Imaging lattice switching with Talbot effect in reconfigurable non-Hermitian photonic graphene

Zhaoyang Zhang; Yuan Feng; Shaohuan Ning; G. Malpuech; D. D. Solnyshkov; Zhongfeng Xu; Yanpeng Zhang; Min Xiao

doi:10.1364/PRJ.447404

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

[2] 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(2017).

[3] L. Feng, R. El-Ganainy, L. Ge. Non-Hermitian photonics based on parity–time symmetry. Nat. Photonics, 11, 752-762(2017).

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

[5] 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).

[6] J. Doppler, A. A. Mailybaev, J. Böhm, U. Kuhl, A. Girschik, F. Libisch, T. J. Milburn, P. Rabl, N. Moiseyev, S. Rotter. Dynamically encircling an exceptional point for asymmetric mode switching. Nature, 537, 76-79(2016).

[7] S. Ozdemir, S. Rotter, F. Nori, L. Yang. Parity-time symmetry and exceptional points in photonics. Nat. Mater., 18, 783-798(2019).

[8] L. Chang, X. Jiang, S. Hua, C. Yang, J. Wen, L. Jiang, G. Li, G. Wang, M. Xiao. Parity–time symmetry and variable optical isolation in active–passive-coupled microresonators. Nat. Photonics, 8, 524-529(2014).

[9] H. F. Jones. The energy spectrum of complex periodic potentials of the Kronig-Penney type. Phys. Lett. A, 262, 242-244(1999).

[10] X.-G. Zhang, K. Varga, S. T. Pantelides. Generalized Bloch theorem for complex periodic potentials: a powerful application to quantum transport calculations. Phys. Rev. B, 76, 035108(2007).

[11] Z. Ahmed. Energy band structure due to a complex, periodic, PT-invariant potential. Phys. Lett. A, 286, 231-235(2001).

[12] K. G. Makris, R. El-Ganainy, D. N. Christodoulides, Z. H. Musslimani. Beam dynamics in PT symmetric optical lattices. Phys. Rev. Lett., 100, 103904(2008).

[13] A. Regensburger, C. Bersch, M.-A. Miri, G. Onishchukov, D. N. Christodoulides, U. Peschel. Parity-time synthetic photonic lattices. Nature, 488, 167-171(2012).

[14] C. Keller, M. K. Oberthaler, R. Abfalterer, S. Bernet, J. Schmiedmayer, A. Zeilinger. Tailored complex potentials and Friedel’s law in atom optics. Phys. Rev. Lett., 79, 3327-3330(1997).

[15] B. Zhen, C. W. Hsu, Y. Igarashi, L. Lu, I. Kaminer, A. Pick, S.-L. Chua, J. D. Joannopoulos, M. Soljačić. Spawning rings of exceptional points out of Dirac cones. Nature, 525, 354-358(2015).

[16] S. Yao, Z. Wang. Edge states and topological invariants of non-Hermitian systems. Phys. Rev. Lett., 121, 086803(2018).

[17] H. Zhou, C. Peng, Y. Yoon, C. W. Hsu, K. A. Nelson, L. Fu, J. D. Joannopoulos, M. Soljačić, B. Zhen. Observation of bulk Fermi arc and polarization half charge from paired exceptional points. Science, 359, 1009-1012(2018).

[18] A. Ghatak, M. Brandenbourger, J. V. Wezel, C. Coulais. Observation of non-Hermitian topology and its bulk-edge correspondence in an active mechanical metamaterial. Proc. Natl. Acad. Sci. USA, 117, 29561-29568(2020).

[19] Z. H. Musslimani, K. G. Makris, R. El-Ganainy, D. N. Christodoulides. Optical solitons in PT periodic potentials. Phys. Rev. Lett., 100, 030402(2008).

[20] S. Assawaworrarit, X. Yu, S. Fan. Robust wireless power transfer using a nonlinear parity–time-symmetric circuit. Nature, 546, 387-390(2017).

[21] H. F. Talbot. Facts relating to optical science. Philos. Mag. J. Sci., 9, 401-407(1836).

[22] L. Rayleigh. On copying diffraction gratings and on some phenomenon connected therewith. Philos. Mag., 11, 196-205(1881).

