Longitudinal Component Of Electric Field Research Articles

Customizing subwavelength stochastic light fields via structured spatial coherence in a high-NA resonator

Interaction of light in the high-numerical aperture (high-NA) systems is crucial for theoretical advances and applications such as superresolution imaging and optical nanofabrication. High coherence is demanded at this scale for intensity and spin profile sculpturing, since the underlying physics being wave interference. Here we report that, even for low-coherence light, 3D light features in a nanometer range can be generated by employing structured coherence states of the light beam in a high-NA resonator system. The generated structures, e.g., 3D helix intensity and transverse spin texture, can survive in rather incoherent optical fields at nanoscale. We also found that, counterintuitively, despite the substantial decrease in spatial coherence of the light field, the longitudinal electric field component and transverse spin density are instead enhanced. The applications of the observed twisted spectral density and spin structures may range from high-resolution imaging to metrology.

A new ER valve composed of multilayer mesh electrodes

In many cases, ER valves are required to be used at lower operating voltages. For example, to develop a two-dimensional Braille matrix display, it is necessary to lay out many ER valves and control each Braille dot independently. If the commonly used parallel plate electrodes are applied, a low voltage can only be used when the electrode gap is very small, which will make the ER valve flow resistance very large, thus making it difficult to achieve effective control. A new type of ER valve composed of multilayer mesh electrodes was designed, which are arranged vertically in the direction of ER fluid flow. The flow rate of the ER valve is determined by the opening ratio of the mesh electrodes. This type of mesh electrode results in a more complex electric field distribution, which has a different action pattern on ER fluid yield stress compared to parallel electrodes. The non-uniform electric field generated by mesh electrodes under different operating voltages was simulated using COMSOL software, and the pressure drops of ER valves with various sizes of mesh electrodes under different voltages were experimentally investigated. The results indicate that the longitudinal electric field component plays a dominant role, and the stress of the ER fluid exhibits a periodic and gradient distribution. This valve exhibits good ER performance when the applied voltage is much lower than that of parallel electrodes. At the same time, the flow rate of the ER valve can be increased by enlarging the opening ratio of the mesh electrodes. Even if the applied voltage is 180 V, the pressure drop of the ER valve is large enough and the operation stability is good. This new type of ER valve makes the device small in size, easy to control intelligently and low cost. Multilayer mesh electrodes also have universal application value in ER technology.

Vectorial characterization of surface wave via one-dimensional photonic-atomic structure

Quantitative assessment of polarization properties of waves opens up the way for effective exploitation of them in many amazing applications. Tamm surface waves (TSW) that propagate on the interface of periodic dielectric media are proposed for many applications in numerous reports. The polarization state of TSW is not simply intuitive and would not be extracted from reflection spectra. Here considering orientation sensitive nature of the interaction between polarized electromagnetic wave and atom, we try to quantitatively characterize the polarization state of TSWs, excited on the surface of the 1D photonic crystal. To do this we performed direct contact between TSW and rubidium atomic gas by fabrication of a one-dimensional photonic crystal-atomic vapor cell and applied a moderate external magnetic field to create geometrical meaning and a sense of directionality to dark lines in reflection intensity. Our experimental results indicate that transition lines in the reflection spectrum of our hybrid system modify dependent on the orientation of the applied magnetic field and the transverse spin of TSW. We have used these changes to redefine the geometry of Voigt and Faraday for evanescent waves, especially Tamm surface waves. In the end, we performed simple mathematical operations on absorption spectra and extract the ratio of longitudinal and transverse electric field components of the polarization vector of TSW equal to 25\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\frac{2}{5}$$\\end{document}.

