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.

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.

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.

Background-penalty-free waveguide enhancement of CARS signal in air-filled anti-resonance hollow-core fiber.

We study coherent anti-Stokes Raman spectroscopy in air-filled anti-resonance hollow-core photonic crystal fiber, otherwise known as "revolver" fiber. We compare the vibrational coherent anti-Stokes Raman signal of N2, at ∼2331 cm-1, generated in ambient air (no fiber present), with the one generated in a 2.96 cm of a revolver fiber. We show a ∼170 times enhancement for the signal produced in the fiber, due to an increased interaction path. Remarkably, the N2 signal obtained in the revolver fiber shows near-zero non-resonant background, due to near-zero overlap between the laser field and the fiber cladding. Through our study, we find that the revolver fiber properties make it an ideal candidate for the coherent Raman spectroscopy signal enhancement.

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.

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.

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.

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.

Optical beam shift as a vectorial pointer of curved-path geodesics: an evolution-operator perspective.

When set to travel along a curved path, e.g., in a bending-waveguide setting, an optical beam tends to re-adjust its position, shifting away from the center of path curvature. This shift is highly sensitive to the spatial profile of the refractive index, providing a vectorial pointer for curved-path geodesics and bending-induced optical tunneling. An evolution-operator analysis of this effect extends an analogy with a time-evolution-operator treatment of quantum dynamics and suggests the routes whereby the ability of an optical beam to sense curved-path geodesics can be understood in terms of the pertinent evolution operators, path integrals, and imaginary-time/path theorems.

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.

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.

Laser-induced tunneling, the Kapitza effective potential, and the limits of perturbative nonlinear optics.

The canonical framework of optical physics connects the validity of perturbative nonlinear optics to the smallness of the optical driver field E compared to a characteristic field Eat that acts on electrons in an atom, a molecule, or a crystal lattice. However, in a vast area of strong-field optical science, the borderline between perturbative and nonperturbative nonlinear optics is defined as γ ~1, where γ is the Keldysh parameter. Not only is this criterion frequency-dependent, in a stark contrast with E/Eat ~1, but it also often dictates much weaker fields at which the perturbative treatment is still valid, leading to a dramatic shrinkage in the convergence radius of perturbation-theory expansions. Here, we identify the physics behind the gap between the E/Eat ~1 and γ ~1 conditions as the limits of perturbative nonlinear optics. We argue that, while the criterion E/Eat << 1 sets a universal upper-bound limit on the validity of perturbative nonlinear optics and its central concept of nonlinear-optical susceptibilities, optical nonlinearities related to photoionization pathways become nonperturbative in much weaker optical fields, with the limits of a perturbative treatment defined by the Keldysh parameter γ rather than the E/Eat ratio.

Linear entropy of multiqutrit nonorthogonal states.

We derive a closed-form analytical expression for the linear entropy of a multipartite qutrit state, providing a quantitative measure for quantum entanglement within the class of n-mode nonorthogonal qutrit states with any n. Conditions for enhanced and maximum quantum entanglement of multipartite qutrit states are identified. The usefulness of the introduced multipartite qutrit states as quantum communication channel resources is analyzed. The Hamiltonians allowing for the generation of multipartite qutrit states can be attained by combining optomechanical cavities with sequences of tunable beam splitters.

Analytical insights into self-phase modulation: beyond the basic theory.

We present a closed-form analytical description of the early stages of spectral broadening of ultrashort laser pulses beyond the basic theory of self-phase modulation (SPM). In the limit of short propagation paths, approximate analytical expressions derived as a part of our treatment recover the canonical SPM-theory results for the nonlinear shift and spectral broadening. For longer propagation paths, these expressions shed light on how dispersion effects enter the scene, decelerating the spectral broadening in the regime of normal dispersion and giving rise to an explosion-like bandwidth growth in anomalous-dispersion high-soliton-number pulse evolution scenarios. Based on this formalism, we will provide an analytical derivation for the relation between the maximum soliton self-compression length and the soliton number, which has been previously treated as purely empirical.

Witnessing quantum entanglement in ensembles of nitrogen-vacancy centers coupled to a superconducting resonator.

A hybrid quantum device consisting of three ensembles of nitrogen-vacancy centers (NVEs) whose spins are collectively coupled to a superconducting coplanar waveguide resonator is shown to enable the generation of controllable tripartite macroscopic entangled states. The density matrix of such NVEs can be encoded to recast a three-qubit system state, which can be characterized in terms of the entanglement witnesses in relation to the Greenberger-Horne-Zeilinger (GHZ) states. We identify the parameter space within which the generated entangled states can have an arbitrarily large overlap with GHZ states, indicating an enhanced entanglement in the system.

Free-beam spectral self-compression at supercritical peak powers.

We demonstrate free-beam spectral self-compression of ~100-GW femtosecond laser pulses due to self-phase modulation (SPM) in a transparent dielectric. While all the earlier studies of SPM-induced spectral narrowing have been performed using optical fibers, experiments and simulations presented in this Letter show that this type of spectral transformation can be implemented as a part of a full three-dimensional field-waveform dynamics and can be extended to peak powers ∼105 times higher than the critical power of self-focusing. With a properly chosen initial chirp, spectral self-compression is accompanied by pulse compression, providing spectral-temporal mode self-compression as a whole.

Spatiotemporal modulation instability as off-axis parametric amplification: insights from the phase.

The canonical linear-stability analysis of spatiotemporal modulation instability (MI), which treats MIs as instabilities of the steady-state solution of the field evolution equation with respect to weak complex harmonic perturbations, is shown to be physically equivalent to a coupled-wave analysis of off-axis parametric amplification of the Stokes and anti-Stokes fields by an intense pump wave. With an appropriate space-evolution transfer matrix, a complex harmonic trial function used in the standard MI model translates into a pair of coupled off-axis waves, of which one is exponentially growing, while the other is exponentially decreasing, thus recovering a two-wave field structure that is inherent in the fields undergoing parametric amplification through four-wave mixing. Analysis of the phase of these fields offers useful physical insights into high-order dispersion effects in spatiotemporal MIs, suggests a physically transparent and accurate method to include high-order dispersion in MI gain calculations, and reveals new spatiotemporal MI effects induced by high-order dispersion.

Coherence brightened laser source for atmospheric remote sensing.

We have studied coherent emission from ambient air and demonstrated efficient generation of laser-like beams directed both forward and backward with respect to a nanosecond ultraviolet pumping laser beam. The generated optical gain is a result of two-photon photolysis of atmospheric O(2), followed by two-photon excitation of atomic oxygen. We have analyzed the temporal shapes of the emitted pulses and have observed very short duration intensity spikes as well as a large Rabi frequency that corresponds to the emitted field. Our results suggest that the emission process exhibits nonadiabatic atomic coherence, which is similar in nature to Dicke superradiance where atomic coherence is large and can be contrasted with ordinary lasing where atomic coherence is negligible. This atomic coherence in oxygen adds insight to the optical emission physics and holds promise for remote sensing techniques employing nonlinear spectroscopy.