Quantum Theory of Surface Polaritons in Semi-Infinite Dielectric Systems

The interaction system of a semi-infinite diatomic dielectric and the electromagnetic field propagating parallelly to the surface is studied. The long-wave optical phonon modes of the semi-infinite dielectric are calculated including the electronic polarizability by a quantum-mechanical theory. Retardation effects are neglected. A quantum field theory method of surface polaritons is developed to calculate the operator describing the interaction between a photon and the phonon polarization fields of the semi-infinite crystal, with explicit inclusion of surface effects. The dispersion relations of the surface phonon-polaritons are derived and discussed. The results are in good agreement with those obtained by the conventional, macroscopic dielectric theory of surface polaritons and experimental ATR (attenuated total reflection) spectra. The dispersion cuwes of polariton leaking modes caused by the interaction between bulk TO mode with surface effect and photons are presented in a graphical form. The k_||-dependence of the electric field strength in each polariton branch is calculated and presented also in a graphical form. We also research the spatial dependence of the field strength in each polariton branch. It is found that these properties are influenced and modulated by the surface phonons because of the interaction between photons and the surface phonon modes of the semi-infinite dielectric system. Hence the divergent nature (diffraction effect) of light propagating along the fib& and waveguides is restrained. We present a method how to use the boundary conditions in the quantum theory, which will be discussed in detail.     

Surface Polaritons in a Wire Medium with Spatial Dispersion

The dispersion relations of the surface polariton in a semi-infinite wire medium with spatial dispersion are analysed. In comparison with the traditional spatial dispersive medium there only exists one branch instead of multibranch for the dispersion curve. The possibility of the experimentally observing the surface polaritons by attenuated total reflection is simulated numerically.     

表面不平整对半无限超晶格表面电磁耦子的影响

本文讨论表面不平整对半无限超晶格表面电磁耦子(polariton)的影响。文中推导了平整表面半无限超晶格情形,Maxwell方程的格林函数。由此导出表面电磁耦子的色散关系。主要结论是:在表面不平整情形,将出现新的模式——表面型TE模表面电磁耦子,可资实验检验。 关键词：     

Theory of nonlinear excitation of surface polaritons in lossy media

The purpose of this paper is to study the nonlinear excitation of surface polaritons taking fully into account the damping of the active medium and the finite cross-section of the nonlinear polarization on the interface. This problem is solved using the guided wave calculation techniques where the EM field at the surface polariton frequency is expanded over a complete set of normal modes of the unperturbed interface. Using a “table method” we find that this set includes one guided mode, which is the surface polariton mode, and two classes of radiation modes. The expressions of all these modes are derived and interpreted physically. We then get the expression of the EM field excited at the surface polariton frequency inside and outside the pumped region and show that, in the general case, it is a mixture of all these normal modes. The end of the paper is mainly devoted to the study of the surface term occurring in the expression of the EM field at the surface polariton frequency: we point out the existence of a resonance phenomenon with two kinds of surface polariton modes: the “spatial” one and the “temporal” one. The corresponding dispersion curves, or resonance curves, are given and it is explained how each of them can be obtained experimentally.     

The near field correlation spectrum of a metallic film

The spatial two-point coherence function of the thermal radiation field at subwave-distance from a metallic film is calculated within fluctuation electrodynamics. Long-range oscillations as a function of lateral separation are seen; we interpret their features by comparing to the dispersion relations of surface plasmon polariton modes on the thin film. The hybridization of the surface modes on the top and bottom interfaces leads to a beatnote in the field correlations, for specific detector setups.     

Analysis of surface and guided wave plasmon polariton modes in insulator–metal–insulator planar plasmonic waveguides

Theoretical and experimental study of the surface plasmon–polariton and guided wave plasmon polariton modes is presented for the Sapphire/Ag/Polycarbonate/Air structure. Theoretical results are obtained by solving complex multilayer eigenvalue equations as well as the reflectivity equation for this structure. It is proposed that the mode attenuation can be significantly reduced by inserting a low index dielectric buffer between the metal and the guiding dielectric layer. The dispersion and attenuation curves are generated. Both the surface plasmon and guided wave plasmon polariton modes are studied experimentally. The experimental values of the effective refractive indices agree well with the theoretical values. The electric field profiles are generated and used to examine the nature of modes. After optimization of various parameters the condition for low loss single mode guiding is obtained for the proposed structure. Effect of metal thickness on surface plasmon mode is also discussed. It is inferred that in a properly optimized plasmonic waveguide, the losses can be reduced by a factor of 4.     

