Drude Metals Research Articles

Radiative Contributions Dominate Plasmon Broadening for Post-Transition Metals in the Ultraviolet

We use classical electrodynamics calculations to investigate the plasmonic properties of the post-transition metals Al, Bi, Ga, In, and Sn, which are active in the ultraviolet, focusing in particular on the material- and resonance-dependent origins of plasmon broadening. Analytic Mie theory, the modified-long wavelength approximation, and the quasistatic dipole approximation together show that radiative processes dominate plasmon dephasing and damping in small (5–25 nm radius) Al, Bi, Ga, In, and Sn spheres. For Al, Ga, In, and Sn, the radiative contribution (∼0.5–2 eV) to the plasmon linewidth is more than 100-fold greater than the nonradiative contribution (0.001–0.02 eV) derived from the bulk dielectric function. This is significantly different than what is observed for Ag spheres, where nonradiative contributions (∼0.1 eV) are the primary source of broadening up to a radius of 25 nm. Overall, these data suggest that the plasmonic properties, dephasing, and lifetimes for Al, Ga, In, and Sn—and to a lesser extent Bi—spheres are qualitatively similar. To develop a more general understanding of the relationship between plasmon energy and linewidth, we use a model for ideal free-electron Drude metals. It is seen that the linewidth increases at higher energies even for lossless Drude metals, suggesting that the increased broadening observed in UV-active metals is a generalizable observation. These data have important implications for the use of these metals for ultraviolet plasmonics. The increased importance of radiative damping for post-transition metals could influence the ability to harvest photons, generate hot carriers, and enhance spectroscopy in the ultraviolet while providing new opportunities for manipulating high-energy photons.

Theory of "Hot" Photoluminescence from Drude Metals.

We provide a complete quantitative theory for light emission from Drude metals under continuous wave illumination, based on our recently derived steady-state nonequilibrium electron distribution. We show that the electronic contribution to the emission exhibits a dependence on the emission frequency which is very similar to the energy dependence of the nonequilibrium distribution, and characterize different scenarios determining the measurable emission line shape. This enables the identification of experimentally relevant situations, where the emission lineshapes deviate significantly from predictions based on the standard theory (namely, on the photonic density of states), and enables the differentiation between cases where the emission scales with the metal object surface or with its volume. We also provide an analytic description (which is absent from the literature) of the (polynomial) dependence of the metal emission on the electric field, its dependence on the pump laser frequency, and its nontrivial exponential dependence on the electron temperature, both for the Stokes and anti-Stokes regimes. Our results imply that the emission does not originate from either Fermion statistics (due to e-e interactions), and even though one could have expected the emission to follow boson statistics due to involvement of photons (as in Planck's Black Body emission), it turns out that it deviates from that form as well. Finally, we resolve the arguments associated with the effects of electron and lattice temperatures on the emission, and which of them can be extracted from the anti-Stokes emission.

Friction Force and Radiative Heat Exchange in a System of Two Parallel Plates in Relative Motion: Corollaries of the Levine–Polevoi–Rytov Theory

It has been shown that the fundamental results obtained in the works by Levine–Polevoi–Rytov (1980) and Rytov (1990) adequately describe the rate of radiative heat exchange and frictional force in a system of two thick parallel plates in relative motion, in full agreement with the results obtained by other authors later. A numerically calculated friction force for Drude metals turns out to be higher by a factor of 107 than the early result obtained by Polevoi. In addition, the friction force significantly increases with increasing the conductivity of the plates or increasing the relaxation time of electrons with decreasing temperature.

Friction and radiative heat exchange in a system of two parallel plates moving sideways: Levin–Polevoi–Rytov theory revisited

It is shown that the fundamental results obtained in the works by Levin et al. (1980) and Polevoi (1990), based on the fluctuation-electromagnetic theory by Levin and Rytov, adequately describe the rate of radiative heat exchange and the frictional force in a system of two parallel thick plates in relative lateral motion. A numerically calculated friction force for Drude metals and thin gaps turns out to be by a factor 107 higher than earlier obtained by Polevoi and increases with decreasing temperature (increasing relaxation time of electrons).

