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 unit vector and the propagation axis acts as a parameter that describes the vectorial property of the beam. The impact of $θ_I$ is investigated on a beam of angular-spectrum field scalar that is independent of the azimuthal angle. The field vector in position space is calculated in the first-order approximation under the paraxial condition. A transverse effect is found that a beam of elliptically-polarized angular spectrum is displaced from the center in the direction that is perpendicular to the plane formed by the fixed unit vector and the propagation axis. The expression of the transverse displacement is obtained. Its paraxial approximation is also given.
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.
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…
In this study, we report on the fractional Talbot effect of nonparaxial self-accelerating beams in a multilevel electromagnetically induced transparency (EIT) atomic configuration, which, to the best of our knowledge, is the first study on this subject. The Talbot effect originates from superposed eigenmodes of the Helmholtz equation and forms in the EIT window in the presence of both linear and cubic susceptibilities. The Talbot effect can be realized by appropriately selecting the coefficients of the beam components. Our results indicate that the larger the radial ifference between beam comp…
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…
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…
A unified description of the free-space cylindrical vector beams is presented, which is an integral transformation solution to the vector Helmholtz equation and the transversality condition. The amplitude 2-form of the angular spectrum involved in this solution can be arbitrarily chosen. When one of the two elements is zero, we arrive at either transverse-electric or transverse-magnetic beam mode. In the paraxial condition, this solution not only includes the known $J_1$ Bessel-Gaussian vector beam and the axisymmetric Laguerre-Gaussian vector beam that were obtained by solving the paraxial wa…
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…
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…
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…
Since 1908, when Mie reported analytical expressions for the fields scattered by a spherical particle upon incidence of an electromagnetic plane-wave, generalizing his analysis to the case of an arbitrary incident wave has proved elusive. This is due to the presence of certain radially-dependent terms in the equation for the beam-shape coefficients of the expansion of the electromagnetic fields in terms of vector spherical wave functions. Here we show for the first time how these terms can be canceled out, allowing analytical expressions for the beam shape coefficients to be found for a comple…
Ultra-BroadBand Electromagnetic Control Using a Triple Circular Ring Metasurface: Surface Wave Propagation, Beam Steering, and RCS reduction (50-100 Ghz)
Sylhet Engineering College（锡尔赫特工程学院）；North South University（北南大学）；Mahdy Research Academy（马迪研究院）
Classical beams of light with non-uniform polarization patterns (e.g. radially and azimuthally polarized doughnut beams) may exhibit quantum-like features as, for instance, inseparability. We establish an exact correspondence between radially and azimuthally polarized classical modes of the electromagnetic field and the two-qubit quantum Bell states. We demonstrate the existence of a special representation for such classical modes by means of a pair of Poincaré spheres. Points on these spheres are described by Stokes parameters associated with such modes, and their explicit expressions are giv…
Analytical solution for optical trapping force on a spherical dielectric particle for an arbitrary positioned focused beam is presented in a generalized Lorenz-Mie and vectorial diffraction theory. In this case the exact electromagnetic field is considered in the focal region. A double tweezers setup was employed to perform ultra sensitive force spectroscopy and observe the forces, demonstrating the selectively couple of the transverse electric (TE), transverse magnetic (TM) modes by means of the beam polarization and positioning, and to observe correspondent morphology-dependent resonances (M…
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…
The derivation of the Helmholtz theorem of vector decomposition of a 3-vector field requires that the field satisfy certain convergence properties at spatial infinity. This paper investigates if time-dependent electromagnetic radiation wave fields, which are of long range, satisfy these requirements. It is found that the requirements are satisfied because the fields give rise to integrals over the radial distance r of integrands of the form sin(kr)/r and cos(kr)/r. These Dirichlet integrals converge at infinity as required.
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 …
Coherent vector beams with involved states of polarization (SOP) are widespread in the literature, having applications in laser processing, super-resolution imaging and particle trapping. We report novel vector beams obtained by transforming a Gaussian beam passing through a biaxial crystal, by means of the conical refraction phenomenon. We analyze both experimentally and theoretically the SOP of the different vector beams generated and demonstrate that the SOP of the input beam can be used to control both the shape and the SOP of the transformed beam. We also identify polarization singulariti…
We report a novel experimental scheme for single-pass second harmonic generation (SHG) of vector vortex beam in the blue. Using an ultrafast Ti:Sapphire laser of pulse width ~17 fs and a set of spiral phase plates in polarization based Mach-Zehnder interferometer (MZI) we have generated vector vortex beams of order as high as lp = 12 at an average power of 860 mW. Given the space-variant polarization of the vector vortex beam, and the dependence of nonlinear frequency conversion processes on the polarization of the interacting beams, using two contiguous bismuth borate crystals with optic axis…
We experimentally demonstrate the Talbot effect resulting from the repeated self-reconstruction of a spatially intensity-modulated probe field under the Fresnel near-field regime. By launching the probe beam into an optically induced atomic lattice (established by interfering two coupling fields) inside a rubidium vapor cell, we can obtain an diffracted probe beam pattern from an formed electromagnetically induced grating (EIG) in a three-level $Λ$-type Doppler-free atomic configuration with the assistance of electromagnetically induced transparency (EIT). The EIG-based diffraction pattern rep…
It is observed that a constant unit vector denoted by $\mathbf I$ is needed to characterize a complete orthonormal set of vector diffraction-free beams. The previously found diffraction-free beams are shown to be included as special cases. The $\mathbf I$-dependence of the longitudinal component of diffraction-free beams is also discussed.
