In general, reciprocity requires that signals travel in the same manner in both forward and reverse directions. It governs the behaviour of the majority of electronic circuits and components, imposing severe restrictions on how they operate. Components that violate reciprocity, such as gyrators, isolators and circulators, are, however, of use in many different electronic applications. Non-reciprocal electronic components have typically been implemented using ferrites, but such magnetic materials cannot be integrated in modern semiconductor fabrication processes and magnetic non-reciprocal components remain bulky and expensive. Creating non-reciprocal components without the use of magnetic materials has a long history, but has recently been reinvigorated due to advancements in semiconductor technology. Here we review the development of non-reciprocal devices and the development of non-magnetic non-reciprocal electronics, focusing on devices based on temporal modulation, which arguably exhibit the greatest potential. We consider approaches based on temporal modulation of permittivity and conductivity, as well as hybrid acoustic–electronic components, which have applications including high-power transmitters for communications, simultaneous transmit and receive radars, and full-duplex wireless radios. We also explore superconducting non-reciprocal components based on temporal modulation of permeability for potential applications in quantum computing and consider the key future challenges in the field.
This is a preview of subscription content, access via your institution
Open Access articles citing this article.
npj Quantum Materials Open Access 01 November 2022
Nature Nanotechnology Open Access 17 March 2022
Subscribe to Nature+
Get immediate online access to Nature and 55 other Nature journal
Subscribe to Journal
Get full journal access for 1 year
only $9.92 per issue
All prices are NET prices.
VAT will be added later in the checkout.
Tax calculation will be finalised during checkout.
Get time limited or full article access on ReadCube.
All prices are NET prices.
Cannell, D. M. George Green: Mathematician and Physicist 1793–1841: The background to his life and work. 2nd edn, 190–192 (Society for Industrial and Applied Mathematics, 2001).
Rayleigh, J. W. S. B. Theory of Sound. 1st edn, Vol. 1 Ch. V. (Macmillan and Co., 1896).
Helmholtz, H. On the physical significance of the principle of least action. J. Reine Angew. Math. 100, 217–222 (1886).
Lorentz, H. A. Het theorema van Poynting over de energie in het electromagnetisch veld en een paar algemeene stellingen over de voortplanting van het licht. In Verslagen der Afdeeling Natuurkunde van de Koninklijke Akademie van Wetenschappen 4, 176–187 (1895).
Carson, J. R. Reciprocal theorems in radio communication. Proc. IRE 17, 952–956 (1929).
Ballantine, S. Reciprocity in electromagnetic, mechanical, acoustical, and interconnected systems. Proc. IRE 17, 927–951 (1929).
Onsager, L. Reciprocal relations in irreversible processes. I. Phys. Rev 37, 405–426 (1931).
Casimir, H. B. G. On Onsager’s principle of microscopic reversibility. Rev. Mod. Phys. 17, 343–350 (1945).
De Hoop, A. T. A reciprocity relation between the transmitting and the receiving properties of an antenna. App. Sci. Res 19, 90–96 (1968).
Jalas, D. et al. What is — and what is not — an optical isolator. Nat. Photon 7, 579–582 (2013).
Fan, S. et al. Comment on ‘Nonreciprocal light propagation in a silicon photonic circuit’. Science 335, 38–38 (2012).
Tellegen, D. The gyrator, a new electric network element. Philips Res. Rep 3, 81–101 (1948).
Hogan, C. L. The ferromagnetic Faraday effect at microwave frequencies and its applications: the microwave gyrator. Bell Syst. Tech. J 31, 1–31 (1952).
Gardner, D. S. et al. Review of on-chip inductor structures with magnetic films. IEEE Trans. Magn. 45, 4760–4766 (2009).
Zhou, J. et al. Integrated full duplex radios. IEEE Commun. Mag. 55, 142–151 (2017).
van Liempd, B. et al. A +70-dBm IIP3 electrical-balance duplexer for highly integrated tunable front-ends. IEEE Trans. Microw. Theory Techn 64, 4274–4286 (2016).
