The spatial profile of several types of focusing two-dimensional shock waves (weak shock regime) created in a thin liquid gap are imaged using a shadowgraph with strobe photography. Their profiles before and after focusing are shown to constitute approximately a Hilbert transform pair, regardless of the range of directional angles involved in the focusing and of whether the focusing is at a single point or an extended caustic. This Hilbert transform relation, observable here from a single image or a pair of images, can be explained in terms of the π/2 Gouy phase shift for focused waves in two dimensions, as was shown elsewhere with experiments involving terahertz pulses in the time domain.

Polarimetric scattering is especially important in the understanding of physical phenomena. A scatterer near a waveguide (an engineered scattering element) can lead to a variety of evanescent field effects that significantly affect both the polarization and angular spectrum of the scattered light. Under direct imaging in a microscope, engineered scattering elements image as point sources where much of the rich physics is obscured. However, the pupil plane of a high-NA imaging system reveals important structure in the vector fields. In this work, we present a multipolar analysis of light scattered from engineered scattering elements using vector spherical harmonics as the basis set to illustrate how a scatterer can emulate an electric and/or magnetic dipole.

Spatiotemporal vortex pulses (STVPs) are wavepackets that carry transverse orbital angular momentum (OAM), whose proper quantification has been the subject of recent debate. In this work, we introduce a simplified mechanical model of STVPs, consisting of a loop of non-interacting point particles traveling at a uniform constant speed but at slightly di!erent angles. We examine di!erent initial conditions for the particle loop, including configurations that are elliptic in space at a given time and configurations that are elliptic in spacetime at a fixed propagation distance. Furthermore, employing a non-uniform mass distribution allows the particle loop to mimic the STVP not only in configuration space but also in momentum space. Remarkably, when supplemented by a semiclassical vorticity quantization condition, our mechanical model exactly reproduces di!erent wave-based OAM results previously reported for paraxial STVPs.

Optical fields polarized along three dimensions are frequent in optical microscopy and nanophotonics, and yet retrieving their polarization distribution is challenging. We present the experimental implementation of three-dimensional (3D) Stokes polarimetric imaging of nonparaxial optical fields with nanoscale spatial resolution. This approach extends classical Stokes polarimetry (traditionally limited to paraxial fields) into the nonparaxial regime. We use an array of gold nanospheres, each acting as a localized electric dipolar scatterer, to probe 3D polarization states over a field of view of tens of micrometers. The scattered signal is collected by a high numerical aperture objective lens and separated into its circular polarization components, providing a very simple imaging system. We introduce a computational algorithm to efficiently extract the physical parameters from the generated dipole spread functions with a high throughput across the whole field of view. Finally, we show that this method can also be applied to single-molecule localization and orientation fluorescence microscopy.

Precise calibration is essential in advanced single-molecule microscopy for accurately measuring fluorophore orientation and localization. Fluorescent beads are commonly used to calibrate and characterize system aberrations and polarization distortions. However, their larger size relative to single fluorophores, along with their unpolarized emission, results in a point spread function (PSF) that does not fully capture the behavior of a single fluorophore. This study employs numerical and semi-analytical methods to evaluate how well a fluorescent bead of a given radius, within a polarizer-assisted microscopy setup, can emulate the properties of a single fluorescent molecule.

Sag- or slope-orthogonal bases have proven effective for characterising aspheric and freeform surfaces on circular apertures. Things are not so straightforward, however, for rectangular apertures when slope orthogonality is desired. While such a basis can be constructed via Gram-Schmidt, we show that the simplifying step offered by separation of variables fails, the basis depends on the domain's aspect ratio, and no recurrence relations exist for efficient computation. In contrast, a characterisation in terms of an RDF basis [Opt. Express27, 32263 (2019)10.1364/OE.27.032263] avoids all three issues. Further, the result is both sag- and slope-orthogonal making it ideal for on-the-fly design constraints.

We present 4D topological textures in (quasi)monochromatic nonparaxial optical lattices that contain all possible polarization ellipses with every combination of ellipticity and orientation in 3D space. These fields span the nonparaxial polarization space (a complex projective plane) and a 4-sphere within specific spatiotemporal regions, forming 4D skyrmionic structures. Constructed from five plane waves with adiabatically varying relative amplitudes, they are experimentally realizable in free space by focusing a temporally variant beam with a high numerical aperture lens.

Imaging both the polarization and the wavefront of a light beam is a complex task that typically demands several inten-sity acquisitions. Furthermore, sequential acquisition solutions are incompatible with the monitoring of ultra-fast processes. As a possible solution for single-shot wavefront and full-Stokes polarimetric imaging, we propose here a vector-beam lateral shearing interferometer. The device, composed of a patterned polarization-modulating Hartmann mask placed in close vicinity to a camera, encodes all the information in the fringe pattern of a single-image acquisi-tion. By extending lateral shearing interferometry to vector beams, this work opens avenues for characterizing complex metasurfaces and biological samples. Published by Optica Publishing Group under the terms of the Creative Commons Attribution 4.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Both the polarization state of coherent bichromatic fields produced by harmonic generation and a class of anisotropic paraxial optical cavities are examples of commensurate two-dimensional harmonic oscillators. The geometric phase for these systems is studied here, both in the classical/ray and quantum/wave regimes. The quantum geometric phase is described in terms of the coherent states of the system, for which recursive expressions are derived that yield the exact result and are numerically stable even for high modal orders.