Optical dipole potential energy of a two-level atom interacting with a tightly focused truncated optical Bessel beam

Truncated optical Bessel (TOB) beams are an orthonormal set of optical vortex beams that possess orbital angular momentum (OAM). It is characterized by a significant longitudinal electric field component at the sub-wavelength scales. The photons of a circularly polarized TOB beam also carry spin angular momentum (SAM) and can interact with a two-level atom, in the far-off resonance regime, giving rise to an optical dipole potential energy that involves a spin–orbit term that stems from the inclusion of the longitudinal field component. When a two-level atom is simultaneously irradiated by two TOB beams, the optical dipole potential energy, in some special cases, is entirely dependent on the OAM–SAM coupling. We explore the cold-atom trapping options enabled by the use of TOB beams, either single ones or combinations thereof. We put emphasis on case in which the OAM–SAM coupling is the dominant contribution. The similarities and differences between the results obtained for the TOB beams and those for the Laguerre–Gaussian beams are also discussed.

Dual channel transformation of scalar and vector terahertz beams along the optical path based on dielectric metasurface

Abstract The research on terahertz wave manipulation based on metasurfaces has gradually deepened, and the number of functions or electromagnetic control dimensions in a single device is constantly increasing. For the spatial dimension of terahertz field regulation, its design degrees of freedom have been expanded from a single transverse plane to the propagation path. In this paper, we propose a novel circularly polarization multiplexed metasurface for dual channel terahertz wave transmission control. Based on the spatial integration of two heterogeneous meta-atoms, which are spin-decoupled and isotropic, respectively, there are four phase channels that can be used at the same time, thus achieving different switching between vector and scalar beams in different circularly polarization channels along the optical path. For linearly polarized wave incidence, the device exhibits conversion between different vector beams longitudinally. To control more electric field components, we combine focused wavefront design with vector or scalar fields and utilize the focusing induced spin–orbit coupling effect, then complex amplitude switching of longitudinal electric field components is obtained. This article extends the manipulation of terahertz waves along the propagation trajectory based on metasurface from single to dual channel for the first time, providing a reference for the design of multifunctional meta-device in terahertz band.

Focusing of Radially Polarized Electromagnetic Waves by a Parabolic Mirror

It is well-known that a strong longitudinal electric field and a small spot size are observed when radially polarized beams are tightly focused using a high numerical aperture parabolic mirror. The longitudinal electric field component can accelerate electrons along the propagation axis at high intensities in the focal region, which opens an application in particle acceleration. In this paper, we present a rigorous derivation of the electric field obtained when a radially polarized, monochromatic, flat-top beam is focused by a parabolic mirror. The formulae were deduced from the Stratton–Chu integral known from vector diffraction theory. We examined the influence of the focusing parameters on the distribution of both the longitudinal and radial electric field components. In the small numerical aperture and short wavelength regimes, excellent agreement was found with the results obtained from the Rayleigh–Sommerfeld formula. The calculation method can be adapted for various beam types and for electromagnetic pulses as well.

Angular momentum-carrying radially-polarised twisted light

It is well-known that the fields of pure radially-polarised optical vortex modes do not possess the usual phase function eiℓϕ of typical twisted light and so they do not carry angular momentum. However, recent work has confirmed that radially-polarised modes with helical wave fronts have been created in the laboratory by several groups and they can now be readily generated using commercially available devices. They are endowed with the phase function eiℓϕ for arbitrary values of the winding number ℓ. Crucially, the original theoretical treatments disregard the longitudinal electric and magnetic field components. We show here that the longitudinal components must be included, not just for the consistency of the treatment, but because only this can lead to angular momentum. We show that for such created modes the cycle-averaged angular momentum is αħℓ where α=(Pw02)/(ħc2) is a dimensionless constant, with P the power in the mode and w0 the mode width at focus.

Longitudinal motion of focused shear wave beams in soft elastic media.

