Dielectric-conductor Interface Research Articles

Interfaces with fractional optical constants and linear reflectance versus angle of incidence for incident unpolarized or circularly polarized light.

For unpolarized or circularly polarized light incident at a dielectric-conductor interface, the intensity reflectance Ru(ϕ) can be made an essentially linear function of the angle of incidence ϕ over a significant range of ϕ at specific values of the normal-incidence intensity reflectance R0 (≈1/3) and the associated normal-incidence reflection phase shift δ0 (≈40°). This places the complex refractive index n-jk of the interface in the domain of fractional optical constants. As demonstrated by specific examples, this is realizable in external reflection at vacuum-metal interfaces in the UV, and in internal reflection in the IR at interfaces between a transparent high-index substrate and an optically opaque thin film of the proper n and k. Fractional optical constants are also achievable for light reflection in air at planar surfaces of appropriately designed, nanostructured, metamaterial substrates.

Light-matter interactions in aligned silver nanorod arrays

This study presents an experimental evaluation of the light-matter interactions in silver nanorod arrays of various lengths fabricated by electron-beam physical vapor deposition. The reflectance of nanorod arrays is found to decrease with increasing nanorod length, reaches to a minimum and then again increases with increasing length. Since nanorod arrays are subwavelength structures, the decrease in reflectance is primarily due to surface plasmon resonance. At the tip of the nanorods, the light excites the surface plasmons, which propagate along the conductor-dielectric interface. Hence, longer and consequently higher surface area nanorod arrays provide more dielectric-conductor interface for light to couple with the surface plasmons and more surface to scatter resulting in lower reflectance.

Total transmission of inhomogeneous electromagnetic waves at planar interfaces

We present the total transmission effect of inhomogeneous electromagnetic waves between dissipative media. The total transmission of a $p$-polarized plane wave at the interface between two lossless dielectrics happens at the Brewster angle. However, when a dielectric-conductor interface is considered, the effect cannot be achieved and there is only a minimum, different from zero, of the reflection coefficient. We prove that, by considering an inhomogeneous plane wave, the total transmission can be obtained both at the interface between two dissipative media and at the dielectric-conductor interface.

Necessary and sufficient conditions for the appearance of a reflectance minimum at oblique incidence when unpolarized or circularly polarized light is reflected at a dielectric-conductor interface

The appearance of a reflectance minimum at oblique incidence when unpolarized or circularly polarized light is reflected at a dielectric-conductor interface requires that the normal-incidence intensity reflectance R(0) of the interface be >1/3 [J. Opt. Soc. A9, 957 (1992)10.1364/JOSAA.9.000957; Appl. Opt.53, 7885 (2014)APOPAI0003-693510.1364/AO.53.007885]. However, R(0) 1/3 is only a necessary but insufficient condition for the interface reflectance to exhibit a minimum at non-normal incidence. A second condition, the subject of this study, restricts the normal-incidence reflection phase shift δ(0) for s-polarized light to one of two non-overlapping bands: (a) 0≤δ(0)<δ(0 max) and (b) δ(0 min)<δ(0)≤180°. These two bands are associated with internal and external reflection, respectively. The limiting phase shifts δ(0 max) and δ(0 min) at the band edges are determined analytically as functions of R(0) .

Angle of incidence of minimum reflectance of a dielectric-conductor interface for incident unpolarized or circularly polarized light.

The angle of incidence ϕ=ϕu min of minimum reflectance for incident unpolarized or circularly polarized light at a dielectric-conductor interface is determined for any complex relative refractive index N=(n,k), and contours of constant ϕu min in the nk plane are presented. The minimum reflectance Ru min at ϕu min is also plotted as a function of the polar angle 0≤θ=arg(N)≤90° along each constant ϕu min contour. Also presented are families of Ru-versus-ϕ curves for values of complex N at θ=30°, ϕu min=45° to 85° in steps of 10°, and values of complex N at ϕu min=75°, θ=0° to 90° in steps of 10°. Finally, a nonpolarimetric method for the determination of n and k of optical materials, which is based on measurements of ϕu min and the normal-incidence reflectance R0, is proposed.

