Optical Theorem Research Articles

Reflected energy flux anomaly under grazing incidence: the Brewster angle analogy

The paper presents thorough theoretical and numerical analysis of the anomalies accompanying light diffraction on periodical structures (gratings). We have developed appropriate theoretical approach allowing to consider strong anomalous effects. Obtained results are presented in the form of analytical expressions for the quntities of interest, both diffracted field amplitudes and the outgoing waves energy fluxes. It is proved existence of the fluxes extrema at the specific grazing angle of incidenceб or wavelength. Namely, the specular reflection can be suppressed even for rather shallow gratings up to approximately total suppression.This effect is accompanied by essential energy redistribution between all outgoing waves depending on the grating profile. It is of essence that the energy maxima exist in all nonspecular diffraction orders at the same point (angle, wavelength) as the minimal specular reflectivity. For small period gratings, such that there do not exist other outgoing waves except the specular one, the reflectance minimum is attended by approximately total absorption of the incident radiation. Thus, we show that the grazing anomaly (GA) can be accompanied by redirection of the incident wave energy into nonspecular diffraction channels and into absorption. The results are applicable in the wide spectral region, from visible and near-infrared to terahertz and high-frequency regions for metals and semiconductors with high permittivity. The anomaly considered is well expressed for high electromagnetic contrast of the adjacent media, say, air and metal or semiconductor. Then the high contrast is due to the high value of the metal/semiconductor dielectric permittivity  ,  1 , and the anomaly corresponds to incidence of TM polarized wave. It is shown that the grazing anomaly (GA) is of rather general type and can take place if other than the specular diffraction order experiencies grazing propagation also. This property follows from the results obtained by strict application of the optical reciprocity theorem to the geometry under consideration. The specific case of harmonic relief grating is discussed in detail. It is demomstrated existence of the characteristic inclination, cr a , of the relief inclinatuion for the grating period comparable with the incident radiation wavelength, 1 cr a  , where  stays for the surface impedance,  1  . The condition cr a a , or greater, corresponds to highly expressed GA. The theoretical results are illustrated by numerical applications to gratings on Cu\vacuum (air) interface in THz region. The results obtained can be simply transferred to the TE polarized waves. For this we have to consider the adjacent media with high contrast magnetic properties, i.e., high value of the magnetic permeability  ,  1 . This case is of high interest for nowaday applications in nanophotonics and metamaterials development. As compared with other anomalies GA is attributed to the resonance-type behaviour of the energy flux, not wave amplitudes, the latter change monotonically within this anomaly contrary to the well known Rayleigh and resonance anomalies, where the wave amplitude experiences fast nonmonotonous dependence on the angle of incidence and wavelength.

Asymptotic behavior of numerical solutions of the Schrodinger equation

Many problems of numerically solving the Schrodinger equation require that we choose asymptoticdistances many times greater than the characteristic size of the region of interaction. The problems ofresonance diffraction for composite particles or the problem of nucleon scattering by nonspherical atomicnuclei are examples of the need to use a large spatial domain for calculations. If the solution to onedimensionalequations can be immediately chosen in a form that preserves unitarity, the invariance ofprobability (in the form of, e.g., fulfilling an optical theorem) is a real problem for two-dimensionalequations. An addition that does not exceed the discretization error and ensures a high degree of unitarityis proposed as a result of studying the properties of a discrete two-dimensional equation.The problem for scattering of rigid molecules by the disks was successfully solved using an improvedsampling scheme that provides the correct asymptotic behavior. Corresponding diffraction scatteringcurves are of a pronounced resonance nature.

Construction of the Approximate Solution to the Problems of Diffraction of Electromagnetic Waves by Small Particles with the Use of the Pattern Equation Method

Evident approximate formulas are given for the integral characteristics of scattering. These formulas can be applied for small 3D scatterers having complex shapes. For some examples, the results of the approximate approach are compared with the exact results obtained with the help of the Pattern Equation Method. It is shown for a wide range of the problem parameters that the accuracy of computations controlled with the use of the calculated balance of the power fluxes for the incident and scattered waves (i.e., with the use of the test of fulfillment of the optical theorem) is quite sufficient for the practice.

Решение задач рассеяния волн телами, имеющими изломы границы, и фракталоподобными телами вращения

AbstractBased on the method of continued boundary conditions, a technique is proposed that allows one to model the scattering characteristics, including averaged over orientation angles, for bodies of practically any geometry. A number of examples of solving problems of diffraction on fractal-like bodies of revolution are given. The correctness of the method is confirmed by verifying the implementation of the optical theorem for various bodies and by comparing with the results of calculations obtained by the method of discrete sources.