[23] H. Ramezani, D. N. Christodoulides, V. Kovanis, I. Vitebskiy, T. Kottos. PT-symmetric Talbot effects. Phys. Rev. Lett., 109, 033902(2012).

[24] S. Wang, B. Wang, P. Lu. PT-symmetric Talbot effect in a temporal mesh lattice. Phys. Rev. A, 98, 043832(2018).

[25] S. Longhi. Talbot self-imaging in PT-symmetric complex crystals. Phys. Rev. A, 90, 043827(2014).

[26] Y. Zhang, J. Wen, S. N. Zhu, M. Xiao. Nonlinear Talbot effect. Phys. Rev. Lett., 104, 183901(2010).

[27] J. Wen, Y. Zhang, M. Xiao. The Talbot effect: recent advances in classical optics, nonlinear optics, and quantum optics. Adv. Opt. Photon., 5, 83-130(2013).

[28] Z. Zhang, L. Yang, J. Feng, J. Sheng, Y. Q. Zhang, Y. P. Zhang, M. Xiao. Parity-time-symmetric optical lattice with alternating gain and loss atomic configurations. Laser Photon. Rev., 12, 1800155(2018).

[29] Z. Zhang, Y. Zhang, J. Sheng, L. Yang, M.-A. Miri, D. N. Christodoulides, B. He, Y. Zhang, M. Xiao. Observation of parity-time symmetry in optically induced atomic lattices. Phys. Rev. Lett., 117, 123601(2016).

[30] K. Hornberger, S. Gerlich, P. Haslinger, S. Nimmrichter, M. Arndt. Colloquium: quantum interference of clusters and molecules. Rev. Mod. Phys., 84, 157-173(2012).

[31] Z. Zhang, X. Liu, D. Zhang, J. Sheng, Y. Zhang, Y. Zhang, M. Xiao. Observation of electromagnetically induced Talbot effect in an atomic system. Phys. Rev. A, 97, 013603(2018).

[32] J. M. Wen, S. Du, H. Chen, M. Xiao. Electromagnetically induced Talbot effect. Appl. Phys. Lett., 98, 081108(2011).

[33] M. S. Chapman, C. R. Ekstrom, T. D. Hammond, J. Schmiedmayer, B. E. Tannian, S. Wehinger, D. E. Pritchard. Near-field imaging of atom diffraction gratings: the atomic Talbot effect. Phys. Rev. A, 51, R14-R17(1995).

[34] J. Gea-Banacloche, Y.-Q. Li, S.-Z. Jin, M. Xiao. Electromagnetically induced transparency in ladder-type inhomogeneously broadened media: theory and experiment. Phys. Rev. A, 51, 576-584(1995).

[35] M. Xiao, Y. Li, S. Jin, J. Gea-Banacloche. Measurement of dispersive properties of electromagnetically induced transparency in rubidium atoms. Phys. Rev. Lett., 74, 666-669(1995).

[36] Z. Zhang, F. Li, G. Malpuech, Y. Q. Zhang, O. Bleu, S. Koniakhin, C. Li, Y. P. Zhang, M. Xiao, D. D. Solnyshkov. Particle like behavior of topological defects in linear wave packets in photonic graphene. Phys. Rev. Lett., 122, 233905(2019).

[37] Z. Zhang, S. Liang, F. Li, S. Ning, Y. Li, G. Malpuech, Y. Zhang, M. Xiao, D. Solnyshkov. Spin–orbit coupling in photonic graphene. Optica, 7, 455-462(2020).

[38] O. Bleu, D. D. Solnyshkov, G. Malpuech. Quantum valley Hall effect and perfect valley filter based on photonic analogs of transitional metal dichalcogenides. Phys. Rev. B, 95, 235431(2017).

[39] C. Guo, X. Yin, L. Zhu, Z. Hong. Analytical expression for phase distribution of a hexagonal array at fractional Talbot planes. Opt. Lett., 32, 2079-2081(2007).

[40] J. Belin, T. Tyc. Talbot effect for gratings with diagonal symmetry. J. Opt., 20, 025604(2018).

[41] Z. Zhang, R. Wang, Y. Q. Zhang, Y. V. Kartashov, F. Li, H. Zhong, H. Guan, K. Gao, F. Li, Y. Zhang, M. Xiao. Observation of edge solitons in photonic graphene. Nat. Commun., 11, 1902(2020).