Optical Theorem Research Articles

Searching for QCD instantons at hadron colliders

QCD instantons are non-perturbative phenomena predicted to arise from the strong force, but which have not been directly observed. However, they may appear as a large number of soft jets in LHC collisions. In this paper the authors provide a state-of-the-art calculation of the event rate for these signals by making use of the optical theorem and higher-order contributions. Despite estimating a large cross-section, they find such searches will be difficult due to trigger thresholds and suggest to look for them in data from low-luminosity runs.

Решение двумерной задачи дифракции волн на фракталоподобных телах методом диаграммных уравнений

The solution of the two-dimensional wave diffraction problem for infinite cylinder of complex cross-section was considered by using the pattern equations method (PEM). A triangle and a Koch snowflake of first iteration were chosen as the geometry of the cross-sections of the cylinder. The numerical algorithms of the PEM for a single scatterer and for a group of bodies with the Dirichlet condition on their boundary are briefly presented, and the results of numerical calculations of the scattering characteristics for the above geometries are obtained using the PEM and the method of continued boundary conditions (MCBC). To check the convergence of the numerical algorithm in both methods, the optical theorem was used. The limits of applicability of the PEM for fractal scatterers are established. It is shown that for all convex bodies the algorithm of the PEM is sufficiently stable and allows obtaining calculation results with an accuracy acceptable in practice. In the case of a non-convex body, namely, a Koch snowflake, the algorithm of the PEM for a single scatterer turns out to be unstable and the acceptable accuracy can be obtained only if this geometry is considered as a group of bodies composed of convex geometries (for example, triangles).

Analysis of Interaction Scattering Cross Sections and Their Physical Bounds for Multiple-Dipole Stimulation of a Three-Dimensional Layered Medium

A three-dimensional layered and isotropic medium is excited by primary spherical waves due to $N$ magnetic dipoles radiating inside or outside the medium. Interaction scattering cross sections (ISCS) are defined as the differences between the overall scattering cross section and the sum of the individual cross sections generated by all dipoles within a layer or by all $N$ dipoles. Optical theorems and physical bounds for the ISCS are established. Extensive numerical investigations are performed for the variations of the ISCS and their physical bounds with respect to the geometrical and physical characteristics of the layered medium. Conditions for which ISCS contribute significantly in the overall cross section are analyzed. It is also demonstrated that the number of excitation layers and the total number $N$ of dipoles can be determined by means of the individual scattering cross sections.

Generalized optical theorem for Rayleigh scattering approximation

A general expression for the optical theorem for probe sources given in terms of propagation invariant beams is derived. This expression is obtained using the far field approximation for Rayleigh regime. In order to illustrate this results is revisited the classical and standard scattering elastic problem of a dielectric sphere for which the incident field can be any arbitrary invariant beam.

Raman scattering in high-refractive-index nanostructures

Abstract The advent of resonant dielectric nanomaterials has provided a new path for concentrating and manipulating light on the nanoscale. Such high-refractive-index materials support a diverse set of low-loss optical resonances, including Mie resonances, anapole states, and bound states in the continuum. Through these resonances, high-refractive-index materials can be used to engineer the optical near field, both inside and outside the nanostructures, which opens up new opportunities for Raman spectroscopy. In this review, we discuss the impact of high-refractive-index nano-optics on Raman spectroscopy. In particular, we consider the intrinsic Raman enhancement produced by different dielectric resonances and their theoretical description. Using the optical reciprocity theorem, we derive an expression which links the Raman enhancement to the enhancement of the stored electric energy. We also address recent results on surface-enhanced Raman spectroscopy based on high-refractive-index dielectric materials along with applications in stimulated Raman scattering and nanothermometry. Finally, we discuss the potential of Raman spectroscopy as a tool for detecting the optical near-fields produced by dielectric resonances, complementing reflection and transmission measurements.

