Wave Vector Difference Research Articles

Interference of co-propagating Rayleigh and Sezawa waves observed with micro-focused Brillouin light scattering spectroscopy

We use micro-focused Brillouin light scattering spectroscopy (BLS) to investigate surface acoustic waves (SAWs) in a GaN layer on a Si substrate at GHz frequencies. Furthermore, we discuss the concept of BLS for SAWs and show that the crucial parameters of SAW excitation and propagation can be measured. We investigate a broad range of excitation parameters and observe that Rayleigh and Sezawa waves are excited simultaneously at the same frequency. Spatially resolved measurements of these co-propagating waves show a periodic pattern, which proves their coherent interference. From the periodicity of the spatial phonon patterns, the wavevector difference between the two waves has been identified and compared to the dispersion relation. The appearance of Sezawa waves related to the finite thickness of the piezoelectric substrate leads to acoustic fields with a time-independent spatial variation similar to the situations realized using counter-propagating waves. This periodicity can have an influence on experimental results in angular momentum conversion experiments, for example, via magneto-elastic fields in hybrid-SAW-structures with additional magnetic layers.

Femtosecond photoemission electron microscopy of surface plasmon polariton beam steering via nanohole arrays

Directional control over surface plasmon polariton (SPP) waves is a prerequisite for the development of miniaturized optical circuitry. Here, the efficacy of single and dual component SPP steering elements is explored through photoemission electron microscopy. Our imaging scheme relies on two-color photoemission and counter-propagating SPP generation, which collectively allow SPPs to be visualized in real space. Wave-vector difference mixing between the two-dimensional nanohole array and photon momenta enables SPP steering with directionality governed by the array lattice constant and input photon direction. In our dual component configuration, separate SPP generation and Bragg diffraction based steering optics are employed. We find that array Bragg planes principally influence the SPP angles through the array band structure, which allows us to visualize both positive and negative refractory waves.

Simulating a quantum commensurate-incommensurate phase transition using two Raman-coupled one-dimensional condensates

We study a transition between a homogeneous and an inhomogeneous phase in a system of one-dimensional, Raman tunnel-coupled Bose gases. The homogeneous phase shows a flat density and phase profile, whereas the inhomogeneous ground state is characterized by periodic density ripples, and a soliton staircase in the phase difference. We show that under experimentally viable conditions the transition can be tuned by the wavevector difference $Q$ of the Raman beams and can be described by the Pokrovsky-Talapov model for the relative phase between the two condensates. Local imaging available in atom chip experiments allows to observe the soliton lattice directly, while modulation spectroscopy can be used to explore collective modes, such as the phonon mode arising from breaking of translation symmetry by the soliton lattice. In addition, we investigate regimes where the cold atom experiment deviates from the Pokrovsky-Talapov field theory. We predict unusual mesoscopic effects arising from the finite size of the system, such as quantized injection of solitons upon increasing $Q$, or the system size. For moderate values of $Q$ above criticality, we find that the density modulations in the two gases interplay with the relative phase profile and introduce novel features in the spatial structure of the mode wave-functions. Using an inhomogeneous Bogoliubov theory, we show that spatial quantum fluctuations are intertwined with the emerging soliton staircase. Finally, we comment on the prospects of the ultra-cold atom setup as a tunable platform studying quantum aspects of the Pokrovsky-Talapov theory in and out-of-equilibrium.

Quantum Scars in Microwave Dielectric Photonic Graphene Billiards**Supported by the National Natural Science Foundation of China under Grant No. 11847067, the Natural Science Foundation of Shanxi Province under Grant No. 201801D221178, the Science and Technology Innovation Project of Shanxi Higher Education under Grant No. 2019L0648, and Taiyuan University of Science and Technology Scientific Research Initial Funding under Grant No. 20152044.

In the band structure of graphene, the dispersion relation is linear around a Dirac point at the corners of the Brillouin zone. The closed graphene system has proven to be the ideal model to investigate relativistic quantum chaos phenomena. The electromagnetic material photonic graphene (PG) and electronic graphene not only have the same structural symmetry, but also have the similar band structure. Thus, we consider a stadium shaped resonant cavity filled with PG to demonstrate the relativistic quantum chaos phenomenon by numerical simulation. It is interesting that the relativistic quantum scars not only are identified in the PG cavities, but also appear and disappear repeatedly. The wave vector difference between repetitive scars on the same orbit is analyzed and confirmed to follow the quantization rule. The exploration will not only demonstrate a visual simulation of relativistic quantum scars but also propose a physical system for observing valley-dependent relativistic quantum scars, which is helpful for further understanding of quantum chaos.

