Effective Wave Vector Research Articles

Transverse Confinement of Photon Position in the Light-Atom Interaction.

In an atom interferometry experiment, the output phase shift depends on the wave vector of photons and the recoil momentum in optical transitions. This Letter puts forward a hypothesis that in light-atom interaction, the atom wave function could provide a transverse confinement to photons and thus could affect the mean recoil momentum. We propose a model to analyze the photon effective wave vector in a monochromatic optical field and calculate the relative shift of |k[over →]_{eff}| to k when an atom with a 3D Gaussian wave function absorbs one photon in a Gaussian beam. This shift could lead to a systematic effect related to the spatial distribution of atoms and the transverse beam profile in high-precision experiments based on atom interferometry.

Homogenization of Maxwell\u2019s equations in a layered system beyond the static approximation

The propagation of electromagnetic waves through a disordered layered system is considered in the paradigm of the homogenization of Maxwell’s equations. Although the accuracy of the effective dielectric permittivity and/or magnetic permeability is still unclear outside the static approximation, we show that the effective wave vector can be correctly introduced even in high-frequency cases. It is demonstrated that both the real and imaginary parts of the effective wave vector are self-averaging quantities connected by the Kramers–Kronig relations. We provide a unified approach to describe the propagation and localization of electromagnetic waves in terms of the effective wave vector. We show that the effective wave vector plays the same role in describing composite materials in electrodynamics as the effective dielectric permittivity does in statics.

Clarifications on the Gouy phase of radially polarized laser beams.

The Gouy phase, which describes how a field accumulates an additional phase shift around the focus compared to a spherical wave, is investigated for the strongly focused TM01 beam in free space. It is shown, using both analytical and numerical solutions, that when the effects of the edges of focusing optics are small, the complete variation of the on-axis Gouy phase of the longitudinal electric field is 2π. It is true even in the strongly focused limit. Moreover, we show, using an appropriate effective wavevector, how to retrieve the Gouy phase when the diffraction caused by the edges is dominant at the focus. We further investigate the off-axis Gouy phase of the TM01 beam and show that any slight variation from the optical axis causes a variation of the Gouy phase of the longitudinal electric field to reduce to π.

Mid-infrared large-angle high-efficiency retroreflector based on subwavelenght metallic metagrating

<sec>How to effectively control the refraction, reflection, propagation and wavefront of dynamic waves or light has become one of hot research points in the field of optics. In the past few years, the concept of phase gradient metasurface has been proposed: it introduces a gradient of the phase discontinuity covering the entire angle 2<i>π</i> along the interface to provide an effective wave vector <inline-formula><tex-math id="M190">\begin{document}$\kappa $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="1-20191144_M190.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="1-20191144_M190.png"/></alternatives></inline-formula> and completely control the direction of outing wave. Therefore, the metasurface can possess many novel optical applications, such as holograms, metalenses, photonic spin Hall effect, etc. In this work, we design a simplified reflection-type optical metagrating. The results demonstrate that the metagrating can achive the function of two-channel retroreflection, that is, redirecting the incident wave back toward the source, with a nearly perfect conversion efficiency.</sec><sec>The metagrating designed in this paper contains only two sub-cells with <i>π</i> reflection phase difference in period. The working wavelength (<i>λ</i>) of metagrating is fixed at 3 μm. The two sub-cells are filled with an impedance matching material (their material relative refractive indexes are <i>n</i><sub>1</sub> = 1 and <i>n</i><sub>2</sub> = 1.5 respectively and their thickness is <i>d</i> = 1.5 μm.).The period length range is 1.5 μm ≤ <i>p</i> ≤ 3 μm(considering reducing the reflection order). When the incident angle is <inline-formula><tex-math id="M1">\begin{document}${\theta _{\rm{i}}}= \pm \arcsin [\lambda /(2p)]$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="1-20191144_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="1-20191144_M1.png"/></alternatives></inline-formula>, the absolute values of the incident angle and the reflected angle are equal, and then retroreflection occurs. When the wavelength is greater than the period (<inline-formula><tex-math id="M2">\begin{document}$\lambda \geqslant p$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="1-20191144_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="1-20191144_M2.png"/></alternatives></inline-formula>), the angle of retroreflection can be adjusted to any value (<inline-formula><tex-math id="M3">\begin{document}$\left| {{\theta _{\rm{i}}}} \right| \geqslant {\rm{3}}{{\rm{0}}^ \circ }$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="1-20191144_M3.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="1-20191144_M3.png"/></alternatives></inline-formula>) by adjusting the period <i>p</i>. In this work, COMSOL MULTIPHYSICS software is used to simulate the retroreflection reflectivity and field pattern of the designed metagrating. The results verify the two-channel retroreflection property of the metagrating. In addition,as the angle of incidence changes from 30° to 60°, the efficiency of retroreflection at any incident angle can reach to more than 95%. When the incident angle is 75.4°, the metagrating still has an efficiency of 80% retroreflection. Therefore, the metagrating also achieves the function of high-efficiency retroreflection at a large-angle. Comparing with multiple sub-cells’ metasurface, the simplified metagrating with two sub-cells enables a similar function of retroreflection, but has many potential advantages, and can play an important role in high-efficiency sensing, imaging and communication.</sec>