Shear waves are employed in medical ultrasound imaging because they reveal variations in viscoelastic properties of soft tissue. Frequencies below 1 kHz are required due to the substantially higher attenuation and lower propagation speeds than for compressional waves. Shear waves exhibiting particle motion in the direction of propagation, referred to as longitudinal shear waves, can be generated with longitudinal motion of a circular disk on the surface of a soft elastic medium. This approach permits imaging of the longitudinal shear wave with a conventional ultrasound transducer that is coaxial with the source of the shear wave. Presented here is a mathematical model describing the complete wave field generated by displacement at the surface of an isotropic elastic half-space. Numerical simulations are shown for longitudinal, transverse, torsional, and radial source polarizations, with emphasis on focused longitudinal shear waves. Predictions are consistent with measurements of light beams revealing that the longitudinal electric field component produces a smaller focal spot than the transverse field component [Dorn, Quabis, and Leuchs, Phys. Rev. Lett. 91, 233901 (2003)]. Simulations are compared with preliminary measurements of a focused longitudinal shear wave beam generated in a soft tissue phantom by longitudinal motion of a spherically concave piston.

Surface excitation of focused shear wave beams in soft elastic media: Theory

Shear wave propagation is employed in medical ultrasound imaging, because it reveals variation in the viscoelastic properties of tissue. Frequencies below 1 kHz are required for imaging with shear waves in soft tissue due to their high attenuation and low propagation speeds, compared to compressional waves with frequencies above 1 MHz used for ultrasound imaging. Shear waves exhibiting particle motion in the direction of propagation, referred to as longitudinally polarized shear waves, can be generated by applying longitudinal motion of a circular disk to the surface of a soft elastic medium. This approach is used in practice because it permits imaging of the longitudinal shear wave with a conventional ultrasound transducer that is coaxial with the source of the shear wave. Presented here are the theoretical framework and numerical simulations that illustrate effects of focusing on longitudinally polarized shear waves. Longitudinal, transverse, radial, and torsional source polarizations are considered. The present investigation was motivated initially by an experimental study in optics due to Dorn et al. [Phys. Rev. Lett. 91, 233901 (2003)]. Our predictions for shear wave beams support their measurements of light beams revealing that the longitudinal electric field component produces a smaller focal spot than the transverse field component.

Fundamental Studies on Electron Dynamics in Exact Paraxial Beams with Angular Momentum

Classical electromagnetic radiation with orbital angular momentum (OAM), described by nonvanishing vector and scalar potentials (namely, Lorentz gauge) and under Lorentz condition, is considered. They are employed to describe paraxial laser beams, thereby including non-vanishing longitudinal components of electric and magnetic fields. The relevance of the latter on electron dynamics is investigated in the reported numerical experiments. The lowest corrections to the paraxial approximation appear to have a negligeable influence in the regimes treated here. Incoherent Thomson scattering (TS) from a sample of free electrons moving subject to the paraxial fields is studied and investigated as a beam diagnosis tool. Numerical computations elucidate the nature and conditions for the so called trapped solutions (electron motions bounded in the transverse plane of the laser and drifting along the propagation direction) in long quasi-steady laser beams. The influence of laser parameters, in particular, the laser beam size and the non-vanishing longitudinal field components, essential for the paraxial approximation to hold, are studied. When the initial conditions of the electrons are sufficiently close to the origin, a simplified model Hamiltonian to the full relativistic one is introduced. It yields results comparing quite well quantitatively with the observed amplitudes, phase relationships and frequencies of oscillation of trapped solutions (at least for wide laser beam sizes). Genuine pulsed paraxial fields with OAM and their features, modeling true ultra-short pulses are also studied for two cases, one of wide laser beam spot (100 μm) and other with narrow beam size of 6.4 μm. To this regard, the asymptotic distribution of the kinetic energy of the electrons as a function of their initial position over the transverse section is analyzed. The relative importance of the transverse structure effects and the role of longitudinal fields is addressed. By including the full paraxial fields, the asymptotic distribution of kinetic energy of an electron population distributed across the laser beam section, has a nontrivial and unexpected rotational symmetry along the optical propagation axis.

