Chapter 14: Spatiotemporal Dynamics and Light Bullets in Nematic Liquid Crystals
Institute for Complex Systems, ISC-CNR, Rome, Italy
We see only what we know.
Johann Wolfgang von Goethe (1749–1832)
Electromagnetic wave packets tend to spread out as they evolve, whatever dimension (time or space) is involved. The fundamental cause of this phenomenon is the propagation at different velocities or directions of the wave packet frequency components. Hence, similar to the beam diffracting in space, pulses spread in time because of the so-called group-velocity-dispersion (GVD), as the energy associated to the various Fourier components of the field tends to temporally shift in propagation. One of the most challenging goals in the study of multidimensional nonlinear field–matter interactions is the generation of wave packets confined in both time and space or light bullets. This term was coined in 1990 by Silberberg  to stress the particle nature of such nonlinear objects. We refer to these self-confined waves, or spatiotemporal solitons (STSs), as (2 + 1 + 1)D solitary waves, where the “2” refers to the confinement along the two transverse spatial dimensions, the former “1” relates to the confinement in the time coordinate and the latter “1” refers to the spatial propagation direction.
The formation of STSs requires the simultaneous nonlinear compensation of GVD and diffraction, respectively, occurring in the (1 + 1)D temporal and (2 + 1)D spatial ...