Conical diffraction modulation in honeycomb lattices

Abstract

We investigate the generation and destruction of asymmetric conical diffraction in honeycomb lattices by adjusting rotation angle θ of the three vectors and considering nonlinearities. For θ = 0° and 60°, the modes of the Dirac cone of the honeycomb lattice are excited, symmetric conical diffraction are obtained. When 0 < θ < 60°, asymmetric conical diffraction with a dark notch appears and the dark notch moves clockwise or anti-clockwise around the outer edge of the bright ring. In addition, it is also demonstrated that both Kerr and saturation nonlinearities can cause triangular deformation of conical diffraction pattern. Under the same nonlinearity, two identical wave centered around different Dirac points can evolve to identical triangular rings pointing in opposite directions. The dark notch at a point of triangular appears and moves in a clockwise or anti-clockwise way for self-focusing and self-defocusing nonlinearity, respectively.