Conical emission from laser filaments and higher-order Kerr effect in   air
  We numerically investigate the conical emission (CE) from ultrashort laser filaments, both considering and disregarding the higher-order Kerr effect (HOKE). While the consideration of HOKE has almost no influence on the predicted CE from collimated beams, differences arise for tightly focused beams. This difference is attributed to the different relative contributions of the non-linear focus and of the modulational instability over the whole filament length. 
Pierre B\'ejot and J\'er\^ome Kasparian
physics.optics