Refraction of space-time wave packets: I. theoretical principles.

Space-time (ST) wave packets are pulsed optical beams endowed with precise spatio-temporal structure by virtue of which they exhibit unique and useful characteristics such as propagation invariance and tunable group velocity. We study in detail here, and in two accompanying papers, the refraction of ST wave packets at planar interfaces between non-dispersive, homogeneous, and isotropic dielectrics. We formulate a law of refraction that determines the change in the ST wave-packet group velocity across such an interface as a consequence of a newly identified optical refractive invariant that we call the "spectral curvature". Because the spectral curvature vanishes in conventional optical fields where the spatial and temporal degrees of freedom are separable, these phenomena have not been observed to date. We derive the laws of refraction for baseband, X wave, and sideband ST wave packets that reveal fascinating refractive phenomena, especially for the former class of wave packets. We predict theoretically, and confirm experimentally in the accompanying papers, refractive phenomena such as group-velocity invariance (ST wave packets whose group velocity does not change across the interface), anomalous refraction (group-velocity increase in higher-index media), group-velocity inversion (change in the sign of the group velocity upon refraction but not its magnitude), and the dependence of the group velocity of the refracted ST wave packet on the angle of incidence.

Refraction of space-time wave packets: II. experiments at normal incidence.

The refraction of space-time (ST) wave packets offers many fascinating surprises with respect to conventional pulsed beams. In the first paper in this sequence [J. Opt. Soc. Am. A38, 1409 (2021)10.1364/JOSAA.430105], we theoretically described the refraction of all families of ST wave packets at normal and oblique incidence at a planar interface between two nondispersive, homogeneous, isotropic dielectrics. Here, in this second paper in the sequence, we present experimental verification of the refractive phenomena predicted for baseband ST wave packets upon normal incidence on a planar interface. Specifically, we observe group velocity invariance, normal and anomalous refraction, and group velocity inversion leading to group delay cancellation. These phenomena are verified in a set of optical materials with refractive indices ranging from 1.38 to 1.76, including MgF2, fused silica, BK7 glass, and sapphire. We also provide a geometrical representation of the physics associated with anomalous refraction in terms of the dynamics of the spectral support domain for ST wave packets on the surface of the light cone.

Refraction of space-time wave packets: III. experiments at oblique incidence.

The refraction of space-time (ST) wave packets at planar interfaces between non-dispersive, homogeneous, isotropic dielectrics exhibits fascinating phenomena, even at normal incidence. Examples of such refractive phenomena include group-velocity invariance across the interface, anomalous refraction, and group-velocity inversion. Crucial differences emerge at oblique incidence with respect to the results established at normal incidence. For example, the group velocity of the refracted ST wave packet can be tuned simply by changing the angle of incidence. In the third paper, we present experimental verification of the refractive phenomena exhibited by ST wave packets at oblique incidence that were in the first paper of this sequence [J. Opt. Soc. Am. A38, 1409 (2021)10.1364/JOSAA.430105]. We also examine a proposal for "blind synchronization," whereby identical ST wave packets arrive simultaneously at different receivers without a priori knowledge of their locations except that they are all located at the same depth beyond an interface between two media. A first proof-of-principle experimental demonstration of this effect is provided.

Free-space optical delay line using space-time wave packets.

An optical buffer featuring a large delay-bandwidth-product-a critical component for future all-optical communications networks-remains elusive. Central to its realization is a controllable inline optical delay line, previously accomplished via engineered dispersion in optical materials or photonic structures constrained by a low delay-bandwidth product. Here we show that space-time wave packets whose group velocity is continuously tunable in free space provide a versatile platform for constructing inline optical delay lines. By spatio-temporal spectral-phase-modulation, wave packets in the same or in different spectral windows that initially overlap in space and time subsequently separate by multiple pulse widths upon free propagation by virtue of their different group velocities. Delay-bandwidth products of  ~100 for pulses of width  ~1 ps are observed, with no fundamental limit on the system bandwidth.

