Vectorial Theory Research Articles

Enhanced scattering from an almost-periodic optical temporal slab

We showcase the impact of almost-periodicity on the parametric amplification associated with the first-order momentum gap in photonic time-crystals with time-varying permittivity. Utilizing a vectorial coupled-wave theory approach, we rigorously analyze the scattering by a temporal slab of the considered medium. We pinpoint a critical regime wherein flaws in material tuning paradoxically enhance amplification due to the coupling of fewer, broader modes, resulting in a higher and broader pulselike amplification envelope. Additionally, we demonstrate that the intensity reflectances of time-reversed waves corresponding to secondary “Bragg” resonances achieve remarkably high levels of subharmonic parametric amplification, with the epsilon-near-zero regime serving as a preferred candidate for experimental implementation. Our counterintuitive findings highlight the potential of intentionally leveraging modulation desynchronization and impurities in the temporal unit cell of photonic time-crystals to enhance both the level and the bandwidth of amplification. Published by the American Physical Society 2024

Structured light routing in CROW-endowed add-drop filters

In this paper, we study the propagation of optical vortices (OVs) through the add-drop filter that comprises a coupled resonator optical waveguide (CROW). We develop a fully vectorial theory not based on transfer matrix formalism and apply it to the description of CROWs based on multimode fibers. We study the transmission of higher-order OVs through a CROW-endowed add-drop filter and demonstrate the possibility of transmitting such OVs along the CROW chain. We show that during such transmission OVs may invert their topological charges and determine the condition under which an OV propagates without such charge inversion. We suggest that such a system can be used for the generation of OV frequency combs. We also study group delay time and show that this system may be used as a time delay line for OVs.

New control strategy to improve power quality using a hybrid power filter

A new control algorithm for a hybrid power filter constituted by a series active filter and a passive filter connected in parallel with the load is proposed. The new control strategy is based on the dual formulation of the vectorial theory of electric power, so that the signal injected by the active filter is able to compensate the reactive power and the harmonics of the load current. To verify the developed theoretical analysis, the control strategy was verified by means of an experimental prototype. The results to verify the effectiveness of the proposed control algorithm are presented.

Compensation of Voltage Unbalance and Current Harmonics with a Series Active Power Filter.

A combined system of shunt passive and series active filter for a four-wire three-phase system has been designed and simulated with Matlab/Simulink. The system combined mitigates the source current harmonics and compensates also unbalance voltages reducing the problems of using only a shunt passive filter. Therefore, a new control method based in the power vectorial theory has been proposed. The compensation principle is presented in detail. To verify the effectiveness of the proposed control, simulation results are presented and discussed.

Field dipole interaction and polarization effects in light-sheet optical fluorescence microscopy

Polarization plays a crucial role in understanding the interaction of fluorescent molecules in a light field. We report the study on the effect of a field–dipole interaction under polarization light-sheet fluorescence microscopy using the vectorial theory of light. The molecule is suitably modeled as a radiating electric dipole in a polarized electric field (both linear and random), and the system point spread function (PSF) is determined for different orientations of the dipole (both fixed and random). PSF analysis and contour plots suggest distinct nature of a field distribution in each case, indicating the importance of a field–dipole interaction for high-quality fluorescence imaging. The analysis suggests that the field spreads gradually along the polarization axis at a high numerical aperture (NA) of the objective lens, whereas it is more isotropic and homogeneous at low NA. Moreover, fast changes are not observed at low NA (i.e., far from the central lobe in the field contour plots), suggesting the absence of high-frequency components. However, sidelobes are prominent for linear polarized (along x) light. On the other hand, rapid variations are evident for randomly polarized light, depicting the presence of high spatial frequencies in the system optical transfer function. The other significant observation is the distinct frequency spectrum (both kx and ky) for random and fixed dipoles, indicating the significance of dipole orientation in a light-sheet field. Compared to the point-illumination-based fluorescence microscopy, sheet based polarization technique provides a high signal-to-noise ratio, a uniform field, an order large field of view, and critical information (related to the micro-environment of a dipole and its short-range interactions). The study is expected to facilitate polarization-sensitive investigation of large biological specimens (both fixed and live).

