arXiv subjects

Ayman F. Abouraddy

Publications and source records attributed to Ayman F. Abouraddy.

At least 19 recordsLinked to original sources

arXiv2026

Limits on the free-space group velocity of optical wave packets incorporating angular dispersion. Part~I, conventional angular dispersion: tutorial

A plane-wave optical pulse travels in free space at a group velocity $c$ (the speed of light in vacuum) measured along its propagation axis. It is sometimes thought that spatially structuring the field in free space reduces the group velocity below $c$ because -- intuitively -- the oblique wave vectors undergirding the wave packet increase the average group delay. Here we show that spatiotemporally structuring a pulsed optical beam (or wave packet) can yield -- in principle -- arbitrary group velocities in free space in contradistinction to this commonly held intuition. We devote our attention here to pulses endowed with angular dispersion (AD) where the propagation angle is wavelength dependent. This class of wave packets is particularly pertinent because their group velocity is constant over the transverse field profile and along the propagation axis, thereby yielding an unambiguous group delay. However, significant deviation of the AD-induced group velocity in free space from~$c$ inevitably requires a large numerical aperture that lies deep in the non-paraxial regime, and such wave packets experience AD-induced group-velocity dispersion. The formulation presented here captures a broad range of results, connecting them in a single framework. In Part~II of this tutorial, we describe recently identified `non-differentiable AD' (associated with propagation-invariant space-time wave packets) that helps circumvent the limits associated with conventional (differentiable) AD as outlined here.

physics.optics↗

arXiv2026

Limits on the free-space group velocity of optical wave packets incorporating angular dispersion. Part~II, non-differentiable angular dispersion: tutorial

In Part~I of this tutorial, we showed that introducing angular dispersion (AD) into a collimated optical pulse allows for tuning the wave packet group velocity in free space. In principle, the group velocity can take on arbitrary values, whether superluminal, subluminal, or even negative. However, any significant deviation of the group velocity from $c$ (the speed of light in vacuum) necessitates propagation at large angles with respect to the optical axis in the non-paraxial regime. In Part~II of this tutorial, we describe the recent discovery of a new form of AD we refer to as `non-differentiable AD', which circumvents the limits imposed by conventional (differentiable) AD. Non-differentiable AD does \textit{not} refer to an AD profile that is discontinuous, contains a kink, or features a singularity. Rather, a non-differentiable AD profile is continuous, smooth, and is differentiable everywhere except for one wavelength at which the derivative is not defined. We show that salutary features follow from this non-differentiability with respect to tuning the group velocity of a pulsed beam in free space; namely, significant deviations in the group velocity away from $c$ are achievable in the paraxial regime while remaining free of group-velocity dispersion and all higher-order dispersive effects. This tutorial presents an outline of these recent results for tuning the group velocity of a wave packet via non-differentiable AD, connecting them with the corresponding results associated with conventional AD -- as outlined in Part~I. Moreover, we show that non-differentiable AD undergirds the unique characteristics of propagation-invariant space-time wave packets, thus unifying a large swathe of results in a single conceptual framework.

physics.optics↗

arXiv2026

Diagonalizing an optical coherence matrix via on-chip Stokes tomography

Structured coherence -- partially coherent light spanned by a finite number of modes -- is emerging as a powerful tool in optical communications, computation, cryptography, and spectroscopy. Key to these prospects is the recent development of on-chip processing of structured coherence, in which large meshes of interferometers implement unitary and non-unitary transformations on the Hermitian coherence matrix representing multimode partially coherent light. Two related critical tasks for the applications of structured coherence are the reconstruction of an unknown coherence matrix and its diagonalization. Stokes tomography has been utilized in reconstructing the coherence matrix, whereas variational processing has been employed in its diagonalization. We show here that Stokes tomography can also be exploited in the on-chip diagonalization of an unknown coherence matrix, which we verify for two-mode and four-mode structured coherence in an integrated hexagonal mesh of Mach-Zehnder interferometers. This photonic circuit implements a predetermined sequence of configurations to estimate the generalized Stokes parameters, which -- in a final step -- inform a reconfiguration of the photonic circuit that diagonalizes the coherence matrix. The field is thus left in a coherent-mode representation comprising uncorrelated, orthogonal modes whose weights correspond to the eigenvalues of the original coherence matrix. Moreover, the integrated photonic circuit can be configured to provide the original field alongside its diagonalized counterpart at the circuit output. We verify the diagonalization procedure for coherence matrices of different coherence rank, entropy, and structure. Finally, we dispel the common notion that O(N^2) steps are required for reconstructing an N x N coherence matrix and show that only O(N) steps are needed.

