Transverse Energy Flux Research Articles

Lamb waves in sandwich structures: Anomalous dispersion and transverse (quasi) resonances

Guided waves propagating in three layered sandwich structures with extremely soft inner layer and thin stiff outer layers reveal peculiar phenomena related to the appearance of dual zero group velocities (ZGV) in the fundamental symmetric branch, transverse (quasi) resonances, and transverse energy fluxes, causing “ringing” of the plates and even material damage. The current research relates to sandwich plates, satisfying the so-called Wiechert condition. The analysis is based on the combined method comprising Cauchy sextic formalism and the exponential fundamental matrix method.

Influence of Off-Axis Noncanonical Vortex on the Dynamics of Energy Flux

In this article, we analyze the impact of the off-axis noncanonical vortex on the dynamics of 3D energy flux. The results reveal that the properties of energy flux are significantly influenced by the anisotropy parameter σc of the off-axis noncanonical vortex. It is demonstrated that by adjusting the anisotropy parameter, we can control the transverse energy flux, from the position of the transverse energy tornado and the distribution of the transverse energy strength to the rotation direction of the transverse energy flux as the beam propagates. The interesting phenomenon, the reversed energy flux, is also closely related to the anisotropy parameter. The position and size of the reversed energy flux region, as well as the production of two energy tornadoes with opposite rotating directions, resembling a Chinese “Taiji” pattern, can be controlled by varying the anisotropy parameter. This result will potentially provide a new freedom for tailoring the 3D optical field and be useful in optical manipulation and processing.

Transverse energy propagation and interference of elliptical Gaussian beams

Elliptical Gaussian beam (EGB) has many different physical properties from circular Gaussian beam. In this paper, the transverse energy flux and intensity of one and two coherent EGBs are studied. In our simulation, the transverse energy flux and intensity varying with waist ratio are discussed in detail. It has been found that through increasing the waist ratio, the transverse energy flux after interference would be strengthened significantly. Although the transverse energy flux is much weaker than the longitudinal energy flux, its signal to noise ratio has been verified to be strong enough for detection. Our derivations are still reasonable for another simulation with general experimental parameters. The simulation results are considered to be helpful for some physical experiments using the transverse energy flux of Gaussian beam, such as an important application in electromagnetic response produced by interaction of high-frequency gravitational waves.

Interference enhancement effect in a single Airyprime beam propagating in free space.

An analytical expression of a single Airyprime beam propagating in free space is derived. Upon propagation in free space, a single Airyprime beam in arbitrary transverse direction is the coherent superposition of the Airyprime and the Airy-related modes, which results in the interference enhancement effect under the appropriate condition. The Airy-related mode is the conventional propagating Airy mode with an additional π/2 phase shift and a weight coefficient of half the normalized propagation distance. Due to the peak light intensity in the initial plane being set to be 1, the strength of interference enhancement effect is characterized by the maximum light intensity. The maximum light intensity of a single Airyprime beam propagating in free space is independent of the scaling factor and is only decided by the exponential decay factor. When the exponential decay factor is above the saturated value, the interference enhancement effect disappears. When the exponential decay factor decreases from the saturated value, the maximum light intensity of a single propagating Airyprime beam increases, and the position of maximum light intensity is getting farther away. With the increase of the scaling factor, the position of maximum light intensity of a single propagating Airyprime beam is extended. The intensity distribution and the transverse Poynting vector of a single propagating Airyprime beam are demonstrated in different observation planes of free space. The flow direction of transverse energy flux effectively supports the interference enhancement effect of a single propagating Airyprime beam. The Airyprime beam is experimentally generated, and the interference enhancement effect is experimentally confirmed. The interference enhancement effect is conducive to the practical application of a single Airyprime beam.

Spin-Orbital Conversion with the Tight Focus of an Axial Superposition of a High-Order Cylindrical Vector Beam and a Beam with Linear Polarization.

In this paper, spin-orbital conversion in the tight focus of an axial superposition of a high-order (order m) cylindrical vector beam and a beam with linear polarization is theoretically and numerically considered. Although such a beam does not have a spin angular momentum in the initial plane and the third projection of its Stokes vector is equal to zero, subwavelength local regions with a transverse vortex energy flow and with the non-zero third Stokes projection (the longitudinal component of the spin angular momentum) are formed in the focal plane for an odd number m. This means that such a beam with an odd m has regions of elliptical or circular polarization with alternating directions of rotation (clockwise and counterclockwise) in the focus. For an even m, the field is linearly polarized at every point of the focal plane, and the transverse energy flux is absent. These beams can be used to create a micromachine in which two microparticles in the form of gears are captured in the focus of the beam into neighboring local areas in which the energy flow rotates in different directions, and therefore, these gears will also rotate in different directions.

