Analytical model of the enhanced light transmission through subwavelength metal slits: Green’s function formalism versus Rayleigh’s expansion

We present an analytical model of the resonantly enhanced transmission of light through a subwavelength nm-size slit in a thick metal film. The simple formulae for the transmitted electromagnetic fields and the transmission coefficient are derived by using the narrow-slit approximation and the Green’s function formalism for the solution of Maxwell’s equations. The resonance wavelengths are in agreement with the semi-analytical model [Y. Takakura, Phys. Rev. Lett. 86, 5601 (2001)], which solves the wave equations by using the Rayleigh field expansion. Our formulae, however, show great resonant enhancement of a transmitted wave, while the Rayleigh expansion model predicts attenuation. The difference is attributed to the near-field subwavelength diffraction, which is not considered by the Rayleigh-like expansion models. PACS 42.25.Bs; 42.65.Fx; 42.79.Ag; 42.79.Dj     

Excitonic susceptibility of semiconducting crystals influenced by a uniform electric field

Summary The Stahl’s polariton equations for crystals, influenced by a uniform electric field, can be solved by means of an appropriate Green’s function. The Green’s function is calculated for the half-space geometry and the field directed along the z-axis. Using its asymptotic form a formula for the excitonic susceptibility is derived.     

Green’s function of a 2D Fermi system undergoing a topological phase transition

An explicit expression is obtained for the single-particle Green’s function of a 2D metallic system with attraction between carriers. It is shown that as a result of transverse phase fluctuations, this function is pole-free throughout the entire region of finite temperatures (both above and below the topological phase transition point) corresponding to a nonzero modulus of the complex order field describing the transition from a nonsuperconducting (in this case normal) state to a superconducting state, whose appearance in the 2D case is not accompanied by spontaneous breaking of charge symmetry. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 2, 126–131 (25 January 1999)     

A detailed study of metallic surface-relief grating

This paper presents a more detailed interaction of an electromagnetics light with a metallic surface-relief subwavelength grating utilizing the rigorous coupled-wave analysis. The focus of this work is the accurate modeling of undetermined aspects of diffraction patterns produced by binary metallic grating structures, specially gold grating. First-order diffraction efficiency for rectangular-groove gold grating with equal groove and ridge widths are presented for various wavelengths as a function of period, groove depth, polarization and angle of incidence. We also studied diffraction efficiency of both of TE and TM polarization modes against increasing of incident angle as well as TE polarization against increment of grating period. As a result, very low reflectivity at zero-order was found out for TE and TM polarizations at the pitch of Λ = 2λ. Having been studied diffraction efficiency of metallic surface-relief gratings, we also examined polarization-dependent efficiency of diffraction orders, for different groove depths. Simulation results have been completely presented.     

Dyadic Green’s function of a PEMC cylinder

The dyadic Green’s function of a PEMC cylinder is derived with the aid of the principle of scattering superposition and Ohm–Rayleigh method. The PEMC boundary conditions are presented in dyadic form and it shows that how the impedance parameter of PEMC and cross-polarized fields appear in the Green’s function. The asymptotic expansions of the dyadic function is calculated in order to attain a closed form for the electrical field.     

Electronic transmission through a ladder with a single side-attached impurity

We study the electronic transmission of a model system composed by two coupled chains with an impurity attached to one of them. Analytical espressions for the transmittivity and for the diagonal and the off-diagonal Green’s function matrix elements are derived. Green’s function behaviour as function of the charge carrier energy is exploited to interpret the system transmittivity calculated by the scattering matrix formalism. We find that while a single substitutional impurity in the ladder may generate a Fano resonance in the transmittivity in the lower or in the higher energy part of the spectrum, in the case of a single side-attached impurity to the ladder, a resonance is found in each energy region. We interpret such resonances in terms of local density of states and off-diagonal Green’s function matrix elements.     

