Solutions of the Lippmann-Schwinger equation for confocal parabolic billiards.

We present analytical and numerical solutions of the Lippmann-Schwinger equation for the scattered wave functions generated by confocal parabolic billiards and parabolic segments with various δ-type potential-strength functions. The analytical expressions are expressed as summations of products of parabolic cylinder functions D_{m}. We numerically investigate the resonances and tunneling in the confocal parabolic billiards by employing an accurate boundary wall method that provides a complete inside-outside picture. The criterion for discretizing the parabolic sides of the billiard is explained in detail. We discuss the phenomenon of transparency at certain eigenenergies.

Quantum states resembling classical periodic trajectories in mesoscopic elliptic billiards.

A quantum wave function with localization on classical periodic orbits in a mesoscopic elliptic billiard has been achieved by appropriately superposing nearly degenerate eigenstates expressed as products of Mathieu functions. We analyze and discuss the rotational and librational regimes of motion in the elliptic billiard. Simplified line equations corresponding to the classical trajectories can be extracted from the quantum state as an integral equation involving angular Mathieu functions. The phase factors appearing in the integrals are connected to the classical initial positions and velocity components. We analyze the probability current density, phase maps, and vortex distributions of the periodic orbit quantum states for both rotational and librational motions; furthermore, they may represent traveling and standing trajectories inside the elliptic billiard.

A Gamma-adapted subunit vaccine induces broadly neutralizing antibodies against SARS-CoV-2 variants and protects mice from infection.

In the context of continuous emergence of SARS-CoV-2 variants of concern (VOCs), one strategy to prevent the severe outcomes of COVID-19 is developing safe and effective broad-spectrum vaccines. Here, we present preclinical studies of a RBD vaccine derived from the Gamma SARS-CoV-2 variant adjuvanted with Alum. The Gamma-adapted RBD vaccine is more immunogenic than the Ancestral RBD vaccine in terms of inducing broader neutralizing antibodies. The Gamma RBD presents more immunogenic B-cell restricted epitopes and induces a higher proportion of specific-B cells and plasmablasts than the Ancestral RBD version. The Gamma-adapted vaccine induces antigen specific T cell immune responses and confers protection against Ancestral and Omicron BA.5 SARS-CoV-2 challenge in mice. Moreover, the Gamma RBD vaccine induces higher and broader neutralizing antibody activity than homologous booster vaccination in mice previously primed with different SARS-CoV-2 vaccine platforms. Our study indicates that the adjuvanted Gamma RBD vaccine is highly immunogenic and a broad-spectrum vaccine candidate.

Streamlines and topological transformation of modified vector Bessel-Gauss beams.

We characterize the streamline patterns of the transverse electric (TE) and transverse magnetic (TM) modes of the vector-modified Bessel-Gauss (BG) beam, which is the Fourier-transformed version of the ordinary BG beam. We derive analytical expressions to approximate the streamline patterns produced by the superposition of TM and TE modes. An analysis of the effect on the streamlines of the vector BG beams produced by some polarization devices, e.g., linear retarders and spiral polarizers, is presented. Additionally, we study the geometrical phase induced by linear retarders into the TM mode of the field. This work contributes to the description and understanding of the vector structure of the focal field of Bessel-Gauss beams.

Elliptic billiard with harmonic potential: Classical description.

The classical dynamics of the isotropic two-dimensional harmonic oscillator confined by an elliptic hard wall is discussed. The interplay between the harmonic potential with circular symmetry and the boundary with elliptical symmetry does not spoil the separability in elliptic coordinates; however, it generates nontrivial energy and momentum dependencies in the billiard. We analyze the equimomentum surfaces in the parameter space and classify the kinds of motion the particle can have in the billiard. The winding numbers and periods of the rotational and librational trajectories are analytically calculated and numerically verified. A remarkable finding is the possibility of having degenerate rotational trajectories with the same energy but different second constant of motion and different caustics and periods. The conditions to get these degenerate trajectories are analyzed. Similarly, we show that obtaining two different rotational trajectories with the same period and second constant of motion but different energy is possible.