Rotation of degree of coherence and redistribution of transverse energy flux induced by non-circular degree of coherence of twisted partially coherent sources.

It is known that a twisted Gaussian Schell-model (TGSM) beam with elliptical Gaussian amplitude will rotate its beam spot upon propagation because of the vortex structure of the transverse energy flux. In this paper, we study a special kind of twisted partially coherent beams named twisted Hermite-Gaussian correlated Schell model (HGCSM) beam whose degree of coherence (DOC) is non-circularly symmetric but the source amplitude is of the circular Gaussian profile. Our results reveal that the beam spot (average intensity distribution) does not rotate during propagation even if the circular symmetry of the beam spot is broken. However, the DOC pattern shows the rotation under propagation. From the investigation of the transverse energy flux and OAM density flux, we attribute the nontrivial rotation phenomenon to the redistribution of the transverse energy flux by non-circular DOC. Furthermore, based on Hyde's approach [J. Opt. Soc. Am. A37, 257 (2020)10.1364/JOSAA.381772], we introduce a method for the generation of this class of twisted partially coherent sources. The non-rotation of the beam spot and rotation of the DOC are demonstrated in experiment.

Spin-orbit and orbit-spin conversion in the sharp focus of laser light: Theory and experiment

Based on the Richards-Wolf theory, it is strictly shown that in the sharp focus of a linearly polarized laser beam, the flux of a spin vector has only transverse components (the effect of photonic wheels or a photonic helicopter). For a linearly polarized optical vortex, the orbit-spin conversion leads to the appearance of both longitudinal and transverse components of the spin angular momentum (SAM) vector in the focus. We show that in the strong focus of a circularly polarized Gaussian beam, the longitudinal component of the SAM is maximal on the optical axis, with the longitudinal component of the orbital angular momentum (OAM) being maximal on a ring. In this way, the effect of SAM and OAM on the motion of a trapped microparticle can be evaluated separately. Spin-orbit conversion is experimentally demonstrated for a circularly polarized Gaussian beam when transverse energy flux (orbital angular momentum) arises in the focus, which is transmitted to a microparticle and causes it to rotate. Switching the handedness of circular polarization (from left to right) switches the direction of microparticle rotation. It is also shown here that an azimuthally polarized vortex beam with an arbitrary integer topological charge generates in the focus a SAM vector with only an axial component (pure magnetization), whereas there is no transverse spin flux.

Transverse Propagation Characteristics and Coherent Effect of Gaussian Beams**Supported by the National Natural Science Foundation of China (Grant No. 11873001) and the Natural Science Foundation of Chongqing (Grant No. cstc2018jcyjAX0767).

As an important electromagnetic field in experiment, Gaussian beams have non-vanishing longitudinal electric and magnetic components that generate significant energy fluxes on transverse directions. We focus on the transverse energy flux and derive the theoretical propagation properties. Unlike the longitudinal energy flux, the transverse energy flux has many unique physical behaviors, such as the odd symmetry on propagation, slower decay rate on resonant condition. By means of the characteristics of transverse energy flux, it is feasible to find the suitable regions where the information of coherent lights could be extracted exactly. With the typical laser parameters, we simulate the energy fluxes on receiver surface and analyze the corresponding distribution for the coherent light beams. Especially for coherent lights, the transverse energy flux on the y–z plane with x = 0 and x–z plane with y = 0, contains pure coherent information. Meanwhile, in the transverse distance |y| < 2W0 (W0 is the waist radius) and |x| < W0/3 the coherent information could also be extracted appropriately.

Transfer of spin angular momentum to a dielectric particle

We show here that in the sharp focus of a linearly polarized laser beam the spin vector flux has only transverse components (the effect of photonic wheels or photonic helicopter). For a linearly polarized optical vortex, the orbit-spin conversion leads to the appearance of both longitudinal and transverse components of the spin density vector in the focus. Spin-orbit conversion is experimentally demonstrated for a circularly polarized Gaussian beam when a transverse energy flux (orbital angular momentum) arises in the focus, which is transmitted to a microparticle and makes it rotate. Switching the handedness of circular polarization (from left to right) switches the microparticle rotation direction. It is also shown here that an azimuthally polarized vortex beam with an arbitrary integer topological charge generates in the focus a spin density vector that only has an axial component (pure magnetization), while the transverse spin flux is absent.

