Extreme-value statistics in nonlinear optics.

We show that, although nonlinear optics may give rise to a vast multitude of statistics, all these statistics converge, in their extreme-value limit, to one of a few universal extreme-value statistics. Specifically, in the class of polynomial nonlinearities, such as those found in the Kerr effect, weak-field harmonic generation, and multiphoton ionization, the statistics of the nonlinear-optical output converges, in the extreme-value limit, to the exponentially tailed, Gumbel distribution. Exponentially growing nonlinear signals, on the other hand, such as those induced by parametric instabilities and stimulated scattering, are shown to reach their extreme-value limits in the class of the Fréchet statistics, giving rise to extreme-value distributions (EVDs) with heavy, manifestly nonexponential tails, thus favoring extreme-event outcomes and rogue-wave buildup.

Modulation instability of incoherent beams revisited.

We examine the spatial modulation instability (MI) of a partially incoherent laser beam. We show that the P < (a/rc)2P0 criterion of beam stability, with a laser peak power P, beam radius a, correlation radius rc, and critical power of self-focusing P0, is applicable only to a limited class of MIs, viz., MIs that can be described as instabilities of a pertinent transverse correlation function found as a solution to the evolution equation, where the expectation of the four-field-product nonlinear source term is factorized as a product of the field intensity and a two-point transverse correlation function. When extended to a more general class of MIs, field evolution analysis of partially coherent beams suggests that MIs can be attenuated, but never completely suppressed. We show that spatial incoherence can lower the MI-buildup rate, thus helping avoid MI-induced beam breakup in physical settings where the MI-buildup length lMI can be kept longer than the length of the nonlinear medium L. Because the lMI > L condition sets a limitation on the field intensity rather than the laser peak power, MI-induced beam breakup can be avoided, even at laser peak powers well above the critical power of self-focusing P0.

First passage time of laser-driven tunneling.

The notion of the first passage time is shown to offer a meaningful extension to quantum tunneling, providing a closed-integral-form analytical unification of the tunneling rate and the tunneling passage time. We demonstrate that, in suitable potential settings, the quantum first passage time, found as a solution to the Fokker-Planck and backward Kolmogorov's equations for the quantum probability density, recovers the hallmark results for the Kramers escape rate, the lifetime of tunneling quasi-stationary wave packets, leads to a classical, distance-over-speed passage time for a free-particle wave function, and offers useful insights into Keldysh's intimation on the electron barrier-traversal time in field-induced ionization.

Hyperglycemia exacerbates ischemic stroke not through increased generation of hydrogen peroxide.

Diabetes is one of the significant risk factors for ischemic stroke. Hyperglycemia exacerbates the pathogenesis of stroke, leading to more extensive cerebral damage and, as a result, to more severe consequences. However, the mechanism whereby the hyperglycemic status in diabetes affects biochemical processes during the development of ischemic injury is still not fully understood. In the present work, we record for the first time the real-time dynamics of H2O2 in the matrix of neuronal mitochondria in vitro in culture and in vivo in the brain tissues of rats during development of ischemic stroke under conditions of hyperglycemia and normal glucose levels. To accomplish this, we used a highly sensitive HyPer7 biosensor and a fiber-optic interface technology. We demonstrated that a high glycemic status does not affect the generation of H2O2 in the tissues of the ischemic core, while significantly exacerbating the consequences of pathogenesis. For the first time using Raman microspectroscopy approach, we have shown how a sharp increase in the blood glucose level increases the relative amount of reduced cytochromes in the mitochondrial electron transport chain in neurons under normal conditions in awake mice.

Probing ultra-fast dephasing via entangled photon pairs.

We demonstrate how the Hong-Ou-Mandel (HOM) interference with polarization-entangled photons can be used to probe ultrafast dephasing. We can infer the optical properties like the real and imaginary parts of the complex susceptibility of the medium from changes in the position and the shape of the HOM dip. From the shift of the HOM dip, we are able to measure 22 fs dephasing time using a continuous-wave (CW) laser even with optical loss > 97 %, while the HOM dip visibility is maintained at 92.3 % (which can be as high as 96.7 %). The experimental observations, which are explained in terms of a rigorous theoretical model, demonstrate the utility of HOM interference in probing ultrafast dephasing.

Implantable graded-index fibers for neural-dynamics-resolving brain imaging in awake mice on an air-lifted platform.