Two-electron bound states in a continuum in quantum dots

A bound state in a continuum (BIC) might appear in open quantum dots for the variation in the dot’s shape. By means of the equations of motion of the Green’s functions, we investigate the effect of strong intradot Coulomb interactions on that phenomenon within the framework of the impurity Anderson model. The equation that the imaginary part of the poles of the Green’s function equals zero yields the condition for BICs. As a result, we show that the Coulomb interactions replicate the single-electron BICs into two-electron ones. The text was submitted by the authors in English.     

Calculation and optimization of parameters of deep groove gratings with multilayer dielectric coating for compression of high-power laser pulses

The method of calculating the electromagnetic wave field diffracted by a holographic grating with a multilayer dielectric coating is developed. The method consists of the representation of the field inside dielectric layers in the form of a plane-wave expansion for weakly damped harmonics and an expansion over functions of the concomitant coordinate system for strongly damped orders. This modification of the method allows calculation of the diffraction efficiency and the electric field strength for the deep groove gratings. It is shown that a diffraction element that possess high efficiency and radiation strength can be obtained even when the profile of the dielectric layers flattens with an increase in the distance from the grating’s metallic layer.     

Spectral functions in the two-dimensional Hubbard model within a spin-charge rotating frame approach

We have performed electronic spectral function calculations for the Hubbard model on the square lattice using recently developed quantum SU(2) × U(1) rotor approach that enables a self-consistent treatment of the antiferromagnetic state. The collective variables for charge and spin are isolated in the form of the space-time fluctuating U(1) phase field and rotating spin quantization axis governed by the SU(2) symmetry, respectively. As a result interacting electrons appear as composite objects consisting of bare fermions with attached U(1) and SU(2) gauge fields. This allows us to write the fermion Green’s function in the space-time domain as a product of the SU(2) gauge fields, U(1) phase propagator and the pseudo-fermion correlation function. Consequently, the calculation of the spectral line shapes now reduces to performing the convolution of spin, charge and pseudo-fermion Green’s functions. The collective spin and charge fluctuations are governed by the effective actions that are derived from the Hubbard model for any value of the Coulomb interaction. The emergence of a sharp peak in the electron spectral function in the antiferromagnetic state indicates the decay of the electron into separate spin and charge carrying particle excitations.     

Effect of metallic surface microroughness on the probability and spectrum of plasmon excitation by a fast charged particle moving parallel to the surface

The Green’s function of the electric field of plasmons is determined in a semi-infinite medium with an abrupt plasma boundary where nonequilibrium conduction electrons either undergo elastic reflection from the boundary or “stick” to it and give rise to a stationary surface charge. The angular reflection of elastically scattered electrons can be either specular or diffuse. The Green’s function is used to find the singleevent spectrum of energy loss by a fast electron moving parallel to the boundary. The effect of electronboundary scattering parameters on the structure of bulk and surface plasmon resonances is analyzed. The probability of transition radiation of bulk plasmon by an electron moving in vacuum is examined. A new type of surface resonance is found under conditions of perfectly elastic scattering of conduction electrons from the plasma boundary, similar in structure to a tangential surface plasmon.     

Ensembles of plasmonic nanospheres at optical frequencies and a problem of negative index behavior

Arrays of metallic nanoparticles support individual and collective plasmonic excitations that contribute to unusual phenomena like surface-enhanced Raman scattering, anomalous transparency, negative index, and subwavelength resolution in various metamaterials. We examined the electromagnetic response of dual Kron’s lattice and films containing up to three monolayers of metallic nanospheres. It appears that open cubic Kron’s lattice exhibits ‘soft’ electromagnetic response but no negative index behavior. The close-packed arrays behave similarly: there are plasmon resonances and very high transmission at certain wavelengths that are much larger than the separation between the particles, and a ‘soft’ magnetic response, with small but positive effective index of refraction. It would be interesting to check these predictions experimentally. PACS 78.20.Ci; 42.30.Wb; 73.20.Mf; 42.25.Bs     

Effect of metallic and hyperbolic metamaterial surfaces on electric and magnetic dipole emission transitions

Spontaneous emission patterns of electric and magnetic dipoles on different metallic surfaces and a hyperbolic metamaterial (HMM) surface were simulated using the dyadic Green’s function technique. The theoretical approach was verified by experimental results obtained by measuring angular-dependent emission spectra of europium ions on top of different films. The results show the modified behavior of electric and magnetic dipoles on metallic and HMM surfaces. The results of numerical calculations agree well with experimental data.     

