arXiv subjects

Layton A. Hall

Publications and source records attributed to Layton A. Hall.

33 records · Page 2Linked to original sources

arXiv2022

Non-differentiable angular dispersion as an optical resource

Introducing angular dispersion into a pulsed field associates each frequency with a particular angle with respect to the propagation axis. A perennial yet implicit assumption is that the propagation angle is differentiable with respect to the frequency. Recent work has shown that the existence of a frequency at which the derivative of the propagation angle does not exist -- which we refer to as non-differentiable angular dispersion -- allows for the optical field to exhibit unique and useful characteristics that are unattainable by endowing optical fields with conventional angular dispersion. Because these novel features are retained in principle even when the specific non-differentiable frequency is not part of the selected spectrum, the question arises as to the impact of the proximity of the spectrum to this frequency. We show here that operating in the vicinity of the non-differentiable frequency is imperative to reduce the deleterious impact of (1) errors in implementing the angular-dispersion profile, and (2) the spectral uncertainty intrinsic to finite-energy wave packets in any realistic system. Non-differential angular dispersion can then be viewed as a resource -- quantified by a Schmidt number -- that is maximized in the vicinity of the non-differentiable frequency. These results will be useful in designing novel phase-matching of nonlinear interactions in dispersive media.

physics.optics↗

arXiv2022

Spectral reorganization of space-time wave packets in presence of normal group-velocity dispersion

Space-time wave packets (STWPs) are pulsed beams that propagate invariantly (without diffraction or dispersion) in linear media. The behavior of STWPs in free space is now well-established, and recently their propagation invariance was confirmed in both the normal and anomalous dispersion regimes. However, yet-to-be-observed rich dynamics of spectral reorganization have been predicted to occur in the presence of normal group-velocity dispersion (GVD). Indeed, propagation invariance in the normal-GVD regime is compatible with spatio-temporal spectra that are X-shaped, hyperbolic, parabolic, elliptical, or even separable along the spatial and temporal degrees-of-freedom. These broad varieties of field structures can be classified in a two-dimensional space parameterized by the group velocity of the STWP and its central axial wave number. Here we observe the entire span of spectral reorganization for STWPs in the paraxial regime in normally dispersive ZnSe at a wavelength $\sim1$~$μ$m with STWPs of on-axis pulse width of $\sim\!200$~fs. By tuning the group velocity and central axial wave number of the STWP, we observe transitions in the structure of the spatio-temporal spectrum and verify the associated change in its intensity profile. These results lay the foundation for initiating novel phase-matched nonlinear processes using STWPs in dispersive media.

physics.optics↗

arXiv2022

Canceling and inverting normal and anomalous group-velocity dispersion using space-time wave packets

Angular dispersion can counterbalance normal group-velocity dispersion (GVD) that increases the wave-vector length in a dispersive medium. By tilting the wave vector, angular dispersion reduces the axial wave number in this case to match the pre-GVD value. By the same token, however, angular dispersion fails to counterbalance anomalous GVD, which in contrast reduces the wave-vector length. Consequently, GVD-cancellation via angular dispersion has not been demonstrated to date in the anomalous dispersion regime. We synthesize here structured femtosecond pulsed beams known as `space-time' wave packets designed to realize dispersion-cancellation symmetrically in either the normal- or anomalous-GVD regimes by virtue of non-differentiable angular dispersion inculcated into the pulsed field. Furthermore, we also verify GVD-inversion: reversing the GVD sign experienced by the field with respect to that dictated by the chromatic dispersion of the medium itself.

physics.optics↗

arXiv2022

Space-time wave packets

"Space-time" (ST) wave packets constitute a broad class of pulsed optical fields that are rigidly transported in linear media without diffraction or dispersion, and are therefore propagation-invariant in absence of optical nonlinearities or waveguiding structures. Such wave packets exhibit unique characteristics, such as controllable group velocities in free space and exotic refractive phenomena. At the root of these behaviors is a fundamental feature underpinning ST wave packets: their spectra are not separable with respect to the spatial and temporal degrees of freedom. Indeed, the spatio-temporal structure is endowed with non-differentiable angular dispersion, in which each spatial frequency is associated with a single prescribed wavelength. Furthermore, deviation from this particular spatio-temporal structure yields novel behaviors that depart from propagation invariance in a precise manner, such as acceleration with an arbitrary axial distribution of the group velocity, tunable dispersion profiles, and Talbot effects in space-time. Although the basic concept of ST wave packets has been known since the 1980's, only very recently has rapid experimental development emerged. These advances are made possible by innovations in spatio-temporal Fourier synthesis, thereby opening a new frontier for structured light at the intersection of beam optics and ultrafast optics.

