Gaussian beams diffracting in time

Abstract

We show how to transform the mathematical expression of any monochromatic paraxial light beam into the expression of a pulsed beam whose diffraction is switched from the axial direction to its temporal structure. We exemplify this transformation with time-diffracting Gaussian beams. The conditions for the obtained diffraction-free wave to be physically meaningful are discussed.

What is the maximum differential group delay achievable by a space-time wave packet in free space?

“…It was immediately recognized after Brittingham's initial work [1] that ideal propagation-invariant ST wave packets have infinite energy [39], and several theoretical approaches explored constructing finite-energy counterparts. The earliest approach was to superpose ideal ST wave packets [40]; a second approach introduces a finite transverse spatial aperture [41,42]; and a third strategy introduces a temporal 'window' co-propagating with the ST wave packet (at a different group velocity) [6,43].…”

“…Ever since Brittingham proposed in 1983 a pulsed optical beam that is transported rigidly in free space at a group velocity equal to the speed of light c [1], there has been significant interest in the study of propagationinvariant wave packets [2][3][4][5][6][7][8][9][10]. A variety of examples have been identified [11][12][13] whose group velocity in free space -intriguingly -take on arbitrary values.…”

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.…”

Self-trapped pulsed beams with finite power in Kerr media excited by time-diffracting, space-time beams

“…The needed couplings between the spatial and temporal frequencies for diffraction-free propagation at arbitrary propagation velocity in free space and in linear dispersive media are known for some decades, mainly in the context of the so-called localized waves or modes [12][13][14][15], but recent advances in pulse and beam shaping techniques have made possible their practical implementation using spatial light modulators and transparent transmissive phase plates [9][10][11]. On the theoretical side, the spatiotemporal shape of these pulsed beam has been shown to reproduce the axial-transversal structure of monochromatic light that experiences diffraction spreading, that is, diffraction appears to be swapped from the longitudinal direction to time [16,17], which is why they are also called time-diffracting beams (TD beams). This allows to use the vast knowledge about monochromatic light beams to write down simple analytical expressions of time-diffracting beams.…”