金属薄膜亚波长微结构的光束集束器件设计

利用时域有限差分方法,模拟了P偏振光高斯光束入射到金属银亚波长细缝与光栅结构的透射情况.由于表面等离子激元波的影响,对称光栅结构透射光呈现对称出射,而非对称结构可以实现小角度定方向的光束集束现象.借助公式推导法及Helmholtz互易定理,可设计出平行入射P偏振光的光束集束器件.由于高斯光束本身的发散性及近场分布的需要,针对高斯光束的器件在结构参量上缩小了12%.在对其他结构参量的优化的基础上,实现了针对633 nm高斯光束的对称出射及光束集束器件的设计.     

Scalar propagator in an instanton field in a closed volume

Scalar matter in an instanton field in a closed volume is studied. A compact expression is found for the exact Green’s function of massless scalar particles in the fundamental representation. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 11, 833–836 (10 June 1996)     

二元矩形金属光栅衍射增强电磁理论

采用耦合波原理计算了TM波经过二元纳米量级金属光栅衍射的电磁场，研究了金属光栅的占空比、光栅深度及TM波入射角对衍射后的光栅表面电磁场的增强的影响，针对金属金、银做了探讨和分析，得出重要的结论. 关键词： 耦合波原理 金属光栅 衍射     

Electrophysical properties of metallic wire photonic crystals

Simple nonintersecting thin metallic wire photonic crystals are studied using the integral equation method based on the Green’s function for periodically arranged sources. A wavenumber- and wavevector-dependent effective permittivity tensor is derived upon homogenization, and the band diagram and the per-mittivity for the lower dispersion branch are calculated.     

The low-energy compton scattering and polarizability of spin-0 Hadrons in a Gaugeinvariant approach

In this work, the amplitude of the interaction of an electromagnetic field with π-mesons has been determined in the context of a relativistic gauge-invariant approach by solving electrodynamic equations with the use of the covariant Green’s function method. Based on this approach, the effective Lagrangian of the two-photon interaction with spin-0 hadrons taking into account the electric and magnetic polarizabilities has been obtained.     

Electromagnetic Diffraction Analysis of 2-D Antireflective Subwavelength Grating with Coned Profile

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Electromagnetic Diffraction Analysis of 2-D Antireflective Subwavelength Grating with Coned Profile

2D subwavelength multilevel (2-, 4-, 8-, etc. levels) columned stairstep grating with coned spatial profile has been designed to reduce reflection. In this paper, the rigorous coupled-wave theory is employed to analyze the electromagnetic diffraction property of the columned stairstep grid grating. The structure is shown to achieve extremely low reflectance over a wide field of view and a wide light wave band.     

Magnetooptical Kerr effect in the near field of a nanowire supporting surface plasmons

In terms of Green’s functions, a theory is developed describing the resonant magnetooptical Kerr effect in light scattering by a linear probe that is parallel to the surface of a magnet and placed at a subwavelength distance from it. The probe is supposed to be a metal nanowire supporting long-lived surface plasmons and forming the near field of the “probe + image” complex. The resonant interaction between the probe and the sample is taken into account within a self-consistent approximation of multiple-scattering theory, and the magnetooptical interaction is included in the linear approximation in magnetization. The problem of scanning near-field magnetooptical microscopy with a linear probe is solved analytically in the case where the magnetization is parallel to both the magnet surface and the plane of incidence of light (longitudinal magnetooptical Kerr effect). The polarization, spectral, and angular characteristics of scattered light modulated by magnetization are discussed. It is shown that the magnetooptical modulation of the scattered light intensity is significantly enhanced when surface plasmons are resonantly excited in the nanowire.