Radial Polarization Research Articles

The investigation of the features of focusing vortex super-Gaussian beams with a variable-height diffractive axicon

Spatial intensity distributions of the Laguerre-superGauss modes (1,0) as well as a super-Gaussian beam with radial and circular polarization were investigated versus changes in the height of a diffractive axicon. The height of the relief of the optical element varied from 0.25λ to 3λ. The modeling by a finite-difference time-domain method showed that variations in the height of the diffractive axicon significantly affect the diffraction pattern in the near field of the axicon. The smallest focal spot size for a super-Gaussian beam was obtained for radial polarization at a height equal to two wavelengths. The minimum size of the focal spot for the Laguerre-superGauss mode (1,0) was obtained for circular "–" polarization with an element height equal to a quarter of the wavelength.

Formation of polarization-dependent optical vortex beams via an engineered microsphere.

In this work, we propose a method that can realize switchable spatial arrangement of the donut-shaped focusing beams through an engineered microsphere, tuned by changing the polarization state of an incident light. In this polarization-dependent light manipulation, the engineered microsphere is designed and fabricated by focused ion beam (FIB). We simulate and experimentally characterize the focus performance of the engineered microsphere. Under the light incidence with radial polarization, multiple focused donut beams are formed along optical axis. By adding an additional linear polarizer with a rotatable relative angle, the pair of donut beams can be re-arranged in the same transverse plane and stay close to each other. Experimental results and numerical simulation are in good agreement. Such tunable polarization-dependent micro-optics can be used for multiplane imaging applications.

Selection rules for the orbital angular momentum of optically produced THz radiation.

In this work, we theoretically study the transduction of orbital angular momentum (OAM) l for infrared pump lasers into the THz domain. In the case of optical rectification, the transduction of OAM occurs only through a spin-orbit interaction, with the selection rule on the OAM l=0 valid for any kind of polarization of the pump, which means that there is no transfer of OAM along the propagation axis. In difference frequency generation, the selection rule for the difference Δl between the OAM of the pump fields with linear or circular polarization is l=Δl, whereas l ranges from Δl-2 to Δl+2 in cases of both radial and azimuthal polarization. Moreover, for THz generation in the latter case, the high diffraction obtained with tightly focused pumps yields l tending to Δl±2, while l tends to zero in the opposite case of large pump beams.

Exploding paraxial beams, vortex beams, and cylindrical beams of light with finite power in linear media, and their enhanced longitudinal field

We present a set of paraxial light beams with cylindrical symmetry, smooth and localized transversal profile carrying finite power, that develop intensity singularities when they are focused in a linear medium, such as vacuum. They include beams with orbital angular momentum and with radial polarization, in which case they develop punctual phase and polarization singularities surrounded by infinitely bright rings, along with singular longitudinal fields. In practice, these effects are manifested in focal intensities and spot sizes, vortex bright ring intensities and radii, and strengths of the longitudinal field, that strongly change with the lens aperture radius. Continuous control of these focal properties is thus exercised without changing the light incident on the lens, with substantially the same collected power, and while maintaining paraxial focusing conditions. As solutions of the Schr\"odinger equation, these exploding beams have analogues in other areas of physics where this equation is the fundamental dynamical model.

Tight focusing of the centrosymmetric shape of hybrid polarized beams by adjustable multi-vortex phases

We propose an approach for achieving various centrosymmetric shapes by employing hybrid polarized Bessel–Gaussian (HPBG) beams with multi-vortex phases, which are obtained by embedding a few first-order off-axis topological charges into vortices separated by equal arc lengths of a circle. According to the Debye–Wolf electromagnetic diffraction formula (which is routinely used to describe focusing by high numerical aperture optical systems), we investigate the evolution of tightly focused intensity profiles of the HPBG beams with multi-vortex phases (which are the vectorial electric field of radial and azimuthal polarization), by tuning the positional vectors of the embedded vortex phases, the number of vortex phases and the ratio of radial to azimuthal polarization of the hybrid polarization. The simulation results show that the number of vortex phases is equal to the number of vertices of hollow polygons, increasing the magnitude of polar vector leads to deformation of the hollow polygons, and that the ratio of the radial and azimuthal polarization magnitudes affects the edge sharpness of the hollow polygon in the focal plane, respectively. We can produce triangles, squares, pentagons, hexagons, and inner crosses in the central hollow region, and outer crosses, embedded stars and snowflakes by manipulating the numbers and sites of multi-vortex phase singularities. The focusing structures are robust to noise and maintain a limited thickness along the optical axis. These specific intensity profiles are significant for potential applications including the trapping of multiple micro-sized particles, nonlinear optics, optical beam shaping, and optical telecommunication applications.