Generalized hybrid anapole modes in all-dielectric ellipsoid particles [Invited

Numerous exciting optical effects in all-dielectric high-refractive-index structures are associated with so-called toroidal electrodynamics. Among these effects are anapoles, nonradiated states caused by interference phenomena, e.g. between electric dipole and toroidal dipole modes. For a spherical particle it is possible to reach simultaneous destructive interference for electric, magnetic, and corresponding toroidal dipole modes (so-called hybrid anapole mode), by varying the refractive index and/or particle size. However, there are no sufficient degrees of freedom within spherical geometry to extend the hybrid anapole mode effect to higher multipoles. Due to the optical theorem, it is also impossible to create the ideal anapole with destructive interference for all multipoles under plane wave illumination. In principle, it is possible to suppress radiation losses for the finite number of multipoles only by constructing the nanoantenna with complex geometry. Our approach of the hybrid anapole state excitation, we demonstrate in ellipsoidal all-dielectric particle providing cancellation of both electric and magnetic scattering up to quadrupole modes. This effect is achieved due to the optimised geometry of the ellipsoidal particle. Moreover, we provide classification of novel anapoles arising due to interference between moments and their mean- square radii (MSR) of electric, magnetic and toroidal family and introduce generalized anapoles for high order interaction between moments. Our concept is useful for the design of light controlling devices, reflectionless metasurfaces, high Q-factor opened resonators and nonscattering particle development.

Silver nanoparticle synthesis, UV-Vis spectroscopy to find particle size and measure resistance of colloidal solution

It is an important part in nanotechnology to produce nanoparticles with specific properties like particle size or resistance. To produce colloidal silver nanoparticles with specific size and resistance by Turkevich method, it is needed to synthesized silver nanoparticle with various molarity of AgNO3 and concentration of Trisodium citrate. UV-Vis spectrum was taken for the colloidal silver nanoparticle and analysed to roughly measure the particle size. That value was also cross checked by the optical theorem and weighed the resistance of colloidal solution for different parameters.

Quaternionic elastic scattering

We study the elastic scattering of quantum particles based on a real Hilbert space approach to quaternionic quantum mechanics (QM) and derive expression for the wave function, the phase shifts, as well as the optical theorem for the case of a hard sphere scattering potential. The strong agreement between these new quaternionic results and the corresponding results in complex quantum mechanics reinforce the validity of the QM generalization of ordinary complex quantum mechanics (QM).

Optical theorem and indefinite metric in λϕ4 delta-theory

A class of effective field theory called delta-theory, which improves ultraviolet divergences in quantum field theory, is considered. We focus on a scalar model with a quartic self-interaction term and construct the delta theory by applying the so-called delta prescription. We quantize the theory using field variables that diagonalize the Lagrangian, which include a standard scalar field and a ghost or negative norm state. As well known, the indefinite metric may lead to the loss of unitary of the [Formula: see text]-matrix. We study the optical theorem and check the validity of the cutting equations for three processes at one-loop order, and found suppressed violations of unitarity in the delta coupling parameter of the order of [Formula: see text].

CFT unitarity and the AdS Cutkosky rules

We derive the Cutkosky rules for conformal field theories (CFTs) at weak and strong coupling. These rules give a simple, diagrammatic method to compute the double-commutator that appears in the Lorentzian inversion formula. We first revisit weakly-coupled CFTs in flat space, where the cuts are performed on Feynman diagrams. We then generalize these rules to strongly-coupled holographic CFTs, where the cuts are performed on the Witten diagrams of the dual theory. In both cases, Cutkosky rules factorize loop diagrams into on-shell sub-diagrams and generalize the standard S-matrix cutting rules. These rules are naturally formulated and derived in Lorentzian momentum space, where the double-commutator is manifestly related to the CFT optical theorem. Finally, we study the AdS cutting rules in explicit examples at tree level and one loop. In these examples, we confirm that the rules are consistent with the OPE limit and that we recover the S-matrix optical theorem in the flat space limit. The AdS cutting rules and the CFT dispersion formula together form a holographic unitarity method to reconstruct Witten diagrams from their cuts.