Wave Vector Difference of Magnetic Bragg Reflections and Low Energy Magnetic Excitations in Charge-stripe Ordered La2NiO4.11

We report on the magnetism of charge-stripe ordered La2NiO4.11±0.01 by neutron scattering and μSR. On going towards zero energy transfer there is an observed wave vector offset in the centring of the magnetic excitations and magnetic Bragg reflections, meaning the excitations cannot be described as Goldstone modes of the magnetic order. Weak transverse field μSR measurements determine the magnetically order volume fraction is 87% from the two stripe twins, and the temperature evolution of the magnetic excitations is consistent with the low energy excitations coming from the magnetically ordered volume of the material. We will discuss how these results contrast with the proposed origin of a similar wave vector offset recently observed in a La-based cuprate, and possible origins of this effect in La2NiO4.11.

Fabrication of two-dimensional micro-nano photonic structures by symmetry-lost beams interference

Micro-nano photonic structures, such as meta-materials and photonic crystals, having special effects on light generation, transmission, detection and sensing on a submicron scale, play an increasingly significant role in optical information fields. Micro-nano photonic structures have great potential applications in surface laser emission, optical waveguide and high-Q laser. There are several methods to fabricate micro-nano photonic structures, including laser direct writing, electron beam direct writing, electrochemical corrosion, and holographic lithography and so on. Holographic lithography employs multi-beam interference to generate periodic patterns and records them on photosensitive materials to form typical structures. What is more, it has advantages of low cost, large area and high efficiency. However, there are still some challenges in fabricating typical micro-nano photonic structures, especially the precise optical alignment, beam polarization and control of the details of local interference pattern. A specially designed prism is employed in this work and we propose a compact symmetry-lost setup with the rapid adjustment of beam configuration and polarization. Based on the theory of multi-beam interference, symmetry-lost four-and five-beam interference with different polarizations are simulated. By changing the combination of beam configuration and polarization, novel two-dimensional micro-nano photonic structures can be achieved. The variations of azimuthal angle and polarization of beam in symmetry-lost system affect the wave vector difference, and thus changing the lattice shape and structure contrast. Branch-like and wave-like structures are generated by symmetry-lost four beams with polarizations of (90, 90, 90, 90) and five beams with polarizations of (90, 90, 90, 90, 0), respectively. An appropriate threshold is selected in simulation, such that the intensity data larger than the threshold are removed, while the smaller data are remained, which is transformed into an optical lattice pattern. The interference structures show different morphologies and structural contrasts, and have a period of several hundred nanometers. In experimental fabrication, a top-cut hexagonal prism is used to generate two-dimensional micro-nano photonic structure on CHP-C positive photoresist by single exposure. The intensity of each beam is about 18-20 mW, and the incident angle is 42. The beam polarization is adjusted by rotating a half waveplate inside the holes of the mask and structure volume fraction is determined by exposure dose controlled by beam intensity and exposure time. The scanning electron microscope images of the samples show good agreement with simulation results. This study could provide an effective method of fabricating novel photonic structures, which can be used as templates of fabricating different types of metal lattice structures, thereby promoting the development and applications of novel photonic devices.

Improvement of the local characteristics of graphene surface plasmon based on guided-mode resonance effect

Graphene is a one-atom-thick planar sheet of sp2-bonded carbon atoms that are densely packed in a honeycomb crystal lattice. Graphene has been found to support plasmons in a wide range from infrared to terahertz. The confinement of plasmons in graphene is stronger than that on metallic surface. Moreover, the plasmon properties can be dynamically adjusted by doping or grating graphene. In this study, a composite structure comprised of graphene and subwavelength grating is proposed. Highly confined plasmons in graphene are excited by using a diffraction grating with guided mode resonance effect. The wave vector of plasmonic wave in graphene is far larger than that of light in vacuum. To excite plasmons in graphene with a freespace optical wave, their large difference in wave vector must be overcome. Optical gratings are widely used to compensate for wave vector mismatches. A diffraction wave generated by the grating structure can overcome the large wave vector difference and excite surface plasmons. The guided-mode resonance can greatly enhance the intensity of the diffraction field and the coupling efficiency between graphene and incident light. When the phase matching between illuminating wave and a guide mode supported by grating is achieved, guided-mode resonance effect occurs. A nearly 100% diffraction efficiency peak in the reflection or transmission spectrum occurs at a certain wavelength. In this study, the influences of graphene and grating structure on the local characteristics (the surface electric field Ex/Ein, quality factor Q, and effective mode area Seff) of surface plasmons are investigated. The effects of the structural parameters (the thickness of the buffer layer T2, the grating period p, the carrier mobility , and the Fermi level EF) on localization properties are analyzed by the finite element method (COMSOL). The results reveal that the localizations of the surface plasmons in the graphene surface is significantly improved at the certain parameters. 1) The increase of T2 will reduce the intensity of electric field on graphene (Ex/Ein), but the quality factor will obtain a certain increase. The excition of highly confined SPPs needs to improve Q and keep the intensity of Ex/Ein, so in this study T2 = 10 nm. 2) By adjusting the quality factor of SPPs can be improved significantly without changing the resonance frequency ( = 0.7 m2(Vs), Qmax = 1793). 3) Small changes in p and EF will make the resonance peak shift obviously, and the electric field on graphene is greatly enhanced (p = 235 nm, Ex/Ein = 3154; EF = 0.72 eV, and Ex/Ein = 3968). Strong localization leads to strong light-matter interaction, and thus the proposed structure has the potential to be used as sensors with high sensitivity and high-efficiency nonlinear optical devices, greatly expanding the application of graphene in nano optics.