Surface plasmon–polariton modes of metallic single-walled carbon nanotubes

Propagation of surface plasmon–polariton modes in metallic single-walled carbon nanotubes is investigated within the framework of the classical electrodynamics. Electronic excitations on the nanotube's surface are modeled by an infinitesimally thin layer of free-electron gas which is described by means of the linearized hydrodynamic theory. General expression of surface modes dispersion is obtained by solving Maxwell and hydrodynamic equations with appropriate boundary conditions. It is shown that the system generally disallows the separation of the transverse electric (TE) modes and transverse magnetic (TM) modes, except for the case of modes with no angular dependence.     

Surface polariton reflection and transmission at a rough surface

A study of surface polariton electric fields incident on a periodic rough surface is done. Expression for the components of the diffuse reflected and transmitted fields are calculated to first order in the roughness amplitude. The frequency dependence of the reflection and transmission factors is found to have a structure within the surface polariton frequency range. Results are illustrated by a rough surface GaP-vacuum system.     

Dispersion and damping of a surface plasmon polariton on a one-dimensional randomly rough metal surface

Abstract

By the use of the reduced Rayleigh equation for the amplitude of a surface plasmon polariton on a one-dimensional randomly rough metal surface that is in contact with vacuum, we calculate the dispersion and damping of the surface electromagnetic wave to the lowest nonzero order in the rms height of the surface. It is found that the frequency of the surface plasmon polariton is depressed by the surface roughness. The attenuation of the surface plasmon polariton in the long wavelength limit is due primarily to its scattering into other surface plasmon polaritons, while in the short wavelength limit it is due primarily to its roughness-induced scattering into volume electromagnetic waves in the vacuum. The energy mean free path of the surface plasmon polariton is shorter on a randomly rough metal surface than it is on a lossy planar metal surface, and the surface plasmon polariton is more tightly bound to a rough surface than to a planar one.     

Josephson dynamics for coupled polariton modes under the atom–field interaction in the cavity

We consider a new approach to the problem of Bose–Einstein condensation (BEC) of polaritons for atom–field interaction under the strong coupling regime in the cavity. We investigate the dynamics of two macroscopically populated polariton modes corresponding to the upper and lower branch energy states coupled via Kerr-like nonlinearity of atomic medium. We found out the dispersion relations for new type of collective excitations in the system under consideration. Various temporal regimes like linear (nonlinear) Josephson transition and/or Rabi oscillations, macroscopic quantum self-trapping (MQST) dynamics for population imbalance of polariton modes are predicted. We also examine the switching properties for time-averaged population imbalance depending on initial conditions, effective nonlinear parameter of atomic medium and kinetic energy of low-branch polaritons. PACS 03.75.Lm; 71.36.+c; 42.50.Fx     

Surface polaritons at the magnetized semiconductor-dielectric interface

Conditions for the existence of a surface polariton at the semiconductor-dielectric interface have been analyzed. With allowance for the gyrotropy and the resonance frequency dispersion of the semiconductor, which manifests itself in an external magnetic field, the dispersion relation, the characteristic frequencies determining the existence region of a surface polariton, the wave fields, and the energy flux distribution in each of the interfacing media have been obtained. A numerical analysis of the influence of the external field and absorption, which lead to the manifestation of nonreciprocal properties of the polariton and to a substantial reconstruction of the spectrum, has been performed.     

Dielectric waveguide model for guided surface polaritons

Although surface polariton modes supported by finite-width interfaces can guide electromagnetic energy in three dimensions, we demonstrate for the first time to our knowledge that such modes can be modeled by the solutions of two-dimensional dielectric slab waveguides. An approximate model is derived by a ray-optics interpretation that is consistent with previous investigations of the Fresnel relations for surface polariton reflection. This model is compared with modal solutions for metal stripe waveguides obtained by full vectorial magnetic-field finite-difference methods. The field-symmetric modes of such waveguides are shown to be in agreement with the normalized dispersion relationship for analogous TE modes of dielectric slab waveguides. Lateral confinement is investigated by comparison of power-density profiles, and implications for the diffraction limit of guided polariton modes are discussed.     

The Investigation of Plasmon-Longitudinal Optical Phonon Coupling and Surface Polariton Modes in Donor Doped GaAs-Al0.33Ga0.67As Multi Quantum Wells

Infrared Fourier transform spectroscopy has been used to investigate phonon, plasmon, surface polariton and plasma-longitudinal optical phonon coupling in highly donor doped multi quantum wells (GaAs/Al_0.33Ga_0.67As) and direct band gap n- type Al_XGa_1-XAs thin layer on GaAs substrate. Using different samples with different concentration of free carriers. The dispersion equation of coupling modes have been calculated by using the condition which the dielectric functions of samples are zero for longitudinal coupled modes and experimental papameters which have been obtained from the best fit p-polarized oblique incidence far infrared reflection spectra. In MQW samples, the free carriers confined to the well and carriers are quasi two dimensional. So, plasmon- LO phonon coupling occur in the well (GaAs). In n- type Al_XGa_1-XAs thin layer, the coupled modes consist of three branches of the high, intermediate and low frequency modes. Their frequencies depend on both concentration and alloy composition. To analyses the surface polariton modes we carry out attenuated total reflection (ATR) measurements. In order to support our assignment the magnetic field profiles and surface polariton dispersion curves have been calculated.     

