Suppression of filamentation in refraction index modulated Kerr media

•The use of a constant photonic crystal does not allow for control of diffraction.•Adiabatic chirping of the photonic crystal allows projection of radiation into a specific mode.•Diffraction can be precisely tuned by controlling the geometry of a chirped photonic crystal.•Chirped photonic crystals can be designed to effectively suppress filamentation. In this work, the possibility of using periodic refractive index modulation – photonic crystals – to counteract the spatial Kerr effect, thus suppressing filamentation, is shown. Numerical simulations by beam propagation method indicate that fine control of the spatial dispersion can be achieved by tuning the photonic crystal geometry and projecting to the appropriate Bloch mode branch by chirping the longitudinal period. Controlling the spatial dispersion allows management of the strength of diffraction. Furthermore, it is shown that photonic crystals can be engineered with such geometry that the designed diffraction compensates for self-focusing, effectively delaying, or entirely eliminating beam filamentation.