The Harper-Hofstadter Hamiltonian and conical diffraction in photonic lattices with grating assisted tunneling

Abstract

We introduce a grating assisted tunneling scheme for tunable synthetic magnetic fields in photonic lattices, which can be implemented at optical frequencies in optically induced one- and two-dimensional dielectric photonic lattices. We demonstrate a conical diffraction pattern in particular realization of these lattices which possess Dirac points in $k$-space, as a signature of the synthetic magnetic fields. The two-dimensional photonic lattice with grating assisted tunneling constitutes the realization of the Harper-Hofstadter Hamiltonian.

are welcome; figures 2c,d obtained with somewhat better parameter values

References in corpus (11)

• Topological Photonics
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• Reflection-Free One-Way Edge Modes in a Gyromagnetic Photonic Crystal
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Cited by in corpus (8)

• Topological Photonics
• $\mathcal{P}\mathcal{T}$ symmetry in a fractional Schrödinger equation
• Meissner-like effect for synthetic gauge field in multimode cavity QED
• Realization of uniform synthetic magnetic fields by periodically shaking an optical square lattice
• Omnidirectional spin Hall effect in a Weyl spin-orbit coupled atomic gas
• Modulation instability in the nonlinear Schrödinger equation with a synthetic magnetic field: gauge matters
• Chiral excitation flows of a multinode network based on synthetic gauge fields
• Laser assisted tunneling in a Tonks-Girardeau gas