Structure of transverse spin in focused random light

We analyze the spin structure of weakly and tightly focused random light beams in view of the characteristic decomposition of the $3\ifmmode\times\else\texttimes\fi{}3$ polarization matrix. We take the incident beam to be a mixture of mutually uncorrelated, orthogonally linearly polarized parts which entails zero spin for the beam but leads to a nonzero purely transverse spin in focusing via the generation of a longitudinal electric-field component. We show that the spin ensuing from the so-called discriminating component of the polarization matrix displays a vortex structure for any degree of polarization and level of focusing, while the spin distribution of the pure component may vary from linear to circular as the incident beam changes from fully polarized to completely unpolarized. The spin of the discriminating component is related to the recently introduced concept of polarimetric nonregularity and emerges only when the degree of nonregularity is different from zero. Our results demonstrate the relationship between the rich polarimetric structure of random three-component light and the composition of the optical electric-field spin.

Spatiotemporal delay in photoionization by polarization-structured laser fields

Focused laser fields with textured polarization on a subwavelength scale allow extracting information on electronic processes which are not directly accessible by homogeneous fields. Here we consider photoionization in radially and azimuthally polarized laser fields and show that, due to the local polarizations of the transversal and the longitudinal laser electric field components, the detected photoelectron spectra depend on the atom position from which the electron originates. The calculation results show the angular dependence of the photoionization amplitude, the quantum phase, and the time delay of the valence shell electrons as the parent atom's position varies across the laser spot. We discuss the possibility of using the photoelectron spectra to identify the position of the ionized atom within the laser spot on the subwavelength scale. The proposal and its illustrations underline the potential for the detection of the atomic position based on attosecond streaking methods.

Surface plasmon polaritons of higher-order mode and standing waves in metallic nanowires.

The surface plasmon polaritons (SPPs) of higher-order mode propagating along a plasmonic nanowire (NW) or an elongated nanorod (NR) are studied theoretically. The dispersion relations of SPPs in NWs of different radii, obtained from a transcendental equation, show that the propagation lengths of SPPs of mode 1 and 2 at a specific frequency are longer than that of mode 0. For the higher-order mode, the spatial phase of the longitudinal component of electric field at a cross section of a NW exhibits the topological singularity, which indicates the optical vortex. Of importance, the streamlines of Poynting vector of these SPPs exhibit a helical winding along NW, and the azimuthal component of orbital momentum density exists in the nearfield of NW to produce a longitudinal orbital angular momentum (OAM). Two types of standing wave of counter-propagating SPPs of mode 1 and 2 are also studied; they perform as a string of beads or twisted donut depending on whether the handedness of two opposite-direction propagating SPPs is same or opposite. In addition, a SPP of mode 1 propagating along an elongated NR can be generated by means of an end-fire excitation of crossed electric bi-dipole with 90° phase difference. If the criterion of a resonator for a mode-1 standing wave (string of beads) is met, the configuration of a plasmonic NR associated with a pair of bi-dipoles with a phase delay (0° or 180°) at the two ends can be applied as a high-efficiency nanoantenna of transmission. Our results may pave a way to the further study of SPPs of higher-order mode carrying OAM along plasmonic waveguides.

Euler\u2013Heisenberg waves propagating in a magnetic background

We derive the Euler–Heisenberg solutions that describe electromagnetic waves propagating through very intense uniform magnetic or electric background, with the effective metric approach. We first explore the case of a magnetic background: as a result of the interaction between the wave and the background there is birefringence and a longitudinal electric field component arises. The two phase velocities depend on the intensity of the external magnetic field and on the polarization of the wave; phase velocities can be slowed down up to the order of hundred thousandths for fields B/B_mathrm{cr}<< 1. The analogous study is done when the wave propagates through a uniform electric field. We then consider the situation when the background is in movement by means of a Lorentz boost, modeling then a magnetized flowing medium. We determined how this motion affects the speed of propagation of the electromagnetic wave, in this case the phase velocities depend on both the magnetic background and the direction and velocity of the boost.