physics.optics↗

arXiv2021

A universal angular-dispersion synthesizer

We uncover a surprising gap in optics with regards to angular dispersion (AD) that has persisted for decades. A systematic examination of pulsed optical-field configurations classified according to their three lowest dispersion orders resulting from AD (the axial phase velocity, group velocity, and group-velocity dispersion) reveals that the majority of possible classes of fields have eluded optics thus far. This gap is due in part to the limited technical reach of the standard components that provide AD such as gratings and prisms, but due in part also to misconceptions regarding the set of physically admissible field configurations that can be accessed via AD. For example, it has long been thought that AD cannot yield normal group-velocity dispersion in free space. To rectify this state of affairs, we introduce a 'universal AD synthesizer': a pulsed-beam shaper that produces a wavelength-dependent propagation angle with arbitrary spectral profile, thereby enabling access to all physically admissible field configurations realizable via AD. This universal AD synthesizer is a versatile tool for preparing pulsed optical fields for dispersion compensation, optical signal processing, and nonlinear optics.

physics.optics↗

arXiv2021

The consequences of non-differentiable angular dispersion in optics: Tilted pulse fronts versus space-time wave packets

Conventional diffractive and dispersive devices introduce angular dispersion (AD) into pulsed optical fields thus producing so-called 'tilted pulse fronts'. Naturally, it is always assumed that the functional form of the wavelength-dependent propagation angle associated with AD is differentiable with respect to wavelength. Recent developments in the study of space-time wave packets -- pulsed beams in which the spatial and temporal degrees of freedom are inextricably intertwined -- have pointed to the existence of non-differentiable AD: field configurations in which the propagation angle does not possess a derivative at some wavelength. Here we investigate the consequences of introducing non-differentiable AD into a pulsed field and show that it is the crucial ingredient required to realize group velocities that deviate from $c$ (the speed of light in vacuum) along the propagation axis in free space. In contrast, the on-axis phase and group velocities are always equal in conventional scenarios. Furthermore, we show that non-differentiable AD is needed for realizing anomalous or normal group-velocity dispersion along the propagation axis, while simultaneously suppressing all higher-order dispersion terms. These and several other consequences of non-differentiable AD are verified experimentally using a pulsed-beam shaper capable of introducing AD with arbitrary spectral profile. Rather than being an exotic phenomenon, non-differentiable AD is an accessible, robust, and versatile resource for sculpting pulsed optical fields.

physics.optics↗

arXiv2021

Arbitrarily accelerating space-time wave packets

All known realizations of optical wave packets that accelerate along their propagation axis, such as Airy wave packets in dispersive media or wave-front-modulated X-waves, exhibit a constant acceleration; that is, the group velocity varies linearly with propagation. Here we synthesize space-time wave packets that travel in free space with arbitrary axial acceleration profiles, including group velocities that change with integer or fractional exponents of the distance. Furthermore, we realize a composite acceleration profile: the wave packet first accelerates from an initial to a terminal group velocity, decelerates back to the initial value, and then travels at a fixed group velocity. These never-before-seen optical-acceleration phenomena are all produced using the same experimental arrangement that precisely sculpts the wave packet's spatio-temporal spectral structure.

physics.optics↗

arXiv2021

Realizing normal group-velocity dispersion in free space via angular dispersion

It has long been thought that normal group-velocity dispersion (GVD) cannot be produced in free space via angular dispersion. Indeed, conventional diffractive or dispersive components such as gratings or prisms produce only anomalous GVD. We identify the conditions that must be fulfilled by the angular dispersion introduced into a plane-wave pulse to yield normal GVD. We then utilize a pulsed-beam shaper capable of introducing arbitrary angular-dispersion profiles to symmetrically produce normal and anomalous GVD in free space, which are realized here on the same footing for the first time.

physics.optics↗

arXiv2021

V-Waves: Spatio-temporally induced group-velocity dispersion in free space

Introducing precise spatio-temporal structure into a pulsed optical field can lead to remarkable changes with its free propagation. `Space-time' (ST) wave packets, for example, propagate rigidly at a tunable group velocity in free space by inculcating a one-to-one relationship between the axial wave numbers and the temporal frequencies. Here we introduce a new class of ST wave packets that we call V-waves (so named because of their characteristically V-shaped spatio-temporal spectrum) in which a linear one-to-one relationship is introduced between the temporal frequencies and the transverse wave numbers (or spatial frequencies). We confirm experimentally that V-waves experience anomalous group velocity dispersion in free space, all the while maintaining the group velocity fixed at the speed of light in vacuum. Extremely large values of group velocity dispersion can be easily realized, which are not accessible with traditional optical materials or photonic structures. Moreover, V-waves are the unique optical wave packets whose diffraction and dispersion lengths are intrinsically equal by virtue of the spatio-temporal structure of the field itself. These results are of interest for optical signal processing and nonlinear optics.

physics.optics↗

arXiv2021

Temporal Talbot effect in free space

The temporal Talbot effect refers to the periodic revivals of a pulse train propagating in a dispersive medium, and is a temporal analog of the spatial Talbot effect with group-velocity dispersion in time replacing diffraction in space. Because of typically large temporal Talbot lengths, this effect has been observed to date in only single-mode fibers, rather than with freely propagating fields in bulk dispersive media. Here we demonstrate for the first time the temporal Talbot effect in free space by employing dispersive space-time wave packets, whose spatio-temporal structure induces group-velocity dispersion of controllable magnitude and sign in free space.

