Observation of parity-time symmetry in time-division multiplexing pulsed optoelectronic oscillators within a single resonator

Hao Ding; Qizhuang Cen; Kun Xu; Ming Li; Yitang Dai

doi:10.1364/PRJ.461637

[1] C. M. Bender, S. Boettcher. Real spectra in non-Hermitian Hamiltonians having PT symmetry. Phys. Rev. Lett., 80, 5243-5246(1998).

[2] S. Longhi. Parity-time symmetry meets photonics: a new twist in non-Hermitian optics. Europhys. Lett., 120, 64001(2017).

[3] Ş. K. Özdemir, S. Rotter, F. Nori, L. Yang. Parity–time symmetry and exceptional points in photonics. Nat. Mater., 18, 783-798(2019).

[4] R. El-Ganainy, K. G. Makris, M. Khajavikhan, Z. H. Musslimani, S. Rotter, D. N. Christodoulides. Non-Hermitian physics and PT symmetry. Nat. Phys., 14, 11-19(2018).

[5] V. V. Konotop, J. Yang, D. A. Zezyulin. Nonlinear waves in PT-symmetric systems. Rev. Mod. Phys., 88, 035002(2016).

[6] S. V. Suchkov, A. A. Sukhorukov, J. Huang, S. V. Dmitriev, C. Lee, Y. S. Kivshar. Nonlinear switching and solitons in PT-symmetric photonic systems. Laser Photon. Rev., 10, 177-213(2016).

[7] A. A. Zyablovsky, A. P. Vinogradov, A. A. Pukhov, A. V. Dorofeenko, A. A. Lisyansky. PT-symmetry in optics. Phys.-Usp., 57, 1063-1082(2014).

[8] R. El-Ganainy, K. Makris, D. Christodoulides, Z. H. Musslimani. Theory of coupled optical PT-symmetric structures. Opt. Lett., 32, 2632-2634(2007).

[9] A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, D. N. Christodoulides. Observation of PT-symmetry breaking in complex optical potentials. Phys. Rev. Lett., 103, 093902(2009).

[10] C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, D. Kip. Observation of parity–time symmetry in optics. Nat. Phys., 6, 192-195(2010).

[11] L. Feng, M. Ayache, J. Huang, Y.-L. Xu, M.-H. Lu, Y.-F. Chen, Y. Fainman, A. Scherer. Nonreciprocal light propagation in a silicon photonic circuit. Science, 333, 729-733(2011).

[12] L. Feng, Y.-L. Xu, W. S. Fegadolli, M.-H. Lu, J. E. B. Oliveira, V. R. Almeida, Y.-F. Chen, A. Scherer. Experimental demonstration of a unidirectional reflectionless parity-time metamaterial at optical frequencies. Nat. Mater., 12, 108-113(2013).

[13] L. Feng, Z. J. Wong, R.-M. Ma, Y. Wang, X. Zhang. Single-mode laser by parity-time symmetry breaking. Science, 346, 972-975(2014).

[14] H. Hodaei, M.-A. Miri, M. Heinrich, D. N. Christodoulides, M. Khajavikhan. Parity-time-symmetric microring lasers. Science, 346, 975-978(2014).

[15] W. Liu, M. Li, R. S. Guzzon, E. J. Norberg, J. S. Parker, M. Lu, L. A. Coldren, J. Yao. An integrated parity-time symmetric wavelength-tunable single-mode microring laser. Nat. Commun., 8, 15389(2017).

[16] M. P. Hokmabadi, A. Schumer, D. N. Christodoulides, M. Khajavikhan. Non-Hermitian ring laser gyroscopes with enhanced Sagnac sensitivity. Nature, 576, 70-74(2019).

[17] W. Wan, Y. Chong, L. Ge, H. Noh, A. D. Stone, H. Cao. Time-reversed lasing and interferometric control of absorption. Science, 331, 889-892(2011).

