Interaction of surface magnetoplasmons and surface optical phonons in polar semiconductors

A theoretical investigation has been carried out of surface polaritons associated with surface magnetoplasmons coupled to surface optical phonons in polar semiconductors. The coupled mode frequencies are calculated for several orientations of the magnetic field relative to the surface and the direction of propagation in the large wave vector (unretarded) limit. Dispersion curves are calculated for the configuration in which the magnetic field is parallel to the surface and is perpendicular to the wave vector. Experimental possibilities for observing the interaction effects are discussed.     

Plasma resonance guiding of surface magnetoplasmons by thin semiconductor films

Theoretical investigation on surface magnetoplasmons maintained by the plasma resonance in a thin (comparing to the wavelength) semiconducting film placed on a perfectly conducting substrate is presented. Dispersion characteristics and nonreciprocal behaviour of surface magnetoplasmons are studied for arbitrary orientation of externally applied magnetostatic field and for various profiles of film inhomogeneity.     

Magnetic field effects on the optical response of a film with a rough surface: Voigt geometry

Using the Rayleigh–Fano modal approach we investigate the optical response of a metallic film with a deterministic rough surface taking into account an external magnetic field in the Voigt geometry. For P-polarized light incident onto a deterministic rough surface we calculate the specular and first-order scattered field amplitudes. We also explore the nonreciprocity property and the coupling of the incident light with the surface magnetoplasmons. It is obtained that the magnetic field strength may increase the gap between two minima produced by the splitting of the minima of the zero-field specular reflection. The dispersion relations of the surface magnetoplasmons predict the possible experimental excitation and detection of these modes.     

The linear dispersion coefficient of surface magnetoplasmons

The dispersion of surface magnetoplasmons supported on a semiconductor-vacuum interface which is normal to an applied magnetic field is investigated. It is assumed that the surface possesses a depletion layer and that the dispersion is of hydrodynamic origin. Dimensionless numerical results are obtained for the magnetic field dependence of the linear dispersion coefficient with special reference being given to n-type InSb.     

Surface plasma waves in silver and gold

The dispersion curves for surface plasma waves (SPW) in Ag have been determined from calculated reflectivity minima as exhibited by attenuated total reflection (ATR spectra) for the prism-air-metal (PAM) configuration and from the direct calculation of the dispersion relation for the same configuration. The dispersion curves for Au have been determined by measuring the ATR spectra for the prism-dielectric-metal (PDM) configuration, by calculating the ATR spectra from published optical constants and from the direct calculation of the despersion relation for the PDM configuration. We have found two general types of solutions from the direct calculation of the dispersion relation for both configurations. The two solutions are the surface or Brewster modes and the virtual modes. The characteristics of both modes are discussed. The effect of electronic damping upon the dispersion curves for Ag which exhibits low electronic damping and Au which exhibits moderate electronic damping is demonstrated. Finally the perturbing effect of the dielectric (referred herein as dielectric shift) upon the displacement of the dispersion curves to higher wave number for the PAM configuration for Ag and for the PDM configuration for Au is shown.     

Surface plasma waves in the noble metals

The dispersoon curves for surface plasma waves (SPW) in Ag have been determined from calculated reflectivity minima as exhibited by attenuated total reflection (ATR spectra) for the prism-metal-air (PMA) configuration and from the direct calculation of the dispersion relation for the same configuration. Comparison is made with published results. The dispersion curves for Au and Cu have been determined for the same configuration from calculated ATR spectra and verified experimentally. Comparison is made with the direct calculation of the dispersion relation. The direct calculation yields two types of modes; namely the surface or Brewster mode and the virtual mode. Both modes are discussed. The marked effect of small electronic damping as exhibited by Ag and moderate electronic damping as exhibited by Au and Cu upon the PMA dispersion curves from ATR spectra is examined. Finally the direct calculation of the dielectric shift (perturbing effect of the prism-metal surface upon the active metal-air surface dispersion curve) is presented for the three metals as a function of film thickness and photon energy.     

