Characterization and control of peak intensity distribution at the focus of a spatiotemporally focused femtosecond laser beam. Simultaneous spatial and temporal focusing of femtosecond pulses. Zhu, G., van Howe, J., Durst, M., Zipfel, W. Influence of spatiotemporal coupling induced by an ultrashort laser pulse shaper on a focused beam profile. Tanab, T., Kannari, F., Korte, F., Koch, J. The general theory of first-order spatio-temporal distortions of Gaussian pulses and beams. The longitudinal iso-phase condition and needle pulses. Diffraction-free pulsed optical beams via space–time correlations. Methods for generating wideband localized waves of superluminal group velocity. Bessel X waves in two- and three-dimensional bidispersive optical systems. One dimensional spatial localization of polychromatic stationary wave-packets in normally dispersive media. Jedrkiewicz, O., Wang, Y.-D., Valiulis, G. Spatiotemporal Bessel beams: theory and experiments. Spontaneously generated X-shaped light bullets. Evidence of X-shaped propagation-invariant localized light waves. Nondiffracting X waves-exact solutions to free-space scalar wave equation and their finite aperture realizations. Focus wave modes in homogeneous Maxwell’s equations: transverse electric mode. Airy–Bessel wave packets as versatile linear light bullets. Localized waves with spherical harmonic symmetries. Diffraction-free and dispersion-free pulsed beam propagation in dispersive media. Subwavelength anti-diffracting beams propagating over more than 1,000 Rayleigh lengths. Non-diffracting Waves (Wiley, Weinheim, 2014). Normalization of optical Weber waves and Weber-Gauss beams. Parabolic nondiffracting optical wave fields. Fundamentals of Photonics (Wiley, Hoboken, 2007). However, most applications require free-space diffraction-free beams. Optical nonlinearities can be exploited to thwart diffractive spreading 10, 11, and in some cases chromatic dispersion is required in the medium to restrain the diffraction of pulsed beams 12, 13. Indeed, a conclusive argument by Michael Berry 9 identified the Airy beam as the only such monochromatic one-dimensional (1D) profile. The situation is altogether different for monochromatic beams with one transverse dimension-or light sheets-where there are only two possible diffraction-free solutions: the cosine wave, which lacks spatial localization, and the Airy beam, which maintains a localized intensity profile but has a centre of mass that undergoes a transverse shift with propagation 8. Monochromatic diffraction-free beams have sculpted two-dimensional (2D) transverse spatial profiles that conform to Bessel 3, Mathieu 4 or Weber 5 functions, among others (see refs 6, 7 for recent taxonomies). As a result, there has been a long-standing fascination with so-called ‘diffraction-free’ beams whose change in shape and scale during propagation is curbed 2. Diffraction sets limits on the optical resolution in microscopy, lithography and photography, on the maximum distance for free-space optical communications and standoff detection, and on the precision of spectral analysis 1. These ‘space–time’ light sheets can be useful in microscopy, nonlinear spectroscopy, and non-contact measurements.ĭiffractive spreading is a fundamental feature of freely propagating optical beams that is readily observed in everyday life. Far from being exceptional, self-similar axial-propagation in free space is a generic feature of fields whose spatial and temporal degrees of freedom are tightly correlated. The spectral loci of such beams are the reduced-dimensionality trajectories at the intersection of the light-cone with spatiotemporal spectral planes. By introducing programmable conical (hyperbolic, parabolic or elliptical) spectral correlations between the beam’s spatiotemporal degrees of freedom, a continuum of families of propagation-invariant light sheets is generated. Here, we demonstrate that the temporal degree of freedom can be exploited to efficiently synthesize one-dimensional pulsed light sheets that propagate self-similarly in free space, with no need for nonlinearity or dispersion. Monochromatic beams that avoid diffractive spreading require two-dimensional transverse profiles and there are no corresponding solutions for profiles restricted to one transverse dimension. Diffraction-free optical beams propagate freely without change in shape and scale.
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