Complex reflection coefficients of p- and s-polarized light at the pseudo-Brewster angle of a dielectric–conductor interface

The complex Fresnel reflection coefficients r(p) and r(s) of p- and s-polarized light and their ratio ρ=r(p)/r(s) at the pseudo-Brewster angle (PBA) φ(pB) of a dielectric-conductor interface are evaluated for all possible values of the complex relative dielectric function ε=|ε|exp(-jθ)=ε(r)-jε(i), ε(i)>0 that share the same φ(pB). Complex-plane trajectories of r(p), r(s), and ρ at the PBA are presented at discrete values of φ(pB) from 5° to 85° in equal steps of 5° as θ is increased from 0° to 180°. It is shown that for φ(pB)>70° (high-reflectance metals in the IR) r(p) at the PBA is essentially pure negative imaginary and the reflection phase shift δ(p)=arg(r(p))≈-90°. In the domain of fractional optical constants (vacuum UV or light incidence from a high-refractive-index immersion medium) 0<φ(pB)<45° and r(p) is pure real negative (δ(p)=π) when θ=tan(-1)(√(cos(2φ(pB)))), and the corresponding locus of ε in the complex plane is obtained. In the limit of ε(i)=0, ε(r)<0 (interface between a dielectric and plasmonic medium) the total reflection phase shifts δ(p), δ(s), Δ=δ(p)-δ(s)=arg(ρ) are also determined as functions of φ(pB).

An Efficient Solution of the Volume-Surface Integral Equation for Electromagnetic Scattering and Radiation of the Composite Dielectric-Conductor Objects With Reduced Number of Unknowns

An efficient method of moments (MoM) solution of the volume-surface integral equation (VSIE) is presented for the analysis of electromagnetic (EM) scattering and radiation of composite objects comprising arbitrarily contacted dielectrics and conductors. In contrast to the conventional Schaubert-Wilton-Glisson (SWG) and Rao-Wilton-Glisson (RWG) basis functions, which were widely used in the MoM solutions of the VSIE, a new hybrid pulse-rooftop basis function is proposed to explicitly enforce the boundary condition of vanishing tangential electric field at the dielectric-conductor interface. As a consequence, the displacement currents in the dielectrics can be efficiently modeled by a reduced number of volume bases on the same set of meshes, particularly when thin dielectric slabs are involved in the composite structures. The numerical results of EM scattering and radiation of several composite objects are shown to illustrate the accuracy and efficiency of the proposed scheme. Since the new hybrid basis function can be easily implemented into the existing fast algorithms, the VSIE solution presented in this paper is promising for EM problems of composite targets with large size.

Difference between the second-Brewster and pseudo-Brewster angles when polarized light is reflected at a dielectric–conductor interface

For a given pseudo-Brewster angle phi(pB) of minimum reflectance |r(p)| of p-polarized light at a dielectric-conductor interface, the second-Brewster angle phi(2B) of minimum reflectance ratio |rho|=|r(p)|/|r(s)| of the p and s polarizations is determined for all possible values of the complex relative dielectric function epsilon that lead to the same phi(pB). The difference phi(2B)-phi(pB) is considered as a function of phi(pB) and theta=arg(epsilon). For any given phi(pB), the difference phi(2B)-phi(pB)=0 at theta=0(epsilon(r)>0,epsilon(i)=0) increases monotonically as a function of theta and reaches maximum value {phi(2B)-phi(pB)}(max) in the limit as theta-->180 degrees (epsilon(r)<0,epsilon(i)=0). This maximum difference {phi(2B)-phi(pB)}(max) has an upper limit of 15.701 degrees when phi(pB)=28.195 degrees.