Chapman, B. J. et al. Widely tunable on-chip microwave circulator for superconducting quantum circuits. Phy. Rev. X 7, 041043 (2017).
JQL Electronics. Accessed on: 2020. [Online]. Available: http://www.jqlelectronics.com/
Reiskarimian, N., Baraani Dastjerdi, M., Zhou, J. & Krishnaswamy, H. Analysis and design of commutation-based circulator-receivers for integrated full-duplex wireless. IEEE J. Solid State Circ 53, 2190–2201 (2018).
Nagulu, A. & Krishnaswamy, H. Non-magnetic CMOS switched-transmission-line circulators with high power handling and antenna balancing: theory and implementation. IEEE J. Solid State Circ 54, 1288–1303 (2019).
Dinc, T. et al. Synchronized conductivity modulation to realize broadband lossless magnetic-free non-reciprocity. Nat. Commun. 8, 795 (2017).
Nagulu, A. et al. Nonreciprocal components based on switched transmission lines. IEEE Trans. Microw. Theory Techn 66, 4706–4725 (2018).
Biedka, M. M., Zhu, R., Xu, Q. M. & Wang, Y. E. Ultra-wide band non-reciprocity through sequentially-switched delay lines. Sci. Rep 7, 40014 (2017).
Reiskarimian, N. & Krishnaswamy, H. Magnetic-free non-reciprocity based on staggered commutation. Nat. Commun. 7, 11217 (2016).
Tanaka, S., Shimomura, N. & Ohtake, K. Active circulators–the realization of circulators using transistors. Proc. IEEE 53, 260–267 (1965).
Mung, S. W. & Chan, W. S. The challenge of active circulators: design and optimization in future wireless communication. IEEE Microw. Mag. 20, 55–66 (2019).
Kodera, T., Sounas, D. L. & Caloz, C. Magnetless nonreciprocal metamaterial (MNM). technology: application to microwave components. IEEE Trans. Microw. Theory Techn 61, 1030–1042 (2013).
Carchon, G. & Nanwelaers, B. Power and noise limitations of active circulators. IEEE Trans. Microw. Theory Techn 48, 316–319 (2000).
Peng, B. et al. Parity-time-symmetric whispering-gallery microcavities. Nat. Phys 10, 394–398 (2014).
Fan, L. et al. An all-silicon passive optical diode. Science 335, 447–450 (2012).
Nazari, F. et al. Optical isolation via PT-symmetric nonlinear Fano resonances. Opt. Express 22, 9574–9584 (2014).
Mahmoud, A. M., Arthur, R. D. & Engheta, N. All-passive nonreciprocal metastructure. Nat. Commun. 6, 8359 (2015).
Sounas, D. L., Soric, J. & Alù, A. Broadband passive isolators based on coupled nonlinear resonances. Nat. Elec 1, 113 (2018).
D’Aguanno, G., Sounas, D. L. & Alù, A. Nonlinearity-based circulator. Appl. Phys. Lett. 114, 181102 (2019).
Hadad, Y., Soric, J. C., Khanikaev, A. B. & Alù, A. Self-induced topological protection in nonlinear circuit arrays. Nat. Elec 1, 178–182 (2018).
Shi, Y., Yu, Z. & Fan, S. Limitations of nonlinear optical isolators due to dynamic reciprocity. Nat. Photon 9, 388–392 (2015).
Sounas, D. L. & Alù, A. Nonreciprocity Based on Nonlinear Resonances. IEEE Antenn. Propag. Lett 17, 1958–1962 (2018).
Reed, E. D. The variable-capacitance parametric amplifier. IRE Trans. Electron. Devices 6, 216–224 (1959).
Kamal, A. A parametric device as a nonreciprocal element. Proc. IRE 48, 1424–1430 (1960).
Baldwin, L. Nonreciprocal parametric amplifier circuits. Proc. IRE 49, 1075 (1961).