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

The group velocity of 'space-time' wave packets - propagation-invariant pulsed beams endowed with tight spatio-temporal spectral correlations - can take on arbitrary values in free space. Here we investigate theoretically and experimentally the maximum achievable group delay that realistic finite-energy space-time wave packets can achieve with respect to a reference pulse traveling at the speed of light. We find that this delay is determined solely by the spectral uncertainty in the association between the spatial frequencies and wavelengths underlying the wave packet spatio-temporal spectrum - and not by the beam size, bandwidth, or pulse width. We show experimentally that the propagation of space-time wave packets is delimited by a spectral-uncertainty-induced 'pilot envelope' that travels at a group velocity equal to the speed of light in vacuum. Temporal walk-off between the space-time wave packet and the pilot envelope limits the maximum achievable differential group delay to the width of the pilot envelope. Within this pilot envelope the space-time wave packet can locally travel at an arbitrary group velocity and yet not violate relativistic causality because the leading or trailing edge of superluminal and subluminal space-time wave packets, respectively, are suppressed once they reach the envelope edge. Using pulses of width ∼ 4 ps and a spectral uncertainty of ∼ 20 pm, we measure maximum differential group delays of approximately ±150 ps, which exceed previously reported measurements by at least three orders of magnitude.

Broadband space-time wave packets propagating 70 m.

The propagation distance of a pulsed beam in free space is ultimately limited by diffraction and space-time coupling. "Space-time" (ST) wave packets are pulsed beams endowed with tight spatio-temporal spectral correlations that render them propagation-invariant. Here we explore the limits of the propagation distance for ST wave packets. Making use of a specially designed phase plate inscribed by gray-scale lithography and having a laser-damage threshold of ∼0.5 J/cm2, we synthesize a ST light sheet of width ≈700 µm and bandwidth ∼20 nm, and confirm a propagation distance of ≈70 m.

Simultaneous cell traction and growth measurements using light.

Characterizing the effects of force fields generated by cells on proliferation, migration and differentiation processes is challenging due to limited availability of nondestructive imaging modalities. Here, we integrate a new real-time traction stress imaging modality, Hilbert phase dynamometry (HPD), with spatial light interference microscopy (SLIM) for simultaneous monitoring of cell growth during differentiation processes. HPD uses holographic principles to extract displacement fields from chemically patterned fluorescent grid on deformable substrates. This is converted into forces by solving an elasticity inverse problem. Since HPD uses the epi-fluorescence channel of an inverted microscope, cellular behavior can be concurrently studied in transmission with SLIM. We studied the differentiation of mesenchymal stem cells (MSCs) and found that cells undergoing osteogenesis and adipogenesis exerted larger and more dynamic stresses than their precursors, with MSCs developing the smallest forces and growth rates. Thus, we develop a powerful means to study mechanotransduction during dynamic processes where the matrix provides context to guide cells toward a physiological or pathological outcome.

Meters-long propagation of diffraction-free space-time light-sheets.

Space-time (ST) wave packets are pulsed beams in which the spatial frequencies and wavelengths are tightly correlated. Proper design of the functional form of these correlations results in diffraction-free and dispersion-free axial propagation; that is, propagation invariance in free space. To date, observed propagation distances of such ST wave packets has been on the order of a few centimeters. Here we synthesize an ST wave packet in the form of a pulsed optical sheet of transverse spatial width ∼200 µm and spectral bandwidth of ∼2 nm, and observe its diffraction-free propagation for approximately 6 meters. For such ST wave packets, we identify the spectral uncertainty - the precision in associating the spatial and temporal frequencies - as a critical parameter in determining the propagation-invariant distance. We present a design strategy and an experimental methodology that enables further increase in the diffraction-free length.

Ratiometric analysis of optical coherence tomography-measured in†vivo retinal layer thicknesses for the detection of early diabetic retinopathy.