Reverse flux of energy of a nonparaxial optical vortex in the near field

In this work, using an expansion in terms of plane waves, we obtain all six components of the electric and magnetic field vectors for an elliptically polarized optical vortex with an arbitrary integer topological charge. We also obtain expressions for the distributions of the field intensity and the Poynting vector components in the initial plane of this optical vortex. For the particular case of a narrow angular spectrum of plane waves (Bessel beam) and for circular polarization, it is shown that in the presence of inhomogeneous evanescent waves in the initial light field, a reverse flux of light energy can occur near the optical axis. It is also shown that in the initial plane the effect of an “angular tractor” occurs, when at different distances from the optical axis the transverse energy flux rotates clockwise or counterclockwise. Using the obtained general expressions, the light flux for other known exact solutions of the Maxwell equations can be analyzed.

Mechanisms of the energy transfer across the magnetic field by Alfvén waves in toroidal plasmas

Physics of the transverse energy transfer by Alfvén waves in toroidal plasmas is elucidated. It is found that, in contrast to the classical Alfvén waves in infinite plasmas, the Alfvén waves in toroidal systems produce plasma compression due to coupling with fast magnetoacoustic waves, which provides the energy transfer. The radial group velocities of the traveling waves constituting the Global Alfvén Eigenmodes and Toroidicity-induced Alfvén Eigenmodes are calculated. It is shown that equations for Alfvén eigenmodes derived in the approximation of vanishing wave field along the equilibrium magnetic field reproduce the longitudinal magnetic field of the wave and lead to correct transverse energy flux. The obtained results explain how Alfvén eigenmodes can provide the spatial energy channeling—the transfer of the energy by these modes from the unstable plasma region to the region where the mode damping dominates.

Radial energy flux during destabilized Alfvén eigenmodes

Equations which determine the density of the transverse energy flux generated by destabilized Alfvén eigenmodes in bounded plasmas are derived and analyzed. It is shown that the energy flux can be directed outwards or inwards. The value, direction, and radial distribution of the flux depend on the instability growth rate and location of the regions driving the instability. The transverse flux provides the growth of the mode amplitude in places where the instability drive is weak or absent. Moreover, it provides the spatial channeling of the energy [the energy transfer by the mode predicted by Kolesnichenko et al. [Phys. Rev. Lett. 104, 075001 (2010)]] from unstable regions to the regions where damping dominates. This improves the plasma energy confinement in the case of an inward flux and deteriorates the confinement in the contrary case. The energy fluxes during some Alfvén instabilities in the tokamak-reactor ITER and the Wendelstein 7-X stellarator are evaluated.

Energy flux density and angular momentum density of radial Pearcey-Gauss vortex array beams in the far field

The longitudinal and transverse energy flux density (EFD) and angular momentum density (AMD) of the radial Pearcey-Gauss vortex array beams are studied by using the vector angular spectrum representation and stationary phase method, where the influence of topological charge, initial phase index, noncanonical strength and the number of beamlet on far-field vectorial structures of the corresponding beam is emphasized. The results show that the topological charge of center optical vortex is always equal to initial phase index for different noncanonical strength. The longitudinal EFDs exhibit different structures by varying initial phase index and the number of beamlet. For an odd-N, the topological charge of center optical vortex can be determined by distinguishing the longitudinal EFD, however for an even-N the topological charge cannot be identified due to the equivalence of longitudinal EFD in the case of positive and negative initial phase index m. The AMD tends to split more branches from the positive and negative direction with increasing the absolute value of topological charge l, The inner structures of AMD are also affected by different beamlets while the zero value of AMD is always retained.

Energy flux density and angular momentum density of Pearcey-Gauss vortex beams in the far field

The longitudinal and transverse energy flux density (EFD) and angular momentum density (AMD) of a Pearcey–Gauss vortex beam in the far field are studied using the vector angular spectrum representation and stationary phase method, where the influence of topological charge, noncanonical strength and off-axis distance of the embedded optical vortex on far-field vectorial structures of the corresponding beam is emphasized. For comparison, the EFD and AMD of the Pearcey–Gauss beam with non-vortex in the far field are also discussed. The results show that the longitudinal EFDs of the Pearcey–Gauss vortex beam exhibit parabolic patterns, and the number of parabolic dark zones equals the absolute value of topological charge of the embedded optical vortex in the input plane. While for the Pearcey–Gauss beam, the dark zones are not found owing to the non-vortex in the input plane. The motion of zero-intensity spot of whole beam appears by varying the off-axis distance. Noncanonical strength and off-axis distance both can adjust the magnitudes and directions of transverse EFD and control the spatial energy distributions of longitudinal EFD, but not change the net AMD.

