Diffraction-free pulsed optical beams via space-time correlations

Abstract

Diffraction places a fundamental limitation on the distance an optical beam propagates before its size increases and spatial details blur. We show here that imposing a judicious correlation between spatial and spectral degrees of freedom of a pulsed beam can render its transverse spatial profile independent of location along the propagation axis, thereby arresting the spread of the time-averaged beam. Such correlation introduced into a beam with arbitrary spatial profile enables spatio-temporal dispersion to compensate for purely spatial dispersion that underlies diffraction. As a result, the spatio-temporal profile in the local time-frame of the pulsed beam remains invariant at all positions along the propagation axis. One-dimensional diffraction-free space-time beams are described - including non-accelerating Airy beams, despite the well-known fact that cosine waves and accelerating Airy beams are the only one-dimensional diffraction-free solutions to the monochromatic Helmholtz equation.

Diffraction-free space–time light sheets

“…where is a constant axial wave number 26,27 . This correlation function between | | and results from intersecting the light-cone with an iso-plane 0 ( = ) in a single branch of a hyperbola (Fig.…”

“…4e), and -in principle -for ST-beams lying in all other spectral planes. In general, the ratio of the spectral-correlation uncertainty to the bandwidth ∆ (that is, ∆ / ) sets the diffraction-free length 26 , which is in general orders-of-magnitude larger than that of a Gaussian beam of the same transverse width.…”

“…In this conception, the spectral loci of ST-beams are reduced-dimensionality trajectories at the intersection of the light-cone with surfaces in the ST spectral domain, such as the conic sections at the intersection of the light-cone with tilted spectral planes. One such plane is the iso-plane 0 of the axial wave number, whose intersection with the light-cone is a branch of a hyperbola that corresponds to beams with no axial ST-dynamics [25][26][27] . Planes tilted with respect to 0 intersect with the light-cone in hyperbolae, parabolas, or ellipses -all of which are spectral loci for families of diffraction-free STbeams.…”

Demonstration of a Free-Space Optical Delay Line Using Space-Time Wave Packets

“…An altogether different approach for tuning the group velocity of a pulse makes use of 'spacetime' (ST) wave packets: propagation-invariant pulsed beams (diffraction-free and dispersionfree) [31][32][33][34][35][36][37][38] endowed with structured spatio-temporal spectra [39][40][41][42][43] in which each spatial frequency is associated with a single wavelength [44][45][46][47][48]. Although it has long been known theoretically that ST wave packets may take on arbitrary group velocities (speed of the wavepacket peak) in free space [49][50][51][52][53], experiments have revealed group-velocity deviations from c of only ∼0.1% [54][55][56], corresponding to group delays of tens or hundreds of femtoseconds -several orders-of-magnitude below the requirements for an optical buffer.…”

“…A different strategy relies on transverse spatial structuring to reduce the group velocity in free space, but only a minute reduction below c has been detected to date [23,24]. Nevertheless, theoretical proposals suggest that pushing this approach to the limit may produce sufficiently large differential group delays for an optical buffer [25,26], but temporal spreading is associated with the propagation of these wave packets [27].Finally, a recent theoretical proposal suggests that optical non-reciprocity can help bypass the usual DBP limits [28], but doubts have been cast on this prospect [29,30].An altogether different approach for tuning the group velocity of a pulse makes use of 'spacetime' (ST) wave packets: propagation-invariant pulsed beams (diffraction-free and dispersionfree) [31][32][33][34][35][36][37][38] endowed with structured spatio-temporal spectra [39][40][41][42][43] in which each spatial frequency is associated with a single wavelength [44][45][46][47][48]. Although it has long been known theoretically that ST wave packets may take on arbitrary group velocities (speed of the wavepacket peak) in free space [49][50][51][52][53], experiments have revealed group-velocity deviations from c of only ∼0.1% [54][55][56], corresponding to group delays of tens or hundreds of femtoseconds -several orders-of-magnitude below the requirements for an optical buffer.…”