Polariton modes in semiconductor superlattices

Polariton electric fields and dispersion relations of some important complex-basis superlattices have been derived by means of electromagnetic theory and the Bloch's theorem. The spatial distribution of the polariton electric fields shows an interesting physical picture: the polaritons are mainly bulk modes as the wavenumber k is small and become typical interface modes with very strong peak intensities as k increases.     

Suppression of radiative losses of surface polaritons on nanostructured thin metal films

The strong electromagnetic coupling between surface plasmon polariton modes on opposite interfaces of a finite thickness periodically nanostructured metal film has been studied. Surface polariton dispersion and associated electromagnetic field distributions have been analyzed. It was shown that at a frequency that corresponds to the crossing of film Bloch modes of different symmetries, the radiative losses of surface polaritons that are related to the polaritons' coupling to light during propagation on the structured surface are suppressed.     

Dispersion relation of LT mixed mode polaritons

Simple equations are presented for polariton dispersion relations in anisotropic medium for an arbitrary direction of wave vector, where LT (longitudinal-transverse) mixed modes occur in general. The use of the polarizability tensor defined for pure external (not for the total) field is essentially important to obtain the simple result. The relation between all the tensor components of the polarizability and dielectric function is also explicitly given. The result can be used for any elementary excitations relevant to dielectric function. In the case of multi-component excitons of LT mixed mode character, the dispersion equation is rewritten in a matrix form, which is useful to obtain the allowed values of polariton wave vector for a given frequency.     

Thermoplasma polariton within scaling theory of single-layer graphene

The electrodynamics of single-layer graphene is studied in the scaling regime. At any finite temperature, there is a weakly damped collective thermoplasma polariton mode whose dispersion and wavelength-dependent damping is determined analytically. The electric and magnetic fields associated with this mode decay exponentially in the direction perpendicular to the graphene layer, but, unlike the surface plasma polariton modes of metals, the decay length and the mode frequency are strongly temperature-dependent. This may lead to new ways of generation and manipulation of these modes.     

The dispersion relations for surface plasmon in a nonlinear-metal-nonlinear dielectric structure

In the asymmetric and symmetric nonlinear-metal-nonlinear dielectric structures, this paper studies the analytic dispersion relation for surface plasmon in a system consisting of a thin metallic film covered on two sides media of intensity-dependent refractive indexes by applying a generalised first integral approach. Especially in the symmetric waveguide structure, two possible modes can exist: the odd mode and the even mode. The dispersion relations of the two modes are obtained. Due to the nonlinear dielectric, the squared magnitude of the electric field at the interface appears and alters the dispersion relations. Numerical results are compared to those from a certain approximate treatment.     

The surface plasmon polariton dispersion relations in a nonlinear-metal-nonlinear dielectric structure of arbitrary nonlinearity

The analytic surface plasmon polaritons(SPPs) dispersion relation is studied in a system consisting of a thin metallic film bounded by two sides media of nonlinear dielectric of arbitrary nonlinearity is studied by applying a generalised first integral approach.We consider both asymmetric and symmetric structures.Especially,in the symmetric system,two possible modes can exist:the odd mode and the even mode.The dispersion relations of the two modes are obtained.Due to the nonlinear dielectric,the magnitude of the electric field at the interface appears and alters the dispersion relations.The changes in SPPs dispersion relations depending on film thicknesses and nonlinearity are studied.     

An analog of the Migdal-Kohn singularity and the radiation width of the high-frequency branch of the polariton spectrum for a bounded crystal of the <Emphasis Type="Italic">J</Emphasis>-aggregate type

The excitation spectra of crystalline ensembles of coherently emitting interacting quantum electric dipole oscillators are investigated. The system of dynamic equations derived for a one-dimensional crystal of the J-aggregate type can be used in various limiting cases for studying optical photons as well as X-ray and gamma quanta. An exact analytic solution to the dispersion equation is obtained for polaritons (mixed states of Frenkel excitons and transverse photons). It is shown that the high-frequency polariton branch with anomalously high radiation broadening has the limiting wave vector corresponding to the spectral edge not because the broadening becomes comparable to the frequency (as was generally accepted earlier), but due to smooth joining of this polariton branch with the other (nonphysical) branch determined from the dispersion equation. At this point, the derivative of the dispersion curve goes to infinity, which is an analog of the well-known Migdal-Kohn singularity in the phonon spectra of metals. It is shown that the low-frequency polariton branch also exhibits slight broadening due to the fact that the proper radiation width is taken into account exactly.