Influence of diabetes mellitus (DM) and diabetic retinopathy (DR) on parafoveal retinal thicknesses and their ratios was evaluated. Six retinal layer boundaries were segmented from spectral-domain optical coherence tomography images using open-source software. Five study groups: (1) healthy control (HC) subjects, and subjects with (2) controlled DM, (3) uncontrolled DM, (4) controlled DR and (5) uncontrolled DR, were identified. The one-way analyses of variance (ANOVA) between adjacent study groups (i. e. 1 with 2, 2 with 3, etc) indicated differences in retinal thicknesses and ratios. Overall retinal thickness, ganglion cell layer (GCL) thickness, inner plexiform layer (IPL) thickness, and their combination (GCL+ IPL), appeared to be significantly less in the uncontrolled DM group when compared to controlled DM and controlled DR groups. Although the combination of nerve fiber layer (NFL) and GCL, and IPL thicknesses were not different, their ratio, (NFL+GCL)/IPL, was found to be significantly higher in the controlled DM group compared to the HC group. Comparisons of the controlled DR group with the controlled DM group, and with the uncontrolled DR group, do not show any differences in the layer thicknesses, though several significant ratios were obtained. Ratiometric analysis may provide more sensitive parameters for detecting changes in DR. Picture: A representative segmented OCT image of the human retina is shown.

Geometric localization of thermal fluctuations in red blood cells.

The thermal fluctuations of membranes and nanoscale shells affect their mechanical characteristics. Whereas these fluctuations are well understood for flat membranes, curved shells show anomalous behavior due to the geometric coupling between in-plane elasticity and out-of-plane bending. Using conventional shallow shell theory in combination with equilibrium statistical physics we theoretically demonstrate that thermalized shells containing regions of negative Gaussian curvature naturally develop anomalously large fluctuations. Moreover, the existence of special curves, "singular lines," leads to a breakdown of linear membrane theory. As a result, these geometric curves effectively partition the cell into regions whose fluctuations are only weakly coupled. We validate these predictions using high-resolution microscopy of human red blood cells (RBCs) as a case study. Our observations show geometry-dependent localization of thermal fluctuations consistent with our theoretical modeling, demonstrating the efficacy in combining shell theory with equilibrium statistical physics for describing the thermalized morphology of cellular membranes.

Ratiometric analysis of in vivo retinal layer thicknesses in multiple sclerosis.

We performed ratiometric analysis of retinal optical coherence tomography images for the first time in multiple sclerosis (MS) patients. The ratiometric analysis identified differences in several retinal layer thickness ratios in the cohort of MS subjects without a history of optic neuritis (ON) compared to healthy control (HC) subjects, and there was no difference in standard retinal nerve fiber layer thickness (RNFLT). The difference in such ratios between HC subjects and those with mild MS-disability, without a difference in RNFLT, further suggests the possibility of using layer ratiometric analysis for detecting early retinal changes in MS. Ratiometric analysis may be useful and potentially more sensitive for detecting disease changes in MS.

Phase correlation imaging of unlabeled cell dynamics.

We present phase correlation imaging (PCI) as a novel approach to study cell dynamics in a spatially-resolved manner. PCI relies on quantitative phase imaging time-lapse data and, as such, functions in label-free mode, without the limitations associated with exogenous markers. The correlation time map outputted in PCI informs on the dynamics of the intracellular mass transport. Specifically, we show that PCI can extract quantitatively the diffusion coefficient map associated with live cells, as well as standard Brownian particles. Due to its high sensitivity to mass transport, PCI can be applied to studying the integrity of actin polymerization dynamics. Our results indicate that the cyto-D treatment blocking the actin polymerization has a dominant effect at the large spatial scales, in the region surrounding the cell. We found that PCI can distinguish between senescent and quiescent cells, which is extremely difficult without using specific markers currently. We anticipate that PCI will be used alongside established, fluorescence-based techniques to enable valuable new studies of cell function.