Statistical Properties of Partially Coherent Higher-Order Laguerre-Gaussian Power-Exponent Phase Vortex Beams

In this paper, partially coherent radially polarized (RP) Laguerre-Gaussian (LG) rotationally symmetrical power-exponent phase vortex (RSPEPV) beams with the LG-correlated Schell-model (LGSM) were introduced. The statistical properties of the tightly focused beams, including intensity distribution, degrees of polarization and coherence, and Stokes vector, were studied based on vectorial Richards-Wolf diffraction integral theory. Moreover, when the distance between focal plane and the observation plane z = 0, the relationships between the tight-focusing properties of RP-LG-RSPEPV beams with LGSM and the order of LGSM p’, topological charges l, power exponent n, spatial correlation δ, and radial index p were investigated. The results show that by changing the order of LGSM, topological charge, power exponent, spatial correlation length, and radial index, the focal spot distribution of various shapes can be obtained. This work provides ideas for the application of partially coherent beams in particle capture and optical tweezers.

Tight Focusing Properties of Ring Pearcey Beams with a Cross Phase

We theoretically investigated the properties of tightly focused ring Pearcey beams with a cross phase (CPRPB). The expressions of the distributions of both electric field and magnetic field in the focal region of an objective were first derived from the vectorial Debye theory, and then numerical calculations were carried out to obtain the focused intensity distribution and the Poynting vector of CPRPB near the focus. Numerical calculations indicate that as CPRPB is focused on an objective of high numerical aperture (NA), two nonuniform self-focusing spots occur at both sides of the geometrical focus of the objective symmetrically, and the angle between their directions is 90 degrees. The stronger is the strength of cross-phase modulation, the flatter are the ellipses of the self-focusing spots, and the smaller is the intensity at the geometrical focus of the objective. Numerical calculations also demonstrate that the optical gradient force produced by tightly focused CPRPB in the focal region can be manipulated in magnitude and in direction by tuning the strength of cross-phase modulation. Due to these properties of tightly focused CPRPB, they might find applications in the manipulation of micro- and nanoparticles and so on.

Structured light transformations and orbital angular momentum control in a three-coil optical snake

In this paper, we studied transformations of structured light and its angular momentum in a three-coil optical snake – a coil resonator composed of 3 evanescently uniformly coupled coils of a multimode fiber. We have suggested a fully vectorial theory of normal modes of the 3-coil resona-tor, which takes account of the spin-orbit interaction. On the basis of the analytical expressions for such normal modes and their propagation constants we have studied transmission of some types of structured light beams – optical vortices, Hermite-Gaussian-like and Laguerre-Gaussian beams – through such a system. We have shown the possibility of a super-efficient parametric control over the topological charge, orbital and spin angular momenta of the outcoming optical field by this system. We have theoretically demonstrated implementation of logic X and Y Pauli gates for light beams carrying orbital angular momentum on the basis of such a 3-coil resonator.

Ultrafast Spin‐to‐Orbit and Orbit‐to‐Local‐Spin Conversions of Tightly Focused Hybridly Polarized Light Pulses

Spin–orbit interaction (SOI) has provided a new viable roadmap for the development of spin‐based photonics devices. However, existing strategies to control the SOI focus commonly on tailoring the spatial dimension of light fields yet neglecting the inherent temporal one. Herein, ultrafast temporal effects on both spin‐to‐orbit and orbit‐to‐local‐spin conversions based on the time‐assistant vectorial diffractive theory and the fast Fourier transformation are first presented. Such interconversions depend upon whether the incident hybridly vectorial light pulse carries vortex phase or not in a single high numerical aperture geometry. For the case of the absence of vortex phase, it is found that it enables orbit angular momentum‐carrying transverse component fields, and the resultant orbit angular momentum embedded within focused light fields remains constantly revolving as time elapses, which indicates that the controllable spin‐to‐orbit conversion occurs. By contrast, it is revealed that hybridly polarized vectorial‐vortex light pulses allow access to the locally excited circular polarization at the focus, and this induced local circular polarization is independent of ultrafast varying time, whereas the resulting spin angular momentum density components experience the alternation between the appearance and annihilation over time, thus giving rise to the tunable orbit‐to‐local‐spin conversion. These exotic ultrafast interconversions not only breathe a new life into the area of ultrafast photonics, but refresh our understanding on the paradigm of photonic SOI.

