Feng Li1, Sergei V. Koniakhin2、3, Anton V. Nalitov4、5、6, Evgeniia Cherotchenko7, Dmitry D. Solnyshkov8、9, Guillaume Malpuech8, Min Xiao10、11, Yanpeng Zhang1, and Zhaoyang Zhang1、*
Author Affiliations
1Xi’an Jiaotong University, Key Laboratory for Physical Electronics and Devices of the Ministry of Education, Shaanxi Key Laboratory of Information Photonic Technique, School of Electronic Science and Engineering, Faculty of Electronics and Information, Xi’an, China2Institute for Basic Science, Center for Theoretical Physics of Complex Systems, Daejeon, Republic of Korea3Korea University of Science and Technology (UST), Basic Science Program, Daejeon, Republic of Korea4Moscow Institute of Physics and Technology, Dolgoprudnyi, Russia5University of Wolverhampton, Faculty of Science and Engineering, Wolverhampton, United Kingdom6ITMO University, St. Petersburg, Russia7Ioffe Institute, St. Petersburg, Russia8Université Clermont Auvergne, Institut Pascal, PHOTON-N2, CNRS, Clermont INP, Clermont-Ferrand, France9Institut Universitaire de France, Paris, France10University of Arkansas, Department of Physics, Fayetteville, Arkansas, United States11Nanjing University, School of Physics, National Laboratory of Solid State Microstructures, Nanjing, Chinashow less
DOI: 10.1117/1.AP.5.6.066007
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Feng Li, Sergei V. Koniakhin, Anton V. Nalitov, Evgeniia Cherotchenko, Dmitry D. Solnyshkov, Guillaume Malpuech, Min Xiao, Yanpeng Zhang, Zhaoyang Zhang. Simultaneous creation of multiple vortex-antivortex pairs in momentum space in photonic lattices[J]. Advanced Photonics, 2023, 5(6): 066007
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Fig. 1. Experimental schemes. (a) Illustrative picture of the experimental setup. The focus lengths of the two lenses are both . (b) The three-level atomic configuration excited by the probe field and the hexagonal coupling field . (c) and (d) Calculated spatial distribution of refractive index for (c) and (d) with , resulting in honeycomb and hexagonal lattices, respectively.
Fig. 2. Momentum space vortex generation in the honeycomb lattice with the two-photon detuning being 20 MHz. (a) Experimentally measured momentum space image interference with the reference beam. The dislocations in fringes correspond to the vortices (marked by white circles). (b) The corresponding phase pattern extracted from the interference image. Black arrows show the rotation direction.
Fig. 3. Numerical solution of the Schrödinger equation showing wave packet expansion in photonic graphene starting from the excitation of a single site. (a) The probability distribution in real space. (b) The probability distribution in momentum space. (c) The reciprocal space phase image of the WF corresponding to panel (b). The left and right vortices are marked with blue and red circles, respectively. (d) The reciprocal space WF interference with a plane wave. Green circles indicate the Dirac points. The snapshot shows that the WF has the symmetry. Panels (e) and (f) show the results of tight-binding calculation and correspond to panels (a) and (d), respectively.
Fig. 4. Numerical solution of the Schrödinger equation showing wave packet expansion in photonic honeycomb and hexagonal lattices with various symmetries of the WFs. (a), (b) Honeycomb lattice, excitation of a single “benzene ring” (): real space probability (a) and momentum space phase (b). (c), (d) The same for a honeycomb lattice, excitation between two sites ( symmetry). (e), (f) The same for a topologically trivial hexagonal lattice with -excitation.
Fig. 5. Phase patterns in momentum space for alternative symmetries and lattices. Panels (a) and (b) demonstrate absence of vortices for the case of symmetry signal in honeycomb lattice. The momentum space interference image shown in panel (a) contains no fork dislocations in fringe pattern and the extracted phase shown in panel (b) also demonstrates no vortex-like phase defects. Panels (c) and (d) show the interference pattern and extracted phase, respectively, for the symmetry signal realized in the honeycomb lattice by excitation between two sites. Panels (e) and (f) are for the interference pattern and extracted phase, respectively, in the case of the symmetry in hexagonal lattice realized experimentally by setting the two-photon detuning .