Detection of retinal blood vessel changes in multiple sclerosis with optical coherence tomography.

Although retinal vasculitis is common in multiple sclerosis (MS), it is not known if MS is associated with quantitative abnormalities in retinal blood vessels (BVs). Optical coherence tomography (OCT) is suitable for examining the integrity of the anterior visual pathways in MS. In this paper we have compared the size and number of retinal blood vessels in patients with MS, with and without a history of optic neuritis (ON), and control subjects from the cross-sectional retinal images from OCT. Blood vessel diameter (BVD), blood vessel number (BVN), and retinal nerve fiber layer thickness (RNFLT) were extracted from OCT images collected from around the optic nerves of 129 eyes (24 control, 24 MS + ON, 81 MS-ON) of 71 subjects. Associations between blood vessel metrics, MS diagnosis, MS disability, ON, and RNFLT were evaluated using generalized estimating equation (GEE) models. MS eyes had a lower total BVD and BVN than control eyes. The effect was more pronounced with increased MS disability, and persisted in multivariate models adjusting for RNFLT and ON history. Twenty-nine percent (29%) of MS subjects had fewer retinal blood vessels than all control subjects. MS diagnosis, disability, and ON history were not associated with average blood vessel size. The relationship between MS and lower total BVD/BVN is not accounted for by RNFLT or ON. Further study is needed to determine the relationship between OCT blood vessel metrics and qualitative retinal blood vessel abnormalities in MS.

High-Resolution Projection Microstereolithography for Patterning of Neovasculature.

To gain a quantitative understanding of the way cells sense, process, and respond to dynamic environmental signals in real-time requires developing in vitro model systems that accurately replicate the 3D structure and function of native tissue. A high-resolution projection stereolithography apparatus (µSLA) capable of multimaterial and grayscale 3D patterning of cells and biomaterials at <5 µm resolution is presented. Murine cells (fibroblasts, myoblasts, endothelial, and bone marrow stromal cells) encapsulated within photosensitive hydrogels using the µSLA remain viable up to two weeks after fabrication. Harnessing the high-resolution fabrication capabilities of this machine, sub-millimeter scale angiogenic cell-encapsulating patches designed to promote targeted growth of neovasculature are printed, as assessed in vitro via enzyme-linked immunosorbent assay (ELISA) and in ovo via a chick chorioallantoic membrane assay (CAM). This application establishes the µSLA as an enabling technology that is widely adaptable to any application that requires high-resolution patterning of cells and cells signals. By providing an efficient and robust method of engineering microscale tissues with encapsulated cells, this apparatus has a range of applications including fundamental studies of extracellular matrix interactions, high throughput drug testing of physiologically relevant substitutes for native tissue, and programmable tissue engineering for applications in regenerative medicine.

Measuring the Nonuniform Evaporation Dynamics of Sprayed Sessile Microdroplets with Quantitative Phase Imaging.

We demonstrate real-time quantitative phase imaging as a new optical approach for measuring the evaporation dynamics of sessile microdroplets. Quantitative phase images of various droplets were captured during evaporation. The images enabled us to generate time-resolved three-dimensional topographic profiles of droplet shape with nanometer accuracy and, without any assumptions about droplet geometry, to directly measure important physical parameters that characterize surface wetting processes. Specifically, the time-dependent variation of the droplet height, volume, contact radius, contact angle distribution along the droplet's perimeter, and mass flux density for two different surface preparations are reported. The studies clearly demonstrate three phases of evaporation reported previously: pinned, depinned, and drying modes; the studies also reveal instances of partial pinning. Finally, the apparatus is employed to investigate the cooperative evaporation of the sprayed droplets. We observe and explain the neighbor-induced reduction in evaporation rate, that is, as compared to predictions for isolated droplets. In the future, the new experimental methods should stimulate the exploration of colloidal particle dynamics on the gas-liquid-solid interface.