A note on the analysis of the dispersion equation for surface magnetoplasmons in the Faraday configuration

The analysis of the dispersion equation for surface magnetoplasmons in the Faraday configuration for the degenerate case of decaying constants being equal is given from the point of view of understanding the non-existence of the “degenerate modes”. This analysis also shows that there exist well defined “degenerate points” on the dispersion curve with electromagnetic fields varying linearly over small distances taken away from the interface.     

Occurrence of a gap in the spectrum of magnetoplasma excitations of a two-dimensional electron disk subjected to a strong in-plane magnetic field

The effect of a parallel magnetic field on the dispersion of bulk and edge magnetoplasmons in a disk-shaped two-dimensional electron system is investigated. It is found that the anisotropy of the electron effective mass that appears in a parallel magnetic field lifts the degeneracy of plasma oscillations in the disk. This is accompanied by the occurrence of a gap in the spectrum of magnetoplasmons, and the magnetic dispersion of these excitations changes from a linear to a parabolic one. The width of the gap is determined by the difference between the frequencies of plasma oscillations along the field and transverse to the field and grows quadratically with the in-plane field strength.     

Observation of acoustic edge magnetoplasmons near the filling factor ν = 1

Investigation of acoustic edge magnetoplasma excitations in micrometer two-dimensional electron disks has been carried out. It has been shown that additional acoustic edge magnetoplasma modes associated with the existence of incompressible strips in the two-dimensional electron system caused by Zeeman spin splitting can appear in the system at temperatures below the Zeeman energy. The magnetic dispersion of the first “spin” branch of acoustic edge magnetoplasmons has been studied. It has been shown that this mode vanishes as the filling factor ν = 1 is approached. The dependence of the relative amplitude of acoustic edge magnetoplasmons on the filling factor has also been investigated.     

On the dispersion relation of magnetoplasmons in a planar graphene-based superlattice

The dispersion relation for magnetoplasmons in a planar superlattice with periodically alternating regions of gapless and gapped modifications of graphene has been derived within the frame of the random-phase approximation. The contribution of virtual transitions between the lower electron miniband and the upper hole miniband to the polarization operator has been taken into account in addition to the contribution of virtual intra-miniband transitions.     

An alternative method for plotting dispersion curves

Solving the frequency equation and plotting the dispersion curves in problems of wave propagation in cylinders and plates, particularly when the material is anisotropic, are complicated tasks. The traditional numerical methods are usually based on determination of the zeros of the frequency equation by using an iterative find-root algorithm. In this paper, an alternative method is proposed which extracts the solution of the frequency equation in the form of dispersion curves from the three-dimensional illustration of the frequency equation. For this purpose, a three-dimensional representation of the real roots of the frequency equation is first plotted. The dispersion curves, which are the numerical solutions of the frequency equation, are then obtained by a suitable cut in the velocity-frequency plane. The advantages of this method include simplicity, high speed, low possibility of numerical error, and presentation of the results in a graphical form that promotes ease of interpretation. This method is not directly applicable to problems which incorporate high damping or leaky waves. However, if the damping is not very high, it could be a good estimate of the true dispersion curves.     

Chiral optical Tamm states at the boundary of the medium with helical symmetry of the dielectric tensor

We report the observation of photovoltage oscillations in back-gated two-dimensional electron systems when tuning the density under incident microwaves and in the absence of a magnetic field. The oscillations are periodic in the inverse of the square root of the density. They originate from the interference of screened bulk plasmons with a linear dispersion. This phenomenon can be exploited to devise a spectrometer-on-a-chip for millimeter waves. The influence of a perpendicular magnetic field is investigated and reveals a transformation of screened bulk plasmons waves into screened edge magnetoplasmons.     

Wave motion and dispersion phenomena: veering, locking and strong coupling effects

The dispersion curves describe wave propagation in a structure, each branch representing a wave mode. As frequency varies the wavenumbers change and a number of dispersion phenomena may occur. This paper characterizes, analyzes, and quantifies these phenomena in general terms and illustrates them with examples. Two classes of phenomena occur. Weak coupling phenomena-veering and locking-arise when branches of the dispersion curves interact. These occur in the vicinity of the frequency at which, for undamped waveguides, the dispersion curves in the uncoupled waveguides would cross: if two dispersion curves (representing either propagating or evanescent waves) come close together as frequency increases then the curves either veer apart or lock together, forming a pair of attenuating oscillatory waves, which may later unlock into a pair of either propagating or evanescent waves. Which phenomenon occurs depends on the product of the gradients of the dispersion curves. The wave mode shapes which describe the deformation of the structure under the passage of a wave change rapidly around this critical frequency. These phenomena also occur in damped systems unless the levels of damping of the uncoupled waveguides are sufficiently different. Other phenomena can be attributed to strong coupling effects, where arbitrarily light stiffness or gyroscopic coupling changes the qualitative nature of the dispersion curves.     