We propose a novel method to generate vector beams in planar photonic crystal cavities with multiple missing-hole defects. Simulating the resonant modes in the cavities, we observe that the optical fields in each defect have different phase and polarization state distributions, which promise the compositions of vector beams by the scattered light from the defects. The far-field radiation patterns of the cavity modes calculated via the Sommerfeld diffraction theory present vector beams possessing hollow intensity profiles and polarization singularities. In addition, the extraction efficiencies …
Negative propagation is an uncommon response produced by the local sign change in Poynting vector components. We present a general Poynting vector expression for all invariant beams with cylindrical symmetry using scalar potentials in order to evaluate the possibility of negative propagation. We analyze the plausibility of negative propagation being independent of mode mixing; we study Weber beams as a particular case. The study of this negative effect allow us to advance in the field of micro manipulation and understanding of optical forces. Applications of these beams are discussed.
A novel method is presented for the beam shaping of far field intensity distributions of coherently combined fiber arrays. The fibers are arranged uniformly on the perimeter of a circle, and the linearly polarized beams of equal shape are superimposed such that the far field pattern represents an effective radially polarized vector beam, or discrete cylindrical vector (DCV) beam. The DCV beam is produced by three or more beams that each individually have a varying polarization vector. The beams are appropriately distributed in the near field such that the far field intensity distribution has a…
In this letter a general method for expanding paraxial beams into multipolar electromagnetic fields is presented. This method is applied to the expansion of paraxial modes with orbital angular momentum (OAM), showing how the paraxial OAM is related to the general angular momentum of an electromagnetic wave. This method can be extended to quasi-paraxial beams, i.e. highly focused laser beams. Some applications to the control of electronic transitions in atoms are discussed.
The angular spectrum of a vectorial laser beam is expressed in terms of an intrinsic coordinate system instead of the usual Cartesian laboratory coordinates. This switch leads to simple, elegant and new expressions such as for the angular spectrum of the Hertz vector corresponding to the electromagnetic fields. As an application of this approach, we consider axially symmetric vector beams, showing non-diffracting properties of these beams, without invoking the paraxial approximation. Further, we indicate the relevance of the method for analyzing nonparaxial resonators, such as microresonators
Dual-Symmetrized Construction of Electromagnetic Beams Beyond the Paraxial Approximation with an Explicit Separation of Scalar and Vectorial Corrections
King Abdulaziz City for Science and Technology (KACST)（沙特阿拉伯国王科学技术城）；School of Chemistry, University of East Anglia（东英吉利大学化学学院）
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…
It is shown that the generally accepted definition of the Poynting vector and the energy flux vector defined by means of the energy density of the electromagnetic field (Umov vector) lead to the prediction of the different results touching electromagnetic energy flux. The experiment shows that within the framework of the mentioned generally accepted definitions the Poynting vector adequately describes the electromagnetic energy flux unlike the Umov vector. Therefore one can conclude that a generally accepted definitions of the electromagnetic energy density and the Poynting vector, in general,…
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…
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…
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…
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 present the classical electromagnetic theory framework of reflection of a light beam carrying Orbital Angular Momentum (OAM) by an in-plane magnetic structure with generic symmetry. Depending on the magnetization symmetry, we find a change in the OAM content of the reflected beam due to magneto-optic interaction and an asymmetric far-field intensity profile. This leads to three types of Magnetic Helicoidal Dichroism (MHD), observed when switching the OAM of the incoming beam, the magnetization sign, or both. In cases of sufficient symmetries, we establish analytical formulas which link an e…
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…
Vector beam, with a spatial nonuniform polarization distribution, is important for many applications due to its unique field characteristics and novel effects when interacting with matter. Here through three-dimensional particle-in-cell simulations, we demonstrate that intense vector beams in the extreme-ultraviolet to x-ray spectral region can be generated by means of high harmonic generation (HHG) in the relativistic regime. The vector features of the fundamental laser beam can be transferred to the higher frequency emission coherently during the extreme nonlinear HHG dynamics from relativis…
We propose a novel numerical approach for the optimal design of wide-area heterogeneous electromagnetic metasurfaces beyond the conventionally used unit-cell approximation. The proposed method exploits the combination of Rigorous Coupled Wave Analysis (RCWA) and global optimization techniques (two evolutionary algorithms namely the Genetic Algorithm (GA) and a modified form of the Artificial Bee Colony (ABC with memetic search phase method) are considered). As a specific example, we consider the design of beam deflectors using all-dielectric nanoantennae for operation in the visible wavelength…
Vector vortex beams are a class of optical beams with singularities in their space-variant polarization. Vector vortex beam lasers have applications in many areas including imaging and communication, where vertical-cavity lasers emitting Gaussian beams have been most widely used so far. Generation of vector vortex beams from vertical-cavity lasers has required external control or modulation. Here, by utilizing a polarization-selective subwavelength grating as one of the reflectors in a vertical semiconductor microcavity, we design the spin textures of the polariton mode and demonstrate polarit…
We demonstrate the use of cylindrical vector beams - beams with spatially varying polarization - for detecting and preparing the spin of a warm rubidium vapor in a spatially dependent manner. We show that a modified probe vector beam can serve as an atomic spin analyzer for an optically pumped medium, which spatially modulates absorption of the beam. We also demonstrate space-variant atomic spin by optical pumping with the vector beams. The beams are thus beneficial for making singleshot polarization-dependent measurements, as well as for providing a means of preparing samples with position-de…