Transversal flexoelectric coefficient for nanostructures at finite deformations from first principles

We present a novel formulation for calculating the transversal flexoelectric coefficient of nanostructures at finite deformations from first principles. Specifically, we introduce the concept of \emph{radial polarization} to make the coefficient a well-defined quantity for uniform bending deformations. We use the framework to calculate the flexoelectric coefficient for group IV atomic monolayers using density functional theory. We find that graphene's coefficient is significantly larger than previously reported, with a charge transfer mechanism that differs from other members of its group.

Generation of Terawatt Attosecond Pulses from Relativistic Transition Radiation.

When a femtosecond duration and hundreds of kiloampere peak current electron beam traverses the vacuum and high-density plasma interface, a new process, that we call relativistic transition radiation (RTR), generates an intense ∼100 as pulse containing ∼1 terawatt power of coherent vacuum ultraviolet (VUV) radiation accompanied by several smaller femtosecond duration satellite pulses. This pulse inherits the radial polarization of the incident beam field and has a ring intensity distribution. This RTR is emitted when the beam density is comparable to the plasma density and the spot size much larger than the plasma skin depth. Physically, it arises from the return current or backward relativistic motion of electrons starting just inside the plasma that Doppler up shifts the emitted photons. The number of RTR pulses is determined by the number of groups of plasma electrons that originate at different depths within the first plasma wake period and emit coherently before phase mixing.

Simulation study of phase-matched THz emission from an axially modulated magnetized plasma

We studied and demonstrated the emission of THz waves by the beating of two CW-laser beams in an axially modulated plasma in the presence of a static magnetic field (applied transversely to the direction of propagation of lasers) from two-dimensional particle-in-cell simulation. The ponderomotive-force-induced nonlinear current drives THz radiation with frequency close to the beat frequency (Δω = ω1 − ω2) that propagates in the forward direction. Inside the plasma, THz radiation consists of a mixture of linear and radial polarization, while outside the plasma, only linear polarization dominates; however, radial polarization is stronger in the case of unmagnetized plasma. When the ripple is used, several modes are excited and the mode excited at Δk = (k1 − k2) − kq that meets the phase matching condition is resonantly enhanced. The THz field amplitude grows resonantly with time and it becomes saturated due to the excited higher-order mode coupling. The saturation level is reached about five times higher than the nonrippled plasma case in the vacuum side.

Flexoelectric-like radial polarization of single-walled nanotubes from first-principles

Flexoelectricity is the polar response of an insulator to strain gradients such as bending. While the size dependence makes it weak in bulk systems in comparison to piezoelectricity, it can play a bigger role in nanoscale systems such as thin films and nanotubes (NTs). In this paper we demonstrate using first-principles calculations that the walls of carbon nanotubes (CNTs) and transition metal dichalcogenide nanotubes (TMD NTs) are polarized in the radial direction, the strength of the polarization increasing as the size of the NT decreases. This is reminiscent of a flexoelectric response in bulk insulators, the strain gradient being achieved by bending the 2D monolayers into NTs. For CNTs and TMD NTs with chiral indices (n, m), the radial polarization of the walls P R diverges below , where C(n, m) is the circumference and a is the monolayer lattice constant. For CNTs, P R drops to zero above this value but for TMD NTs there is a non-zero polarization, which is ionic rather than electronic. The size dependence of P R in the TMD NTs is interesting: it increases gradually and reaches a maximum of P R ∼ 100 C cm−2 at C(n, m)/a ∼ 15, then decreases until C(n, m)/a ∼ 10 where it starts to diverge. Measurements of the radial strain on the bonds with respect to the monolayers shows that this polarization is the result of a larger strain on the outer bonds than the inner bonds, but did not explain the peculiar size dependence. These results suggest that while the walls of smaller CNTs and TMD NTs are polarized, the walls of larger TMD NTs are also polarized due to a difference in strain on the inner and outer bonds.

Tailoring multi-singularity structure induced by a focused radially polarized beam

A structured optical field with controllable three-dimensional intensity and multiple polarization singularities is demonstrated by utilizing a combination of a radially polarized (RP) beam, a designed phase mask, and a high numerical aperture lens. Owing to the tight focusing property of RP beams as well as the interference of multiple linearly polarized non-coplanar plane waves, various lattice-like optical structures can emerge at the focal plane with multiple structured singularities in the transverse plane and optical needle array along with propagation. Compared with recently proposed phase and polarization engineering methods with spatial light modulators, the method presented here is convenient and flexible, and can easily realize the generation of V-point and C-point lattices. More importantly, a structured longitudinal field, namely, an optical needle array, with steerable positive and reverse energy flows may be extensively applied in multi-particle acceleration and trapping, optical microscopes, and second-harmonic generation.