physics.optics↗

arXiv2026

Structured coherence: A modern perspective on optical coherence as a resource

Optical coherence is a well-established branch of physical optics in which the statistical properties of fluctuating optical fields are described in terms of correlation functions over continuous spatial and temporal degrees of freedom (DoFs). Nevertheless, in any practical setting, only discrete DoFs are ever accessible. In these scenarios, the modes are fixed, stable, and deterministic, and partial coherence arises from random relative complex amplitudes, a configuration we refer to as 'structured coherence'. Advances in structured coherence have recently unveiled new conceptual ground in optical communications and information processing in which partial coherence may be preferable to full coherence, which we call a 'coherence advantage'. We formulate structured coherence in terms of coherence matrices to investigate these recent theoretical and experimental breakthroughs. We first review optical fields characterized by a binary DoF via 2x2 Hermitian coherence matrices and introduce key concepts that take on new significance for larger-dimensional modal sets. Next, we examine the structured coherence of two binary DoFs, which can be described by 4x4 coherence matrices. We introduce the concept of coherence rank, entropy swapping, and optical cross-purity. In the perspective outlined here, coherence is viewed as a 'resource', which can be exchanged between DoFs, concentrated into a DoF or into particular modes, or spread over the DoFs. We then examine larger-dimensional modal sets, which allow for more versatile applications in optical information processing. The formulation presented here lends itself particularly to the manipulation of partial optical coherence in integrated photonic platforms, thereby opening myriad avenues for novel fundamental investigations of structured coherence and exploiting the coherence advantage in optical communications and information processing.

physics.optics↗

arXiv2026

Selective avoidance of multiple line-of-sight obstacles at 130~m using locally bending space-time wave packets

Self-accelerating optical beams follow curved trajectories rather than propagating rectilinearly, which raises the prospect for avoiding line-of-sight (LoS) obstacles blocking the beam path. However, if a conventional laser beam is intercepted by an obstacle en route to an intended LoS target, then replacing this beam with a bending beam is not adequate: the obstacle is avoided but the target cannot be concomitantly reached. Rather, a laser beam that \textit{locally} bends around the obstacle -- before continuing along its rectilinear path -- is needed. Here we show that engineering the spatiotemporal spectrum of a pulsed beam yields a space-time wave packet whose propagation dynamics can be tuned at will to locally bend around one or multiple obstacles, thereby avoiding them, to selectively reach a designated target. We carry out our experiments over distances extending to 130~m from the source, carried out in an open-air environment. In one scenario, the beam is incident on a target placed between two LoS obstacles, one preceding it and one following it -- both of which are avoided. In a second scenario, the locally bending beam avoids one and then two LoS obstacles preceding the intended target. These results may contribute to applications requiring selective incidence on targets in remote sensing, stand-off detection, directed energy, for optical and radio-frequency communications in presence of LoS obstacles, and for selectively delivered radiation therapies.

physics.optics↗

arXiv2026

Avoiding a line-of-sight obstacle via deep sub-Rayleigh shadow-projection utilizing space-time wave packets

A challenge in optics, which is shared by other sources of radiation, is to direct a coherent beam to impinge on a target behind an obstacle intervening in the line-of-sight (LoS). While self-accelerating or bending beams can help avoid an LoS obstacle, the beam does not reach the LoS target downstream beyond the obstacle. If one instead avoids the obstacle by projecting a \textit{transverse} null or shadow onto the axial plane at which it is located, an associated \textit{axial} shadow is cast that extends over the effective Rayleigh length, which reduces the utility of this approach. Unless either the wavelength or the transverse shadow width is changed, this Rayleigh length can only be reduced by modifying the structure of the illumination beam. Here we show that space-time wave packets (STWPs), in which each spatial frequency is tightly associated with a single wavelength, when used as an illumination beam, can dramatically reduce the axial extent of the cast shadow. Indeed, by utilizing STWPs we produce deep sub-Rayleigh-length shadows, in some cases with a more than two orders-of-magnitude reduction below the conventional Rayleigh length. For example, a 5-mm-wide transverse shadow in a Gaussian beam at a wavelength of $\sim1$~$μ$m has a Rayleigh length of $\sim25$~m, whereas the same shadow projected by an STWP extends only $\sim0.15$~m. We demonstrate this sub-Rayleigh-length reduction in the axially cast shadow accompanying transverse nulls whose widths extend over a broad span of widths from 80~$μ$m to 48~mm -- almost three orders-of-magnitude. These results may lead to advances in safe radiation therapy, non-LoS optical and wireless communications, selective stand-off detection, three-dimensional photolithography, and laser ablation and micro-machining.

