron 1, 113–119 (2018).

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