Low-temperature behavior of the Casimir-Polder free energy and entropy for an atom interacting with graphene

The analytic expressions for the free energy and entropy of the Casimir-Polder interaction between a polarizable and magnetizable atom and a graphene sheet are found in the limiting case of low temperature. In so doing, the response of graphene to electromagnetic fluctuations is described in the framework of the Dirac model by means of the polarization tensor in (2+1)-dimensional space-time. It is shown that the dominant contribution to the low-temperature behavior is given by an explicit dependence of the polarization tensor on temperature as a parameter. We demonstrate that the Lifshitz theory of atom-graphene interaction satisfies the Nernst heat theorem, i.e., is thermodynamically consistent. On this basis possible reasons of thermodynamic inconsistency arising for the Casimir-Polder and Casimir interactions in the case of Drude metals are discussed. The conclusion is made that although large thermal effect arising in the Casimir interaction between Drude metals at short separations should be considered as an artifact, the giant thermal effect predicted for graphene systems is an important physical phenomenon which awaits for its experimental observation.

Сила трения и радиационный теплообмен в системе двух параллельных пластин при их относительном движении: следствия теории Левина--Полевого--Рытова

AbstractIt has been shown that the fundamental results obtained in the works by Levine–Polevoi–Rytov (1980) and Rytov (1990) adequately describe the rate of radiative heat exchange and frictional force in a system of two thick parallel plates in relative motion, in full agreement with the results obtained by other authors later. A numerically calculated friction force for Drude metals turns out to be higher by a factor of 10^7 than the early result obtained by Polevoi. In addition, the friction force significantly increases with increasing the conductivity of the plates or increasing the relaxation time of electrons with decreasing temperature.

Calculation and analysis of the complex band structure of dispersive and dissipative two-dimensional photonic crystals

Numerical calculation of modes in dispersive and absorptive systems is performed using the finite element method. The dispersion is tackled in the frame of an extension of Maxwell's equations where auxiliary fields are added to the electromagnetic field. This method is applied to multi-domain cavities and photonic crystals including Drude and Drude-Lorentz metals. Numerical results are compared to analytical solutions for simple cavities and to previous results of the literature for photonic crystals, showing excellent agreement. The advantages of the developed method lie on the versatility of the finite element method regarding geometries, and in sparing the use of tedious complex poles research algorithm. Hence the complex spectrum of resonances of non-hermitian operators and dissipative systems, like two-dimensional photonic crystal made of absorbing Drude metal, can be investigated in detail. The method is used to reveal unexpected features of their complex band structures.

Surface Plasmon Resonance in Bimetallic Core–Shell Nanoparticles

Colloidal metal nanoparticles have unique surface plasmon resonance (SPR) properties for applications in optics, medicine, photocatalysis, and photovoltaics. In this work, we use the Mie theory to investigate the SPR properties of bimetallic core–shell nanoparticles having a spherical shape and consisting of Drude metals. We find that there exists a special SPR mode whose energy is concentrated at the interface between the core and the shell, and we call it the extraordinary SPR mode. This mode can interact with the conventional SPR mode whose energy is concentrated at the outer surface of the bimetallic nanoparticle, which is called the ordinary SPR mode. The ordinary and extraordinary SPR modes together determine the line shape of the extinction spectrum as well as the shift of SPR peak (to shorter or longer wavelengths) as a function of various geometric parameters. When extended to practical noble metals such as Au, Ag, Pd, and Pt, we find that the SPR of both Au@Pt and Au@Pd nanoparticles can occur in the visible region with high tunability, which is beneficial to the enhancement of photocatalytic properties of both Pd and Pt. The theoretical studies would open up new avenues for engineering the plasmonic properties of bimetallic nanoparticles to enhance their applications related to fluorescence, Raman spectroscopy, optical sensing, photocatalysis, photovaltaics, and biomedical research.

