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Two field lines of the Poynting vector for the same dipole as in Fig. 1, but now the dipole is embedded in a medium with ε r = 1 + 0.07 i and μ r = 1 . Due to the damping, the rotations of the field lines near the dipole are much less dense, as compared to Fig. 1, and the cone shapes of Fig. 1 become funnels.
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When a circular electric dipole moment, rotating in the x – y plane, is embedded in a material with relative permittivity ε r and relative permeability μ r , the field lines of energy flow of the emitted radiation are dramatically influenced by the surrounding material. For emission in free space, the field lines swirl around the z axis and lie on...
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Citations
... There is no explicit dependence on ε r . Equation (14) in [3] gives the expression for σq for the case of an embedded electric dipole. The terms in braces are identical, with ε r and μ r switched. ...
An oscillating magnetic dipole moment emits radiation. We assume that the dipole is embedded in a medium with relative permittivity and relative permeability , and we have studied the effects of the surrounding material on the flow lines of the emitted energy. For a linear dipole moment in free space the flow lines of energy are straight lines, coming out of the dipole. When located in a medium, these field lines curve toward the dipole axis, due to the imaginary part of . Some field lines end on the dipole axis, giving a nonradiating contribution to the energy flow. For a rotating dipole moment in free space, each field line of energy flow lies on a cone around the axis perpendicular to the plane of rotation of the dipole moment. The field line pattern is an optical vortex. When embedded in a material, the cone shape of the vortex becomes a funnel shape, and the windings are much less dense than for the pattern in free space. This is again due to the imaginary part of . When the real part of is negative, the field lines of the vortex swirl around the dipole axis opposite to the rotation direction of the dipole moment. For a near-single-negative medium, the spatial extent of the vortex becomes huge. We compare the results for the magnetic dipole to the case of an embedded electric dipole.
... Therefore, vortices under the current investigation are not singular and carry no topological charges. Our key results presented in Fig. 1 display streamlines of Poynting vectors indicated by arrows [1], [2]. Here, the eye-circle indicated in green refers to a very thin layer of gain material. ...
... Fig. 2(b) shows the axial component S ρ and angular component S θ of a Poynting vector both in metal and vacuum [12]. We employ a generic parameterε of the relative dielectric constant, either metal in the interior of a cylinder or vacuum in its exterior [2], [20] ...
... In contrast, S θ < 0 in metal as seen from (4) or the angular flow is clockwise (or backward) for n > 0 because ε r < 0 for metal. In comparison, S θ > 0 in vacuum, namely, the angular flow is counterclockwise (or forward) [2], [13]. Let us define the Poyning-vector swirl ratio (PVSR) σ S , which is readily evaluated through (4) where each vertical bar denotes the migration of σ S as ρ varies from the eye-circle at ρ = R to the center at ρ = 0. ...
We examine electromagnetic waves propagating on the cross-sectional plane of a single cylindrical metal nanowire. For continuous waves to be sustained, gain medium is placed around the periphery of wire, thus compensating for the material loss of metal. The thickness of gain layer is assumed to be infinitely thin, whereby a threshold gain is defined as the jump in the radial component of Poynting energy. Resulting energy-flow patterns exhibit resemblance to atmospheric typhoon, but with a relative quietness within its eye region. In addition, we analyze optical-compressor aspects of the resulting swirl flows. On theoretical sides, we focus on the spatially transverse features of angular propagations associated with asymmetry, which arises in turn from the temporal irreversibility of Drude model for metal. Besides, we find relationships of vector and scalar potentials to Poynting vectors.
... As regards metamaterials, the EM-energy aspect receives correspondingly intense attention [8,9]. The EM energy and the Poynting-vector dynamics in particular find renewed importance in light vortices for their possible implications for quantum vortices [10][11][12]. In addition, electronic vortices are common with type-II high-temperature superconductors (HTSCs) [11,13,14]. ...
... In the presence of material loss, the frequency is complex-valued such that ω ≡ ω r + iω i [16,17]. The stability condition ω i < 0 is enforced along with the entropy-increase condition that γ ω r > 0 [4,12,16]. To fix the idea, we choose ω r > 0, and hence γ > 0 as well [16]. ...
... Besides, the factor exp(2ω i t) signifies temporal attenuation [4,12,16]. Details are provided in appendix B. ...
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... Even though the imaginary part of ε r is very small for the illustration in Figure 7, the effect is dramatic. The rotation of the field lines near the source leads to a displacement of the dipole image in the far field, as in Figure 5 [14]. Just as for the dipole in free space, this provides a possible method for experimental observation of this phenomenon. ...
