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.

The Role of Virtual Reality and Artificial Intelligence in Cognitive Pain Therapy: A Narrative Review.

PURPOSE OF REVIEW: This review investigates the roles of artificial intelligence (AI) and virtual reality (VR) in enhancing cognitive pain therapy for chronic pain management. The work assesses current research, outlines benefits and limitations and examines their potential integration into existing pain management methods. RECENT FINDINGS: Advances in VR have shown promise in chronic pain management through immersive cognitive therapy exercises, with evidence supporting VR's effectiveness in symptom reduction. AI's personalization of treatment plans and its support for mental health through AI-driven avatars are emerging trends. The integration of AI in hybrid programs indicates a future with real-time adaptive technology tailored to individual needs in chronic pain management. Incorporating AI and VR into chronic pain cognitive therapy represents a promising approach to enhance management by leveraging VR's immersive experiences and AI's personalized tactics, aiming to improve patient engagement and outcomes. Nonetheless, further empirical studies are needed to standardized methodologies, compare these technologies to traditional therapies and fully realize their clinical potential.

Continuous-Time Modeling of the Bidirectional Relationship Between Incidental Affect and Physical Activity.

BACKGROUND: Previous research suggests that there is a bidirectional relationship between incidental affect (i.e., how people feel in day-to-day life) and physical activity behavior. However, many inconsistencies exist in the body of work due to the lag interval between affect and physical activity measurements. PURPOSE: Using a novel continuous-time analysis paradigm, we examined the temporal specificity underlying the dynamic relationship between positive and negative incidental affective states and moderate-to-vigorous physical activity (MVPA). METHODS: A community sample of adults (n = 126, Mage = 27.71, 51.6% Male) completed a 14-day ambulatory assessment protocol measuring momentary positive and negative incidental affect six times a day while wearing a physical activity monitor (Fitbit). Hierarchical Bayesian continuous-time structural equation modeling was used to elucidate the underlying dynamics of the relationship between incidental affective states and MVPA. RESULTS: Based on the continuous-time cross-effects, positive and negative incidental affect predicted subsequent MVPA. Furthermore, engaging in MVPA predicted subsequent positive and negative incidental affect. Incidental affective states had a greater relative influence on predicting subsequent MVPA compared to the reciprocal relationship. Analysis of the discrete-time coefficients suggests that cross-lagged effects increase as the time interval between measurements increase, peaking at about 8 h between measurement occasions before beginning to dissipate. CONCLUSIONS: The results provide support for a recursive relationship between incidental affective states and MVPA, which is particularly strong at 7-9 hr time intervals. Future research designs should consider these medium-term dynamics, for both theory development and intervention.

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.

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.

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.

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.

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.

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.

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.

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.

Geometric phase morphology of Jones matrices.

We demonstrate an innovative technique based on the Pancharatnam-Berry phase that can be used to determine whether an optical system characterized by a Jones matrix is homogeneous or inhomogeneous, containing orthogonal or nonorthogonal eigenpolarizations, respectively. Homogeneous systems have a symmetric geometric phase morphology showing line dislocations and sets of polarization states with an equal geometric phase. In contrast, the morphology of inhomogeneous systems exhibits phase singularities, where the Pancharatnam-Berry phase is undetermined. The results show an alternative to extract polarization properties such as diattenuation and retardance, and can be used to study the transformation of space-variant polarized beams.

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.

Web Use for Symptom Appraisal of Physical Health Conditions: A Systematic Review.

BACKGROUND: The Web has become an important information source for appraising symptoms. We need to understand the role it currently plays in help seeking and symptom evaluation to leverage its potential to support health care delivery. OBJECTIVE: The aim was to systematically review the literature currently available on Web use for symptom appraisal. METHODS: We searched PubMed, EMBASE, PsycINFO, ACM Digital Library, SCOPUS, and Web of Science for any empirical studies that addressed the use of the Web by lay people to evaluate symptoms for physical conditions. Articles were excluded if they did not meet minimum quality criteria. Study findings were synthesized using a thematic approach. RESULTS: A total of 32 studies were included. Study designs included cross-sectional surveys, qualitative studies, experimental studies, and studies involving website/search engine usage data. Approximately 35% of adults engage in Web use for symptom appraisal, but this proportion varies between 23% and 75% depending on sociodemographic and disease-related factors. Most searches were symptom-based rather than condition-based. Users viewed only the top search results and interacted more with results that mentioned serious conditions. Web use for symptom appraisal appears to impact on the decision to present to health services, communication with health professionals, and anxiety. CONCLUSIONS: Web use for symptom appraisal has the potential to influence the timing of help seeking for symptoms and the communication between patients and health care professionals during consultations. However, studies lack suitable comparison groups as well as follow-up of participants over time to determine whether Web use results in health care utilization and diagnosis. Future research should involve longitudinal follow-up so that we can weigh the benefits of Web use for symptom appraisal (eg, reductions in delays to diagnosis) against the disadvantages (eg, unnecessary anxiety and health care use) and relate these to health care costs.

Creation operators for Cartesian and circular beams.

Creation operators of fractional order, to derive the general Cartesian beams and circular beams from the lowest-order Gaussian beam, are introduced and discussed. Finding the creation operator for these general cases is a way to find the creation operator of all the special cases of Cartesian and circular beams.

Shaping optical beams with non-integer orbital-angular momentum: a generalized differential operator approach.

We introduce an analytical procedure to construct an optical beam with an arbitrary value of orbital-angular momentum (OAM) by keeping the flexibility of shaping its transverse intensity distribution without changing its OAM. We apply the general theory of fractional differential operators in Fourier domain to derive general expressions for the OAM content in the beam and find the relevant parameters that determine its OAM value and those that can be freely modified without affecting it.