Tunable mode-locked fiber laser to generate ultrashort cylindrical vector beams

In this work, we report a tunable mode-locked fiber laser that can produce ultrashort laser pulses with polarization vortex. Two vortex wave plates (VWPs) are employed in this laser to convert the intracavity beam states between the Gaussian mode and cylindrical vector mode. By adjusting the angle between a diffraction grating and the light beam in the cavity, the center wavelength of the mode-locked pulse can be tuned from 1015 nm to 1030 nm. Mode-locked pulses with full width at half maximum of 1.51 ps with the maximum single pulse energy of 2.2 nJ have been obtained. Through synchronously adjusting the orientations of the two VWPs, the output mode can be switched between radial polarization and azimuthal polarization states. The output vortex pulse from the tunable mode-locked fiber laser may find many applications such as optical manipulation, imaging and laser micro-machining.

Sub-7 fs radially-polarized pulses by post-compression in thin fused silica plates.

We experimentally demonstrate the post-compression of radially polarized 25 fs pulses at 800 nm central wavelength in a multiple thin plate arrangement for the first time, to the best of our knowledge. Sub-7 fs pulses with 90 µJ energy were obtained after dispersion compensation, corresponding to a compression factor of more than 3.5. Preservation of radial polarization state was confirmed by polarized intensity distribution measurements. Linear projections of the radially polarized pulses were also fully characterized in the temporal domain.

Scattering of a high-order vector Bessel Gaussian beam by a spherical marine aerosol

Based on the generalized Lorenz-Mie theory (GLMT) and the angular spectrum decomposition method (ASDM), we derive the beam shape coefficients (BSCs) of high-order vector Bessel Gaussian beams (H-VBGB), and investigate the interaction mechanism of H-VBGB illuminating a spherical marine aerosol. Linear (x, y), circular (left, right), azimuthal and radial polarizations are considered. The effects of various parameters characterizing the incident beam and the aerosol on the normalized differential scattering cross section (DSCS) are investigated. Numerical results show that the normalized DSCS is very sensitive to fluctuations in the parameters, and that the distinctions of incident beams may highly influence results. The relative humidity of aerosol performs similar effects on results for all polarizations, so it is not feasible to recognize the relative humidity of aerosol environment by using the differences of normalized DSCS for various polarization states. We provide a reference for the practical use of the scattering features of non-diffractive beams illuminating spherical calibrators.

Statistical properties of a return wave generated from an arbitrary rough target in atmospheric turbulence by a partially coherent beam with radial polarization

The interaction of a radially polarized partially coherent beam with an arbitrary rough target embedded in a bi-static LIDAR system in the presence of atmospheric turbulence was illustrated. The target could modelled as a combination of a Goodman-like thin random phase screen and a Gaussian lens. Within the framework of paraxial approximation, the analytical formulas for the cross-spectral density matrix elements of the beam at the source plane, at the target plane, just after the target and at the receiver plane were derived. It was found that the statistical properties of the return wave were dependent not only upon the transverse correlation width of the target, but also on the turbulence. In addition, it was possible to predict the target type by measuring the spectrum and polarization properties of the return beam in the receiver plane.

Polarization-insensitive, high-gain parametric amplification of radially polarized femtosecond pulses

Radially polarized lasers, in contrast to the conventional Gaussian laser mode, possess unique features such as sharp focusing and strong longitudinal fields. Thus far, radially polarized femtosecond pulses have been produced only by low-power devices such as mode-locked resonators and segmented half-wave plates. It is imperative to solve the bottleneck problem in generating higher powers and shorter durations. This paper reports on a polarization-insensitive, high-gain optical parametric amplifier for radially polarized femtosecond pulses, which works at type-II phase-matching and approximately degenerate wavelength. We experimentally demonstrate > --> 1000 -fold amplification of radially polarized ∼ 400 f s pulses at 1610 nm, via chirped ∼ 280 f s pumping at 800 nm, with the axially symmetric intensity profile and radial polarization state both being well-maintained within a 20 nm spectral range. With currently available high-energy picosecond pumping, the demonstrated amplification scheme will be promising to create radially polarized femtosecond pulses with ultrahigh powers and may facilitate future applications such as strong-field physics.

Dynamic control of magnetization spot arrays with three-dimensional orientations.