Hamasaki, J. A theory of a unilateral parametric amplifier using two diodes. Bell Syst. Tech. J 43, 1123–1147 (1964).
Galland, C., Ding, R., Harris, N. C., Baehr-Jones, T. & Hochberg, M. Broadband on-chip optical non-reciprocity using phase modulators. Opt. Express 21, 14500–14511 (2013).
Doerr, C. R., Chen, L. & Vermeulen, D. Silicon photonics broadband modulation-based isolator. Opt. Express 22, 4493–4498 (2014).
Lira, H., Yu, Z., Fan, S. & Lipson, M. Electrically driven nonreciprocity induced by interband photonic transition on a silicon chip. Phys. Rev. Lett. 109, 033901 (2012).
Kang, M., Butsch, A. & Russell, P. S. J. Reconfigurable light-driven opto-acoustic isolators in photonic crystal fibre. Nat. Photon 5, 549–553 (2011).
Yu, Z. & Fan, S. Complete optical isolation created by indirect interband photonic transitions. Nat. Photon 3, 91–94 (2008).
Qin, S., Xu, Q. & Wang, Y. Nonreciprocal components with distributedly modulated capacitors. IEEE Trans. Microw. Theory Techn 62, 2260–2272 (2014).
Fleury, R., Sounas, D. L., Sieck, C. F., Haberman, M. R. & Alù, A. Sound isolation and giant linear nonreciprocity in a compact acoustic circulator. Science 343, 516–519 (2014).
Sounas, D. L. & Alù, A. Angular-momentum-biased nanorings to realize magnetic-free integrated optical isolation. ACS Photon 1, 198–204 (2014).
Estep, N. A., Sounas, D. L., Soric, J. & Alù, A. Magnetic-free non-reciprocity and isolation based on parametrically modulated coupled-resonator loops. Nat. Phys 10, 923–927 (2014).
Kord, A., Sounas, D. L. & Alù, A. Pseudo-linear time-invariant magnetless circulators based on differential spatiotemporal modulation of resonant junctions. IEEE Trans. Microw. Theory Tech 66, 2731–2745 (2018).
Kord, A., Tymchenko, M., Sounas, D. L., Krishnaswamy, H. & Alù, A. CMOS integrated magnetless circulators based on spatiotemporal modulation angular-momentum biasing. IEEE Trans. Microw. Theory Tech 67, 2649–2662 (2019).
Tyagi, S. et al. An advanced low power, high performance, strained channel 65nm technology. In 2005 IEEE Int. Electron Devices Meet. Tech. Digest 245–247 (IEEE, 2005).
Mohr, R. J. A new nonreciprocal transmission line device. Proc. IEEE 52, 612 (1964).
Ghaffari, A., Klumperink, E. A. M., Soer, M. C. M. & Nauta, B. Tunable high-Q N-path band-pass filters: modeling and verification. IEEE J. Solid State Circ 46, 998–1010 (2011).
Busignies, H. & Dishal, M. Some relations between speed of indication, bandwidth, and signal-to-random-noise ratio in radio navigation and direction finding. Proc. IRE 37, 478–488 (1949).
LePage, W. R., Cahn, C. R. & Brown, J. S. Analysis of a comb filter using synchronously commutated capacitors. Trans. Am. Inst. Electric. Eng. I 72, 63–68 (1953).
Nagulu, A. & Krishnaswamy, H. Non-magnetic 60GHz SOI CMOS circulator based on loss/dispersion-engineered switched bandpass filters. In 2019 IEEE Int. Solid State Circuits Conf. (ISSCC) 446–448 (IEEE, 2019).
Lu, R., Krol, J., Gao, L. & Gong, S. Frequency independent framework for synthesis of programmable non-reciprocal networks. Sci. Rep 8, 14655 (2018).
Torunbalci, M. M., Odelberg, T. J., Sridaran, S., Ruby, R. C. & Bhave, S. A. An FBAR circulator. IEEE Microw. Compon. Lett 28, 395–397 (2018).