[18] B. Peng, Ş. K. Özdemir, F. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. Fan, F. Nori, C. M. Bender, L. Yang. Parity–time-symmetric whispering-gallery microcavities. Nat. Phys., 10, 394-398(2014).

[19] H. Hodaei, A. U. Hassan, S. Wittek, H. Garcia-Gracia, R. El-Ganainy, D. N. Christodoulides, M. Khajavikhan. Enhanced sensitivity at higher-order exceptional points. Nature, 548, 187-191(2017).

[20] C. Hang, G. Huang, V. V. Konotop. PT symmetry with a system of three-level atoms. Phys. Rev. Lett., 110, 083604(2013).

[21] A. Perez-Leija, R. Keil, A. Kay, H. Moya-Cessa, S. Nolte, L.-C. Kwek, B. M. Rodríguez-Lara, A. Szameit, D. N. Christodoulides. Coherent quantum transport in photonic lattices. Phys. Rev. A, 87, 012309(2013).

[22] Y. Li, Y.-G. Peng, L. Han, M.-A. Miri, W. Li, M. Xiao, X.-F. Zhu, J. Zhao, A. Alù, S. Fan, C.-W. Qiu. Anti–parity-time symmetry in diffusive systems. Science, 364, 170-173(2019).

[23] J. Schindler, A. Li, M. C. Zheng, F. M. Ellis, T. Kottos. Experimental study of active LRC circuits with PT symmetries. Phys. Rev. A, 84, 040101(2011).

[24] M. Sakhdari, M. Hajizadegan, Y. Li, M. M.-C. Cheng, J. C. H. Hung, P.-Y. Chen. Ultrasensitive, parity–time-symmetric wireless reactive and resistive sensors. IEEE Sens. J., 18, 9548-9555(2018).

[25] Y. Choi, C. Hahn, J. W. Yoon, S. H. Song. Observation of an anti-PT-symmetric exceptional point and energy-difference conserving dynamics in electrical circuit resonators. Nat. Commun., 9, 2182(2018).

[26] J. Zhang, L. Li, G. Wang, X. Feng, B.-O. Guan, J. Yao. Parity-time symmetry in wavelength space within a single spatial resonator. Nat. Commun., 11, 3217(2020).

[27] Y.-H. Lai, Y.-K. Lu, M.-G. Suh, Z. Yuan, K. Vahala. Observation of the exceptional-point-enhanced Sagnac effect. Nature, 576, 65-69(2019).

[28] H. Zhang, R. Huang, S.-D. Zhang, Y. Li, C.-W. Qiu, F. Nori, H. Jing. Breaking anti-PT symmetry by spinning a resonator. Nano Lett., 20, 7594-7599(2020).

[29] L. Li, Y. Cao, Y. Zhi, J. Zhang, Y. Zou, X. Feng, B.-O. Guan, J. Yao. Polarimetric parity-time symmetry in a photonic system. Light Sci. Appl., 9, 169(2020).

[30] S. V. Suchkov, F. Fotsa-Ngaffo, A. Kenfack-Jiotsa, A. D. Tikeng, T. C. Kofane, Y. S. Kivshar, A. A. Sukhorukov. Non-Hermitian trimers: PT-symmetry versus pseudo-Hermiticity. New J. Phys., 18, 065005(2016).

[31] Y. Liu, T. Hao, W. Li, J. Capmany, N. Zhu, M. Li. Observation of parity-time symmetry in microwave photonics. Light Sci. Appl., 7, 38(2018).

[32] J. Zhang, J. Yao. Parity-time–symmetric optoelectronic oscillator. Sci. Adv., 4, eaar6782(2018).

[33] Z. Fan, W. Zhang, Q. Qiu, J. Yao. Widely tunable parity-time-symmetric optoelectronic oscillator based on a silicon microdisk resonator. International Topical Meeting on Microwave Photonics (MWP), 1-4(2019).