Coherence refers to correlations between field vibrations at two separate points in degrees of freedom such as space, time, and polarization. In the context of space, coherence theory has been formulated between two transverse positions which can be described either in the Cartesian coordinates or in the cylindrical coordinates. When expressed in cylindrical coordinates, spatial coherence is described in terms of azimuthal and radial coordinates. The description of spatial coherence in radial degree of freedom has been formulated only recently in JOSA A40, 411 (2023)10.1364/JOSAA.474724. In the present article, we demonstrate an efficient experimental technique for measuring radial coherence, and we report measurement of radial coherence of two different types of radially partially coherent optical fields.

The use of multipoles, otherwise called spherical wavefunctions, has been explored for acoustic fields that can be omnidirectional, for example, in scattering theory. Less developed is the use of spherical harmonic multipoles for the construction of directed beams, such as the Gaussian unfocused beampattern, which is an important reference beam in many practical applications. We develop the straightforward construction of a Gaussian unfocused beam using the special properties of the sum of spherical harmonics; these include the use of an imaginary offset in directing the forward propagation to the desired beampattern. Examples are given for narrowband and broadband pulse propagation in the ultrasound MHz range, with comparisons against a classical acoustics formulation of the Gaussian beam. The use of spherical harmonics forms an alternative framework for devising beampatterns, with apodization and concentration issues of the beam linked to an array of a limited number of discrete multipoles at the source.

The design of high-NA optical systems such as those used for advanced single molecule microscopy require careful modeling of polarization and its impact on the point spread function. When the system is engineered specifically with a polarization-dependent point spread function, it is possible to recover information such as molecule location, orientation, and wobble. SOLID comprises five principles of software design that, when implemented in software designed for modeling a microscope, can provide significant flexibility in the shape of a fluorescent source and its polarization distribution while incorporating such novel elements as stress-engineered optics in the imaging path. We will describe a modeling architecture implemented in Python and provide examples relevant to experimental single molecule microscopy systems.

Imaging both the polarization and the wavefront of a light beam is a complex task that typically demands several intensity acquisitions. Furthermore, sequential acquisition solutions are incompatible with the monitoring of ultra-fast processes. As a possible solution for single-shot wavefront and full-Stokes polarimetric imaging, we propose here a vector-beam lateral shearing interferometer. The device, composed of a patterned polarization-modulating Hartmann mask placed in the close vicinity of a camera, encodes all the information in the fringe pattern of a single image acquisition.

Spatiotemporal optical vortices (STOVs) are a type of optical pulse carrying tranverse orbital momentum. Here, we present analytical expressions modeling STOVs that are as round as possible. We obtain those expressions by applying mathematical differential operators to light "blobs" presenting a Poissonian spectrum and modeled with a complex focus method.

We introduce and produce experimental optical beams exhibiting periodic skyrmionic polarization lattices at each transverse plane of propagation. These textures are meron lattices formed by tiles mapping hemispheres of the Poincare sphere. All of the presented fields are combinations of a small number of plane waves. First, we propose square lattices with a Skyrme density (the Jacobian of the mapping between the Poincare sphere and physical space) that oscillates in sign but whose intensity distribution is constant. Second, we present triangular lattices preserving the Skyrme density's sign. Both lattices are invariant under propagation. Finally, we introduce a family of lattices with a uniform Skyrme density sign, composed of square tiles that map to the same hemisphere of the Poincare sphere. In these lattices, the polarization state undergoes a uniform local periodic rotation during propagation, thus preserving the texture's Skyrme density distribution.

We find periodic skyrmionic textures via conformal cartographic projections that map either an entire spherical parameter space or a hemisphere onto every regular polygon that provides regular tessellations of the plane. These textures minimize the energy inherent to the mapping and preserve the sign of the Skyrme density throughout the entire space. We show that 2D spinor fields (e.g., 2D polarization) that present periodic textures preserving the sign of the Skyrme density unavoidably exhibit zeros. We implement these textures in the polarization state of a laser beam.

Spatiotemporal optical vortices (STOVs) are short pulses that present a vortex whose axis is perpendicular to the main propagation direction. We present analytic expressions for these pulses that satisfy exactly Maxwell's equation, by applying appropriate differential operators to complex focus pulses with Poisson-like frequency spectrum. We also provide a simple ray picture for understanding the deformation of these pulses under propagation. Finally, we use these solutions to propose a type of pulse with sagittal skyrmionic polarization distribution covering all states of transverse polarization.

The classical solution to the Helmholtz wave equation in spherical coordinates is well known and has found many important applications in wave propagation, scattering, and imaging in optics and acoustics. The separable solution is comprised of spherical Bessel functions in the radial direction and spherical harmonics in the angular directions. The nature of the spherical Bessel functions includes a long asymptotic oscillatory tail at large radii, not conducive to applications where a tight concentration of wave amplitude around a ring is desired, for example in toroidal configurations. However, we have found that certain practical bandpass spectral shapes, centered around a peak frequency, can create a superposition of spherical Bessel functions that effectively concentrate the wave amplitude around a defined ring at the time instant of coherent addition, avoiding the long tail asymptotic oscillations of the single frequency solution. Theoretical solutions are shown for different bandpass spectra applied to the spherical Bessel functions, along with numerical solutions of transient wave propagation using practical hemispherical source shapes. These findings introduce a framework by which ring or toroidal concentrated waves can be produced with a simple bandpass superposition applied to hemispherical source shapes and with reference to the classical solutions in spherical coordinates.