Safety and immunogenicity of a SARS-CoV-2 Gamma variant RBD-based protein adjuvanted vaccine used as booster in healthy adults.

A Gamma Variant RBD-based aluminum hydroxide adjuvanted vaccine called ARVAC CG was selected for a first in human clinical trial. Healthy male and female participants (18-55 years old) with a complete COVID-19-primary vaccine scheme were assigned to receive two intramuscular doses of either a low-dose or a high-dose of ARVAC CG. The primary endpoint was safety. The secondary objective was humoral immunogenicity. Cellular immune responses were studied as an exploratory objective. The trial was prospectively registered in PRIISA.BA (Registration Code 6564) and ANMAT and retrospectively registered in ClinicalTrials.gov (NCT05656508). Samples from participants of a surveillance strategy implemented by the Ministry of Health of the Province of Buenos Aires that were boosted with BNT162b2 were also analyzed to compare with the booster effect of ARVAC CG. ARVAC CG exhibits a satisfactory safety profile, a robust and broad booster response of neutralizing antibodies against the Ancestral strain of SARS-CoV-2 and the Gamma, Delta, Omicron BA.1 and Omicron BA.5 variants of concern and a booster effect on T cell immunity in individuals previously immunized with different COVID-19 vaccine platforms.

General stigmatic surfaces.

Given an arbitrary input wavefront, we derive the analytical refractive surface that refracts the wavefront into a single image point. The derivation of the surface is fully analytical without paraxial or numerical approximations. We evaluate the performance of the surface with several cases, and the results were as expected.

The field of values of Jones matrices: classification and special cases.

The concept of field of values (FoV), also known as the numerical range, is applied to the 2 × 2 Jones matrices used in polarization optics. We discover the relevant interplay between the geometric properties of the FoV, the algebraic properties of the Jones matrices and the representation of polarization states on the Poincaré sphere. The properties of the FoV reveal hidden symmetries in the relationships between the eigenvectors and eigenvalues of the Jones matrices. We determine the main mathematical properties of the FoV, discuss the special cases that are relevant to polarization optics, and describe its application to calculate the Pancharatnam-Berry phase introduced by an optical system to the input state.

Uniqueness of stigmatic solutions.

We compare two analytical methods for designing stigmatic lenses that are based on very different paradigms published recently [Appl. Opt.57, 9341 (2018)APOPAI0003-693510.1364/AO.57.009341; J. Opt. Soc. Am. A37, 1155 (2020)JOAOD60740-323210.1364/JOSAA.392795]. In the process, we derive a third hybrid approach, which is the result of combining the two original methods. Given the same initial conditions, an accurate numerical analysis shows that the three methods yield the same results. This is clear evidence that the problem of designing a stigmatic lens for a known boundary condition has a unique solution independent of the formalism used.

Pancharatnam-Berry phase algorithm to calculate the area of arbitrary polygons on the Poincaré sphere.

We introduce a very efficient noniterative algorithm to calculate the signed area of a spherical polygon with arbitrary shape on the Poincaré sphere. The method is based on the concept of the geometric Berry phase. It can handle diverse scenarios like convex and concave angles, multiply connected domains, overlapped vertices, sides and areas, self-intersecting polygons, holes, islands, cogeodesic vertices, random polygons, and vertices connected with long segments of great circles. A set of MATLAB routines of the algorithm is included. The main benefits of the algorithm are the ability to handle all manner of degenerate shapes, the shortness of the program code, and the running time.

How inhomogeneous can an inhomogeneous Jones matrix be?

We determine the interval of the inhomogeneity parameter of a Jones matrix to get physically realizable optical systems satisfying the passivity condition. It is found that the inhomogeneity parameter depends on the inner product of the eigenvectors of the Jones matrix, but its maximum value depends exclusively on its eigenvalues.

General formula to design a freeform singlet free of spherical aberration and astigmatism: reply.

The comment made by Valencia-Estrada and García-Márquez [Appl. Opt.59, 3422 (2020)APOPAI0003-693510.1364/AO.379238] to our paper [Appl. Opt.58, 1010 (2019)APOPAI0003-693510.1364/AO.58.001010] consists of a trivial generalization of our formulation.