physics.optics↗

arXiv2026

On-chip measurement of the modal Stokes-Gell-Mann parameters for partially coherent three-mode light

The Stokes parameters are three real parameters that completely characterize partially coherent optical fields spanned by two modes -- whether a pair of polarization or spatial modes -- and their use is thus ubiquitous in optics. Because the Stokes parameters are defined through an expansion of the $2\times2$ coherence matrix in terms of the Pauli matrices, they cannot be applied to optical fields comprising three modes, which are described by a $3\times3$ coherence matrix. Examples of such fields include the polarization of non-paraxial fields (spanned by three orthogonal polarization modes), and fields comprising three spatial or temporal modes. It has long been theorized that the $3\times3$ Gell-Mann matrices -- developed in high-energy particle physics -- can serve as a basis for $3\times3$ optical coherence matrices, with 8~expansion coefficients known as the Stokes-Gell-Mann (SGM) parameters, but the measurement procedure is daunting, and the SGM parameters have not been measured directly to date in optics. Here we present the first measurements of the SGM parameters for partially coherent three-mode light in a photonic integrated platform comprising a hexagonal mesh of Mach-Zehnder interferometers. Measuring the SGM parameters on chip, from which we reconstruct the $3\times3$ coherence matrix facilitates exploring the full space of iso-entropy fields that can be inter-converted into each other unitarily, and those that share the same value of entropy and yet cannot be inter-converted unitarily. These results pave the way to utilizing multimode partially coherent light in applications involving optical communications, sensing, and information processing.

physics.optics↗

arXiv2026

Self-healing of the Montgomery pattern

Self-healing -- the ability of a structured beam to reconstruct its transverse profile after partial obstruction -- has been demonstrated for diffraction-free beams, where the recovery distance varies continuously with obstruction size. Here, we investigate self-healing in the Montgomery pattern, a self-imaging of tightly localized optical fields. Using Babinet's principle, we show theoretically that the recovery distance is quantized in integer multiples of the self-imaging period -- a qualitative distinction from all previously studied self-healing beams. We confirm these predictions experimentally using a programmable holographic setup with circular disk obstructions of size up to $20\times$ of the spot size of the Montgomery pattern at the self-imaging plane, establishing the robustness of the Montgomery pattern against scatterers and obstructions in the beam path.

physics.optics↗

arXiv2026

On-chip control of the coherence matrix of four-mode partially coherent light: rank, entropy, and modal Stokes parameters

Partially coherent light offers salutary capabilities in optical information processing that cannot be matched by coherent light. To date, this `coherence advantage' has been confirmed in proof-of-principle optical communications protocols using bulk optics. Taking full advantage of such opportunities necessitates processing multimode partially coherent light in integrated photonics platforms that alone provide the requisite stability for cascaded operations on a large scale. Here we demonstrate on-chip manipulation of four-mode partially coherent light described by a $4\times4$ Hermitian coherence matrix. Starting with generic maximally incoherent light, we utilize an on-chip hexagonal mesh of Mach-Zehnder interferometers to perform all the unitary and non-unitary tasks that are critical for realizing structured coherence: controlling the coherence rank (the number of non-zero eigenvalues of the coherence matrix); tuning the field entropy; molding the structure of the coherence matrix via $4\times4$ unitary transformations constructed out of sequences of $2\times2$ unitaries acting on pairs of modes; and tomographic reconstruction of the coherence matrix by measuring the modal Stokes parameters associated with Kronecker-Pauli matrices. These results confirm the scalability of utilizing $2\times2$ on-chip building blocks for the synthesis and reconstruction of high-dimensional coherence matrices, and provide a decisive step towards large-scale on-chip manipulation of massively moded partially coherent light for applications in optical information processing.

physics.optics↗

arXiv2026

Programmable on-chip synthesis and reconstruction of partially coherent two-mode optical fields

Partially coherent light is typically studied in the context of freely propagating continuous fields. Recent developments have indicated the existence of a `coherence advantage' in multimode optical communications, where partially coherent light outperforms coherent light. However, exploiting partial coherence in such applications requires manipulating multimode field coherence in programmable on-chip platforms. We present here the first example of on-chip synthesis and characterization of two-mode optical fields in an integrated on-chip hexagonal mesh of Mach-Zehnder interferometers. Starting with incoherent two-mode light, we adjust the degree of coherence on the chip with non-unitary transformations, construct $2\times2$ unitary transformations to synthesize prescribed coherence matrices, and reconstruct the coherence matrices via measurements of the spatial Stokes parameters. These results indicate the possibility of deploying programmable photonics for producing large-dimensional structured partially coherent light for applications in communications, cryptography, sensing, and spectroscopy.

