Beam propagation in the photonic crystal of the local super-collimation regions.

We investigate the beam propagation behavior in the photonic crystal (PhC) of the local super-collimation (LSC) regions both theoretically and numerically. A theory based on the cubic dispersion model in the LSC regions is established, which is a powerful tool to predict the beam evolution after a long propagation distance. The numerical experiments are also implemented, whose results agree well with those from our theory. Both the theoretical and simulation results show the new phenomenon of the asymmetric beam broadening for beams in the LSC regions, which is quite different from the traditional symmetric broadening. Physical reasons of such asymmetric broadening are explained by the cubic dispersion model and the solution to suppress the asymmetric broadening is proposed. Since the LSC beams could be widely used in photonic devices, such as hypersensitive spectrometers and demultiplexers, the deep insights of the beam propagation behavior in the LSC regions can help us to optimize our designs, such as choosing the proper beam width and the proper working range in the phase space.