Yu, Y. et al. Highly-linear magnet-free microelectromechanical circulators. IEEE J. Microelectromechanical Systems 28, 933–940 (2019).
Yu, Y. et al. Magnetic-free radio frequency circulator based on spatiotemporal commutation of MEMS resonators. In Proc. IEEE Micro Electro Mech. Syst. (MEMS) 154–157 (IEEE, 2018).
Xu, C. & Piazza, G. Magnet-less circulator using AlN mems filters and CMOS RF switches. J. Microelectromech. Syst 28, 409–418 (2019).
Bahamonde, J., Kymissis, I., Alù, A. & Krishnaswamy, H. 1.95-GHz circulator based on a time-modulated electro-acoustic gyrator. In Proc. IEEE Int. Symp. Antennas and Propagation and USNC-URSI Radio (IEEE, 2018).
Ranzani, L. & Aumentado, J. Circulators at the quantum limit: recent realizations of quantum-limited superconducting circulators and related approaches. IEEE Microw. Mag. 20, 112–122 (2019).
Castellanos-Beltran, M. A. & Lehnert, K. W. Widely tunable parametric amplifier based on superconducting quantum interference device array resonator. Appl. Phys. Lett. 91, 083509 (2007).
Josephson, B. D. Possible new effects in superconductive tunneling. Phys. Lett. 1, 251–253 (1962).
Anderson, P. W. & Rowell, J. M. Probable observation of the Josephson superconducting tunneling effect. Phys. Rev. Lett. 10, 230–232 (1963).
Abdo, B., Brink, M. & Chow, J. M. Gyrator operation using Josephson mixers. Phys. Rev. Appl 8, 034009 (2017).
Abdo, B., Kamal, A. & Devoret, M. H. Nondegenerate three-wave mixing with the Josephson ring modulator. Phys. Rev. B 87, 014508 (2013).
Lecocq, F. et al. Nonreciprocal microwave signal processing with a field-programmable Josephson amplifier. Phys. Rev. Appl 7, 024028 (2017).
Sliwa, K. M. et al. Reconfigurable Josephson circulator/directional amplifier. Phys. Rev. X 5, 041020 (2015).
Levy, C. S., Asbeck, P. M. & Buckwalter, J. F. A CMOS SOI stacked shunt switch with sub-500ps time constant and 19-Vpp breakdown. In 2013 IEEE Compound Semiconductor Intg. Circuit Symp. (CSICS) 1-4 (IEEE, 2013).
Hill, C., Levy, C. S., AlShammary, H., Hamza, A. & Buckwalter, J. F. RF watt-level low-insertion-loss high-bandwidth SOI CMOS switches. IEEE Trans. Microw. Theory Tech. 66, 5724–5736 (2018).
Kazior, T.E. et al. High performance mixed signal and RF circuits enabled by the direct monolithic heterogeneous integration of GaN HEMTs and Si CMOS on a silicon substrate. In 2011 IEEE Compound Semiconductor Int. Circuit Symp. (CSICS), 1-4 (IEEE,2011).
Baraani Dastjerdi, M., Reiskarimian, N., Chen, T., Zussman, G. & Krishnaswamy, H. Full duplex circulator-receiver phased array employing self-interference cancellation via beamforming. 2018 IEEE Radio Freq. Int. Circuits Symp. (RFIC) 108–111 (IEEE, 2018).
Baraani Dastjerdi, M., Jain, S., Reiskarimian, N., Natarajan, A. & Krishnaswamy, H. Analysis and design of a full-duplex two-element MIMO circulator-receiver with high TX power handling exploiting MIMO RF and shared-delay baseband self-interference cancellation. IEEE J. Solid State Circ 54, 3525–3540 (2019).
Serrano, D. C. et al. Nonreciprocal graphene devices and antennas based on spatiotemporal modulation. IEEE Ant. Wireless Prop. Lett 15, 1529–1532 (2016).