Spin-wave spectroscopy and application of its methods to heterostructures of silicon dioxide with Co nanoparticles on a GaAs substrate

A method has been developed for determining magnetic and electrical characteristics of film nanostructures containing magnetic nanoparticles from dispersion curves of surface spin waves propagating in these nanostructures. The dispersion curves of spin waves are determined by the dynamics of the spin component described by the generalized Landau-Lifshitz equations and an alternating electromagnetic field induced by a spin wave. Since spin waves are very sensitive to inhomogeneity of magnetic parameters, spin disorder, and conductivity of an object near or inside which these waves propagate, they can be used for determining magnetic and electrical characteristics of the objects under investigation. The developed calculation method, which can be employed both in spin-wave spectroscopy and in analysis of dispersion curves obtained by other methods, has been used for determining parameters of heterostructures consisting of a SiO₂ film with Co nanoparticles on a GaAs substrate. It has been found from the shape of dispersion curves of the surface spin waves that, in the film near the interface, spins of the nanoparticles are close to a ferromagnetic ordering, whereas near the free surface, the spin orientation of nanoparticles is more chaotic. It has been revealed that a conducting layer is formed in GaAs, and the SiO₂(Co) film near the interface has an increased conductivity.     

Theory of the effect of a dc current on surface polaritons in n-type silicon

A theoretical investigation has been made of the effect of a drift current on surface polaritons in n-type silicon. The current direction is taken to be the same as the propagation direction of the surface polaritons. Retardation is included, but damping is neglected. In obtaining the dispersion relation, the specular-reflection/mirror-image technique of Kliewer and Fuchs is used to handle the boundary conditions. The results indicate that an interaction takes place between the current and polaritons which gives rise to polariton instabilities for certain frequency ranges. These instabilities are a consequence of the presence of the surface.     

Theory of surface polaritons in n-type silicon in the presence of a dc current,including the electron thermal pressure gradient

A theoretical investigation has been made of the effect of a drift current, including the electron thermal pressure gradient, on surface polaritons in n-type Si. The polariton propagation and drift current directions are taken to be either parallel or antiparallel. Retardation is included, but damping is neglected. The specular reflection approach of Kliewer and Fuchs is used to obtain the polariton dispersion relation. The results show that the drift current and surface polaritons interact, leading to evanescent waves for certain frequencies. However, no wave amplification is obtained.     

On the observation of surface magnetoplasmons

It is shown that, of the two techniques (grating or prism coupling) proposed for the observation of surface magnetoplasmons, the prism technique appears far superior. An analytic reflectivity formula is presented which will be necessary in the analysis of surface magnetoplasmon experimental data.     

Sensitivity of surface plasmon dispersion and damping to alkali adsorption

I have studied the sensitivity to alkali adsorption of the linear coefficients of surface plasmon dispersion and damping, through the use of self-consistent surface potential barriers which have been shown by Lang to give a good account of the work function changes due to such adsorption. The coefficient of dispersion increases strongly with alkali adsorption on an r_S = 2 substrate, while the coefficient of damping changes less.     

Virtual excitation type surface polaritons on anisotropic media

We discuss the nature of a new type of surface polariton which occurs on anisotropic media, involving a photon coupled to a surface virtual excitation. Dispersion curves are calculated for α-quartz, where both real excitation type and virtual excitation type surface polaritons are predicted. The dispersion curves for virtual excitation surface polaritons are found to remain at small wavevector, and the endpoints of the dispersion curves terminate on the bulk polariton dispersion curves in the two media. The virtual excitation surface polaritons which occur on gyromagnetic and gyrodielectric media are also noted.