Realization of one-way electromagnetic modes at the interface between two dissimilar metals

We calculate the dispersion relations for electromagnetic waves propagating at the interface between two dissimilar Drude metals in an external magnetic field B parallel to the interface. The propagating modes are bound to the inteface and travel perpendicular to B. In certain frequency ranges, the waves can propagate in one direction only. The frequency range for these one-way modes increases with increasing B. One group of modes occurs at moderate frequencies, between the lower and upper plasma frequencies of the two metals. The other occurs at much lower frequencies, between their lower and upper cyclotron frequencies. We discuss possible ways to realize such modes in real materials, including dissimilar superconductors.

Complex relaxation rates of the Drude metals and their effects on the lifetime and symmetry of plasmon resonances

The Drude model for metal is extended to include complex relaxation rates. As a test for what happens to the surface plasmon resonances with such metals, the lifetime is examined for propagating waves across a single planar metal-dielectric interface. By analytically solving the dispersion relation being fourth-order in the complex frequency, group-velocity dispersion and quality factors are explicitly found. Due to the symmetry breaking between the forward and backward waves, standing waves are not allowed in general.

Erratum: Thermal Casimir effect for Drude metals in the plane-sphere geometry [Phys. Rev. A82, 012511 (2010)

Erratum: Thermal Casimir effect for Drude metals in the plane-sphere geometry [Phys. Rev. A<b>82</b>, 012511 (2010)

Casimir-Foucault interaction: Free energy and entropy at low temperature

It was recently found that thermodynamic anomalies which arise in the Casimir effect between metals described by the Drude model can be attributed to the interaction of fluctuating Foucault (or eddy) currents [Phys. Rev. Lett. 103, 130405 (2009)]. We show explicitly that the two leading terms of the low-temperature correction to the Casimir free energy of interaction between two plates, are identical to those pertaining to the Foucault current interaction alone, up to a correction which is very small for good metals. Moreover, a mode density along real frequencies is introduced, showing that the Casimir free energy, as given by the Lifshitz theory, separates in a natural manner in contributions from eddy currents and propagating cavity modes, respectively. The latter have long been known to be of little importance to the low-temperature Casimir anomalies. This convincingly demonstrates that eddy current modes are responsible for the large temperature correction to the Casimir effect between Drude metals, predicted by the Lifshitz theory, but not observed in experiments.

Thermal Casimir effect for Drude metals in the plane-sphere geometry

We compute the Casimir interaction between a plane and a sphere, the configuration employed in the most precise experiments. The scattering formula is developed by taking a suitably chosen plane-wave and multipole basis and is valid for arbitrary values of the sphere radius, interplate distance, temperature, and arbitrary dielectric functions for both sphere and plate. Our analytical and numerical results for metallic surfaces show a nontrivial interplay between the effects of curvature, temperature, finite conductivity, and dissipation.

Quantum and thermal Casimir interaction between a sphere and a plate: Comparison of Drude and plasma models

We calculate the Casimir interaction between a sphere and a plate, both described by the plasma model, the Drude model, or generalizations of the two models. We compare the results at both zero and finite temperatures. At asymptotically large separations we obtain analytical results for the interaction that reveal a non-universal, i.e., material dependent interaction for the plasma model. The latter result contains the asymptotic interaction for Drude metals and perfect reflectors as different but universal limiting cases. This observation is related to the screening of a static magnetic field by a London superconductor. For small separations we find corrections to the proximity force approximation (PFA) that support correlations between geometry and material properties that are not captured by the Lifshitz theory. Our results at finite temperatures reveal for Drude metals a non-monotonic temperature dependence of the Casimir free energy and a negative entropy over a sizeable range of separations.