Nonlocal homogenisation scheme for lossless and anisotropic metafluids and phononic crystals

We present a systematic homogenisation approach to describe macroscopic dynamics of generic periodic acoustic materials composed of a rigid structure filled with a lossless fluid. This approach takes temporal dispersion as well as spatial dispersion effects into account, and can characterise, in a general manner, the oblique propagation and anisotropic effects. The theory is formulated such that all effects are encoded in, only, the effective frequency and wavevector dependent density, which can be calculated through a source-driven problem. Also, we demonstrate that the theory can homogenise materials even in frequency band gaps, including those that correspond to local-resonance phenomena or to Bragg scattering.We present a systematic homogenisation approach to describe macroscopic dynamics of generic periodic acoustic materials composed of a rigid structure filled with a lossless fluid. This approach takes temporal dispersion as well as spatial dispersion effects into account, and can characterise, in a general manner, the oblique propagation and anisotropic effects. The theory is formulated such that all effects are encoded in, only, the effective frequency and wavevector dependent density, which can be calculated through a source-driven problem. Also, we demonstrate that the theory can homogenise materials even in frequency band gaps, including those that correspond to local-resonance phenomena or to Bragg scattering.

Superchiral photons unveil magnetic circular dichroism

Polarization-dependent photon spectroscopy (dichroism) using signal-enhancing superchiral beams is shown to be sensitive to magnetic properties of the sample, whereas previous investigations explored charge-like electronic properties of chiral samples. In the process of unveiling the potential to observe magnetic circular dichroism (MCD), we underline an affinity between spectroscopies using the Borrmann effect, twisted beams and superchiral beams. Use of an effective wavevector in a quantum-mechanical theory unites the aforementioned spectroscopies and vastly improves our understanding of their advantages. Exploiting an effective wavevector for superchiral beams, natural circular dichroism (NCD) is derived from electric dipole - magnetic dipole (E1-M1) and electric dipole - electric quadrupole (E1-E2) absorption events, and MCD is derived from electric quadrupole-electric quadrupole (E2-E2) absorption. Signal enhancement by superchiral beams is a straightforward gain for the user because NCD and MCD are otherwise precisely the same as for a circularly polarized beam, according to our calculations. Our analysis shows that enhancement of E2-E2 is superior to that available for parity-odd events under consideration. Electronic degrees of freedom in all dichroic signals are encapsulated in atomic multipoles that are frequently used in theoretical interpretations of several established experimental techniques.

Chip-Integrated Geometric Metasurface As a Novel Platform for Directional Coupling and Polarization Sorting by Spin–Orbit Interaction

The focus of the research in metasurfaces has mainly been on the manipulation of the electromagnetic waves in free space during the past few years, which generally require thousands of subwavelength meta-atoms or even more. In this paper, we propose a conceptually new approach that chip-integrated metasurface can behave as a promising compact platform to control the propagation of guided waves when it is integrated with optical waveguide. As a proof of the concept, geometric metasurfaces consisting of only seven rotating anisotropic antennas, both metallic and dielectric, are integrated with silicon-on-insulator waveguide. Benefiting from the geometric phase shift stemming from spin–orbit interaction in metasurfaces, linearly gradient wavefront is generated along the waveguide, which is equivalent to introduce a unidirectional effective wavevector and thus leads to directional coupling. Inspired by the spin dependent gradient wavefront, opposite light flow is excited in the integrated waveguide by switching the handedness of incidence, which may provide a potential pathway to integrated polarization sorters and switchers.