Optical phase of inhomogeneous Jones matrices: retardance and ortho-transmission states.

We determine the optical phase $ \psi $ψ (dynamic and geometric) introduced by a system described by an inhomogeneous Jones matrix. We show that there are two possible scenarios: (a) $ \psi $ψ has a finite range of $ \psi \in [{\psi _{\min }},{\psi _{\max }}] $ψ∈[ψmin,ψmax]. We calculate both limits and their corresponding polarization states analytically. (b) $ \psi $ψ spans the full range of $ \psi \in ( - \pi ,\pi ] $ψ∈(-π,π]. This scenario leads to the existence of two input polarization states whose output states are orthogonal. We call these states ortho-transmission states (OTSs) and find them analytically. We study the inverse problem of designing an optical system with OTSs given by the user.

Analytic design of a spherochromatic singlet.

We derive the analytic formula of the output surface of a spherochromatic lens. The analytic solution ensures that all the rays for a wide range of wavelengths fall inside the Airy disk. So, its amount of spherical aberration is small enough to consider the lens as diffracted limited. We test the singlet lens using ray-tracing methods and find satisfactory results, including spot diagram analysis for three different Abbe wavelengths.

Morphological transformation of generalized spirally polarized beams by anisotropic media and its experimental characterization.

We present a generalization of the known spirally polarized beams (SPBs) which we will call generalized spirally polarized beams (GSPBs). We characterize in detail both theoretically and experimentally the streamline morphologies of the GSPBs and their transformation by arbitrary polarization optical systems described by complex Jones matrices. We find that the description of the passage of GSPBs through a polarization system is equivalent to the stability theory of autonomous systems of ordinary differential equations. While the streamlines of the GSPB exhibit a spiral geometry, the streamlines of the output field may exhibit spirals, saddles, nodes, ellipses, and stars as well. Using a novel experimental technique based on a Sagnac interferometer, we have been able to generate in the laboratory each one of the different cases of GSPBs and record their corresponding characteristic streamline morphologies.

Generation of light beams with custom orbital angular momentum and tunable transverse intensity symmetries.

We introduce a novel and simple modulation technique to tailor optical beams with a customized amount of orbital angular momentum (OAM). The technique is based on the modulation of the angular spectrum of a seed beam, which allows us to specify in an independent manner the value of OAM and the shape of the resulting beam transverse intensity. We experimentally demonstrate our method by arbitrarily shaping the radial and angular intensity distributions of Bessel and Laguerre-Gauss beams, while their OAM value remains constant. Our experimental results agree with the numerical and theoretical predictions.

Singlet lens for generating aberration-free patterns on deformed surfaces.

We introduce a general closed-form analytic formula to design special lenses that generate spherical aberration-free extended images specified previously by the user. The formula considers arbitrary and non-conventional patterns. The formalism is tested with well-established ray tracing techniques.

General formula to design a freeform singlet free of spherical aberration and astigmatism.

In this paper, an analytical closed-form formula for the design of freeform lenses free of spherical aberration and astigmatism is presented. Given the equation of the freeform input surface, the formula gives the equation of the second surface to correct the spherical aberration. The derivation is based on the formal application of the variational Fermat principle under the standard geometrical optics approximation.

Generalization of the axicon shape: the gaxicon.

We generalize the shape of the traditional axicon by analytically finding the function of the output surface when the input surface is not flat but an arbitrary continuous function that possesses rotational symmetry. Several illustrative examples are presented and tested using ray tracing techniques without the paraxial approximation.

On-demand tailored vector beams.

We introduce an effective optical system to produce optical beams with arbitrary, inhomogeneous polarization states. Using our system, we are capable of generating vector beams with discretionarily chosen transverse complex fields in a straightforward way. We generate several different instances of well-known vector beams and the less common spirally polarized vector beams, as well as a full Poincaré beam. We visually show the continual transition between azimuthally and radially polarized beams via a collection of spirally polarized beams. We experimentally determine the polarization states of the generated beams and quantitatively assess the performance of our system. We find that the measured polarization distributions accurately coincide with the intended input polarization distributions.