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The nonlinear effect from the interplay between the nonlinearity and the supercollimation of photonic crystal

The authors theoretically and numerically investigate the beam propagation near the supercollimation frequency ωs0 in a photonic crystal made of nonlinear material. Since the value and sign of the equal-frequency-contour curvature which dominates the beam behaviors can be nonlinearly tuned near ωs0, a kind of nonlinear effect is generated. The envelope equation with unique form is also obtained. Beam-control mechanisms are theoretically predicted and observed in numerical experiments, such as tunable collimation, tunable beam-divergence angle, and self-lock of collimation. These mechanisms can be utilized to function as fiber, lens and coupler, or to design photonic devices.