Nonlinear X-wave formation by femtosecond filamentation in Kerr media

Abstract

We investigate the formation of X waves during filamentation in Kerr media. From the standard model developed for femtosecond filamentation in liquids, solids, and gases, the influence of several physical effects and parameters is numerically studied in the strongly nonlinear regime where group velocity dispersion alone is insufficient to arrest collapse. The collapse is shown to be arrested by multiphoton absorption and plasma defocusing, but not by dispersion. The postcollapse dynamics takes the form of a pulse splitting, which induces large gradients in the near field and seeds the formation of X waves, appearing both in the near and far fields. We discuss the universal features of the X-wave patterns, among which the long arms in the far field that follow the linear dispersive properties of the medium [Conti, Phys. Rev. Lett. 90, 170406 (2003); Kolesik, Phys. Rev. Lett. 92, 253901 (2004)] and are accompanied by a strong modulated axial emission.

Ultrafast supercontinuum generation in bulk condensed media

“…These findings led to the interpretation of femtosecond filaments as conical waves, assuming that the input wave packet will try to evolve toward a final stationary state that has the form of either an Xwave in the range of normal GVD or an O-wave in the range of anomalous GVD. Nonlinear Xwaves [93,94] and O-waves [95] are named because of their evident X-like and O-like shapes, respectively, which appear in both the near-and the far-fields. Moreover, the interpretation of light filaments in the framework of conical waves readily explains the distinctive propagation features of light filaments such as the sub-diffractive propagation in the free space [83,92] and self-reconstruction after hitting physical obstacles [96][97][98], which are universal and regardless of the sign of material GVD, and which were verified experimentally as well.…”

Efficient four-wave parametric amplification and spatial soliton generation in transparent isotropic medium with Kerr nonlinearity

“…With E p = 80 µJ, pump pulse alone (with no seed) breaks up into an array of multiple filaments, which in turn prompts pulse splitting in time into two sub-pulses, as shown by 3-peak autocorrelation function in Fig. 6(c), appearance of conical emission, and, finally, formation of the X-waves [27]. By contrast, temporal splitting of the pump pulse is quenched when a seed signal is launched, and a clean amplified signal with a Gaussian profile is measured, see Fig.…”

Nonlinear localization of light

“…The details of experiment are described elsewhere [38]. most importantly, nonlinear X wave generation is foreseen for a wide parameter range, whatever is the physical mechanism arresting the collapse [28]. Another relevant and still poorly investigated case refers to filamentation phenomena in the regime of anomalous group velocity dispersion.…”

“…(1), while nonlinear terms 4 and 5 stand for self-focusing and multiphoton absorption, respectively. With account for plasma defocusing, equation takes more complex form, including evolution equation for the free electron density, which accounts also for multiphoton and avalanche ionization, plasma absorption, optical shock terms, etc., see the full model described in [28]. However, some basic properties can be evaluated with the help of the propagation equation in the simplified form as given by Eq.…”