Chromatic confocal measurement method using a phase Fresnel zone plate.

A chromatic confocal measurement method based on a phase Fresnel zone plate (FZP) is described. Strong dispersion of FZP results in significant axial focal shift. The axial dispersion curve is close to linear within a certain wavelength range determined by the quantitative calculation using the vectorial angular spectrum theory. A 11.27 mm diameter phase FZP with a primary focal length of 50 mm was processed using standard photolithography technology and used as the dispersive objective in a homemade chromatic confocal measurement system. The calibrated axial measurement range exceeds 16 mm, the axial resolution reaches 0.8 µm, and the measurement accuracy of displacement is better than 0.4%. This chromatic confocal sensor has been practically used in the measurement of step height, glass thickness, and 3D surface profile. The proposed method has the obvious characteristics of simplicity, greatly reduced cost and superior performance. It is believed that this sensing method has broad application prospects in glass, coating, machinery, electronics, optics and other industries.

Vectorial theory surpasses the local theory in explaining the origin of P-wave dispersion

BackgroundLocal theory and the vectorial theory are used to explain the origin of P-wave dispersion (PWD). There are no previous studies that analyze both at the same time. ObjectivesWe set out to determine the implication of local and vectorial theories in the origin of PWD. MethodsCross-sectional study in 153 randomly selected patients aged 18–70 years, undergoing electrophysiological study. Inhomogeneous atrial conduction was evaluated by atrial electrogram dispersion in terms of duration (EGMdurdis) and morphology (EGMmorph dis). P-distal coronary sinus interval (P-DCS) was also measured. P-wave was measured twice, firstly at a calibration of 20 mm/mV and a sweep speed of 50 mm/s, enhancement 10× (basic measurement [BM]), and second time at sweep speed of 150 mm/s, enhancement 80-160× (high precision measurement [HPM]). ResultsPWD with BM was 48 ms [36–54 ms] while with HPM it was 4 ms [0–10 ms], p < 0.001. With BM, maximum and minimum P- wave duration presented a moderate correlation (r = 0.342; p < 0.001), using HPM it becomes strong (r = 0.750; p < 0.001). In cases with P-DCS < 80 ms (r = 0.965; p < 0.001), but not with P-DCS ≥ 80 ms (r = 0.649; p < 0.001), the previous correlation became almost perfect with HPM. EGMdurdis and EGMmorphdis were weak but significantly correlated with PWD. This correlation became moderate in patients with P-DCS ≥ 80 ms and disappeared in those with P-DCS, using BM and HPM. ConclusionVectorial theory explains almost entirely the PWD phenomenon. Inhomogeneous conduction could be an additional mechanism to explain PWD, but its contribution is small.

Scheme-independent series for anomalous dimensions of higher-spin operators at an infrared fixed point in a gauge theory

We consider an asymptotically free vectorial gauge theory, with gauge group $G$ and $N_f$ fermions in a representation $R$ of $G$, having an infrared fixed point of the renormalization group. We calculate scheme-independent series expansions for the anomalous dimensions of higher-spin bilinear fermion operators at this infrared fixed point up to $O(\Delta_f^3)$, where $\Delta_f$ is an $N_f$-dependent expansion variable. Our general results are evaluated for several special cases, including the case $G={\rm SU}(N_c)$ with $R$ equal to the fundamental and adjoint representations.

