Lorentz reciprocity is a fundamental characteristic of the vast majority of electronic and photonic structures. However, non-reciprocal components such as isolators, circulators and gyrators enable new applications ranging from radio frequencies to optical frequencies, including full-duplex wireless communication and on-chip all-optical information processing. Such components today dominantly rely on the phenomenon of Faraday rotation in magneto-optic materials. However, they are typically bulky, expensive and not suitable for insertion in a conventional integrated circuit. Here we demonstrate magnetic-free linear passive non-reciprocity based on the concept of staggered commutation. Commutation is a form of parametric modulation with very high modulation ratio. We observe that staggered commutation enables time-reversal symmetry breaking within very small dimensions (λ/1,250 × λ/1,250 in our device), resulting in a miniature radio-frequency circulator that exhibits reduced implementation complexity, very low loss, strong non-reciprocity, significantly enhanced linearity and real-time reconfigurability, and is integrated in a conventional complementary metal–oxide–semiconductor integrated circuit for the first time.

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Recent research has explored the spatiotemporal modulation of permittivity to break Lorentz reciprocity in a manner compatible with integrated-circuit fabrication. However, permittivity modulation is inherently weak and accompanied by loss due to carrier injection, particularly at higher frequencies, resulting in large insertion loss, size, and/or narrow operation bandwidths. Here, we show that the presence of absorption in an integrated electronic circuit may be counter-intuitively used to our advantage to realize a new generation of magnet-free non-reciprocal components. We exploit the fact that conductivity in semiconductors provides a modulation index several orders of magnitude larger than permittivity. While directly associated with loss in static systems, we show that properly synchronized conductivity modulation enables loss-free, compact and extremely broadband non-reciprocity. We apply these concepts to obtain a wide range of responses, from isolation to gyration and circulation, and verify our findings by realizing a millimeter-wave (25 GHz) circulator fully integrated in complementary metal-oxide-semiconductor technology.