Chirality-enabled optical dipole potential energy for two-level atoms

We consider the optical dipole potential energy, which arises from the interaction of a two-level atom with a circularly polarized Laguerre-Gaussian laser beam of small waist. The beam is characterized by the existence of a longitudinal electric field component which is responsible for the appearance of a chiral term in the optical dipole potential energy. This term reverses sign if either the winding number or the wave polarization of the beam reverses sign. We propose a scheme of a bi-chromatic vortex interaction with the two-level atom in which the resulting optical dipole potential is fully chiral.

Influence of longitudinal mode components on second harmonic generation in III-V-on-insulator nanowires.

The large index contrast and the subwalength tranverse dimensions of nanowires induce strong longitudinal electric field components. We show that these components play an important role for second harmonic generation in III-V wire waveguides. To illustrate this behavior, an efficiency map of nonlinear conversion is determined based on full-vectorial calculations. It reveals that many different waveguide dimensions and directions are suitable for efficient conversion of a fundamental quasi-TE pump mode around the 1550 nm telecommunication wavelength to a higher-order second harmonic mode.

Second-harmonic generation enabled by longitudinal electric-field components in photonic wire waveguides

We investigate type I second harmonic generation in III-V semiconductor wire waveguides aligned with a crystallographic axis. In this direction, because of the single nonzero tensor element of III-V semiconductors, only frequency conversion by mixing with the longitudinal components of the optical fields is allowed. We experimentally study the impact of the propagation direction on the conversion efficiency and confirm the role played by the longitudinal components through the excitation of an antisymmetric second harmonic higher order mode.

Field Coupling to Transmission Line Model Accounting for the Effect of Dielectric Coatings

This article proposed a modified electromagnetic field coupling to transmission line (TL) model with the objective to accounting for the impact of complex dielectric coatings. Classic TL model neglects the perturbation effects of coatings on the incident electric field; the validation of this simplification is disproved in this article for TL structure with complex dielectric coatings. Through analysis, it is corroborated that coating effect could be neglected only for longitudinal electric field component, whereas the perturbation on transverse field component needs to be taken into account by a newly introduced parameter called coating coefficient. The proposed method is verified through a case study on a differential line system, where a simulation method based on the 2-D finite element method is also proposed to evaluate the value of the coating coefficient.

A Novel Chevron-Shape Double-Staggered Grating Waveguide Slow Wave Structure for Terahertz Traveling Wave Tubes

A novel slow wave structure (SWS), called the chevron-shaped double-staggered grating waveguide structure, is proposed for traveling wave tube (TWT) amplifier for the terahertz (THz) region. The potential of this SWS is that it provides higher interaction impedance and has low phase velocity; thus, higher output power can be expected at a lower beam voltage. The electromagnetic characteristics and particle-in-cell (PIC) large-signal simulations were performed with CST Microwave Studio software. The SWS was optimized for the central frequency of 200 GHz, which synchronizes with a beam voltage of 18.8 kV in the second spatial harmonic ( ${2}\pi -{3}\pi $ ). A sheet electron beam with a current density of ${133}~\text {A/cm}^{{2}}$ was used to excite the structure, which interacts with the longitudinal electric field component to provide gain. The reflection coefficient at the port interface is less than −15 dB over the frequency range 181–220 GHz, and a small-signal gain of 30.98 dB is achieved for a tube length of 60 mm.

Floquet engineering of interlayer couplings: Tuning the magic angle of twisted bilayer graphene at the exit of a waveguide

We introduce a new approach that allows one complete control over the modulation of the effective twist angle change in few-layer van der Waals heterostructures by irradiating them with longitudinal waves of light at the end of a waveguide. As a specific application, we consider twisted bilayer graphene and show that one can tune the magic angles to be either larger or smaller, allowing in-situ experimental control of the phase diagram of this and other related materials. A waveguide allows one to circumvent the free-space constraints on the absence of longitudinal electric field components of light. We propose to place twisted bilayer graphene at a specific location at the exit of a waveguide, such that it is subjected to purely longitudinal components of a transverse magnetic modes (TM) wave.