Realistic, Vectorial Modeling of the Detection Point Spread Function for Single Molecule and Brightfield Microscopy

In previous work, we presented a rigorous, vectorial theory for the illumination point spread function (PSF). Here, we extend this approach to model the detection PSF, which is responsible for optical image formation in virtually all microscopy applications, such as conventional widefield microscopy, confocal scanning microscopy, fluorescence correlation spectroscopy, single molecule imaging, and super-resolution microscopy. We cover the most general case of a single dipolar scatterer or emitter, such as a single fluorescent molecule, which is imaged by a microscope objective-tube lens combination. The dipole radiation passes through stratified media composed of up to three layers (sample medium, glass coverslip, and immersion medium). The theoretical model accounts for a high numerical aperture tube lens and microscope objective (corrected for refractive indices of coverslip/immersion medium and coverslip thickness), a finite detector or detection pinhole, and an optional Babinet-Soleil compensator and polarization analyzer in the detection path. The resulting equations are readily evaluated, and multiple application examples will be discussed, such as the influence of dipole orientation and polarization detection on the detection PSF.

Effect of laser illumination conditions on focusing performance of super-oscillatory lens

Super-oscillatory lens (SOL), a new type of planar optical element developed in recent years, may play an important role in the integrated optics, microscopy, advanced sensor, and astronomy. Based on the vectorial angular spectrum theory and genetic algorithm, both binary amplitude-type and phase-type SOLs are designed. Various sub-diffraction focusing properties can be realized by optimizing the design procedure. In order to investigate the focusing characteristics of SOLs under different illumination conditions, rigorous electromagnetic simulation calculations of the diffracted focusing light field are implemented by the finite-difference time-domain method. The results show that when the beam waist radius &lt;i&gt;w&lt;/i&gt;&lt;sub&gt;0&lt;/sub&gt; of the illuminating laser is less than the SOL radius &lt;i&gt;a&lt;/i&gt;, not only the capability of super-diffraction limit focusing will decrease significantly, but also the intensity of the focal spot will attenuate by more than 50%. Comparing with the amplitude-type SOL, the waist radius &lt;i&gt;w&lt;/i&gt;&lt;sub&gt;0&lt;/sub&gt; has a strong effect on the phase-type SOL and causes a significant focus to shift in the positive direction. However, if &lt;i&gt;w&lt;/i&gt;&lt;sub&gt;0&lt;/sub&gt; is larger than 2&lt;i&gt;a&lt;/i&gt;, the ideal focusing characteristics of SOL can be maintained. Under the condition of oblique illumination, the high numerical aperture amplitude-type SOL generally only allows a small inclination angle of less than 10°, while the phase-type SOL has a wide inclination adaptability (can exceed 40°) regardless of the numerical aperture. For the latter, the focal spot will expand laterally and the intensity will decrease sharply with the increase of inclination angle. As for low numerical aperture phase-type SOL, the focusing characteristics, including focal spot size, focusing intensity and the angular position of the focus, can keep stable within an inclination angle of 18°. For imaging infinitely distant objects, the oblique illumination will produce a fluctuating field curvature and significant negative distortion for high numerical aperture SOLs, while for the low numerical aperture SOLs, the field curvature increases with inclination angle increasing and the distortion disappears almost. The research results of this paper provide an important theoretical basis for practical applications of super-oscillatory lens in the fields of sub-diffraction light focusing, super-resolution microscopic imaging, and micro-nano processing of femtosecond laser direct writing.

Vectorial perturbation theory for axisymmetric whispering gallery resonators

We propose a vectorial perturbation theory for axially symmetric, generally nonspherical whispering gallery resonators made of isotropic and anisotropic optical materials. It is based on analysis of the leading terms in the coupled equations for independent light-field components, as derived from Maxwell's equations, and true boundary conditions. Strong localization of the whispering gallery modes (WGMs) near the resonator rim, controlled by the azimuth modal number $m$, is the main prerequisite for our analysis. The theory gives high-precision expressions for the WGM frequencies and modal functions, including the evanescent effects. One of important applications of the theory is analysis of anticrossings of the WGM resonances in anisotropic resonators detected in experiments. Simple relations for the frequency avoidance gaps during the anticrossings are derived and compared with experimental data obtained in lithium-niobate-based WGM resonators. We show also that the vectorial effects substantially restrict the field of applicability of the scalar WGM models.

Tight focusing properties of a circular partially coherent Gaussian beam.

