Abstract
We investigate linear and nonlinear evolution dynamics of light beams propagating along a dislocated edge-centered square lattice. The band structure and Brillouin zones of this novel lattice are analyzed analytically and numerically. Asymmetric Dirac cones as well as the corresponding Bloch modes of the lattice are obtained. By adopting the tight-binding approximation, we give an explanation of the asymmetry of Dirac cones. By utilizing the appropriate Bloch modes, linear and nonlinear asymmetric conical diffraction are demonstrated. We find that both the focusing and defocusing nonlinearities can enhance the asymmetry of the conical diffractions.
Highlights
Two-dimensional photonic lattices with novel spatial periodic arrangements can serve as good platforms for manipulating the spatial behavior of light propagating through waveguide arrays formed by the lattices [1,2,3,4,5]
In summary, we have investigated both the linear and nonlinear asymmetric conical diffraction in the dislocated edge-centered square lattice, which possesses four bands and six Dirac cones between each nearest two bands
The Bloch modes of the asymmetric Dirac cones are obtained using the one-dimensional band of the strained lattice
Summary
Two-dimensional photonic lattices with novel spatial periodic arrangements can serve as good platforms for manipulating the spatial behavior of light propagating through waveguide arrays formed by the lattices [1,2,3,4,5]. We design an edge-centered square lattice with dislocation but without distortion, which possesses tilted type-I Dirac cones and abundantly displays asymmetric conical diffraction. One finds that there are 6 Dirac cones between the two neighboring bands, but they are tilted and elliptic, and are not located at the 6 corners of the first Brillouin zone This is significantly different from the honeycomb lattice [34, 37]. The Gaussian beams will inevitably excite the bulk modes as well and lead to radiation mixed with the conical diffraction, because the locations of the Dirac cones in the three band gaps are different. One finds that the size of the asymmetric diffraction rings increases linearly with the propagation distance
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