Irving Rondon, F. Soto-Eguibar
We present a description of the electromagnetic field for propagation invariant beams using scalar potentials. Fundamental dynamical quantities are obtained: the energy density, the Poynting vector and the Maxwell stress tensor. As an example, all these quantities are explicitly calculated for the Bessel beams, which are the invariant beams with circular cylindrical symmetry.
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We show that in addition to well known Bessel, Hermite-Gauss, and Laguerre-Gauss beams of electromagnetic radiation, one may also construct exponential beams. These beams are characterized by a fall-off in the transverse direction described by an exponential function of rho. Exponential beams, like Bessel beams, carry definite angular momentum and are periodic along the direction of propagation, but unlike Bessel beams they have a finite energy per unit beam length. The analysis of these beams is greatly simplified by an extensive use of the Riemann-Silberstein vector and the Whittaker represe…
We present a mathematical formalism describing the propagation of a completely general electromagnetic wave in a birefringent medium. Analytic formulas for the refraction and reflection from a plane interface are obtained. As a particular example, a Bessel beam impinging at an arbitrary angle is analyzed in detail. Some numerical results showing the formation and destruction of optical vortices are presented.
The new symmetry axis of a well-behaved electromagnetic beam advanced in paper Physical Review A 78, 063831 (2008) is not purely a mathematical concept. The experimental result reported by Hosten and Kwiat in paper Science 319, 787 (2008) is shown to demonstrate the existence of this symmetry axis that is neither perpendicular nor parallel to the propagation axis.
In a coherent monoenergetic beam of non-interacting particles, the phase velocity and the particle transport velocity are functions of position, with the strongest variation being in the focal region. These velocities are everywhere parallel to each other, and their product is constant in space. For a coherent monochromatic electromagnetic beam, the energy transport velocity is never greater than the speed of light, and can even be zero. The phase velocities (one each for the non-zero components of the electric and magnetic fields, in general) can be different from each other and from the ener…
Spectral electromagnetic Gaussian Schell-model (SEGSM) beam is a generalization of Gaussian Schell model beam having parameters with spectral dependence, which offers a basic classical model for random electromagnetic wide-sense statistically stationary beam-like fields. We study degree of polarization (DOP) of a SEGSM beam passing through 2-f and 4-f lens systems. It is observed that for a 2-f lens system, the spectral DOP at the back focal plane of the lens changes with respect to the transverse position from the optic axis, and the spectral parameters of the beam. For a 4-f lens system, the…
On-axis polarization of beams radiated by electromagnetic circularly coherent sources
本文提出具有柱对称和无限延伸的部分相干电磁源，利用汉克尔函数基函数展开给出交叉谱密度矩阵，并研究其辐射场的谱密度和三维偏振度，定义了一类相干矢量模式与基函数一致的柱对称源。
The polarization properties of monochromatic light beams are studied. In contrast to the idealization of an electromagnetic plane wave, finite beams which are everywhere linearly polarized in the same direction do not exist. Neither do beams which are everywhere circularly polarized in a fixed plane. It is also shown that transversely finite beams cannot be purely transverse in both their electric and magnetic vectors, and that their electromagnetic energy travels at less than c. The electric and magnetic fields in an electromagnetic beam have different polarization properties in general, but …
In this paper, we utilize the deformation transformation optics (DTO) method to design electromagnetic beam bender, which can change the direction of electromagnetic wave propagation as desire. According to DTO, the transformed material parameters can be expressed by deformation tensor of the spatial transformation. For a beam bender, since the three principal stretches at each point induced by the spatial transformation are independent to each other, there are many possibilities to simplify the transformed material parameters of the bender by adjusting the stretches independently. With the DT…
Cross-spectral purity of the Stokes parameters in random nonstationary electromagnetic beams
本研究从斯托克斯参数角度探究随机非平稳电磁光束的交叉谱纯度，推导得出符合Mandel原始定义的纯度条件及含偏振相关第三因子的约化公式，为相关矢量光干涉研究提供基础性进展。