Surface plasmon polaritons at the interface between dielectric and anisotropic nanocomposite

Specific features of surface-wave propagation along the interface between an isotropic dielectric and an anisotropic nanocomposite containing ellipsoidal metal inclusions whose axes of rotation are perpendicular to the interface between the media have been studied. Frequency dependences of the propagation constant and wave-vector transverse components, of the penetration depths and propagation lengths in each of the media, and of the longitudinal and transverse energy fluxes have been obtained. The effect of the shape of the inclusions on the wave and energy characteristics of the surface waves is shown.

Surface polaritons in a dielectric – anisotropic nanocomposite system

We have studied the peculiarities of propagation of surface polaritons at a planar interface between an isotropic dielectric and anisotropic nanocomposite with metal inclusions of ellipsoidal shape. For the case when the axes of all nanoellipsoids of revolution are perpendicular to the propagation direction and parallel to the medium interface, we have obtained frequency dependences of the propagation constant and transverse wave vector components, penetration depth and path length, longitudinal and transverse energy fluxes for surface polaritons. The shape of nanoellipsoids is shown to have an effect on the wave characteristics of surface polaritons.

Energy flux of a Gaussian beam in microwave band beyond the paraxial approximation

Through the analytic method beyond the paraxial approximation, the energy flux for the general fields of a Gaussian laser beam in microwave band (∼108–1010Hz) with different diffraction angles and longitudinal positions are derived. The results indicate a Gaussian beam (GB) has a certain number of transverse energy flux, and it would be enhanced with larger diffraction angle. In the range of beyond paraxial approximation, the transverse flux plays an important role in energy distribution, so that it cannot be ignored when the GB is highly focused. Meanwhile both transverse and longitudinal energy decay along the propagation direction, and the proportion of transverse energy far from beam axis is much more than the counterpart in paraxial area. The transverse energy as mainly characteristic of GB will be much useful for the interactions between electromagnetic field and other field.

Study on photonic angular momentum states in coaxial magneto-optical waveguides

By rigorously solving Maxwell's equations, we develop a full-wave electromagnetic theory for the study of photonic angular momentum states (PAMSs) in coaxial magneto-optical (MO) waveguides. Paying attention to a metal-MO-metal coaxial configuration, we show that the dispersion curves of the originally degenerated PAMSs experience a splitting, which are determined by the off-diagonal permittivity tensor element of the MO medium. We emphasize that this broken degeneracy in dispersion relation is accompanied by modified distributions of field component and transverse energy flux. A qualitative analysis about the connection between the split dispersion behavior and the field distribution is provided. Potential applications are discussed.

Manipulation of dark photonic angular momentum states via magneto-optical effect for tunable slow-light performance

We propose a novel scheme in realizing tunable slow-light performance by manipulating dark photonic angular momentum states (PAMSs) in metamaterials via the magneto-optical effect. We show that by applying a static magnetic field B, some pairs of sharp transmission dips can be observed in the background transparency window of a complex metamaterial design. Each pair of transmission dips are related to the excitation of dark PAMSs with opposite topological charges -m and +m, with a lifted degeneracy due to the classic analogue of Zeeman effect. Nonreciprocal characteristics can be observed in the distributions of field amplitude and transverse energy flux. The performance of slow light, including the group index ng, its abnormal feature, the associated strong absorption and the dependence with B are also discussed.

Nonlinear dynamics of planar gyrotrons with transverse diffraction coupling of radiation

We propose that the planar geometry of the interaction space and transverse (relative to the direction of translatory motion of electrons) power extraction be used for increasing the integrated radiation power of short-wavelength gyrotrons. The advantage of such a scheme over the traditional cylindrical geometry of gyrotrons is the possibility to ensure coherence of radiation for a large superdimensionality factor due to diffraction mechanism of mode selection in the open transverse coordinate and locking of radiation from various fractions of the ribbon-shaped polyhelical electron beam by transverse energy fluxes. Simulation of the non-linear dynamics of a planar gyrotron demonstrates the possibility of attaining the output power of hundreds of kilowatts at frequencies of up to 1 THz. A further increase in the output power to the megawatt level can be attained by using resonators with a nonuniform profile, for which the gap between the plates increases from the center to the periphery. Such a configuration is analogous to unstable optical resonators used in some powerful lasers.