The effects of background fields on vector financial rogue wave pattern

We study the structure of financial rogue waves with variable stock volatility. We find that there are mainly three types of rogue wave patterns in the coupled system, namely eye-shaped, anti-eye-shaped, and four-petaled. The transition between them can be induced by relative wave vector and amplitude difference between the two background fields. The results will help us achieve a deep understanding of financial rogue waves and suggest a number of implications.

Experimental solution for scattered imaging of the interference of plasmonic and photonic mode waves launched by metal nano-slits.

Using an L-shaped metal nanoslit to generate waves of the pure photonic and plasmonic modes simultaneously, we perform an experimental solution for the scattered imaging of the interference of the two waves. From the fringe data of interference, the amplitudes and the wavevector components of the two waves are obtained. The initial phases of the two waves are obtained from the phase map reconstructed with the interference of the scattered image and the reference wave in the interferometer. The difference in the wavevector components gives rise to an additional phase delay. We introduce the scattering theory under Kirchhoff's approximation to metal slit regime and explain the wavevector difference reasonably. The solution of the quantities is a comprehensive reflection of excitation, scattering and interference of the two waves. By decomposing the polarized incident field with respect to the slit element, the scattered image produced by slit of arbitrary shape can be solved with the nanoscale Huygens-Fresnel principle. This is demonstrated by the experimental intensity pattern and phase map produced by a ring-slit and its consistency with the calculated results.

Proposal for a Datta-Das transistor in the quantum Hall regime

We propose a resonant spin-field-effect transistor for chiral spin-resolved edge states in the integer quantum Hall effect with Rashba spin-orbit interaction. It employs a periodic array of voltage-controlled top gates that locally modulate the Rashba spin-orbit interaction. Strong resonant spin-field effect is achieved when the array periodicity matches the inverse of the wave-vector difference of the two chiral states involved. Well-known techniques of separately contacting the edge states make it possible to selectively populate and read out the edge states, allowing full spin readout. The resonant nature of the spin-field effect and the adiabatic character of the edge states guarantee a high degree of robustness with respect to disorder. Our device represents the quantum Hall version of the all-electrical Datta-Das spin-field effect transistor.

Effects of thermal motion on electromagnetically induced absorption

We describe the effect of thermal motion and buffer-gas collisions on a four-level closed N system interacting with strong pump(s) and a weak probe. This is the simplest system that experiences electromagnetically induced absorption (EIA) due to transfer of coherence via spontaneous emission from the excited to ground state. We investigate the influence of Doppler broadening, velocity-changing collisions (VCC), and phase-changing collisions (PCC) with a buffer gas on the EIA spectrum of optically active atoms. In addition to exact expressions, we present an approximate solution for the probe absorption spectrum, which provides physical insight into the behavior of the EIA peak due to VCC, PCC, and wave-vector difference between the pump and probe beams. VCC are shown to produce a wide pedestal at the base of the EIA peak, which is scarcely affected by the pump-probe angular deviation, whereas the sharp central EIA peak becomes weaker and broader due to the residual Doppler-Dicke effect. Using diffusion-like equations for the atomic coherences and populations, we construct a spatial-frequency filter for a spatially structured probe beam and show that Ramsey narrowing of the EIA peak is obtained for beams of finite width.

Theory of Dicke narrowing in coherent population trapping

The Doppler effect is one of the dominant broadening mechanisms in thermal vapor spectroscopy. For two-photon transitions one would naively expect the Doppler effect to cause a residual broadening, proportional to the wave-vector difference. In coherent population trapping (CPT), which is a two-photon narrow-band phenomenon, such broadening was not observed experimentally. This has been commonly attributed to frequent velocity-changing collisions, known to narrow Doppler-broadened one-photon absorption lines (Dicke narrowing). Here we show theoretically that such a narrowing mechanism indeed exists for CPT resonances. The narrowing factor is the ratio between the atom's mean free path and the wavelength associated with the wave-vector difference of the two radiation fields. A possible experiment to verify the theory is suggested.