physics.optics↗

arXiv2021

Engineering the optical vacuum: Arbitrary magnitude, sign, and order of dispersion in free space using space-time wave packets

Spatial structuring of an optical pulse can lead in some cases upon free propagation to changes in its temporal profile. For example, introducing conventional angular dispersion into the field results in the pulse encountering group-velocity dispersion in free space. However, only limited control is accessible via this strategy. Here we show that precise and versatile control can be exercised in free space over the dispersion profile of so-called `space-time' wave packets: a class of pulsed beams undergirded by non-differentiable angular dispersion. This abstract mathematical feature allows us to tune the magnitude and sign of the different dispersion orders without introducing losses, thereby realizing arbitrary dispersion profiles, and achieving dispersion values unattainable in optical materials away from resonance. Unlike optical materials and photonic structures in which the values of the different dispersion orders are not independent of each other, these orders are addressable separately using our strategy. These results demonstrate the versatility of space-time wave packets as a platform for structured light and point towards their utility in nonlinear and quantum optics.

physics.optics↗

arXiv2021

The space-time Talbot effect

The Talbot effect, epitomized by periodic revivals of a freely evolving periodic field structure, has been observed with waves of diverse physical nature in space and separately in time, whereby diffraction underlies the former and dispersion the latter. To date, a combined spatio-temporal Talbot effect has not been realized in any wave field because diffraction and dispersion are independent physical phenomena, typically unfolding at incommensurable length scales. Here we report the observation of an optical 'space-time' Talbot effect, whereby a spatio-temporal optical lattice structure undergoes periodic revivals after suffering the impact of both diffraction and dispersion. The discovered space-time revivals are governed by a single self-imaging length scale, which encompasses both spatial and temporal degrees of freedom. Key to this effect is the identification of a unique pulsed optical field structure, which we refer to as a V-wave, that is endowed with intrinsically equal diffraction and dispersion lengths in free space, thereby enabling self-imaging to proceed in lockstep in space and time.

physics.optics↗

arXiv2021

Space-time wave packets violate the universal relationship between angular dispersion and pulse-front tilt

Introducing angular dispersion into a pulsed field tilts the pulse front with respect to the phase front. There exists between the angular dispersion and the pulse-front tilt a universal relationship that is device-independent, and also independent of the pulse shape and bandwidth. We show here that this relationship is violated by propagation-invariant space-time (ST) wave packets, which are pulsed beams endowed with precise spatio-temporal structure corresponding to a particular form of angular dispersion. We demonstrate theoretically and experimentally that underlying ST wave packets is -- to the best of our knowledge -- the first example in optics of non-differentiable angular dispersion, resulting in pulse-front tilt that depends on the pulse bandwidth even at fixed angular dispersion.

physics.optics↗

arXiv2020

Spectrally recycling space-time wave packets

'Space-time' (ST) wave packets are propagation-invariant pulsed optical beams that travel rigidly in linear media without diffraction or dispersion at a potentially arbitrary group velocity. These unique characteristics are a result of spatio-temporal spectral correlations introduced into the field; specifically, each spatial frequency is associated with a single temporal frequency (or wavelength). Consequently, the spatial and temporal bandwidths of ST wave packets are correlated, so that exploiting an optical source with a large temporal bandwidth or achieving an ultralow group velocity necessitate an exorbitantly large numerical aperture. Here we show that `spectral recycling' can help overcome these challenges. 'Recycling' or `reusing' each spatial frequency by associating it with multiple distinct but widely separated temporal frequencies allows one to circumvent the proportionality between the spatial and temporal bandwidths of ST wave packets, which has been one of their permanent characteristics since their inception. We demonstrate experimentally that the propagation invariance, maximum propagation distance, and group velocity of ST wave packets are unaffected by spectral recycling. We also synthesize a ST wave packet with group velocity c/14.3 (c is the speed of light in vacuum) with a reasonable numerical aperture made possible by spectral recycling.

physics.optics↗

arXiv2020

Veiled Talbot effect

A freely propagating optical field having a periodic transverse spatial profile undergoes periodic axial revivals - a well-known phenomenon known as the Talbot effect or self-imaging. We show here that introducing tight spatio-temporal spectral correlations into an ultrafast pulsed optical field with a periodic transverse spatial profile eliminates all axial dynamics in physical space while revealing a novel space-time Talbot effect that can be observed only when carrying out time-resolved measurements. Indeed, 'time-diffraction' is observed whereupon the temporal profile of the field envelope at a fixed axial plane corresponds to a segment of the spatial propagation profile of a monochromatic field sharing the initial spatial profile and observed at the same axial plane. Time-averaging, which is intrinsic to observing the intensity, altogether veils this effect.

physics.optics↗