Graviton scattering and a sum rule for the c anomaly in 4D CFT

4D CFTs have a scale anomaly characterized by the coefficient c, which appears as the coefficient of logarithmic terms in momentum space correlation functions of the energy-momentum tensor. By studying the CFT contribution to 4-point graviton scattering amplitudes in Minkowski space we derive a sum rule for c in terms of TT mathcal{O} OPE coefficients. The sum rule can be thought of as a version of the optical theorem, and its validity depends on the existence of the massless and forward limits of the 〈TTTT〉 correlation functions that contribute. The finiteness of these limits is checked explicitly for free scalar, fermion, and vector CFTs. The sum rule gives c as a sum of positive terms, and therefore implies a lower bound on c given any lower bound on TT mathcal{O} OPE coefficients. We compute the coefficients to the sum rule for arbitrary operators of spin 0 and 2, including the energy-momentum tensor.

Perturbative unitarity and higher-order Lorentz symmetry breaking

We study perturbative unitarity in the scalar sector of the Myers-Pospelov model. The model introduces a preferred four-vector $n$ which breaks Lorentz symmetry and couples to a five-dimension operator. When the preferred four-vector is chosen in the pure timelike or lightlike direction, the model becomes a higher time derivative theory, leading to a cubic dispersion relation. Two of the poles are shown to be perturbatively connected to the standard ones, while a third pole, which we call the Lee-Wick-like pole, is associated to a negative metric, in Hilbert space, threatening the preservation of unitarity. The pure spacelike case is a normal theory in the sense that it has only two solutions both being small perturbations over the standard ones. We analyze perturbative unitarity for purely spacelike and timelike cases using the optical theorem and considering a quartic self-interaction term. By computing discontinuities in the loop diagram, we arrive at a pinching condition which determines the propagation of particles and Lee-Wick-like particles through the cut. We find that the contribution for Lee-Wick-like particles vanishes for any external momenta, leaving only the contribution of particles, thus preserving one-loop unitarity in both cases.

Conformal basis, optical theorem, and the bulk point singularity

We study general properties of the conformal basis, the space of wavefunctions in $(d+2)$-dimensional Minkowski space that are primaries of the Lorentz group $SO(1,d+1)$. Scattering amplitudes written in this basis have the same symmetry as $d$-dimensional conformal correlators. We translate the optical theorem, which is a direct consequence of unitarity, into the conformal basis. In the particular case of a tree-level exchange diagram, the optical theorem takes the form of a conformal block decomposition on the principal continuous series, with OPE coefficients being the three-point coupling written in the same basis. We further discuss the relation between the massless conformal basis and the bulk point singularity in AdS/CFT. Some three- and four-point amplitudes in (2+1) dimensions are explicitly computed in this basis to demonstrate these results.

Generalization of the optical theorem: experimental proof for radially polarized beams

The optical theorem, which is a consequence of the energy conservation in scattering processes, directly relates the forward scattering amplitude to the extinction cross-section of the object. Originally derived for planar scalar waves, it neglects the complex structure of the focused beams and the vectorial nature of the electromagnetic field. On the other hand, radially or azimuthally polarized fields and various vortex beams, essential in modern photonic technologies, possess a prominent vectorial field structure. Here, we experimentally demonstrate a complete violation of the commonly used form of the optical theorem for radially polarized beams at both visible and microwave frequencies. We show that a plasmonic particle illuminated by such a beam exhibits strong extinction, while the scattering in the forward direction is zero. The generalized formulation of the optical theorem provides agreement with the observed results. The reported effect is vital for the understanding and design of the interaction of complex vector beams carrying longitudinal field components with subwavelength objects important in imaging, communications, nanoparticle manipulation, and detection, as well as metrology.

Symmetries of scattering factors and diffraction efficiencies in grating theory.

This paper theoretically discusses basic topics on the reciprocity theorem and the optical theorem in the grating theory for plane wave reflection and transmission from a periodic rough interface between two-layered homogeneous media. Based on the shadow theory, symmetries of the scattering factors and diffraction efficiencies are newly presented in several formulas.