Spatiotemporal characterization of a fibrin clot using quantitative phase imaging.

Studying the dynamics of fibrin clot formation and its morphology is an important problem in biology and has significant impact for several scientific and clinical applications. We present a label-free technique based on quantitative phase imaging to address this problem. Using quantitative phase information, we characterized fibrin polymerization in real-time and present a mathematical model describing the transition from liquid to gel state. By exploiting the inherent optical sectioning capability of our instrument, we measured the three-dimensional structure of the fibrin clot. From this data, we evaluated the fractal nature of the fibrin network and extracted the fractal dimension. Our non-invasive and speckle-free approach analyzes the clotting process without the need for external contrast agents.

Diffraction phase microscopy: monitoring nanoscale dynamics in materials science [invited].

Quantitative phase imaging (QPI) utilizes the fact that the phase of an imaging field is much more sensitive than its amplitude. As fields from the source interact with the specimen, local variations in the phase front are produced, which provide structural information about the sample and can be used to reconstruct its topography with nanometer accuracy. QPI techniques do not require staining or coating of the specimen and are therefore nondestructive. Diffraction phase microscopy (DPM) combines many of the best attributes of current QPI methods; its compact configuration uses a common-path off-axis geometry which realizes the benefits of both low noise and single-shot imaging. This unique collection of features enables the DPM system to monitor, at the nanoscale, a wide variety of phenomena in their natural environments. Over the past decade, QPI techniques have become ubiquitous in biological studies and a recent effort has been made to extend QPI to materials science applications. We briefly review several recent studies which include real-time monitoring of wet etching, photochemical etching, surface wetting and evaporation, dissolution of biodegradable electronic materials, and the expansion and deformation of thin-films. We also discuss recent advances in semiconductor wafer defect detection using QPI.

Optical assay of erythrocyte function in banked blood.

Stored red blood cells undergo numerous biochemical, structural, and functional changes, commonly referred to as storage lesion. How much these changes impede the ability of erythrocytes to perform their function and, as result, impact clinical outcomes in transfusion patients is unknown. In this study we investigate the effect of the storage on the erythrocyte membrane deformability and morphology. Using optical interferometry we imaged red blood cell (RBC) topography with nanometer sensitivity. Our time-lapse imaging quantifies membrane fluctuations at the nanometer scale, which in turn report on cell stiffness. This property directly impacts the cell's ability to transport oxygen in microvasculature. Interestingly, we found that cells which apparently maintain their normal shape (discocyte) throughout the storage period, stiffen progressively with storage time. By contrast, static parameters, such as mean cell hemoglobin content and morphology do not change during the same period. We propose that our method can be used as an effective assay for monitoring erythrocyte functionality during storage time.

Dissolution chemistry and biocompatibility of single-crystalline silicon nanomembranes and associated materials for transient electronics.

Single-crystalline silicon nanomembranes (Si NMs) represent a critically important class of material for high-performance forms of electronics that are capable of complete, controlled dissolution when immersed in water and/or biofluids, sometimes referred to as a type of "transient" electronics. The results reported here include the kinetics of hydrolysis of Si NMs in biofluids and various aqueous solutions through a range of relevant pH values, ionic concentrations and temperatures, and dependence on dopant types and concentrations. In vitro and in vivo investigations of Si NMs and other transient electronic materials demonstrate biocompatibility and bioresorption, thereby suggesting potential for envisioned applications in active, biodegradable electronic implants.

Nanoscale topography and spatial light modulator characterization using wide-field quantitative phase imaging.

We demonstrate an optical technique for large field of view quantitative phase imaging of reflective samples. It relies on a common-path interferometric design, which ensures high stability without the need for active stabilization. The technique provides single-shot, full-field and robust measurement of nanoscale topography of large samples. Further, the inherent stability allows reliable measurement of the temporally varying phase retardation of the liquid crystal cells, and thus enables real-time characterization of spatial light modulators. The technique's application potential is validated through experimental results.