We demonstrate a versatile framework for cellular brain imaging in awake mice based on suitably tailored segments of graded-index (GRIN) fiber. Closed-form solutions to ray-path equations for graded-index waveguides are shown to offer important insights into image-transmission properties of GRIN fibers, suggesting useful recipes for optimized GRIN-fiber-based deep-brain imaging. We show that the lengths of GRIN imaging components intended for deep-brain studies in freely moving rodents need to be chosen as a tradeoff among the spatial resolution, the targeted imaging depth and the degree of fiber-probe invasiveness. In the experimental setting that we present in this paper, the head of an awake mouse with a GRIN-fiber implant is fixed under a microscope objective, but the mouse is free to move around an in-house-built flat-floored air-lifted platform, exploring a predesigned environment, configured as an arena for one of standard cognitive tests. We show that cellular-resolution deep-brain imaging can be integrated in this setting with robust cell-specific optical neural recording to enable in vivo studies with minimal physical restraints on animal models. The enhancement of the information capacity of the fluorescence signal, achieved via a suitable filtering of the GRIN-fiber readout, is shown to open routes toward practical imaging modalities whereby the deep-brain neuronal dynamics and axonal connections underpinning the integrative functions of essential brain structures can be studied in awake rodent models.

Real-time fiber-optic recording of acute-ischemic-stroke signatures.

We present an experimental framework and methodology for in vivo studies on rat stroke models that enable a real-time fiber-optic recording of stroke-induced hydrogen peroxide and pH transients in ischemia-affected brain areas. Arrays of reconnectable implantable fiber probes combined with advanced optogenetic fluorescent protein sensors are shown to enable a quantitative multisite time-resolved study of oxidative-stress and acidosis buildup dynamics as the key markers, correlates and possible drivers of ischemic stroke. The fiber probes designed for this work provide a wavelength-multiplex forward-propagation channel for a spatially localized, dual-pathway excitation of genetically encoded fluorescence-protein sensors along with a back-propagation channel for the fluorescence return from optically driven fluorescence sensors. We show that the spectral analysis of the fiber-probe-collected fluorescence return provides means for a high-fidelity autofluorescence background subtraction, thus enhancing the sensitivity of real-time detection of stroke-induced transients and significantly reducing measurement uncertainties in in vivo acute-stroke studies as inherently statistical experiments operating with outcomes of multiply repeated measurements on large populations of individually variable animal stroke models.

State-vector geometry and guided-wave physics behind optical super-resolution.

We examine the state-vector geometry and guided-wave physics underpinning spatial super-resolution, which can be attained in far-field linear microscopy via a combination of statistical analysis, quantum optics, and spatial mode demultiplexing. A suitably tailored guided-wave signal pickup is shown to provide an information channel that can distill the super-resolving spatial modes, thus enabling an estimation of sub-Rayleigh space intervals ξ. We derive closed-form analytical expressions describing the distribution of the ξ-estimation Fisher information over waveguide modes, showing that this information remains nonvanishing as ξ → 0, thus preventing the variance of ξ estimation from diverging at ξ → 0. We demonstrate that the transverse refractive index profile nQ(r) tailored to support the optimal wave function ψQ(r) for super-resolving ξ estimation encodes the same information about ξ as the entire manifold of waveguide modes needed to represent ψQ(r). Unlike ψQ(r), nQ(r) does not need a representation in a lengthy manifold of eigenmodes and can be found instead via adaptive feedback-controlled learning.

Imaging through a scattering medium: the Fisher information and the generalized Abbe limit.

Enhanced-resolution imaging in complex scattering media is revisited from a parameter estimation perspective. A suitably defined Fisher information is shown to offer useful insights into the limiting precision of parameter estimation in a scattering environment and, hence, into the limiting spatial resolution that can be achieved in imaging-through-scattering settings. The Fisher information that defines this resolution limit via the Cramér-Rao lower bound is shown to scale with the number of adaptively controlled space-time modes of the probe field, suggesting a physically intuitive generalization of the Abbe limit to the spatial resolution attainable for complex scattering systems. In a conventional, direct-imaging microscopy setting, this bound is shown to converge to the canonical Abbe limit.

In vivo dynamics of acidosis and oxidative stress in the acute phase of an ischemic stroke in a rodent model.

