In-plane Component Of Electric Field Research Articles

Revealing local structural properties of an atomically thin MoSe2 surface using optical microscopy

Using a triangular molybdenum diselenide (MoSe2) flake as surface-enhanced Raman spectroscopy (SERS) platform, we demonstrate the dependency of the Raman enhancement on laser beam polarization and local structure using copper phthalocyanine (CuPc) as probe. Second harmonic generation (SHG) and photoluminescence spectroscopy and microscopy are used to reveal the structural irregularities of the MoSe2 flake. The Raman enhancement in the focus of an azimuthally polarized beam, which possesses exclusively an in-plane electric field component is stronger than the enhancement by a focused radially polarized beam, where the out-of-plane electric field component dominates. This phenomenon indicates that the face-on oriented CuPc molecules strongly interact with the MoSe2 flake via charge transfer and dipole–dipole interaction. Furthermore, the Raman scattering maps on the irregular MoSe2 surface show a distinct correlation with the SHG and photoluminescence optical images, indicating the relationship between local structure and optical properties of the MoSe2 flake. These results contribute to understand the impacts of local structural properties on the Raman enhancement at the surface of the 2D transition-metal dichalcogenide.

Spatially confined vector fields at material-induced resonances in near-field-coupled systems.

Local electric fields play the key role in near-field optical examinations and are especially appealing when exploring heterogeneous or even anisotropic nano-systems. Scattering-type near-field optical microscopy (s-SNOM) is the most commonly used method applied to explore and quantify such confined electric fields at the nanometer length scale: while most works so far did focus on analyzing the z-component oriented perpendicular to the sample surface under p-polarized tip/sample illumination only, recent experimental efforts in s-SNOM report that material resonant excitation might equally allow to probe in-plane electric field components. We thus explore this local vector-field behavior for a simple particle-tip/substrate system by comparing our parametric simulations based on finite element modelling at mid-IR wavelengths, to the standard analytical tip-dipole model. Notably, we analyze all the 4 different combinations for resonant and non-resonant tip and/or sample excitation. Besides the 3-dimensional field confinement under the particle tip present for all scenarios, it is particularly the resonant sample excitations that enable extremely strong field enhancements associated with vector fields pointing along all cartesian coordinates, even without breaking the tip/sample symmetry! In fact, in-plane (s-) resonant sample excitation exceeds the commonly-used p-polarized illumination on non-resonant samples by more than 6 orders of magnitude. Moreover, a variety of different spatial field distributions is found both at and within the sample surface, ranging from electric fields that are oriented strictly perpendicular to the sample surface, to fields that spatially rotate into different directions. Our approach shows that accessing the full vector fields in order to quantify all tensorial properties in nanoscale and modern-type materials lies well within the possibilities and scope of today's s-SNOM technique.

Essential differences between TE and TM band gaps in periodic films at the first Bragg condition.

In photonic lattices with thin-film geometry, TE modes possess an in-plane electric field component parallel to the film surface, whereas TM modes have a magnetic field component similarly oriented. This study reports the essential properties of, and differences between, TE and TM band gaps induced by laterally periodic thin-film photonic lattices at the first Bragg condition. Because TE and TM guided waves obey different wave equations, TE and TM band gaps exhibit different evolution as the film thickness varies. The first TM band exhibits both band gap closure and band flips wherein the symmetry properties of the band-edge modes are reversed by variation of film thickness. In the first TE band, in contrast, there is neither band gap closure nor band flip. The work provides an insightful semianalytical formulation whose results are verified by rigorous computations.

Large Near-Field Enhancement in Terahertz Antennas by Using Hyperbolic Metamaterials with Hole Arrays

Terahertz antennas can greatly enhance the near fields and enable strong light–matter interactions, and thus have been widely used in applications such as terahertz sensing and detection. Here we propose a novel approach to further enhance the near fields in terahertz antennas. We show that by sandwiching hyperbolic metamaterials that are composed of InSb and SiO 2 multilayer and that are dressed with hole arrays, between a terahertz dipole antenna and the substrate, the near-field electric field intensities in the antenna can be further enhanced by more than three times. Simulations reveal that this enhancement originates from the doubly enhanced in-plane electric field component and the significantly enhanced out-of-plane electric field component. We expect this work will advance the design of terahertz antennas that are widely used in sensors and detectors.

Plasmonic mode conversion in individual tilted 3D nanostructures.