High-Compton-frequency, parity-independent, mesoscopic Schrödinger-cat-state atom interferometer with Heisenberg-limited sensitivity

We present a protocol for an atomic interferometer that reaches the Heisenberg Limit (HL), within a factor of $\sim$ $\sqrt{2}$, via collective state detection and critical tuning of one-axis twist spin squeezing. It generates a Schr\"odinger cat (SC) state, as a superposition of two extremal collective states. When this SC interferometer is used as a gyroscope, the interference occurs at an ultrahigh Compton frequency, corresponding to a mesoscopic single object with a mass of $Nm$, where $N$ is the number of particles in the ensemble, and $m$ is the mass of each particle. For $^{87}$Rb atoms, with $N=10^{6}$, for example, the intereference would occur at a Compton frequency of $\sim$ $2 \times 10^{31}$ Hz. Under this scheme, the signal is found to depend critically on the parity of $N$. We present two variants of the protocol. Under Protocol A, the fringes are narrowed by a factor of $N$ for one parity, while for the other parity the signal is zero. Under Protocol B, the fringes are narrowed by a factor of $N$ for one parity, and by a factor of $\sqrt{N}$ for the other parity. Both protocols can be modified in a manner that reverses the behavior of the signals for the two parities. Over repeated measurements under which the probability of being even or odd is equal, the averaged sensitivity is smaller than the HL by a factor of $\sim$ $\sqrt{2}$ for both versions of the protocol. We show that when the SC interferometer is configured as an accelerometer, the effective two-photon wave vector is enhanced by a factor of $N$, leading to the same degree of enhancement in sensitivity. We also show that such a mesoscopic single object can be used to increase the effective base frequency of an atomic clock by a factor of $N$, with a sensitivity that is equivalent to the HL, within a factor of $\sim$ $\sqrt{2}$.

A unified formulation of dichroic signals using the Borrmann effect and twisted photon beams

Dichroic X-ray signals derived from the Borrmann effect and a twisted photon beam with topological charge l = 1 are formulated with an effective wavevector. The unification applies for non-magnetic and magnetic materials. Electronic degrees of freedom associated with an ion are encapsulated in multipoles previously used to interpret conventional dichroism and Bragg diffraction enhanced by an atomic resonance. A dichroic signal exploiting the Borrmann effect with a linearly polarized beam presents charge-like multipoles that include a hexadecapole. A difference between dichroic signals obtained with a twisted beam carrying spin polarization (circular polarization) and opposite winding numbers presents charge-like atomic multipoles, whereas a twisted beam carrying linear polarization alone presents magnetic (time-odd) multipoles. Charge-like multipoles include a quadrupole, and magnetic multipoles include a dipole and an octupole. We discuss the practicalities and relative merits of spectroscopy exploiting the two remarkably closely-related processes. Signals using beams with topological charges l ≥ 2 present additional atomic multipoles.

Time delay and the effect of the finite speed of light in atom gravimeters

The propagation time delay due to the finite speed of light (FSL) in atom gravimeters introduces a bias in the gravity measurement, as well as that in classical free-falling corner-cube gravimeters, which is usually termed the FSL effect. For a typical atom gravimeter, the FSL time delay is about several nanoseconds, resulting in the FSL effect, a non-negligible bias in the gravity-acceleration measurement. However, a time delay of about several microseconds, achieved by controlling the Raman-pulse timing directly, contributes a negligible effect. This interesting phenomenon motivates us to make clear two questions: first, what are the origins of the FSL effect in atom gravimeters, and second, what is the difference between the two time delays? Our analysis shows that the FSL effect in atom gravimeters is not just a matter of FSL time delay to a great extent but also the change in the effective wave vector; moreover, the FSL time delay can be quantitatively regarded as the same as the pulse time delay since both actually affect the gravity measurement by changing the two interferometer pulse separations.