Application of the Pattern Equation Method to the Analysis of Electromagnetic Wave Scattering by a Thin Cylinder of an Arbitrary Cross Section

An approximate approach based on application of the pattern equation method is developed for solution of the problem of scattering by a thin cylinder. Explicit formulas for integral scattering characteristics that are applicable to cylindrical scatterers of a complex shape are derived. The accuracy of these formulas is controlled by checking fulfillment of the “optical theorem.”

Nonlocal vertices and analyticity: Landau equations and general Cutkosky rule

We study the analyticity properties of amplitudes in theories with nonlocal vertices of the type occurring in string field theory and a wide class of nonlocal field theory models. Such vertices are given in momentum space by entire functions of rapid decay in certain (including Euclidean) directions ensuring UV finiteness but are necessarily of rapid increase in others. A parametric representation is obtained by integrating out the loop (Euclidean) momenta after the introduction of generalized Schwinger parameters. Either in the original or parametric representation, the well-defined resulting amplitudesare then continued in the complex space of the external momenta invariants. We obtain the alternative forms of the Landau equations determining the singularity surfaces showing that the nonlocal vertices serve as UV regulators but do not affect the local singularity structure. As a result the full set of singularities known to occur in local field theory also occurs here: normal and anomalous thresholds as well as acnodes, crunodes, and cusps that may under certain circumstances appear even on the physical sheet. Singularities of the second type also appear as shown from the parametric representation. We obtain the general Cutkosky discontinuity rule for encircling a singularity by employing contour deformations only in the finite plane. The unitarity condition (optical theorem) is thendiscussed as a special application of the rule across normal thresholds and the hermitian analyticity property of amplitudes.

Asymptotic Behavior of Solutions in Finite Difference Schemes

In many problems of numerically solving the Schrodinger equation, it is necessary to choose asymptotic distances that are many times greater than the characteristic size of the region of interaction. If the solutions to one-dimensional equations can be immediately chosen in a form that preserves unitarity, the preservation of probability (in, e.g., the form of optical theorem implementation) is then a real problem for two-dimensional equations. As result of studying the properties of a discretized two-dimensional equation, an additional term is found that does not exceed the sampling error and ensures a high degree of unitarity preservation.

Quantum Forces from Dark Matter and Where to Find Them

We observe that sub-GeV dark matter (DM) induces Casimir-Polder forces between nucleons that can be accessed by experiments from nuclear to molecular scales. We calculate the nucleon-nucleon potentials arising in the DM effective theory and note that their main features are fixed by dimensional analysis and the optical theorem. Molecular spectroscopy and neutron scattering turn out be DM search experiments and are found to be complementary to nucleon-based DM direct detection. Existing data set limits on DM with mass up to ∼3-50 MeV and with effective interaction up to the O(10-100) MeV scale, constraining a region typically difficult to reach for other experiments.

Initial State Radiation Measurements at BESIII

A difference of more than three standard deviations between is currently observed between the direct experimental measurement and the Standard Model prediction of the anomalous magnetic moment of the muon (g−2)μ. The hadronic vacuum polarization contributions can be related to hadronic cross sections using the optical theorem. Precision measurements of the hadronic cross sections e+e−→π+π−, π+π−π0, π+π−2π0, ωπ0 and π+π−3π0 are performed at the BESIII experiment located in Beijing, China. The initial state radiation method is used to access the energy regions of interest for (g−2)μ. Our results will improve the precision of the Standard Model prediction of (g−2)μ.

Singular lensing from the scattering on special space\u2013time defects

It is well known that certain special classes of self-gravitating point-like defects, such as global (non gauged) monopoles, give rise to non-asymptotically flat space–times characterized by solid angle deficits, whose size depends on the details of the underlying microscopic models. The scattering of electrically neutral particles on such space–times is described by amplitudes that exhibit resonant behaviour when thescattering and deficit angles coincide. This, in turn, leads to ring-like structures where the cross sections are formally divergent (“singular lensing”). In this work, we revisit this particular phenomenon, with the twofold purpose of placing it in a contemporary and more general context, in view of renewed interest in the theory and general phenomenology of such defects, and, more importantly, of addressing certain subtleties that appear in the particular computation that leads to the aforementioned effect. In particular, by adopting a specific regularization procedure for the formally infinite Legendre series encountered, we manage to ensure the recovery of the Minkowski space–time, and thus the disappearance of the lensing phenomenon, in the no-defect limit, and the validity of the optical theorem for the elastic total cross section. In addition, the singular nature of the phenomenon is confirmed by means of an alternative calculation, which, unlike the original approach, makes no use of the generating function of the Legendre polynomials, but rather exploits the asymptotic properties of the Fresnel integrals.