[34] P. Li, Z. Dai, Z. Fan, L. Yan, J. Yao. Parity–time-symmetric frequency-tunable optoelectronic oscillator with a single dual-polarization optical loop. Opt. Lett., 45, 3139-3142(2020).

[35] X. S. Yao, L. Maleki. Optoelectronic microwave oscillator. J. Opt. Soc. Am. B, 13, 1725-1735(1996).

[36] Y. K. Chembo, D. Brunner, M. Jacquot, L. Larger. Optoelectronic oscillators with time-delayed feedback. Rev. Mod. Phys., 91, 035006(2019).

[37] T. Hao, Y. Liu, J. Tang, Q. Cen, W. Li, N. Zhu, Y. Dai, J. Capmany, J. Yao, M. Li. Recent advances in optoelectronic oscillators. Adv. Photon., 2, 044001(2020).

[38] Z. Dai, Z. Fan, P. Li, J. Yao. Frequency-tunable parity-time-symmetric optoelectronic oscillator using a polarization-dependent Sagnac loop. J. Lightwave Technol., 38, 5327-5332(2020).

[39] C. Teng, X. Zou, P. Li, C. Xie, Y. Sun, W. Pan, L. Yan. Fine tunable PT-symmetric optoelectronic oscillator based on laser wavelength tuning. IEEE Photon. Technol. Lett., 32, 47-50(2020).

[40] P. Liu, P. Zheng, H. Yang, D. Lin, G. Hu, B. Yun, Y. Cui. Parity-time symmetric frequency-tunable optoelectronic oscillator based on a Si₃N₄ microdisk resonator. Appl. Opt., 60, 1930-1936(2021).

[41] Q. Cen, T. Hao, H. Ding, S. Guan, Z. Qin, K. Xu, Y. Dai, M. Li. Microwave photonic ising machine(2020).

[42] E. C. Levy, M. Horowitz, C. R. Menyuk. Modeling optoelectronic oscillators. J. Opt. Soc. Am. B, 26, 148-159(2009).

[43] K.-H. Kim, M.-S. Hwang, H.-R. Kim, J.-H. Choi, Y.-S. No, H.-G. Park. Direct observation of exceptional points in coupled photonic-crystal lasers with asymmetric optical gains. Nat. Commun., 7, 13893(2016).

[44] K. Takata, K. Nozaki, E. Kuramochi, S. Matsuo, K. Takeda, T. Fujii, S. Kita, A. Shinya, M. Notomi. Observing exceptional point degeneracy of radiation with electrically pumped photonic crystal coupled-nanocavity lasers. Optica, 8, 184-192(2021).

[45] K. Takata, N. Roberts, A. Shinya, M. Notomi. Imaginary couplings in non-Hermitian coupled-mode theory: Effects on exceptional points of optical resonators. Phys. Rev. A, 105, 013523(2022).

[46] H. Benisty, C. Yan, A. Degiron, A. Lupu. Healing near-PT-symmetric structures to restore their characteristic singularities: analysis and examples. J. Lightwave Technol., 30, 2675-2683(2012).

[47] N. B. Nguyen, S. A. Maier, M. Hong, R. F. Oulton. Recovering parity-time symmetry in highly dispersive coupled optical waveguides. New J. Phys., 18, 125012(2016).

[48] J. D. Hart, D. C. Schmadel, T. E. Murphy, R. Roy. Experiments with arbitrary networks in time-multiplexed delay systems. Chaos, 27, 121103(2017).

[49] M. H. Matheny, J. Emenheiser, W. Fon, A. Chapman, A. Salova, M. Rohden, J. Li, M. Hudoba de Badyn, M. Pósfai, L. Duenas-Osorio, M. Mesbahi, J. P. Crutchfield, M. C. Cross, R. M. D’Souza, M. L. Roukes. Exotic states in a simple network of nanoelectromechanical oscillators. Science, 363, eaav7932(2019).