Time development of a persistent hole burning in multiple-scattering media

We investigated the time development of persistent hole burning in photoreactive and multiple-scattering media. In this hole burning, a writing laser beam recodes the volume speckle pattern inside the medium through the photoreactive process, and then the luminescence intensity excited by a reading beam is measured as a function of the frequency or wave vector difference between the writing and reading beams. The time development reflects the statistics of the intensity fluctuations in the speckle inside the medium. One of the striking results is that the maximum hole depth is approximately 0.26 . We distinguish three types of samples according to the geometric configurations and the photoreactive processes and discuss the hole shape, hole width, and the depth during time development. Hole burning experiments were also performed using a spiropyran derivative photochromic dye. The experimental results showed good agreement with the theory.

Oxygen ordering and strain-related morphology in YBa2Cu3-xMxO7 systems, where M is a trivalent atom.

Monte Carlo simulations were performed on an anisotropic lattice-gas model which well represents the interactions between oxygen atoms in ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7}$ systems doped with trivalent impurity atoms M such as Fe or Al. Concentration wave amplitudes obtained from these simulations were used to calculate the diffuse x-ray scattering intensity caused by the resulting displacement field using a concentration-wave--displacement-wave approach, and the results are compared with x-ray and electron diffraction data. The results suggest that the small orthorhombic domains (short-range ordering) associated with the oxygen ``cross-links'' around impurity atoms M cause the diffuse scattering intensity to fall off with the scattering wave-vector difference q from a Bragg peak as 1/${\mathit{q}}^{2}$ for small q and as 1/${\mathit{q}}^{4}$ for larger q. We show that the average size of such domains can be obtained from diffuse x-ray scattering data.

Polarization dependences of degenerate backward four-wave mixing in dye doped boric acid glass

The three components of third-order nonlinear susceptibilities responsible for degenerate backward four-wave mixing are calculated for an isotropic medium and their dependence with respect to wave-vector difference between the two beams are shown. Comparisons are made with their experimental values in dye doped boric acid glass. The results are in very good agreement with theory.

Picosecond Holographic-Grating Spectroscopy

Interfering light waves produce an optical interference pattern in any medium that interacts with light. This modulation of some physical parameter of the system acts as a classical holographic grating for optical radiation. When such a grating is produced through interaction of pulsed light waves with an optical transition, a transient grating is formed whose decay is a measure of the relaxation time of the excited state. Transient gratings can be formed in real space or in frequency space depending on the time ordering of the interfering light waves. The two gratings are related by a space-time transformation and contain complementary information on the optical dynamics of a system. The status of a grating can be probed by a delayed third pulse, which diffracts off this grating in a direction determined by the wave vector difference of the interfering light beams. This generalized concept of a transient grating can be used to interpret many picosecond-pulse optical experiments on condensed-phase systems. Examples of some low-temperature experiments will be presented. In principle, many of these experiments could also be performed by using stochastic broad-band excitation. In these nonlinear photon-interference experiments the time resolution is determined by the correlation time of the light source rather than its pulse width.

Variationally optimized T matrices for elastic scattering

Trial T matrices depending only on the wave vector difference ki−kf have been employed to obtain optimum elastic scattering amplitudes. These amplitudes are the values assumed by a variational functional evaluated at the optimum trial T and thus have a more complex dependence on ki and kf than the trial T. By way of illustration, two examples are presented: scattering from an attractive Yukawa potential, and scattering from an attractive well. In both instances the results compare very favorably with other methods of solution.

Theory of Magnetically Assisted indirect Transitions in Magnetic Semiconductors

The optical absorption coefficient for ferromagnetic semiconductors has been calculated for an indirect transition in which spin-fluctuation scattering takes the place of the usual phonon scattering. The resulting absorption coefficient is found to be proportional to $〈{|{S}_{{\stackrel{\ensuremath{\rightarrow}}{\mathrm{Q}}}_{Z}}|}^{2}〉$, where $\stackrel{\ensuremath{\rightarrow}}{\mathrm{Q}}$ is the wave-vector difference between the valence-band maximum and the conduction-band minimum. The fact that this decreases with decreasing temperature below the Curie point can lead to an apparent blue shift of the absorption edge similar to what is observed in Cd${\mathrm{Cr}}_{2}$${\mathrm{S}}_{4}$.