High-frequency response of subwavelength-structured metals in the petahertz domain

Electromagnetic plane waves, incident on and reflecting from a dielectric-conductor interface, set up a standing wave in the dielectric with the B-field adjacent to the conductor. It is shown here how the harmonic time variation of this B-field induces an E-field and a conduction current J (c) within the skin depth of a real metal; and that at frequencies in the visible and near-infrared range, the imaginary term sigmai of the complex conductivity sigma = sigma(r) + isigma(i) dominates the optical response. Continuity conditions of the E-field through the surface together with the in-quadrature response of the conductivity determine the phase relation between the incident E-M field and J(c). If slits or grooves are milled into the metal surface, a displacement current in the dielectric gap and oscillating charge dipoles at the structure edges are established in quadrature phase with incident field. These dipoles radiate into the aperture and launch surface waves from the edges. They are the principle source of light transmission through the apertures.

Plurality of principal angles for a given pseudo-Brewster angle when polarized light is reflected at a dielectric-conductor interface

The pseudo-Brewster angle phi(pB) of minimum reflectance for p-polarized light and the principal angle phi at which incident linearly polarized light of the proper azimuth is reflected circularly polarized are considered as functions of the complex relative dielectric function epsilon of a dielectric-conductor interface over the entire complex epsilon plane. In particular, the spread of phi for a given phi (pB) is determined, and the maximum difference(phi -phi(pB))(max) is obtained as a function of phi(pB). The maximum difference (phi -phi(pB))(max) approaches 45 degrees and 0 in the limit as phi(pB)-->phi 0 and 90 degrees , respectively. For phi(pB)<22.666 degrees , multiple principal angles phi (i), i=1,2,3, appear for each epsilon in a subdomain of fractional optical constants. This leads to an elaborate pattern of multiple solution branches for the difference phi (i)-phi(pB), i=1,2,3, as is illustrated by several examples.

Poynting’s theorem for plane waves at an interface: A scattering matrix approach

We write Poynting’s theorem in a form that allows us to introduce a natural definition of the scattering matrix S. For a dielectric-dielectric interface this balance equation leads to energy flux conservation and the unitarity property of S. For the dielectric-conductor interface the scattering matrix is no longer unitary due to the presence of losses in the conductor, and we denote it by S̃. The dissipative term in Poynting’s theorem can be interpreted as due to a single parasitic channel or excitation of the absorptive interface. We define an S matrix that includes the parasitic channel, so that S is unitary.

Quasi index matching for minimum reflectance at a dielectric-conductor interface for obliquely incident p- and s-polarized light

Conditions for reducing the reflectance of a dielectric-conductor interface for p- and s-polarized light to a minimum at any angle of incidence phi are determined. The refractive indices of a transparent immersion medium (liquid) that achieve minimum reflectance at normal incidence, phi=0, and at phi=45 degrees are independent of polarization. These indices provide sufficient data to determine the real and imaginary parts of the complex refractive index of an absorbing substrate. Reflection at a dielectric-Au interface at 500 nm wavelength is considered as an example. It is shown that the lowest possible reflectance is attained for p-polarized light at phi=45 degrees and that the associated p-reflection phase shift is also minimum at that angle. For phi> or =65 degrees the lowest reflectance of p-polarized light occurs when the ambient is vacuum or air. However, this lowest reflectance at the air-Au interface is not a true minimum in a mathematical sense.

Efficiency of linear-to-circular polarization conversion for light reflection at the principal angle by a dielectric-conductor interface

The efficiency eta(LC) of linear-to-circular polarization conversion when light is reflected at a dielectric-conductor interface is determined as a function of the principal angle phi and principal azimuth psi . Constant-eta(LC) contours are presented in the phi , psi plane for values of eta(LC) from 0.5 to 1.0 in steps of 0.05, and the corresponding contours in the complex plane of the relative dielectric function are also determined. As specific examples, efficiencies > or = 88% are obtained for light reflection by a Ag mirror in the visible and near-IR (400-1200 nm) spectral range, and > or =40% for the reflection of extreme ultraviolet (EUV) and soft x-ray radiation by a SiC mirror in the 60-120 nm wavelength range.