A representation theory of finite electromagnetic beams in free space is formulated by factorizing the field vector of the plane-wave component into a $3 \times 2$ mapping matrix and a 2-component Jones-like vector. The mapping matrix has one degree of freedom that can be described by the azimuthal angle of a fixed unit vector with respect to the wave vector. This degree of freedom allows us to find out such a beam solution in which every plane-wave component is specified by the same fixed unit vector $\mathbf{I}$ and has the same normalized Jones-like vector. The angle $θ_I$ between the fixed…
During the last 2 years, it was shown that an electromagnetic beam configuration can be bent after propagation through an asymmetrically shaped (Janus) dielectric particle, which adds a new degree of simplicity for generation of a curved light beam. This effect is termed "photonic hook" (PH) and differs from Airy-family beams. PH features the smallest curvature radius of electromagnetic waves ever reported which is about 2 times smaller than the wavelength of the electromagnetic wave. The nature of a photonic hook is a the dispersion of the phase velocity of the waves inside a trapezoid or com…
Many nanophotonic applications require precise control and characterization of electromagnetic field properties at the nanoscale. The chiral properties of the field are among its key characteristics, yet measurement of optical chirality at dimensions beyond the diffraction limit has proven difficult. Here we theoretically show that the chiral properties of light can be characterized down to the nanometer scale by means of force detection. To measure the chiral properties of a beam of given handedness at the nanoscale, we determine the photo-induced force exerted on a sharp tip, which is illumi…
The transformation media concept based on the form-invariant Maxwell's equations under coordinate transformations has opened up new possibilities to manipulate the electromagnetic fields. In this paper we report on applying the finite-embedded coordinate transformation method to design electromagnetic beam modulating devices both in the Cartesian coordinates and in the cylindrical coordinates. By designing the material constitutive tensors of the transformation optical structures through different kinds of coordinate transformations, either the beam width of an incident Gaussian plane wave cou…
It is shown that three-dimensional nonparaxial beams are described by the oblate spheroidal exact solutions of the Helmholtz equation. For the first time, their beam behaviour is investigated and their corresponding parameters are defined. Using the fact that the beam width of the family of paraxial Gaussian beams is described by an hyperbola, the connection between the physical parameters of nonparaxial spheroidal beam solutions and those of paraxial beams is formally stablished. These results are also helpful to investigate the exact vector nonparaxial beams.
We present a new class of exact nonsingular solutions for the Maxwell equations in vacuum, which describe the electromagnetic field of the counterpropagating focused laser beams and the subperiod focused laser pulse. These solutions are derived by the use of a modification of the "complex source method", investigated and visualized.
We present a solution to the problem of partial reflection and refraction of a polarized paraxial Gaussian beam at the interface between two transparent media. The Fedorov--Imbert transverse shift of the centers of gravity of the reflected and refracted beams are calculated. Our results differ in general case from ones derived previously by other authors. In particular, they obey general conservation law for the beams' total angular momentum but do not obey one-particle conservation laws for individual photons, which have been proposed by Onoda et al. [Phys. Rev. Lett. 93, 083901 (2004)]. We a…
Majorana constellations for optical scalar beams and vector fields
本文利用光角动量的su(2)对称性，在黎曼球面上构建标量光束与矢量场的马约拉纳星座表示，揭示拉盖尔-高斯、厄米-高斯及部分庞加莱场的几何结构，并探讨猫态码与量子性之王的类比及其光通信应用潜力。
High Refractive Index (HRI) dielectric particles smaller than the wavelength, isolated or forming a designed ensemble are ideal candidates as new multifunctional elements for building optical devices. Their directionality effects are traditionally analyzed through forward and backward measurements, even if these directions are not suitable for practical purposes. Here we present unambiguous experimental evidence in the microwave range that, for a dimer of HRI spherical particles, a perfect switching effect (perfect means off = null intensity) is observed out of those directions as a consequenc…
Probing the electromagnetic response of dielectric antennas by vortex electron beams
本研究通过理论分析涡旋电子束能量损失谱学，揭示了其可高效探测介电纳米天线的电与磁模式，并通过调节涡旋性或加速电压控制探测效率，为表征光学激发提供了新途径。
