Spatiotemporal bessel beams: theory and experiments

Dallaire, Michael; McCarthy, Nathalie; Piché, Michel

doi:10.1364/oe.17.018148

Cited by 63 publications

(53 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The last point is supported by the existence, as mentioned before, of the 2D spatially localized BB, or of the 2D STBB characterized in [18], both stationary in propagation. In both cases, the ringlike spatial spectrum of the BB or the ringlike spatiotemporal spectrum of the STBB leads to a Bessel profile in the near field, and to its localization in space and in space-time, respectively.…”

Section: Introductionsupporting

confidence: 53%

See 1 more Smart Citation

Simultaneous stationarity and localization of linear wave packets: The importance of dimensionality and broad spectral support

et al. 2014

View full text Add to dashboard Cite

In this paper we review the conditions needed for the localization and stationarity of a wave packet during propagation in a linear transparent medium. The requirements on the dimensionality and spatiotemporal frequency content for wave packets with such characteristics are discussed. In particular, we demonstrate how the localization of the stationary two-dimensional solution of the propagation equation depends on the features and shape of its spatiotemporal spectral bandwidth. The spatiotemporal properties of the one-dimensional (1D) spatial and 1D temporal beams stationarily propagating in dispersive materials are illustrated both in the normal and in the anomalous dispersion regime

show abstract

Section: Introductionsupporting

confidence: 53%

“…A similar stationary propagating WP is the two-dimensional spatiotemporal Bessel beam (STBB), also featured by infinite energy [18]. Analogously, the three-dimensional X waves and O waves are stationary wave packets in linear media when having unlimited energy [3][4][5][6]8,9].…”

Section: Introductionmentioning

confidence: 99%

Simultaneous stationarity and localization of linear wave packets: The importance of dimensionality and broad spectral support

et al. 2014

View full text Add to dashboard Cite

show abstract

“…By controllably associating each with a unique , programmable correlations are introduced into the ST-spectrum � ( , ). Recombining the spectrum via a second grating reconstitutes the pulse and simultaneously overlaps all the spatial frequencies, so the ST-beam is immediately realized along with no need for a spatial Fourier transform 40,41 .…”

Section: Methodsmentioning

confidence: 99%

Diffraction-free space–time light sheets

Kondakci¹,

Abouraddy²

2017

Nature Photon

289

283

View full text Add to dashboard Cite

Diffraction-free optical beams propagate freely without change in shape and scale. Monochromatic beams that avoid diffractive spreading require two-dimensional transverse profiles, and there are no corresponding solutions for profiles restricted to one transverse dimension. Here, we demonstrate that the temporal degree of freedom can be exploited to efficiently synthesize onedimensional pulsed optical sheets that propagate self-similarly in free space. By introducing programmable conical (hyperbolic, parabolic, or elliptical) spectral correlations between the beam's spatio-temporal degrees of freedom, a continuum of families of axially invariant pulsed localized beams is generated. The spectral loci of such beams are the reduced-dimensionality trajectories at the intersection of the light-cone with spatio-temporal spectral planes. Far from being exceptional, self-similar axial propagation is a generic feature of fields whose spatial and temporal degrees of freedom are tightly correlated. These one-dimensional 'space-time' beams can be useful in optical sheet microscopy, nonlinear spectroscopy, and non-contact measurements.Diffractive spreading is a fundamental feature of freely propagating optical beams that is readily observed in everyday life. 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 1,2 . As a result, there has been a long-standing fascination with socalled 'diffraction-free' beams whose change in shape and scale during propagation is curbed when compared to other beams of comparable transverse size 3 . Monochromatic diffraction-free beams have sculpted two-dimensional (2D) transverse spatial profiles that confirm to Bessel 4 , Mathieu 5 , or Weber 6 functions, among other examples (see Refs. [7,8] for recent taxonomies). The situation is altogether different for monochromatic beams with one transverse dimension -or optical sheets -where there are only two possible diffraction-free solutions: the cosine wave that lacks spatial localization and the Airy beam that maintains a localized intensity profile but whose center-of-mass undergoes a transverse shift with propagation 9,10 . Indeed, a conclusive argument by Michael Berry 11 identified the Airy beam as the only such monochromatic one-dimensional (1D) profile. Optical nonlinearities can be exploited to thwart diffractive spreading 12,13 , and in some cases chromatic dispersion is required in the medium to restrain the diffraction of pulsed beams [14][15][16] . However, most applications require free-space diffraction-free beams.Here, we exploit the temporal degree of freedom (DoF) in conjunction with the spatial DoF to realize a variety of diffraction-free pulsed solutions having arbitrary 1D transverse profiles. By establishing a correlation between the spatial and temporal DoFs, diffractive spreading is reined-in and the time-averaged spatial profile propagates self-similarly. ...

show abstract

“…But, they require a nonlinearity to preserve their shape. It was pointed out by Durnin that nonlinearity is not a necessity for invariant propagation; indeed, he proved that Bessel beams can propagate in a purely linear material without deformation (Durnin, 1987;Dallaire et al, 2009). On the other hand, Lopez and Helmerson have recently demonstrated that non-diffracting beams with arbitrary transverse shapes can be generated (Lopez-Mariscal and Helmerson, 2010).…”

Section: Introductionmentioning

confidence: 99%