Absorption of infrared radiation by a giant enhancement of two-phonon lattice modes at a dielectric-conductor interface

Absorption of infrared radiation by a giant enhancement of two-phonon lattice modes at a dielectric-conductor interface

Absorption of infrared radiation by a giant enhancement of two-phonon lattice modes at a dielectric-conductor interface

Abstract Recent experimental work has shown that, at certain frequencies of infrared radiation, there is a giant absorption at the interface between a nanosize graphite substrate doped with copper and diamond nanocrystals grown on the substrate. We propose a model for this absorption based on the Born approach which uses a set of dynamie surface dipoles induced in a conducting medium at its interface with a dielectric and where the frequency of radiation corresponds to a combination of two-lattice vibrations. The wavenumber at which the enhancement oceurs can be determined from the fundamental freauency of the vibrations and the functional dependence of the extinction coefficient as a function of wavenumber can be determined from the relaxation times and the plasma frequencies. An analytical expression for the enhancement absorption factor is derived and it is shown how the cut-off of the absorption band can be used to ascertain the size and shape of conductive nanocrystals.

Limaçon of Pascal locus of the complex refractive indices of interfaces with maximally flat reflectance-versus-angle curves for incident unpolarized light

For an interface between two isotropic media the power reflectance Rν(ϕ) is an even function, Rν(ϕ) = Rν(−ϕ) of the angle of incidence ϕ; hence all the odd derivatives, Rν(n) = dnRν/dϕn (n odd), are identically 0 at ϕ = 0, independent of the incident polarization ν. When the incident light is unpolarized (ν = u), the second derivative, Ru(2) is also 0 at ϕ = 0, so that the flatness of the Ru-versus-ϕ curve over an initial range of ϕ starting from ϕ = 0 is determined by the fourth derivative, Ru(4). The condition that Ru(4) = 0 at ϕ = 0 gives the maximally flat response and leads to a specific constraint on the complex relative refractive index N, namely, that Re[(N − 1)2/N3] = 2/NN*. The corresponding complex plane contour is the limaçon of Pascal, η=2 cos θ±3 in polar form, where N = η exp(jθ). The two branches of this contour constitute the boundary lines that separate the region of the complex plane in which the function Ru(ϕ) is monotonic from that in which the function exhibits a minimum at oblique incidence. Families of curves that illustrate the maximally flat response in external and internal reflection are presented. New equations that determine the angle of incidence of minimum unpolarized-light reflectance of a dielectric–dielectric or a dielectric–conductor interface are derived.

Enhanced backscattering from a rough dielectric film on a reflecting substrate

We carry out computer simulations of the scattering of a beam of light with p or s polarization from a transparent dielectric film (BaSO4) on a perfectly conducting substrate. The dielectric–vacuum interface is assumed to be a random grating; the dielectric–conductor interface is assumed to be planar. It is found that for incident light of either polarization the angular dependence of the incoherent contribution to the mean intensity of the scattered light has a well-defined peak when the scattering angle corresponds to the retroreflection direction (enhanced backscattering). The existence of enhanced backscattering of p-polarized light in this geometry contrasts with its absence in the scattering of p-polarized light from a random grating on a semi-infinite dielectric medium that is characterized by the same roughness parameters and index of refraction. The enhanced backscattering that is observed in the scattering of s-polarized light from a random grating on a semi-infinite dielectric medium is stronger when the scattering takes place from the structure studied. For both polarizations the enhancement is most pronounced when the distance of the perfectly conducting substrate from the mean dielectric–vacuum interface is several (2–10) times the distance of the focusing plane of the rough interface from the mean interface.

Surface-traction boundary condition at a dielectric-conductor interface

Abstract A variational principle is used to obtain the boundary conditions for the applied surface tractions at a dielectric-conductor interface.