## 2 Linear Light Bullets  
### Medium-Free Generation of Linear Light Bullets  
The search for stable, non-spreading solutions of wave equations for electromagnetic waves like those of Maxwell, Schroedinger or Helmholtz type, quantum mechanic wave functions and acoustic waves resulted in wave phenomena called \"undistorted progressive\" [7], \"diffraction-less\" [8; 9; 10] or \"localized waves\" [11]. Among the propagation-invariant solutions is the important Bessel beam which is characterized by a radially symmetric intensity profile following the square of a zero-order first kind Bessel function. The perfect theoretical monochromatic Bessel beam has an unlimited depth of focus (DOF) and consists of an infinite number of concentric rings surrounding a central maximum in all transversal planes. Practical realizations, however, work with conical phase elements (axicons) of finite diameter. In this case, the DOF and the number of fringes is limited. In frame of ultrasound studies it was found that the spatio-spectral interference of pulsed conical waves with large spectral bandwidths leads to the formation of X-shaped waves (X-waves) [12, 13]. In their maximum, Bessel-X-pulses can reach giant intensities by focusing the energy in space and time. Optical Bessel-X-waves were first shaped with high pressure lamps of few-fs coherence time with conical axicons and indicated by cross correlation experiments [14]. Ultrashort-pulsed Bessel-X-pulses were demonstrated by shaping pulses of a Ti:sapphire laser with transparent and reflective thin-film axicons and detecting the characteristic features by spatially resolved autocorrelation [11, 15, 16].  
In contrast to other types of linear light bullets, the generation of optical X-pulses does not require a dispersive medium. The bullet structure, _i.e._, the spatial and temporal confinement and propagation invariance, is the result of a linear superposition and constructive interference of many contributing spectral modes with approximately identical angular spectra. It has to be noticed that an analogous effect might contribute to the spontaneous generation of extreme water waves (rogue or monster waves), in regions of deep ocean water which can not simply be explained by shallow water models (the similarity was addressed in [17], p. 193). [PERSON] _et al._ extended the X-wave concept to the nonlinear regime [18, 19]. The spontaneous generation of nonlinear X-waves was first experimentally demonstrated in [20]. For linear, normally dispersive media, a certain class of finite energy light bullets was identified which allows arbitrary spatio-temporal profiles [21]. Recently, several variations of linear and nonlinear light bullets emerged in the literature, most of which are close relatives of Bessel beams, e.g., [PERSON] [22], Airy [23], Pearsey [24], Weber [25], or Helmholtz beams [26]. It was found that such beams are self-healing after distortion (for the self-reconstruction of Bessel-X-pulses, see [11]). This results from the subsequent constructive interference of conical waves which continues again behind a shadow zone. The detailed theoretical interpretation of nondiffracting wave phenomena is still a subject of discussion.