Ischemic cerebral stroke is one of the leading causes of death and disability in humans. However, molecular processes underlying the development of this pathology remain poorly understood. There are major gaps in our understanding of metabolic changes that occur in the brain tissue during the early stages of ischemia and reperfusion. In particular, it is generally accepted that both ischemia (I) and reperfusion (R) generate reactive oxygen species (ROS) that cause oxidative stress which is one of the main drivers of the pathology, although ROS generation during I/R was never demonstrated in vivo due to the lack of suitable methods. In the present study, we record for the first time the dynamics of intracellular pH and H2O2 during I/R in cultured neurons and during experimental stroke in rats using the latest generation of genetically encoded biosensors SypHer3s and HyPer7. We detect a buildup of powerful acidosis in the brain tissue that overlaps with the ischemic core from the first seconds of pathogenesis. At the same time, no significant H2O2 generation was found in the acute phase of ischemia/reperfusion. HyPer7 oxidation in the brain was detected only 24 h later. Comparison of in vivo experiments with studies on cultured neurons under I/R demonstrates that the dynamics of metabolic processes in these models significantly differ, suggesting that a cell culture is a poor predictor of metabolic events in vivo.

Laser filaments as pulsed antennas.

Secondary radiation emission of laser-induced filaments is revisited from a perspective of transient antenna radiation. Solutions for transient-antenna radiation fields are shown to provide an accurate description of the spectral and polarization properties, radiation patterns, and the angular dispersion of terahertz and microwave radiation emitted by laser filaments. Time-domain pulsed-antenna analysis offers a physically clear explanation for the bandwidth of this radiation, relating the low-frequency cutoff in its spectrum to the filament length, thus explaining efficient microwave generation in laser filamentation experiments.

Analysis of intensity correlation enhanced plasmonic structured illumination microscopy.

We propose to enhance the performance of localized plasmon structured illumination microscopy (LP-SIM) via intensity correlations. LP-SIM uses sub-wavelength illumination patterns to encode high spatial frequency information. It can enhance the resolution up to three-fold before gaps in the optical transfer function (OTF) support arise. For blinking fluorophores or for quantum antibunching, an intensity correlation analysis induces higher harmonics of the illumination pattern and enlarges the effective OTF. This enables ultrahigh resolutions without gaps in the OTF support, and thus a fully deterministic imaging scheme. We present simulations that include shot and external noise and demonstrate the resolution power under realistic photon budgets. The technique has potential in light microscopy where low-intensity illumination is paramount while aiming for high spatial but moderate temporal resolutions.

Keldysh time bounds of laser-driven ionization dynamics.

We revisit the energy-time uncertainty underpinning of the pointwise bounds of laser-driven ionization dynamics. When resolved within the driver pulse and its field cycle, these bounds are shown to manifest the key signature tendencies of photoionization current dynamics-a smooth growth within the pulse in the regime of multiphoton ionization and an abrupt, almost stepwise photocurrent buildup within a fraction of the field cycle in the limit of tunneling ionization. In both regimes, the Keldysh time, defined as the ratio of the Keldysh parameter to the driver frequency, serves as a benchmark for the minimum time of photoionization, setting an upper bound for the photoelectron current buildup rate.

Light-induced uncertainty and information limits of optical neural recording.

Cutting-edge methods of laser microscopy combined with fluorescent protein engineering and spectral analysis provide a unique resource for high-resolution neuroimaging, enabling a high-fidelity, high-contrast detection of fine structural details of neural cells and intracellular compartments. In addition to their extraordinary imaging abilities in real space, such methods can help resolve the neural states in a multidimensional space of neural responses whereby individual neurons and neural populations encode information on external stimuli. This study shows, however, that laser-induced biochemical processes in neural cells can give rise to an uncertainty of neural states, setting an upper bound on the information that optical measurements can provide on neural states, neural encodings, and neural dynamics. Comparison of absorbed laser power with the native biochemical energy budget of neuronal firing suggests that each readout photon in optical recording comes at a cost of precision of neural encoding and a loss of information encoded by the neural response. A quantitative measure for such a measurement-induced neural uncertainty can be defined, as this study shows, in terms of the Fisher information, relating the lower bound of this uncertainty to the loss of the Shannon information capacity of neural states.

Enhanced-contrast two-photon optogenetic pH sensing and pH-resolved brain imaging.