physics.optics↗

arXiv2025

Observation of spatially structured Montgomery effect in free space

We report the first direct observation of the spatially structured Montgomery effect, a lensless self-imaging phenomenon that generalizes the Talbot effect to aperiodic structures, unfolding repeated tightly focused spots (~10 $μ$m) in free space. Using a dynamic optical hologram to discretize radial spatial frequencies, we demonstrate self-imaging at distances ranging from 30 to 100 mm. Our method independently controls the focal spot size and self-imaging period, enabling dynamic three-dimensional light patterns. We also show the arbitrary tunability of the transverse profile by demonstrating revivals of Laguerre-Gaussian, Hermite-Gaussian, Ince-Gaussian modes, and Airy beams. These findings open opportunities for multi-plane microscopy, optical atom traps, and quantum atomic systems.

physics.optics↗

arXiv2025

Bridging the gap between ultrafast optics and resonant photonics via omni-resonance

High-finesse planar Fabry-P{é}rot (FP) cavities spectrally filter the incident field at discrete resonances, and thus cannot be utilized to resonantly enhance the field of ultrashort pulses. Introducing judicious angular dispersion into a pulse can give rise to `omni-resonance', whereby the entire bandwidth of a spatiotemporally structured ultrafast pulse couples to a single longitudinal cavity resonance, even when the pulse bandwidth far exceeds the resonant linewidth. Here we show that omni-resonance increases the intra-cavity peak intensity above that of a pulse having equal energy and bandwidth when tightly focused in free space -- maintained across its entire bandwidth and along a cavity longer than the Rayleigh length of the focused pulse. This paves the way towards broadband resonant enhancement of nonlinear optical effects, thereby bridging the gap between ultrafast optics and resonant photonics.

physics.optics↗

arXiv2025

Broadband entangled-photon omni-resonance in a planar optical cavity

Resonant field enhancement in an optical cavity is a promising pathway towards realizing optical nonlinearities at the few-photon level. This quest is hampered by inevitable narrowing of the resonant linewidth as the cavity finesse is increased, which necessitates striking a compromise between the magnitude of the field enhancement and the bandwidth over which it is harnessed. This difficulty is exacerbated for broadband entangled-photon pairs, which are typically frequency-anticorrelated, so that the two photons cannot be simultaneously admitted to a cavity except when the degenerate wavelength coincides with a cavity resonance. Here we show that introducing judicious angular dispersion into single-photon and entangled-photon states before incidence on a planar Fabry-P{é}rot (FP) cavity renders these non-classical fields omni-resonant: the entire spectrum is coupled to a single longitudinal cavity mode. Making use of a planar FP cavity of finesse $\approx100$, resonant linewidth $\approx0.3$~nm, and free spectral range $\approx22$~nm in the near-infrared, we couple single-photon states and frequency-anticorrelated entangled-photon states of 20-nm bandwidth to a broadband achromatic resonance associated with a single underlying narrowband longitudinal FP-cavity mode -- thereby preserving the entangled spectral structure. In general, pre-conditioning the optical field by introducing angular dispersion enables coupling non-classical states of light to a single longitudinal cavity mode, even if the field bandwidth far exceeds the resonant linewidth, or even exceeds the cavity free-spectral-range. These results pave the way to broadband resonant interactions with non-classical states of light in photon-starved applications.

physics.optics↗

arXiv2025

Bending space-time wave packets

Optical beams with certain asymmetric profiles, such as the Airy beam, can depart from rectilinear propagation and instead travel along curved (typically parabolic) trajectories. Here we show that sculpting the spatiotemporal spectrum of optical pulses yields self-accelerating beams that have symmetric profiles, remain diffraction-free, and travel along power-law curves with propagation distance having arbitrary positive exponent (integer or fractional). We build upon propagation-invariant space-time wave packets (STWPs), in which each spatial frequency is associated with a single wavelength. A linear tilt in the propagation path of an STWP is produced by a corresponding tilt in the spectral domain. A curved trajectory is then produced through locally changing the tilt direction along the propagation axis, which requires associating a prescribed finite-bandwidth spatial spectrum to each wavelength. Using this approach, we realize symmetric STWPs traveling along curved trajectories that follow linear, quadratic, cubic, or even square-root power laws with an acceleration rate that is independent of the beam spatial scale. These novel bending STWPs open new avenues for realizing target-avoidance with electromagnetic waves.