Analytical properties of the effective refractive index

The propagation of a plane wave through a periodic layered system is considered in terms of the effective parameters. The problem of introduction of effective parameters is discussed. It was demonstrated that although the effective admittance cannot be introduced, it is possible to introduce the effective refractive index, which tends toward the Rytov value when the system size increases. It was shown that the effective wave vector derivative is an analytical function of frequency. In particular, the Kramers–Kronig-like relations for real and imaginary parts of the effective wave vector derivative were obtained. The Kramers–Kronig-like relations for the effective refractive index were also considered. The results obtained numerically were proved by exact solution of Maxwell's equations in the specific case of an “equi-impedance” system.

Capillary wave Hamiltonian for the Landau–Ginzburg–Wilson density functional

We study the link between the density functional (DF) formalism and the capillary wave theory (CWT) for liquid surfaces, focused on the Landau–Ginzburg–Wilson (LGW) model, or square gradient DF expansion, with a symmetric double parabola free energy, which has been extensively used in theoretical studies of this problem. We show the equivalence between the non-local DF results of Parry and coworkers and the direct evaluation of the mean square fluctuations of the intrinsic surface, as is done in the intrinsic sampling method for computer simulations. The definition of effective wave-vector dependent surface tensions is reviewed and we obtain new proposals for the LGW model. The surface weight proposed by Blokhuis and the surface mode analysis proposed by Stecki provide consistent and optimal effective definitions for the extended CWT Hamiltonian associated to the DF model. A non-local, or coarse-grained, definition of the intrinsic surface provides the missing element to get the mesoscopic surface Hamiltonian from the molecular DF description, as had been proposed a long time ago by Dietrich and coworkers.

Atom Interferometry in the Presence of an External Test Mass

The influence of an external test mass on the phase of the signal of an atom interferometer is studied theoretically. Using traditional techniques in atom optics based on the density matrix equations in the Wigner representation, we are able to extract the various contributions to the phase of the signal associated with the classical motion of the atoms, the quantum correction to this motion resulting from atomic recoil that is produced when the atoms interact with Raman field pulses and quantum corrections to the atomic motion that occur in the time between the Raman field pulses. By increasing the effective wave vector associated with the Raman field pulses using modified field parameters, we can increase the sensitivity of the signal to the point where such quantum corrections can be measured. The expressions that are derived can be evaluated numerically to isolate the contribution to the signal from an external test mass. The regions of validity of the exact and approximate expressions are determined.

Analytic derivation of electrostrictive tensors and their application to optical force density calculations

Using multiple scattering theory, we derived for the first time analytical formulas for electrostrictive tensors for two dimensional metamaterial systems. The electrostrictive tensor terms are found to depend explicitly on the symmetry of the underlying lattice of the metamaterial and they also depend explicitly on the direction of a local effective wave vector. These analytical results enable us to calculate light induced body forces inside a composite system (metamaterial) using the Helmholtz stress tensor within the effective medium formalism in the sense that the fields used in the stress tensor are those obtained by solving the macroscopic Maxwell equation with the microstructure of the metamaterial replaced by an effective medium. Our results point to some fundamental questions of using an effective medium theory to determine optical force density. In particular, the fact that Helmholtz tensor carries electrostrictive terms that are explicitly symmetry dependent means that the standard effective medium parameters cannot give sufficient information to determine body force density, even though they can give the correct total force. A more challenging issue is that the electrostrictive terms are related to a local effective wave vector, and it is not always obtainable in systems with boundary reflections within the context of a standard effective medium approach.

Effective quantities and effective rules in two-dimensional ferromagnetic antidot lattices

In this paper the metamaterial properties of two-dimensional arrays of circular antidots (holes) embedded into a ferromagnetic medium of Permalloy are studied according to both micromagnetic and analytical calculations. The periodicity of the arrays and the diameters of the antidots are in the nanometric range. The collective mode dynamics is described by means of effective physical quantities for the scattering geometry with the external magnetic field applied perpendicularly to the Bloch wave vector in the antidot plane. As an example, the definition of an effective field, incorporating the demagnetizing effects due to the holes, permits to describe the dynamical properties of collective modes in terms of effective properties in the travelling regime. An effective wavelength and a small wave vector are introduced both for extended and localized magnonic modes. By means of these effective quantities it is shown that holes play the role of point defects affecting the spin dynamics in the microwave range. Relations between the effective wavelength and the Bloch wavelength and between the corresponding small wave vector and the Bloch wave vector are found. Some effective rules on the dynamic magnetization, based upon the effective wavelength and the corresponding small wave vector, are derived. An application that exploits the definition of the small wave vector is proposed and an experiment based upon the notion of effective wavelength and small wave vector is suggested.