Hadad, Y., Soric, J. C. & Alù, A. Breaking temporal symmetries for emission and absorption. Proc. Natl Acad. Sci. USA 113, 3471–3475 (2016).
Taravati, S. & Caloz, C. Mixer-duplexer-antenna leaky-wave system based on periodic space-time modulation. IEEE Trans. Ant. Prop 65, 442–452 (2017).
Tymchenko, M., Sounas, D. L., Nagulu, A., Krishnaswamy, H. & Alù, A. Quasielectrostatic wave propagation beyond the delay-bandwidth limit in switched networks. Phys. Rev. X 9, 031015 (2019).
Fleury, R., Sounas, D. L. & Alù, A. Subwavelength ultrasonic circulator based on spatiotemporal modulation. Phys. Rev. B 91, 174306 (2015).
Estep, N. A., Sounas, D. L. & Alù, A. Magnetless microwave circulators based on spatiotemporally modulated rings of coupled resonators. IEEE Trans. Microw. Theory Tech 64, 502–518 (2016).
Soer, M. C. M., Klumperink, E. A. M., Boer, P. T. D., Vliet, F. E. V. & Nauta, B. Unified frequency-domain analysis of switched-series-RC passive mixers and samplers. IEEE Trans. Circuits Syst. I 57, 2618–2631 (2010).
Reiskarimian, N., Zhou, J., Chuang, T. H. & Krishnaswamy, H. Analysis and design of two-port N-path bandpass filters with embedded phase shifting. IEEE Trans. Circuits Syst. II 63, 728–732 (2016).
Hameed, S., Rachid, M., Daneshrad, B. & Pamarti, S. Frequency-domain analysis of N-path filters using conversion matrices. IEEE Trans. Circuits Syst. II Express Briefs 63, 74–78 (2016).
Pavan, S. & Klumperink, E. A. M. Generalized analysis of high-order switch-RC N-path mixers/filters using the adjoint network. IEEE Trans. Circuits Syst. I 65, 3267–3278 (2018).
Xu, C. & Piazza, G. A generalized model for linear periodically-time-variant circulators. Sci. Rep 9, 8718 (2019).
Kane, C. L. & Mele, E. J. Z2 topological order and the quantum spin Hall effect. Phys. Rev. Lett. 95, 146802 (2005).
Qi, X.-L. & Zhang, S.-C. Topological insulators and superconductors. Rev. Mod. Phys. 83, 1057 (2011).
Khanikaev, A. B., Fleury, R., Mousavi, S. H. & Alù, A. Topologically robust sound propagation in an angular-momentum-biased graphene-like resonator lattice. Nat. Commun. 6, 8260 (2015).
Fleury, R., Khanikaev, A. B. & Alù, A. Floquet topological insulators for sound. Nat. Commun. 7, 11744 (2016).
Haldane, F. D. M. & Raghu, S. Possible realization of directional optical waveguides in photonic crystals with broken time-reversal symmetry. Phys. Rev. Lett. 100, 013904 (2008).
Yu, Z., Veronis, G., Wang, Z. & Fan, S. One-way electromagnetic waveguide formed at the interface between a plasmonic metal under a static magnetic field and a photonic crystal. Phys. Rev. Lett. 100, 023902 (2008).
Wang, Z., Chong, Y., Joannopoulos, J. D. & Soljaćić, M. Observation of unidirectional backscattering-immune topological electromagnetic states. Nature 461, 772–775 (2009).
This work was supported by the National Science Foundation, the Air Force Office of Scientific Research, and the Defense Advanced Research Projects Agency. We wish to thank T. Olsson and T. Hancock for useful feedback and comments.
The authors declare no competing interests.
Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
About this article
Cite this article
Nagulu, A., Reiskarimian, N. & Krishnaswamy, H. Non-reciprocal electronics based on temporal modulation. Nat Electron 3, 241–250 (2020). https://doi.org/10.1038/s41928-020-0400-5
This article is cited by
Nature Nanotechnology (2022)
npj Quantum Materials (2022)
Nature Nanotechnology (2022)