Transient Electromagnetic Field of an Electric Line Source above a Plane Drude Model Plasmonic Half-space

The enhancement of the electromagnetic fleld at the surface of a Drude metal is classifled as the so called surface plasmon efiect. This surface plasmon efiect in a classical Drude model has been investigated extensively in the frequency domain. However, to understand what is actually happening to the electromagnetic fleld at the near vicinity of a Drude metal a thorough analysis in the space-time domain is needed. Once the space-time domain counterpart of the surface plasmon efiect is found, one is able to describe and classify the physical phenomena that are playing a role in the occurrence of this efiect. The phenomenon of surface plasmon resonance of metallic structures has been known and theoret- ically described for more than flfty years. Nowadays, the plasmonic nanostructures are used in a variety of applications, such as molecular sensing and imaging devices, optical devices and meta- materials. One of the materials in which plasmonic efiects are encountered are metals that have a frequency dependant conductivity described by the Drude model. Many researchers investigated Drude model metals in the frequency domain in order to determine the optical behaviour of metals within a certain frequency range. However, to understand what phenomena are at work when the electromagnetic fleld interacts in the near vicinity with a Drude model metal, a thorough analysis in the space-time domain is needed. Once the space-time domain counterpart of the surface plasmon efiect is identifled, a description and classiflcation of the physical phenomena that occur can be given. These results can be of great importance in the fleld of time-domain terahertz spectroscopy. The pulsed electromagnetic radiation from a line source above a plane plasmonic half-space, modeled by a classical Drude model, is investigated. In order to obtain closed-form expressions for the re∞ected electric fleld anywhere above the plasmonic half-space, the re∞ection factor RE that corresponds to the Drude metal half-space is mathematically written in the form of a Laplace transform integral, enabling the application of the Cagniard-de Hoop method. In the Cagniard-de Hoop method the Laplace transform with respect to time is used, in which the Laplace parameter s is kept real and positive in order to ensure causality in the space-time domain expressions for the electromagnetic fleld. Attention is paid to investigate which parts of the Laplace transform integral representation of RE give rise to the surface-plasmon efiect by means of enhancement of the re∞ected electromagnetic fleld at the near vicinity of the Drude metal interface. The derived space-time domain expressions for the re∞ected electric fleld explicitly show the special time and space dependence that exists in the re∞ection factor at the interface of the plasmonic half-space. Consequently, leading to a better understanding of the physical efiects, that occur at the interface of classical Drude metals in the space-time domain. Finally, a suitable source signature is proposed, which enables, without loss of generality, a suitable determination of analytical closed-form inverse Laplace transforms of the distinct source functions. Numerical results that support the conclusions made in this paper will be presented at the Symposium. 2. DESCRIPTION OF THE CONFIGURATION

Simulation of subwavelength metallic gratings using a new implementation of the recursive convolution finite-difference time-domain algorithm

We introduce a new implementation of the finite-difference time-domain (FDTD) algorithm with recursive convolution (RC) for first-order Drude metals. We implemented RC for both Maxwell's equations for light polarized in the plane of incidence (TM mode) and the wave equation for light polarized normal to the plane of incidence (TE mode). We computed the Drude parameters at each wavelength using the measured value of the dielectric constant as a function of the spatial and temporal discretization to ensure both the accuracy of the material model and algorithm stability. For the TE mode, where Maxwell's equations reduce to the wave equation (even in a region of nonuniform permittivity) we introduced a wave equation formulation of RC-FDTD. This greatly reduces the computational cost. We used our methods to compute the diffraction characteristics of metallic gratings in the visible wavelength band and compared our results with frequency-domain calculations.

Cellular automaton approach to electromagnetic wave propagation in dispersive media

Extensions of Białynicki-Birula's cellular automaton are proposed for studies of the one-dimensional propagation of electromagnetic fields in Drude metals, as well as in both transparent, dispersive and lossy dielectrics. These extensions are obtained by representing the dielectrics with appropriate matter fields, such as polarization together with associated velocity fields. To obtain the different schemes for the integration of the resulting systems of linear partial differential equations, split-operator ideas are employed. Possible further extensions to two-dimensional propagation and for the study of left-handed materials are discussed. The stability properties of the cellular automaton treated as a difference scheme are analysed.

