Abstract

The continuum produced by intense femtosecond laser pulses has been widely studied in various transparent media, such as air, liquids and dielectrics (see [1] for review). This spectral broadening is in general caused by self-phase modulation (SPM). In self-guiding regime, femtosecond pulses, whose power is above the critical power for self-focusing, develop a collapse dynamics that becomes saturated by the generation of a tenuous plasma created by photo-ionization of the ambient molecules. The resulting structure is an ultrashort filament clamped at high intensity (> 10 TW/cm²), able to propagate over distances exceeding the beam diffraction limit. The spectrum is expected to become all the broader as the maximum pulse intensity is high, the pulse duration is short and the filamentation range is large. In addition to SPM, other mechanisms such as spacetime focusing, self-steepening and third harmonic generation (THG) can noticeably alter the pulse spectrum. In connection, the choice of the central laser wavelength also influence the effective broadening to some extent [2]. We here analyze numerically supercontinuum generation for the three laser wavelengths of 248 nm, 800 nm and 1550 nm, on the basis of different nonlinear Schrödinger-like equations for the electric field envelope involving or not space-time focusing and self-steepening operators, and an unidirectional propagation equation avoiding any Taylor expansion of the dispersion relation. Several photo-ionization models, fixing the level of the filament intensity in the range of 10 to 100 TW/crn², are investigated. Emphasis is put on the long-range propagation over several meters in air. Spectral enlargements are directly linked to the level of the maximum intensity: Steepening operators as well as THG broaden all the more the spectra as the peak intensity in the filament is high. The higher this peak intensity, the wider the blueshift induced by steepening effects. Also, the overall length of the filament plays a crucial role in supercontinuum generation: Successive cycles of focusing and defocusing events promote the creation of shorter and shorter peaks in the pulse temporal profile and lead to a maximal extension of the spectrum. Several input durations ranking from 20 to 500 fs have been tested. They condition the saturation intensity and the spectral broadening reached during the early focusing events only [3]. However, a long propagation produces short peaks along the focusing/defocusing sequences. These eventually enlarge the spectra to similar extents, whatever the input pulse duration may be. The central laser wavelength appears as a more crucial quantity, since supercontinuum generation is more efficient at larger wavelengths, which is illustrated in Fig. 1.

© 2007 IEEE