Star product representation of coherent state path integrals

In this paper, we determine the star product representation of coherent path integrals. By employing the properties of generalized delta functions with complex arguments, the Glauber–Sudarshan P-function corresponding to a non-diagonal density operator is obtained. Then, we compute the Husimi–Kano Q-representation of the time evolution operator in terms of the normal star product. Finally, the optical equivalence theorem allows us to express the coherent state path integral as a star exponential of the Hamiltonian function for the normal product.

The total reaction cross section of heavy-ion reactions induced by stable and unstable exotic beams: the low-energy regime

In this review paper we present a detailed account of the extraction and the calculation of the total reaction cross section of strongly bound and weakly bound, stable and unstable, exotic, nuclei. We discuss the optical model and the more general coupled channels model of direct reactions. The effect of long-range absorption due to the coupling to excited states in the target and to the breakup continuum in the projectile is also discussed. The generalized optical theorem for charged particle scattering and the resulting sum-of differences method is then discussed. The so-called "quarter-point recipe" is discussed next, and the quarter-point angle is introduced as a simple and rapid mean to obtain the total reaction cross section. The last topic discussed is the reduction of the total reaction cross section that would allow a large body of data to sit on a single universal function. Such a universal function exists in the case of the fusion data, and the aim of this last topic of the review is to extend the fusion case to the total reaction, by adding the direct reaction contribution. Also discussed is the inclusive breakup cross section and how it can be used to extract the total reaction cross section of the interacting fragment with the target. This method is also known as the Surrogate method and represents a case of hybrid reactions. The sum of the integrated inclusive breakup cross section with the complete fusion cross section supplies the total fusion cross section. The main experimental methods to determine the total reaction cross section are also discussed, with emphasis in recent techniques developed to deal with reactions induced by unstable beams.

Excitation of a layered medium by 𝑁 sources: Scattering relations, interaction cross sections and physical bounds

A layered medium is excited by N N external or internal point sources. Boundary-value problems for the generated acoustic waves are formulated. General scattering and optical theorems are established relating the involved fields and far-field patterns due to groups of sources. Interaction scattering cross sections are defined and associated physical bounds are derived. The large- N N behavior of these cross sections is also investigated. Numerical results are presented demonstrating the variations of the interaction cross sections and their physical bounds.

Influence of the illumination direction on the optical extinction by a scatterer close to a dielectric interface

The intrinsic optical response of a scattering object is known to be modified when it is placed on a substrate. Moreover, the total extinction through ohmic losses and Rayleigh scattering is basically dependent on the reversal of the direction of the excitation wave. Considering, as stated by the generalized optical theorem, that the total extinction of the incident wave is shared among the extinction of the waves transmitted and reflected by the non-absorbing substrate, we show that only the contribution of the transmitted wave is insensitive to the direction of illumination, by analogy with the textbook case of transmission through a planar stratified medium. This property was recently confirmed experimentally [J. Phys. Chem. C 123, 15217 (2019)] and is established here on theoretical grounds in the frameworks of the Green's function integral equation method and the Lorentz reciprocity theorem. Some of its limitations with regard to the incidence and the polarization of the excitation wave are also discussed in detail.

A Tutorial on the Classical Theories of Electromagnetic Scattering and Diffraction

AbstractStarting with Maxwell’s equations, we derive the fundamental results of the Huygens-Fresnel-Kirchhoff and Rayleigh-Sommerfeld theories of scalar diffraction and scattering. These results are then extended to cover the case of vector electromagnetic fields. The famous Sommerfeld solution to the problem of diffraction from a perfectly conducting half-plane is elaborated. Far-field scattering of plane waves from obstacles is treated in some detail, and the well-known optical cross-section theorem, which relates the scattering cross-section of an obstacle to its forward scattering amplitude, is derived. Also examined is the case of scattering from mild inhomogeneities within an otherwise homogeneous medium, where, in the first Born approximation, a fairly simple formula is found to relate the far-field scattering amplitude to the host medium’s optical properties. The related problem of neutron scattering from ferromagnetic materials is treated in the final section of the paper.