Sensitivity of metal nanoparticle plasmon resonance band position to the dielectric environment as observed in scattering

Electrodynamic simulations of gold nanoparticle scattering spectra were used to investigate the sensitivity of localized surface plasmon band position to the refractive index, n, of the medium for moderately high aspect ratio nanoparticles of various shapes and hollow nanoshells of various sizes. For the sub-150 nm particles investigated here, the sensitivity of the peak scattering wavelength, λ*, to refractive index, n, is found to increase linearly with peak wavelength. The refractive index sensitivities of scattering peak location, thus, are found to have the same dependence upon peak position as was previously observed to characterize the sensitivities of extinction peak position. Whereas the plasmon bands of solid nanospheres display peak scattering at longer wavelengths than the wavelengths of peak extinction, the scattering and extinction peaks of high aspect ratio particles of comparable sizes have scattering and extinction spectra that are more closely overlapping. Thus, for these particles, band position sensitivities are independent both of the nature of the spectral measurement and the particle shape, except through shape control of the location of the resonance. Using an analytical expression for the sensitivity of peak wavelength to index of refraction of the medium that captures the dependence of the sensitivity upon the slope of the real part, e', of the particle dielectric function as a function of wavelength, the peak wavelength dependences of the sensitivities were characterized in terms of parameters derived from both linear and quadratic fits to e' in the visible wavelength range. Comparison of sensitivities determined by electrodynamic simulation with the predictions based upon these two dielectric function models indicates that sensitivity estimates based upon linear fit parameters provided better estimates of the sensitivities of plasmon bands in the visible than do estimates based upon quadratic fits appropriate to true Drude metals. The bulk refractive index sensitivities presented here serve as upper bounds to sensitivities of nanoparticles on dielectric substrates and sensitivities of nanoparticles to local refractive index changes, such as those associated with biomolecule sensing.

Surface plasmons in Drude metals

We present here a detailed derivation of the dispersion relations for surface plasmons in classical Drude metals, taking into account the fact that the relative permittivity at high frequency may be different from 1, as in the case of dielectrics. We also retain the imaginary part of the dielectric response in the derivation of the dispersion relations for the surface plasmon, which exists up to a maximum frequency, ω s. This treatment has not previously been published. We compare the model with experiment, and show the importance of the relative permittivity in understanding the value of ω s in Ag. We show that the observed ratios of surface to volume plasmon peak energies in electron energy loss spectra can be understood in terms of the simple model, but that considerable care is needed in interpreting the physical circumstances of such experiments.

Applications of the wave packet method to resonant transmission and reflection gratings

Scattering of femtosecond laser pulses on resonant transmission and reflection gratings made of dispersive (Drude metals) and dielectric materials is studied by a time-domain numerical algorithm for Maxwell's theory of linear passive (dispersive and absorbing) media. The algorithm is based on the Hamiltonian formalism in the framework of which Maxwell's equations for passive media are shown to be equivalent to the first-order equation, ∂Ψ/ ∂t= HΨ , where H is a linear differential operator (Hamiltonian) acting on a multi-dimensional vector Ψ built of the electromagnetic inductions and auxiliary matter fields describing the medium response. The initial value problem is then solved by means of a modified time leapfrog method in combination with the Fourier pseudospectral method applied on a non-uniform grid that is constructed by a change of variables and designed to enhance the sampling efficiency near medium interfaces. The algorithm is shown to be highly accurate at relatively low computational costs. An excellent agreement with previous theoretical and experimental studies of the gratings is demonstrated by numerical simulations using our algorithm. In addition, our algorithm allows one to see real time dynamics of long living resonant excitations of electromagnetic fields in the gratings in the entire frequency range of the initial wide band wave packet as well as formation of the reflected and transmitted wave fronts.