When electromagnetic energy propagates through a material medium, the paths of energy flow may be altered, as compared to propagation in free space. We consider radiation emitted by an electric dipole, embedded in a medium with permittivity and permeability . For a linear dipole in free space, the field lines of energy flow are straight, but when the imaginary part of is finite, the field lines in the material become curves in the near field of the dipole. Therefore, the energy flow is redistributed due to the damping in the material. For a circular dipole in free space, the field lines of energy flow wind around the axis perpendicular to the plane of rotation of the dipole moment. When has an imaginary part, this flow pattern is altered drastically. Furthermore, when the real part of is negative, the direction of rotation of the flow lines reverses. In that case, the energy in the field rotates opposite to the direction of rotation of the dipole moment. It is indicated that in metamaterials with a negative index of refraction this may lead to an observable effect in the far field.
The net angular momentum of light remains conserved during propagation. This conservation leads to a spin transport which becomes evident when light encounters a refractive index gradient, i.e., when it is reflected, refracted, or scattered. The phenomenon is so‐called as the spin‐orbit interaction (SOI) of light has paved the way to manipulate the light‐matter interaction at the nanoscale and has remained the core of many recent studies. Particularly, the photonic spin Hall effect (PSHE) of light which is the microscopic spin splitting into circular polarization has given rise to novel applications, for example, precision metrology. The PSHE is well explored at planar interfaces, however much less attention is given to it when the optical potential gradient is of higher dimensionality, i.e., for nanoparticles. In this review, the theoretical description of the PSHE as well as the SOI in the scattering of light from nanoparticles are covered. Recent advances and trends in the PSHE in nanoparticles are reviewed. The review is concluded with suggestions for some novel directions in the field of PSHE of nanoparticles.
The field lines of energy flow of radiation emitted by an oscillating electric dipole in free space are either straight lines (linear dipole) or they form a vortex (rotating dipole). When the dipole is embedded in a material, the properties of the medium affect the direction of energy flow. Damping due to the imaginary part of the relative permittivity (Formula presented.) makes the field lines curve for the case of a linear dipole, and for a rotating dipole, the shape of the vortex is altered. In addition, a negative value of the real part of (Formula presented.) has the effect that the rotation direction of the vortex reverses for the case of a rotating dipole. The value of the relative permeability (Formula presented.) has in general not much effect on the redistribution of the direction of energy propagation. We show that a dramatic effect occurs when the embedding material is near-single-negative (both (Formula presented.) and (Formula presented.) approximately real, and the real parts of opposite sign). The curving of field lines is in general a sub-wavelength phenomenon. For near-single-negative materials, however, this curving extends over large distances from the dipole. In particular, the small free-space vortex of a rotating dipole becomes a vortex of enormous dimensions when the radiation is emitted into a near-single-negative material.
Shenqi pill, a traditional Chinese herbal formula, is widely prescribed for hypertensive patients with kidney yang deficiency syndrome in China. This study aims to examine the efficacy and safety of Shenqi pill for the treatment of hypertension.
A systematic search of the Cochrane Central Register of Controlled Trials, PubMed, EMBASE, the Chinese National Knowledge Infrastructure, the Chinese Scientific Journal Database, the Chinese Biomedical Literature Database, and the Wanfang Database was conducted from their inception up to October 7, 2014. All randomized controlled trials (RCTs) testing Shenqi pill alone or combined with western medicine against placebo, no intervention or western medicine in hypertensive patients were included.
A total of 4 RCTs comparing Shenqi pill plus western medicine with western medicine were included. Shenqi pill as complementary therapy exhibited a relatively small with no significant reduction on blood pressure, and showed remarkable improvement on sexual function, lipid profile and some biochemical indicators of hypertensive renal damage compared to western medicine used alone. The safety of Shenqi pill is still unknown.
This systematic review firstly provided no definite evidence for the efficacy and safety of Shenqi pill for hypertension based on the insufficient data. More rigorously designed RCTs focusing on sexual dysfunction and hypertensive renal damage are warranted to give high level of evidence.
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We consider an oscillating electric dipole, embedded in a uniform medium with relative permittivity epsilon(1) and relative permeability mu(1). The dipole is located near an interface with a layer with uniform material parameters epsilon(2) and mu(2), and the second interface borders a uniform medium with parameters epsilon(3) and mu(3). We have obtained the solutions for the electric and magnetic fields in the various regions, without any restrictions on the parameters and for any state of oscillation of the dipole (elliptical, in general). The solution involves a set of auxiliary functions, which are given as integral representations containing the Fresnel coefficients for plane waves. With this solution, the field lines of energy flow can be obtained, and we have considered the flow pattern for the simple case of a dipole oscillating perpendicular to the interface. When the material of the layer is optically thicker than the embedding medium of the dipole, energy flows more or less along straight lines. At an interface, the field lines refract, similar to optical rays. When the layer material is optically thinner, the energy flow lines curve. A portion of the energy that propagates toward the interface bends away from it before reaching the interface. Other field lines of energy flow cross the interface, but then return to the area of the dipole by crossing the interface again. This leads to an oscillation of energy back and forth through the interface. In the neighborhood of this oscillation, a concentric set of vortex tori appears.