Application of the Method of Extended Boundary Conditions to the Solution of the Problem of Wave Diffraction by Magnetodielectric Scatterers Having a Compound Geometry

A technique allowing to model scattering characteristics for bodies of arbitrary geometries is suggested on the basis of the method of extended boundary conditions. The scattering characteristics include those ones, which are averaged over orientation angles. The 2D problem of diffraction of a plane wave by dielectric bodies having a complicated geometry of the cut and, in particular, by bodies similar to fractals is considered. The numerical algorithms of the diffraction problem solution on the basis of the systems of integral equations of the first and second kinds are compared. The correctness of the method is confirmed with the help of the verification of the optical theorem fulfillment for various bodies and by comparing with the calculation results obtained by the modified method of discrete sources.

Scattering cross-section under external magnetic field using the optical theorem

The cross-section for the lowest order $2\rightarrow2$ elastic scattering between two charged scalars under external magnetic field mediated via a neutral scalar, has been computed in strong as well as weak magnetic field limits. This has been done by applying the optical theorem where the cross-section is expressed in terms of the imaginary parts of different one-loop graphs contributing to the forward scattering amplitudes. The modification in the amplitudes due to the external magnetic field has been done by means of replacing the charged scalar propagators with the Schwinger proper-time ones. Significant modifications of the cross-sections with respect to the vacuum cross-section are observed due to the external magnetic field.

Solution of the Problem of Diffraction by a Plane Screen in a Plane Layered Medium with the Help of the Method of Continued Boundary Conditions

The 3D problem of diffraction of the field of a point source by a plane screen located on the interface of a plane layered medium is considered. The algorithm of the numerical solution of this problem is developed on the basis of the method of continued boundary conditions. In particular, the case, when the screen is located on the interface between two media and on the upper boundary of a dielectric layer surrounded by identical dielectric half-spaces, is considered. The correctness of the obtained results is controlled by verifying the accuracy of the fulfillment of the optical theorem. The angular dependences of the scattering pattern are constructed for the screens having circular, rectangular, and elliptic shapes.

Upper bounds on absorption and scattering

A general framework for determining fundamental bounds in nanophotonics is introduced in this paper. The theory is based on convex optimization of dual problems constructed from operators generated by electromagnetic integral equations. The optimized variable is a contrast current defined within a prescribed region of a given material constitutive relations. Two power conservation constraints analogous to the optical theorem are utilized to tighten the bounds and to prescribe either losses or material properties. Thanks to the utilization of matrix rank-1 updates, modal decompositions, and model order reduction techniques, the optimization procedure is computationally efficient even for complicated scenarios. No dual gaps are observed. The method is well-suited to accommodate material anisotropy and inhomogeneity. To demonstrate the validity of the method, bounds on scattering, absorption, and extinction cross sections are derived first and evaluated for several canonical regions. The tightness of the bounds is verified by comparison to optimized spherical nanoparticles and shells. The next metric investigated is bi-directional scattering studied closely on a particular example of an electrically thin slab. Finally, the bounds are established for Purcell’s factor and local field enhancement where a dimer is used as a practical example.

Mutual extinction and transparency of multiple incident light waves

When a wave is incident on a complex scattering medium, the transmitted intensity differs from the incident one due to extinction. In the absence of absorption, the extinguished power is equal to the total scattered power, a well-known conservation law termed the optical theorem. Here, we extend the case of a single incident wave to the situation of scattering and extinction by multiple incoming waves. The emerging generalized optical theorem has the exciting consequence that multiple incident waves show mutual extinction and mutual transparency, phenomena that do not exist in common forward scattering or self-extinction. Based on both exact calculations of realistic three-dimensional (3D) samples containing many (up to 104) scatterers and on approximate Fraunhofer diffraction theory we make the striking observation that the total extinction of two incident waves is greatly enhanced, called mutual extinction, or greatly reduced, mutual transparency, by up to 100% of the usual single-beam extinction. In view of the surprisingly strong mutual extinction and transparency, we propose new experiments to observe mutual extinction and transparency, namely in two-beam experiments with either elastic and absorbing scatterers, in optical wavefront shaping, in dynamic light scattering, and we discuss possible applications.