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Proper alignment is critical to obtain the desired performance from focused spatially chirped beams, for example in simultaneous spatial and temporal focusing (SSTF). We present a simple technique for inspecting the beam paths and focusing conditions for the spectral components of a broadband beam. We spectrally resolve the light transmitted past a knife edge as it was scanned across the beam at several axial positions. The measurement yields information about spot size, M2, and the propagation paths of different frequency components. We also present calculations to illustrate the effects of defocus aberration on SSTF beams.

Simultaneous spatially and temporally focussing (SSTF) of ultrashort pulses allows for an unprecedented control of the intensity distribution of light. It has therefore a great potential for widespread applications ranging from nonlinear microscopy, ophthalmology to micro-machining. SSTF also allows to overcome many bottlenecks of ultrashort pulse micro-machining, especially non-linear effects like filamentation and self-focussing. Here, we describe and demonstrate in detail how SSTF offers an additional degree of freedom for shaping the focal volume. In order to obtain a SSTF beam, the output of an ultrafast laser is usually split by a grating into an array of copies of the original beam, which we refer to as beamlets. The ratio of the beamlet array width to the width of the invidual beamlet is the beam aspect ratio. The focal volume of the SSTF beam can now be tailored transversally by shaping the cross-section of the beamlets and axially by choosing the right beam aspect ratio. We will discuss the requirements of the setup for a successful implementation of this approach: Firstly, the group velocity dispersion and the third order dispersion have to be compensated in order to obtain a high axial confinement. Secondly, the beamlet size and their orientation should not vary too much spectrally. Thirdly, beamlet and SSTF focus should match. We will hence demonstrate how SSTF allows to inscribe tailored three-dimensional structures with fine control over their aspect ratio. We also show how the SSTF focus can be adapted for various glasses and crystals.

Spatial chirp can be manipulated to control the focusing conditions for materials processing. Our double-ABCD nonparaxial analysis helps to understand and exploit the mechanisms for intensity localization, pulse front tilt, and grating formation, and includes initial spectral phase and detuning of the wavelength crossing plane. We also present a novel method for creating high density, high intensity interference patterns with crossed beams that have no relative pulse front tilt. 1. Non-paraxial double ABCD tracing The properties of space-time focused beams are strongly dependent of the nature of the spatial overlap of the frequency components. The analysis of optical systems with spatial chirp is therefore critical both for understanding the unusual properties of these beams and for designing systems to exploit these properties for materials processing. In a recent paper, we developed an analytical approach to calculate the propagation of spatially chirped beams. A ray is traced that represents the central axis of the Gaussian beamlet for each frequency component. Since one form of the calculation is nonparaxial, the beamlet angles can be large and the calculation is valid over a wider range of conditions than direct Fresnel propagation. Our technique explains, for example, how the evolution of the beamlet radius of curvature leads to an axial variation of the spectral chirp through the focus, contributing to the axial intensity localization. It also allows the derivation of simple scaling properties of the beam, showing that the improvement of the localization over the confocal parameter of the focused beamlets depends primarily on the degree of spatial chirp, not on the initial pulse duration or the focal length.

Space-time focusing of spatially-chirped Ti:Sapphire laser pulses is used to generate a plasma in air axially localized to 28× less than the confocal parameter, suppressing filamentation on the way to the focus.

Space-time focusing of spatially-chirped Ti:Sapphire laser pulses is used to generate a plasma in air axially localized to 28x less than the confocal parameter, suppressing filamentation on the way to the focus.