We report a new paradigm for achieving magnetization spot arrays with controllable three-dimensional (3D) orientations. Toward this aim, we subtly design a tailored incident beam containing three parts and further demonstrate that the designed incident beam is phase-modulated radial polarization. Based on the raytracing model under tight focusing condition and the inverse Faraday effect on the magneto-optic (MO) film, the magnetization field components along the y-axis and z-axis directions are generated through the focus. In particular, we are able to garner orientation-tunable 3D magnetization under different numerical apertures of the focusing objectives by adjusting the ratios between the three parts of incident beam. Apart from a single magnetization spot, magnetization spot arrays capable of dynamically controlling 3D orientation in each spot can also be achieved by multi-zone plate (MZP) phase filter. Such a robust magnetization pattern is attributed to not only the constructive interferences of three orthogonal focal field components, but also the position translation of each magnetization spot resulting from shifting phase of the MZP phase filter. It is expected that the research outcomes can be beneficial to spintronics, magnetic encryption and multi-value MO parallelized storage.

LIPSS-covered annular ablation region induced on ZnO surface by focusing femtosecond laser beam spatially shaped by bubbles in cedar oil

In this paper, without circular scanning of laser focus, annular ablation region was reported to be induced by femtosecond laser static irradiation of ZnO surface immersed in oil, and these annular ablation regions were all covered by laser-induced periodic surface structures (LIPSS) upon irradiation of either linearly-polarized light or circularly-polarized light. This novel phenomenon was found to be related to the bubbles in-situ generated and attached at laser focus inside oil during irradiation process. With increasing irradiation pulse number, the shallow annular ablation region transited to a deep annular groove, and the unablated region surrounded by the annular ablation region was finally ablated to a LIPSS-covered spherical-crown-shaped bump. Finite-difference-time-domain (FDTD) simulation shows that the bubble at the laser focus may act as a beam shaping device to partly transform a Gaussian-intensity-profile beam to an annular-intensity-profile beam and the increased bubble size induces a decrease of the radius of the annular beam, which can roughly explain the experimentally observed morphology transformation phenomenon. Further analysis of light field transformation based on matrix optics further demonstrates that the annular intensity profile is originated from hollow beams generated after incident light passing through the bubble-type radial polarizer.

Comparison of Transition rates with the LG (0, 1)* spiral-phase mode field distribution in the frame of three ionization theories

We discussed the tunneling ionization of an Argon atom placed in a strong low-frequency field of Ti: Sapphire laser. The transition rate of the electron obtained with radial polarization LG (0, 1)* spiral-phase mode field distribution included are compared to the basic transition rate. All analyses are given in the frame of the three different ionization theories-Keldysh, PPT, and ADK. We demonstrated that the tunneling transition rate is sensitive to laser polarization and a set field distribution. As well as changes in the azimuthal angle as a parameter on which the given distribution depends.

Few Percent Efficient Polarization-Sensitive Conversion in Nonlinear Plasmonic Interactions Inside Oligomeric Gold Structures.

The backscattering spectra of a 500 nm thick gold film, which was excited near the 525 nm transverse localized plasmon resonance of its constituent, self-organized, vertically-aligned nanorods by normally incident 515 nm, 300 fs laser pulses with linear, radial, azimuthal and circular polarizations, revealed a few-percent conversion into Stokes and anti-Stokes side-band peaks. The investigation of these spectral features based on the nanoscale characterization of the oligomeric structure and numerical simulations of its backscattering response indicated nonlinear Fano-like plasmonic interactions, particularly the partially degenerate four-wave mixing comprised by the visible-range transverse plasmon resonance of the individual nanorods and an IR-range collective mode of the oligomeric structure. Such oligomeric structures in plasmonic films may greatly enhance inner nonlinear electromagnetic interactions and inner near-IR hotspots, paving the way for their engineered IR tunability for broad applications in chemosensing and biosensing.

Mueller Matrix Polarimetric Imaging Analysis of Optical Components for the Generation of Cylindrical Vector Beams

In this work, we performed a Mueller matrix imaging analysis of two commercial optical components usually employed to generate and manipulate vector beams—a radial polarizer and a liquid-crystal q-plate. These two elements generate vector beams by different polarization mechanisms—polarizance and retardance, respectively. The quality of the vector beams relies on the quality of the device that generates them. Therefore, it is of interest to apply the well-established polarimetric imaging techniques to evaluate these optical components by identifying their spatial homogeneity in diattenuation, polarizance, depolarization, and retardance, as well as the spatial variation of the angles of polarizance and retardance vectors. For this purpose, we applied a customized imaging Mueller matrix polarimeter based on liquid-crystal retarders and a polarization camera. Experimental results were compared to the numerical simulations, considering the theoretical Mueller matrix. This kind of polarimetric characterization could be very helpful to the manufacturers and users of these devices.