physics.optics↗

arXiv2025

Optical communications through highly scattering channels using the coherence-rank

In optical communications, logical bits are encoded in physical degrees-of-freedom (DoFs) of the electromagnetic field. Consequently, optical scattering in a communications channel compromises the information transfer. In the worst-case-scenario, bit-to-bit stochastically varying scattering that couples the DoFs to each other -including even unused DoFs -can decouple the transmitter and receiver when relying on conventional physical encoding schemes, and preclude the utilization of adaptive techniques as a counter-measure. Here we show that partially coherent optical fields help circumvent the worst-case-scenario of rapidly varying, strong optical scattering, even when the channel is rendered informationally opaque for conventional approaches. Using a channel in which the spatial and polarization DoFs are relevant, we encode the logical bits in the unitarily invariant coherence rank (the number of non-zero eigenvalues of the field coherence matrix) and prepare our partially coherent fields with maximal entropies of 0, 1, 1.585, and 2 bits for rank-1, rank-2, rank-3, and rank-4 coherence matrices, respectively. This scheme demonstrates scattering-immune optical communications with 100 % fidelity. These results unveil an unexpected utility for partially coherent light in optical communications through challenging environments.

physics.optics↗

arXiv2025

Universality and non-differentiability: A new perspective on angular dispersion in optics

Angular dispersion (AD) is a ubiquitous phenomenon in optics after light traverses a diffractive or dispersive device, whereby each wavelength propagates at a different angle. AD is useful in a variety of applications; for example, modifying the group velocity or group-velocity dispersion of pulsed lasers in free space or optical materials, which are essential ingredients in group-velocity matching and dispersion compensation. Conventional optical components introduce `differentiable' AD, so that the propagation angle can be expanded perturbatively around a fixed frequency, in which only a few low AD-orders are typically relevant. However, this model does not encompass newly emerging classes of propagation-invariant pulsed optical fields, such as `space-time wave packets', which incorporate a new form of AD that we call `non-differentiable AD'. This is a surprising feature: there exists a frequency at which the derivative of the propagation angle with respect to frequency is not defined. Consequently, the propagation angle cannot be expanded perturbatively at this frequency, and a large number of independently controllable AD orders are needed to approximate this condition. Synthesizing these new AD-induced field configurations requires constructing a `universal AD synthesizer' capable of accessing the magnitude and sign of any AD order, a capability missing from any single optical component to date. This Perspective article provides a unified schema for studying differentiable and non-differentiable AD, shows that non-differentiable AD enables circumventing many well-established constraints in optics -- thereby giving rise to new applications, and outlines the requirements for a universal AD synthesizer capable of producing both forms of AD.

physics.optics↗

arXiv2025

Long-distance axial spectral encoding using space-time wave packets

Space-time wave packets (STWPs) are pulsed optical beams whose spatiotemporal structure enables propagation invariance. However, STWPs allow for a unique propagation configuration that we call axial spectral encoding, in which the spectrum on the propagation axis changes with distance. We demonstrate here axial spectral encoding over distances extending for hundreds of meters in an open-field laser range. We verify two distinct configurations: in the first, the on-axis spectrum blue-shifts or red-shifts with propagation distance; and in the second, the spectrum changes at a fixed axial position by altering an internal parameter of the STWP without modifying the wave packet spectrum. These results indicates the potential for using spectral measurements for ranging in LIDAR and sensing applications.

physics.optics↗

arXiv2025

Optical spatiotemporal Fourier synthesis: Tutorial

Fourier synthesis is one of the foundations of physical optics. Spatial Fourier optics is a basis for understanding optical imaging, microscopy, and holography. In conventional Fourier optics, the complex spatial field distribution in the Fourier plane constitutes the spatial spectrum of the field to be realized in physical space. Analogously, in temporal Fourier optics the complex temporal spectrum can be manipulated for ultrafast pulse-shaping. We present here a tutorial on the emerging field of spatiotemporal Fourier optics whereby the spatial and temporal spectra are manipulated jointly to produce spatiotemporally structured optical fields that display unique propagation characteristics. In this tutorial, we focus on a subset of the overall class of non-separable spatiotemporally structured fields; namely, cylindrically symmetric fields in which each radial spatial frequency is associated with a single wavelength. This subset of fields comprises propagation-invariant wave packets that travel rigidly in linear media at a tunable group velocity, and includes space-time wave packets and other closely related structured fields. We describe a spatiotemporal Fourier synthesis system capable of preparing arbitrary optical fields belonging to this subclass.

physics.optics↗