We present experiments on cell cultures and brain slices that demonstrate two-photon optogenetic pH sensing and pH-resolved brain imaging using a laser driver whose spectrum is carefully tailored to provide the maximum contrast of a ratiometric two-photon fluorescence readout from a high-brightness genetically encoded yellow-fluorescent-protein-based sensor, SypHer3s. Two spectrally isolated components of this laser field are set to induce two-photon-excited fluorescence (2PEF) by driving SypHer3s through one of two excitation pathways-via either the protonated or deprotonated states of its chromophore. With the spectrum of the laser field accurately adjusted for a maximum contrast of these two 2PEF signals, the ratio of their intensities is shown to provide a remarkably broad dynamic range for pH measurements, enabling high-contrast optogenetic deep-brain pH sensing and pH-resolved 2PEF imaging within a vast class of biological systems, ranging from cell cultures to the living brain.

Light and corona: guided-wave readout for coronavirus spike protein-host-receptor binding.

We show that waveguide sensors can enable a quantitative characterization of coronavirus spike glycoprotein-host-receptor binding-the process whereby coronaviruses enter human cells, causing disease. We demonstrate that such sensors can help quantify and eventually understand kinetic and thermodynamic properties of viruses that control their affinity to targeted cells, which is known to significantly vary in the course of virus evolution, e.g., from SARS-CoV to SARS-CoV-2, making the development of virus-specific drugs and vaccine difficult. With the binding rate constants and thermodynamic parameters as suggested by the latest SARS-CoV-2 research, optical sensors of SARS-CoV-2 spike protein-receptor binding may be within sight.

Multisite cell- and neural-dynamics-resolving deep brain imaging in freely moving mice with implanted reconnectable fiber bundles.

We demonstrate a reconnectable implantable ultraslim fiber-optic microendoscope that integrates a branching fiber bundle (BFB) with gradient-index fiber lenses, enabling a simultaneous fluorescence imaging of individual cells in distinctly separate brain regions, including brain structures as distant as the neocortex and hippocampus. We show that fluorescence images of individual calcium-indicator-expressing neurons in the brain of freely moving transgenic mice can be recorded, via the implanted BFB probe, in parallel with time- and cell-resolved traces of calcium signaling, thus enabling correlated circuit-dynamics studies at -multiple sites within the brain of freely moving animals.

High-energy self-mode-locked Cr:forsterite laser near the soliton blowup threshold.

At the level of peak powers needed for a Kerr-lens mode-locked operation of solid-state soliton short-pulse lasers, a periodic perturbation induced by spatially localized pulse amplification in a laser cavity can induce soliton instability with respect to resonant dispersive-wave radiation, eventually leading to soliton blowup and pulse splitting of the laser output. Here, we present an experimental study of a high-peak-power self-mode-locking Cr:forsterite laser, showing that, despite its complex, explosion-like buildup dynamics, this soliton blowup can be captured and quantitatively characterized via an accurate cavity-dispersion- and gain-resolved analysis of the laser output. We demonstrate that, with a suitable cavity design and finely tailored balance of gain, dispersion, and nonlinearity, such a laser can be operated in a subcritical mode, right beneath the soliton blowup threshold, providing an efficient source of sub-100-fs 15-20 MHz repetition-rate pulses with energies as high as 33 nJ.

Two- and three-photon absorption cross-section characterization for high-brightness, cell-specific multiphoton fluorescence brain imaging.

We demonstrate an accurate quantitative characterization of absolute two- and three-photon absorption (2PA and 3PA) action cross sections of a genetically encodable fluorescent marker Sypher3s. Both 2PA and 3PA action cross sections of this marker are found to be remarkably high, enabling high-brightness, cell-specific two- and three-photon fluorescence brain imaging. Brain imaging experiments on sliced samples of rat's cortical areas are presented to demonstrate these imaging modalities. The 2PA action cross section of Sypher3s is shown to be highly sensitive to the level of pH, enabling pH measurements via a ratiometric readout of the two-photon fluorescence with two laser excitation wavelengths, thus paving the way toward fast optical pH sensing in deep-tissue experiments.

A high-N00N output of harmonically driven cavity QED.

A harmonically driven cavity QED system consisting of two cavities and a two-level qubit is shown to enable the generation of a vast class of maximally entangled states suitable for measurements with a Heisenberg-limit precision. As one of its modalities, this system can serve as a quantum beam splitter, converting an |N〉 ⊗ |0〉 input into a maximally entangled N00N state (|N〉 ⊗ |0〉 + |0〉 ⊗ |N〉)/[Formula: see text] at its output. A network of such quantum beam splitters is shown to provide a source of multimode N00N-type entanglement.