Phase stability and diffraction effects in self-focused white light filaments in water and glass

Three aspects of filament formation due to self-focusing are investigated. In the first the generation of a horizontal array of stable white light (super) continuum (WLC) filaments in water has been observed using a cylindrical planoconvex lens. Far field interference patterns are observed suggesting that the optical paths and phase stability between neighbouring filaments is remarkably constant. The pattern created by a filament pair is similar to that due to a pair of Young's slits. The experimental results agree well with theoretical predictions based on the number of fringes and the fringe spacing. These observations suggest that regular arrays of WLC filaments may be treated as phased arrays to steer the beam in the far field. In the second investigation the effect of beam quality on self-focusing has been studied. The small intrinsic aberration of a high quality TEM₀₀ beam is shown to cause hot-spots leading to multiple filaments. In the third investigation a circular aperture is used to create a Fresnel diffraction pattern. It is shown that self-focusing (a prerequisite for filament formation) occurs in the presence of the aperture but that no formation is observed when the aperture is removed, even though the beam has higher power well above the threshold for critical power. An analytical solution to the Huygens-Fresnel diffraction integral shows that the axial intensity oscillates between maxima and minima as the distance from the aperture increases and that filament formation coincides with the presence of an axial maximum.