Hadronic vacuum polarization and e+e− → μ+μ− cross section: Reanalysis with new precise data for σh with 4π final states included

The interference effect between leptonic radiative corrections and hadronic polarization functions is calculated via optical theorem for μ–pair production in vicinity of narrow resonances. Within seven most dominant exclusive channels of the production cross section σh(e+e− → hadrons) one achieves high acuracy which is necessary for the comparison with experiments. The result is compared with KLOE and KLOE2 experiments for μ−μ+ and μ−μ+γ productions at φ and ω/ρ meson energy.

Absorption, scattering, and radiation force efficiencies in the longitudinal wave scattering by a small viscoelastic particle in an isotropic solid.

Analytical expressions of the absorption, scattering, and elastic radiation force efficiency factors are derived for the longitudinal plane wave scattering by a small viscoelastic particle in a lossless solid matrix. The particle is assumed to be much smaller than the incident wavelength, i.e., the so-called long-wavelength (Rayleigh) approximation. The efficiencies are dimensionless quantities that represent the absorbed and scattering powers and the elastic radiation force on the particle. In the quadrupole approximation, they are expressed in terms of contrast functions (bulk and shear moduli, and density) between the particle and solid matrix. The results for a high-density polyethylene particle embedded in an aluminum matrix agree with those obtained with the partial wave expansion method. Additionally, the connection between the elastic radiation force and forward scattering function is established through the optical theorem. The present results should be useful for ultrasound characterization of particulate composites, and the development of implanted devices activated by radiation force.

Scattering of a longitudinal Bessel beam by a sphere embedded in an isotropic elastic solid.

The scattering of a longitudinal Bessel beam of arbitrary order by a sphere embedded in an isotropic solid matrix is theoretically analyzed. The spherical inclusion can be made of a viscoelastic, elastic, or fluid-filled isotropic material. In the analysis, the absorbing, scattering, and extinction efficiency factors are obtained, e.g., the corresponding power per characteristic beam intensity per sphere's cross-section area. Furthermore, the extended optical theorem, which expresses the extinction efficiency in terms of an integral of the longitudinal scattering function is derived. Several features of zeroth- and first-order Bessel beams scattering in solids are illustrated considering a polymer adhesive (cured) sphere embedded in a stainless steel matrix. For instance, omnidirectional scattering can be achieved by choosing specific values of the half-cone angle of the Bessel beam, which is the beam's geometrical parameter. Additionally, it is demonstrated that mode suppression leads to lower absorption inside the inclusion when compared to plane wave scattering results.

Prediction of deviations from the Rutherford formula for low-energy Coulomb scattering of wavepackets

We calculate the nonrelativistic scattering of a wavepacket from a Coulomb potential and find deviations from the Rutherford formula in all cases. These generally occur only at low scattering angles, where they would be obscured by the part of the incident beam that emerges essentially unscattered. For a model experiment, the scattering of helium nuclei from a thin gold foil, we find the deviation region is magnified for low incident energies (in the keV range), so that a large shadow zone of low probability around the forward direction is expected to be measurable. From a theoretical perspective, the use of wavepackets makes partial wave analysis applicable to this infinite-range potential. It allows us to calculate the everywhere finite probability for a wavepacket to wavepacket transition and to relate this to the differential cross section. Time delays and advancements in the detection probabilities can be calculated. We investigate the optical theorem as applied to this special case.

Daylighting System Based on Novel Design of Linear Fresnel lens

In this paper, we present a design and optical simulation of a daylighting system using a novel design of linear Fresnel lens, which is constructed based on the conservation of optical path length and edge ray theorem. The linear Fresnel lens can achieve a high uniformity by using a new idea of design in which each groove of the lens distributes sunlight uniformly over the receiver so that the whole lens also uniformly distributes sunlight over the receiver. In this daylighting system, the novel design of linear Fresnel lens significantly improves the uniformity of collector and distributor. Therefore, it can help to improve the performance of the daylighting system. The structure of the linear Fresnel lenses is designed by using Matlab. Then, the structure of lenses is appreciated by ray tracing in LightToolsTM to find out the optimum lens shape. In addition, the simulation is performed by using LightToolsTM to estimate the efficiency of the daylighting system. The results show that the designed collector can achieve the efficiency of ~80% with the tolerance of ~0.60 and the concentration ratio of 340 times, while the designed distributor can reach a high uniformity of >90%.