Unveiling the Link Between Fractional Schrödinger Equation and Light Propagation in Honeycomb Lattice |
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| Authors: | Da Zhang Yiqi Zhang Zhaoyang Zhang Noor Ahmed Yanpeng Zhang Fuli Li Milivoj R. Belić Min Xiao |
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| Affiliation: | 1. Key Laboratory for Physical Electronics and Devices of the Ministry of Education & Shaanxi Key Lab of Information Photonic Technique, Xi'an Jiaotong University, Xi'an, China;2. Department of Applied Physics, School of Science, Xi'an Jiaotong University, Xi'an, China;3. Science Program, Texas A & M University at Qatar, Doha, Qatar;4. Department of Physics, University of Arkansas, Fayetteville, Arkansas, USA;5. National Laboratory of Solid State Microstructures and School of Physics, Nanjing University, Nanjing, China |
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| Abstract: | We suggest a real physical system — the honeycomb lattice — as a possible realization of the fractional Schrödinger equation (FSE) system, through utilization of the Dirac‐Weyl equation (DWE). The fractional Laplacian in FSE causes modulation of the dispersion relation of the system, which becomes linear in the limiting case. In the honeycomb lattice, the dispersion relation is already linear around the Dirac point, suggesting a possible connection with the FSE, since both models can be reduced to the one described by the DWE. Thus, we propagate Gaussian beams in three ways: according to FSE, honeycomb lattice around the Dirac point, and DWE, to discover universal behavior — the conical diffraction. However, if an additional potential is brought into the system, the similarity in behavior is broken, because the added potential serves as a perturbation that breaks the translational periodicity of honeycomb lattice and destroys Dirac cones in the dispersion relation. |
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| Keywords: | Fractional Schrö dinger equation Honeycomb lattice Linear dispersion Dirac‐Weyl equation |
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