We investigate mode conversion in 3D asymmetric nanocones using angle-dependent linear optical spectroscopy and second-harmonic generation microscopy supported by corresponding simulations. The results prove the efficient excitation of the plasmonic out-of-plane mode that enhances the electric near-field at the sharp tip. Furthermore, we introduce two advanced fabrication processes including either etch mask transfer by tilted etching into a metallic layer or tilted electron-beam lithography followed by tilted evaporation and lift-off. These processes enable the fabrication of tilted nanostructures which can be optimized for a given purpose. The combination of the optical properties and the introduced fabrication processes enables a new design of plasmonic nanostructures for ultra-compact sensors or photon sources.

Near-field observation of a surface-plasmon wave interacting with a three-dimensional wedge-shaped structure

We experimentally investigate the near field of a surface-plasmon wave that is interacting with a three-dimensional wedge-shaped resist structure using phase resolved near-field scanning optical microscopy. Upon entering the resist structure the surface-plasmon wave is exposed to a continuously increasing effective refractive index. As a consequence the dispersion relation of the surface plasmon varies accordingly. Similar to the shoaling of tsunami waves that are entering shallow water, the wavelength and the group velocity of the surface plasmon are reduced while the in-plane electric field component simultaneously increases. We provide measurements, simulations, and a theoretical analysis of the described behavior.

Layerwise mixed models for analysis of multilayered piezoelectric composite plates using least-squares formulation

This work provides an assessment of layerwise mixed models using least-squares formulation for the coupled electromechanical static analysis of multilayered plates. In agreement with three-dimensional (3D) exact solutions, due to compatibility and equilibrium conditions at the layers interfaces, certain mechanical and electrical variables must fulfill interlaminar C0 continuity, namely: displacements, in-plane strains, transverse stresses, electric potential, in-plane electric field components and transverse electric displacement (if no potential is imposed between layers). Hence, two layerwise mixed least-squares models are here investigated, with two different sets of chosen independent variables: Model A, developed earlier, fulfills a priori the interlaminar C0 continuity of all those aforementioned variables, taken as independent variables; Model B, here newly developed, rather reduces the number of independent variables, but also fulfills a priori the interlaminar C0 continuity of displacements, transverse stresses, electric potential and transverse electric displacement, taken as independent variables. The predictive capabilities of both models are assessed by comparison with 3D exact solutions, considering multilayered piezoelectric composite plates of different aspect ratios, under an applied transverse load or surface potential. It is shown that both models are able to predict an accurate quasi-3D description of the static electromechanical analysis of multilayered plates for all aspect ratios.

Photogalvanic current in a double quantum well

We study the in-plane stationary current caused by phototransitions between the states of a double quantum well. The electric polarization of light has both vertical and in-plane components. The stationary current originates from the periodic vibration of electrons between two non-equivalent quantum wells caused by the normal component of the alternating electric field with simultaneous in-plane acceleration/deceleration by the in-plane component of electric field. The quantum mechanism of the stationary current is conditioned by in-plane transition asymmetry which appears due to the indirect phototransitions with the participation of impurity scattering. The photocurrent has a resonant character corresponding to the equality of the photon energy to the distance between subbands. It is found that the current appears as a response to the linear-polarized light.

Photogalvanic current in a parabolic well

We study the in-plane stationary photocurrent in a parabolic potential well. The well has vertical asymmetry due to inhomogeneous distribution of scatterers. The electric field of light has both vertical and in-plane components. The photogalvanic effect originates from the periodic oscillation of electrons in a vertical direction caused by the normal component of the alternating electric field with simultaneous in-plane acceleration/deceleration by the in-plane component of electric field. The problem is considered in classical approximation assuming inhomogeneously-distributed friction. Photocurrent has a resonance character. Resonance occurs at light frequencies close to a characteristic well frequency. The effect of in-plane magnetic field is also studied.

Assessment of a layerwise mixed least-squares model for analysis of multilayered piezoelectric composite plates

A layerwise mixed finite element model is developed based on the least-squares formulation for the coupled electromechanical static analysis of multilayered plates with piezoelectric and composite layers. The model assumes a layerwise variable description for displacements, transverse stresses and in-plane strains, along with the electrostatic potential, transverse electric displacement and in-plane electric field components, taken as independent variables. This original choice for the layerwise mixed formulation is intended to ensure the a priori and complete fulfilment of the interlaminar C0 continuity of both mechanical and electrical variables, which is due to compatibility and equilibrium conditions. Numerical applications are shown for assessment of the model predictive capabilities by comparison with available exact three-dimensional solutions, considering multilayered piezoelectric composite plates of various side-to-thickness ratios, under an applied load or surface potential.

