Localized and stationary light wave modes in dispersive media

In recent experiments, localized and stationary optical wave packets have been generated in second-order nonlinear processes with femtosecond pulses, whose asymptotic features relate to those of nondiffracting and nondispersing polychromatic Bessel beams in linear dispersive media. We investigate the nature of these linear waves and show that they can be identified with the X-shaped (O-shaped) modes of the hyperbolic (elliptic) wave equation in media with normal (anomalous) dispersion. Depending on the relative strengths of mode phase mismatch, group velocity mismatch with respect to a plane pulse, and the defeated group velocity dispersion, these modes can adopt the form of pulsed Bessel beams, focus wave modes, and X waves (O waves), respectively.