An analytical discontinuity is reported in what was thought to be the discontinuity-free exact nonparaxial vortex beam phasor obtained within the complex source/sink model. This discontinuity appears for all odd values of the orbital angular momentum mode. Such discontinuities in the phasor lead to nonphysical discontinuities in the real electromagnetic field components. We identify the source of the discontinuities, and provide graphical evidence of the discontinuous real electric fields for the first and third orbital angular momentum modes. A simple means of avoiding these discontinuities i…
The study of an optical beam interacting with material structures is a fundamental of nanophotonics. Computational electromagnetic solvers facilitate the rapid calculation of the scattering from material structures with arbitrary geometry and complexity, but have limited efficiency when employing structured excitation fields. We have developed a post-processing method and package that can efficiently calculate the full three-dimensional electric and magnetic fields for any optical beam incident on a particle or structure with at least one axis of continuous rotational symmetry, called an axisy…
In Part I (physics/0405091), it was shown that it is possible to achieve efficient heating of cylindrical targets by electromagnetic beams with transverse dimensions that are several orders of magnitude greater than those of the cylinder. Part II contains derivation of the detailed conditions of efficient heating in the longitudinal geometry and establishes a broader domain of parameters providing efficient heating in the transverse geometry. One possible implementation using currently available technology is considered: a nanotube (length 1 cm, diameter 15 nm) may be heated in the transverse …
Asymptotic Solution for Skin Heating by an Electromagnetic Beam at an Incident Angle
针对斜入射毫米波电磁束加热皮肤问题，本文利用穿透深度远小于横向尺度的渐近分析推导任意入射角下温度分布首项解，并给出皮肤温度与伤害感受器激活体积的标度律。
Scalar and vector electromagnetic solitary waves in nonlinear hyperbolic media
该研究针对双曲非线性介质中的电磁波传播问题，通过Hirota双线性方法推导标量和矢量电磁孤波的精确解析形式，发现双曲横向色散可抑制奇异性形成，且孤波具备传统介质中没有的独特传播特性，为双曲非线性超材料的电磁波传播分析提供支撑。
Dual-Symmetrized Construction of Electromagnetic Beams Beyond the Paraxial Approximation with an Explicit Separation of Scalar and Vectorial Corrections
该研究提出了一种超越傍轴近似的电磁光束构造的双对称微扰框架，可显式分离标量与矢量修正，适用于任意傍轴包络和输入琼斯偏振，解决了矢量修正分配依赖构造的问题。
The quasi-optical segmented mirror for a formation of the target irradiation field was manufactured and investigated. It was designed for the high power THz beam of the free electron laser (FEL) using as a target a dust particle cloud, simulating cosmic dust. Numerical calculation of the beam shape and its low power laboratory measurements was made in the spectral region 1 - 3 THz of the first phase of the Novosibirsk FEL construction. The theoretical calculations of the diffraction effects reveal a speckle structure of a target spot, which was confirmed by the laboratory experiment. The beamf…
A theory for the characterization of the fourth moment of electromagnetic wave beams is presented in the case when the source is partially coherent. A Gaussian-Schell model is used for the partially coherent random source. The white-noise paraxial regime is considered, which holds when the wavelength is much smaller than the correlation radius of the source, the beam radius of the source, and the correlation length of the medium, which are themselves much smaller than the propagation distance. The complex wave amplitude field can then be described by the Itô-Schrödinger equation. This equation…
The electromagnetic scalar product in spatially-bounded domains
针对现有电磁标量积表达式无法直接适用于空间有界域内电磁场的问题，本文推导了仅含闭合曲面积分的辐射场电磁标量积表达式，可用于计算光脉冲的光子数等物理量，扩展了Maxwell求解器的功能。
Previous work [I. Bialynicki-Birula, Phys. Rev. Lett. {\bf 93}, 20402 (2004)] is extended to cover more realistic examples of electromagnetic waves, viz. the Bessel beams. It is shown that electrons may be guided by a Bessel beam with nonvanishing orbital angular momentum. The mechanism for trapping the electrons near the electromagnetic vortex line of such a wave field is the same as for the Trojan states of Rydberg electrons produced by a circularly polarized wave. The main difference is that in the present case the transverse motion of electrons in a beam is confined under the action of the…
Propagation properties of partially coherent electromagnetic hyperbolic-sine-Gaussian vortex beam through anisotropic atmospheric turbulence
该研究推导了部分相干电磁双曲正弦高斯涡旋光束在各向异性大气湍流中传输的解析公式，分析了其光强、相干度、偏振度的演化规律，并通过随机相位屏模拟验证了理论结果的一致性。
Absorption of electromagnetic energy by a dissipative material is one of the most fundamental electromagnetic processes that underlies a plethora of applied problems, including sensing and molecular detection, radar detection, wireless power transfer, and photovoltaics. Perfect absorption is a particular regime when all of the incoming electromagnetic energy is absorbed by the system without scattering. Commonly, the incident energy is delivered to the absorbing system by a plane wave, hence perfect absorption of this wave requires an infinitely extended planar structure. Here, we demonstrate …