Tight focusing properties of a circular partially coherent Gaussian (CPCG) beam with linear polarization have been studied based on vectorial Debye theory. Expressions for the intensity distribution and degree of coherence near the focus are derived. Numerical calculations are performed to show the intensity distribution and degree of coherence of the CPCG beam in the focal region. It is interesting to find that after focusing the CPCG beam through a high numerical-aperture objective we can obtain a super-length optical needle (>12λ) with homogeneous intensity along the propagation axis and wavelength beam size (∼λ). Moreover, the numerical calculations of coherence illustrate that, in the range of full width at half-maximum of the optical needle, for any two of the parallel electric field components of the optical needle the coherence is close to 1, but for any two of orthometric electric field components the value of coherence is between 0.4 and 0.9. Such a non-diffracting optical needle may have potential applications in atom optical experiments, such as in atom traps and atom switches.

Confocal microscopy with a radially polarized focused beam.

Rigorous vectorial focusing theory is used to study the imaging of small adjacent particles with a confocal laser scanning system. We consider radially polarized illumination with an optimized amplitude distribution and an annular lens to obtain a narrower distribution of the longitudinal component of the field in focus. A polarization convertor at the detector side is added to transform radial polarization to linear polarization in order to make the signal detectable with a single mode fiber.

Arbitrarily spin-orientated and super-resolved focal spot.

In this Letter, we propose a facile approach for achieving a robust focal spot bearing both super-resolution and arbitrary spin orientation. Toward this aim, we meticulously devise a structured incident light consisting of three sorts of beams, which can be produced definitely by the superposition of a radially polarized beam and an azimuthally polarized beam. Based on the vectorial diffraction integral and spin density theory, such newly configurable beams are tightly focused and isotropically interfered in a 4π microscopic configuration to create three polarized field components perpendicular to each other beyond the diffraction limit, thus enabling us to yield a super-resolved focal spot possessing spatial spin axis. By further willfully adjusting the amplitude factors of the reconstituent fields, the photonic spin direction can be freely tunable. The demonstrated results in this Letter may hold great potential for the spin photonics.

Electromagnetic exploration of focusing properties of high-numerical-aperture micro-Fresnel zone plates

Focusing properties of high-numerical-aperture micro-Fresnel zone plates (FZP) have been rigorously investigated at the wavelength from deep ultraviolet to visible based on the combination of the vectorial angular spectrum theory and three-dimensional finite-difference time-domain method. New insights are found. The axial spot size evaluated by full-width-at-half-maximum is in direct proportion to the inverse of the total annulus number. Linearly negative focal shift phenomenon can be observed due to the wavelength dispersion over a finite range of tens of nanometers. A proper wavelength deviation can lead to the maximum focal intensity. A simple method has been demonstrated to probe either multi-focus or a light needle using a composite microstructure based on high-NA FZPs. The findings of this study expand the common understandings of the classic widely-used FZPs.

Vectorial nonlinear potential theory

We settle the longstanding problem of establishing pointwise potential estimates for vectorial solutions u\colon \Omega \to \mathbb R^{N} to the non-homogeneous p -Laplacean system -\mathrm{div} (|Du|^{p-2}Du)=\mu \qquad \text{in}\ \Omega \subset \mathbb R^{n}\,, where \mu is a \mathbb R^{N} -valued measure with finite total mass. In particular, for solutions u \in W^{1,1}(\mathbb R^{n}) , the global estimates via Riesz and Wolff potentials |Du(x_0)|^{p-1} \lesssim \int_{\mathbb R^{n}}\frac{d|\mu|(x)}{|x-x_0|^{n-1}} and |u(x_0)|\lesssim {\bf W}^{\mu}_{1, p}(x_0,\infty) = \int_0^\infty \left(\frac{|\mu|(B_\varrho(x_0))}{\varrho^{n-p}}\right)^{1/(p-1)}\, \frac{d\varrho}{\varrho} respectively, hold at every point x_0 such that the corresponding potentials are finite. The estimates allow to give sharp descriptions of fine properties of solutions which are the exact analog of the ones in classical linear potential theory. For instance, sharp characterisation of Lebesgue points of u and Du and optimal regularity criteria for solutions are provided exclusively in terms of potentials.