Asymmetry of spin wave dispersions in a hexagonal magnonic crystal

We report a study of the dispersion of spin waves in a hexagonal array of interacting ferromagnetic nanodisks for two orthogonal orientations of the in-plane applied magnetic field, i.e., either parallel or perpendicular to the direction of first neighbour disks. The experimental data were modelled using the dynamical matrix method, and the results were interpreted in terms of the effective wave vector model. We have found that spin waves propagating in the two orthogonal directions exhibit marked asymmetry concerning the existence of maxima/minima in their dispersion curves and the sign of their group velocities.

Micro-Raman phonon scattering by InAs/AlAs quantum dot superlattices

We present the results of micro-Raman scattering study of acoustic phonons of InAs/AlAs quantum dot superlattices grown by molecular beam epitaxy in the Stranski–Krastanow growth mode.Raman scattering from the planar surface and the cleaved (110)-oriented edge of the nanostructures was investigated. Doublets of folded longitudinal acoustic (FLA) phonons up to 7th order were observed in the Raman spectra measured in the z(x,x)-z scattering geometry whose energy positions are well described by the elastic continuum model of Rytov. The in-plane Raman scattering spectra measured in the y′(x′,x′)-y′ geometry reveal the changing energy positions and intensities of the FLA doublet components which are consistent with the changing effective wave vector in the nanostructures induced by the momentum transfer of the light. The Raman selection rules for the FLA phonons with different symmetries are discussed.

Metamaterial properties of ferromagnetic antidot lattices

In this paper the metamaterial properties of two-dimensional arrays of circular antidots (holes) embedded into a ferromagnetic medium of Permalloy are studied according to both micromagnetic and analytical calculations. The periodicity of the arrays and the diameters of the antidots are in the nanometric range. The collective mode dynamics is described by means of effective physical quantities for the scattering geometry with the external magnetic field applied perpendicularly to the Bloch wave vector in the antidot plane. As an example, the definition of an effective field, incorporating the demagnetizing effects due to the holes, permits to describe the dynamical properties of collective modes in terms of effective properties in the travelling regime. An effective wavelength and a small wave vector are introduced both for extended and localized magnonic modes. By means of these effective quantities it is shown that holes play the role of point defects affecting the spin dynamics in the microwave range. Relations between the effective wavelength and the Bloch wavelength and between the corresponding small wave vector and the Bloch wave vector are found. Some effective rules on the dynamic magnetization, based upon the effective wavelength and the corresponding small wave vector, are derived. An application that exploits the definition of the small wave vector is proposed and an experiment based upon the notion of effective wavelength and small wave vector is suggested.

The order of filling transitions in acute wedges

Using a square-gradient density functional model we test the prediction that the filling transition for a fluid in a wedge geometry changes from continuous to first-order as the wedge becomes more acute. Our numerical findings confirm such a change of order, but the value of the tilt angle at which it occurs, α* ≈ 45°, is considerably smaller than the original theoretical prediction. We critically reassess this work, which was based on allowing for the self-interaction of the fluid interface, and argue that the interfacial curvature and effective wavevector dependent surface tension can further lower the predicted value of α*, in keeping with our numerical findings. Interfacial fluctuation effects, occurring beyond mean-field level, are also discussed using effective Hamiltonian theory and are shown to substantially increase the value of α*.

Band Diagram of Spin Waves in a Two-Dimensional Magnonic Crystal

The dispersion curves of collective spin-wave excitations in a magnonic crystal consisting of a square array of interacting saturated nanodisks have been measured by Brillouin light scattering along the four principal directions of the first Brillouin zone. The experimental data are successfully compared to calculations of the band diagram and of the Brillouin light scattering cross section, performed through the dynamical matrix method extended to include the dipolar interaction between the disks. We found that the fourfold symmetry of the geometrical lattice is reduced by the application of the external field and therefore equivalent directions of the first Brillouin zone are characterized by different dispersion relations of collective spin waves. The dispersion relations are explained through the introduction of a bidimensional effective wave vector that characterizes each mode in this magnonic metamaterial.