We present a solution to the problem of reflection/refraction of a polarized Gaussian beam on the interface between two transparent media. The transverse shifts of the beams' centers of gravity are calculated. They always satisfy the total angular momentum conservation law for beams, however, in general, do not satisfy the conservation laws for individual photons in consequence of the lack of the ``which path'' information in a two-channel wave scattering. The field structure for the reflected/refracted beam is analyzed. In the scattering of a linearly-polarized beam, photons of opposite helic…
Breaking the reciprocity of electromagnetic interactions is of paramount importance in photonic and microwave technologies, as it enables unidirectional power flows and other unique electromagnetic phenomena. Here we explore a method to break the reciprocity of electromagnetic guided waves utilizing an electron beam with a constant velocity. By introducing an effective dynamic conductivity for the beam, we theoretically demonstrate how nonreciprocal guided waves and a one-way propagating regime can be achieved through the interaction of swift electrons with electromagnetic waves in two-dimensi…
A comparative study of focusing with scalar and vector beams in an active Raman gain system
本研究在四态原子 active-Raman-gain 系统中推导了标量与矢量探测光束的线性和三阶非线性极化率，发现巨大的 cross-Kerr 非线性可使标量光束聚焦成更小光斑，而矢量光束呈增益诱导变窄，为提升显微分辨率提供了新途径。
We present a general theory of three-dimensional nonparaxial spatially-accelerating waves of the Maxwell equations. These waves constitute a two-dimensional structure exhibiting shape-invariant propagation along semicircular trajectories. We provide classification and characterization of possible shapes of such beams, expressed through the angular spectra of parabolic, oblate and prolate spheroidal fields. Our results facilitate the design of accelerating beams with novel structures, broadening scope and potential applications of accelerating beams.
We construct a novel Lagrangian representation of acoustic field theory that describes the local vector properties of longitudinal (curl-free) acoustic fields. In particular, this approach accounts for the recently-discovered nonzero spin angular momentum density in inhomogeneous sound fields in fluids or gases. The traditional acoustic Lagrangian representation with a ${\it scalar}$ potential is unable to describe such vector properties of acoustic fields adequately, which are however observable via local radiation forces and torques on small probe particles. By introducing a displacement ${\…
Scalar axion field of toroidal electromagnetic pulses
研究环状电磁脉冲在自由空间中的叠加如何产生非零E·B区域，通过轴子电磁动力学生成时空局域的伪标量场。
Certain models involving ALPs (axion-like-particles) allow for the coupling of scalars and pseudoscalars to fermions. A derivation of the total rate for production of massive scalars and pseudoscalars by an electron in a monochromatic, circularly-polarised electromagnetic background is presented. In addition, a derivation and the total rate for the decay of massive scalars and pseudoscalars into electron-positron pairs in the same electromagnetic background is given. We conclude by approximating the total yield of ALP production for a typical laser-particle experimental scenario.
Cylindrical vector beam (CVB) is a structured lightwave characterized by its topologically nontrivial nature of the optical polarization. The unique electromagnetic field configuration of CVBs has been exploited to optical tweezers, laser accelerations, and so on. However, use of CVBs in research fields outside optics such as condensed matter physics has not progressed. In this paper, we propose potential applications of CVBs to those fields based on a general argument on their absorption by matter. We show that pulse azimuthal CVBs around terahertz (THz) or far-infrared frequencies can be a u…
Under conditions of strong scattering, a dilemma often arises regarding the best numerical method to use. Main competitors are the Born series, the Beam Propagation Method, and direct solution of the Lippmann-Schwinger equation. However, analytical relationships between the three methods have not yet, to our knowledge, been explicitly stated. Here, we bridge this gap in the literature. In addition to overall insight about aspects of optical scattering that are best numerically captured by each method, our approach allows us to derive approximate error bounds to be expected under various scatte…
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