A coupled refined high-order global-local theory and finite element model for static electromechanical response of smart multilayered/sandwich beams

In the present study, a coupled refined high-order global-local theory is developed for predicting fully coupled behavior of smart multilayered/sandwich beams under electromechanical conditions. The proposed theory considers effects of transverse normal stress and transverse flexibility which is important for beams including soft cores or beams with drastic material properties changes through depth. Effects of induced transverse normal strains through the piezoelectric layers are also included in this study. In the presence of non-zero in-plane electric field component, all the kinematic and stress continuity conditions are satisfied at layer interfaces. In addition, for the first time, conditions of non-zero shear and normal tractions are satisfied even while the bottom or the top layer of the beam is piezoelectric. A combination of polynomial and exponential expressions with a layerwise term containing first order differentiation of electrical unknowns is used to introduce the in-plane displacement field. Also, the transverse displacement field is formulated utilizing a combination of continuous piecewise fourth-order polynomial with a layerwise representation of electrical unknowns. Finally, a quadratic electric potential is used across the thickness of each piezoelectric layer. It is worthy to note that in the proposed shear locking-free finite element formulation, the number of mechanical unknowns is independent of the number of layers. Excellent correlation has been found between the results obtained from the proposed formulation for thin and thick piezoelectric beams with those resulted from the three-dimensional theory of piezoelasticity. Moreover, the proposed finite element model is computationally economic.

Does the leakage radiation profile mirror the intensity profile of surface plasmon polaritons?

Although the leakage radiation (LR) image intensity is considered to be in proportion to the surface plasmon polariton (SPP) intensity at the metal-air interface, it has not been proven experimentally, to the best of our knowledge. Here we investigate the relationship between the measured LR intensity profile of SPP interference fringes, which are produced by two SPP launching gratings, and the simulated SPP intensity. The experimental modulation depths agree well with the simulation result of the in-plane electric field component of SPPs, which demonstrates that the image intensity in LR microscopy provides the intensity profile of the in-plane component.

Observation of Polarization Singularities at the Nanoscale

With a phase-sensitive near-field microscope we measure independently the two in-plane electric field components of light propagating through a 2D photonic crystal waveguide and the phase difference between them. Consequently, we are able to reconstruct the electric vector field distribution with subwavelength resolution. In the complex field distribution we observe both time-dependent and time-independent polarization singularities and determine the topology of the surrounding electric field.

Intrasubband and intersubband transitions in lightly and heavily dopedGaAs/AlxGa1−xAsmultiple quantum wells

We use a polarizer to investigate quantum-well infrared absorption, and report experimental results as follows. The intrasubband transition was observed in ${\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}/\mathrm{A}\mathrm{l}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{As}$ multiple quantum wells (MQWs) when the incident infrared radiation (IR) is polarized parallel to the MQW plane. According to the selection rule, an intrasubband transition is forbidden. Up to now, most studies have only observed the intersubband transition between two states with opposite parity. However, our experiment shows not only the intersubband transitions, but also the intrasubband transitions. In our study, we also found that for light doping in the well $(4\ifmmode\times\else\texttimes\fi{}{10}^{18}{\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}),$ the intrasubband transition occurs only in the lowest subband, while for the heavy doping $(8\ifmmode\times\else\texttimes\fi{}{10}^{18}{\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}),$ such a transition occurs not only in the lowest subband, but also in the first excited one, because of the electron subband filling. Further experimental results show a linear dependence of the intrasubband transition frequency on the root of the well doping density. These data are in good agreement with our numerical results. Thus we strongly suggest that such a transition can be attributed to plasma oscillation. Conversely, when the incident IR is polarized perpendicular to the MQW plane, intersubband-transition-induced signals appear, while the intrasubband-transition-induced spectra disappear for both light and heavy well dopings. A depolarization blueshift was also taken into account to evaluate the intersubband transition spectra at different well dopings. Furthermore, we performed a deep-level transient spectroscopy (DLTS) measurement to determine the subband energies at different well dopings. A good agreement between DLTS, infrared absorption, and numerical calculation was obtained. In our experiment, two important phenomena are noteworthy: (1) The polarized absorbance is one order of magnitude higher than the unpolarized spectra. This puzzling result is well explained in detail. (2) When the IR, polarized perpendicular to the well plane, normally irradiates the 45\ifmmode^\circ\else\textdegree\fi{}-beveled edge of the samples, we only observed intersubband transition spectra. However, the intrasubband transition signals caused by the in-plane electric-field component are significantly absent. The reason is that such in-plane electric-field components can cancel each other out everywhere during the light propagating in the samples. The spectral widths of bound-to-bound and bound-to-continuum transitions were also discussed, and quantitatively compared to the relaxation time \ensuremath{\tau}, which is deduced from the electron mobility. The relaxation times deduced from spectral widths of bound-to-bound and bound-to-continuum transitions are also discussed, and quantitatively compared to the relaxation time deduced from electron mobility.