S-polarized Waves Research Articles

Coupling of evanescent s-polarized waves to the far field by waveguide modes in metallic arrays

In this paper we show that enhanced optical transmission through a 1D periodic slit array comprising real metallic cylinders is possible for s-polarization when the array is near a dielectric interface. We investigate the behaviour of this structure under s-polarized illumination, in which case surface plasmons are not excited. Numerical results show that the transmitted intensity appears as a periodic function of the slit depth, for propagating as well as for evanescent incidence, suggesting that this behaviour is related to the excitation of waveguide modes in the slits. In particular, the coupling of evanescent to propagating electromagnetic waves is investigated. It is shown that s-polarized evanescent waves generated at the interface can be transformed into propagating waves if the optical width of the slits allows propagation of the first waveguide mode. As the interface approaches the array, the transmitted intensity increases for evanescent incidence.

Bloch vector dependence of the plasma frequency in metallic photonic crystals

In this paper, a wire mesh metallic photonic crystal is modelized as a stack of gratings of period d made of very thin infinitely metallic rods (the conductivity is assumed to be infinite) of radius a (a<<d) . This structure is illuminated by a s-polarized plane wave of wavelength lambda. First, we give the diffracted field in closed form for very large wavelengths compared to the period (lambda>>d) . We derive a very accurate formula for the cut wavelength and we show that the plasma frequency in wire photonic crystals depends upon the Bloch vector. This latest formula is checked numerically.

Microarrays of silver nanowires embedded in anodic alumina membrane templates: size dependence of polarization characteristics

Polarization characteristics of microarrays of silver nanowires embedded in an anodic alumina membrane are theoretically investigated. The microarrays mainly transmit the p-polarized wave, whereas they strongly attenuate the s-polarized wave in the near- and mid-infrared spectral range. We show that the sizes (e.g., diameter, spacing, and ratio of diameter to spacing) of the nanowires strongly affect the optical losses for the polarized waves. It is predicted that large extinction ratios and small insertion losses can be simultaneously achieved by an appropriate choice of the ratio and the diameter. An optimized design of a nanowire grid polarizer at near- and mid-infrared wavelengths is presented.

Refinement in the Reflection Properties of Electromagnetic Waves at a Stratigraphic Interface

The travel time of electromagnetic waves in conductive strata has a quantitative relation to the conductivity, permittivity, and permeability of the strata. Using these parameters, geologists can determine the lithology of rocks. But current logging and exploration methods take the time between incidence and reflection as zero and do not take into account the effect of the lateral shift delay when the electromagnetic wave is reflected on the interface of strata. In this article, the lateral shift delay will be considered and a more accurate relationship between petrophysics and electromagnetic wave travel time will be derived. The lateral shift delay of quasi-total reflection of inhomogeneous s-polarized electromagnetic waves (whose electric field is perpendicular to the incident plane) caused by the Goos–Hanchen effect is derived using the phase shift of the wave. The result fits both low and high frequency electromagnetic waves. But for geologists, the most valuable frequency range is between 106 and 109 Hz (1 MHz–1 GHz, wavelengths between 0.1 and 100 m). A numerical example where the frequency equals to 1 GHz. shows three discontinuous points at the critical angle of phase shift, the critical angle of attenuation and 90∘. When the incident angle equals one of these three angles, the lateral shift delay will become infinite. That is, the electromagnetic wave will propagate along the interface. Even when the incident angle is close to one of them, the lateral shift delay is very large. The results also indicate that the two critical angles have an important relation to conductivity and permittivity of the two strata, and that the lateral shift delay has a relation to the incident angle. These results can be used to determine the lithology of the strata and to divide the strata more effectively. It is suggested that this approach may prove useful in electromagnetic logging analysis and, perhaps, in the design of logging instruments.

Linear s-polarized surface waves in a medium inhomogeneous in one dimension

Linear s-polarized surface waves can exist at the boundary between an isotropic homogeneous medium and a medium inhomogeneous in one dimension (1D-inhomogeneous medium). This is related to deformation of the spatial envelope of the electric and magnetic components of the surface wave propagating in the 1D-inhomogeneous medium (in particular, in a plane-stratified medium). Such linear s-polarized surface waves can appear only provided that the refractive index of the inhomogeneous medium increases with the distance from the interface.

Partial focusing of radiation by a slab of indefinite media

Negative refraction can occur at the interface between vacuum and an indefinite medium—an anisotropic medium for which not all elements of the permittivity and permeability tensors have the same sign. We show experimentally and via simulations that a metamaterial composed of split ring resonators, designed to provide a permeability equal to −1 along the longitudinal axis, will redirect s-polarized electromagnetic waves from a nearby source to a partial focus. The dispersion characteristics of indefinite media prohibit the possibility of true aplanatic points for a planar slab; however, by contouring the surfaces aplanatic points may be realized, as well as other geometrical optical behavior.

Surface plasmon polariton scattering by a small particle placed near a metal surface: An analytical study

Scattering of light by a small particle placed near a metal surface is studied via analytical calculations of the particle extinction cross section. Considering a small spherical particle, we express the extinction cross section via the total electric-field Green's tensor of a metal-dielectric interface structure. Analytic expressions are derived for the parts of Green's tensor that govern the excitation of p- and s-polarized waves propagating away from the interface, and waves propagating along and being localized at the interface, viz., surface plasmon polaritons (SPP's). This allows us in turn to divide the extinction cross section into parts associated with scattering of light into different types of electromagnetic waves. The scattering cross sections related to SPP-to-SPP scattering, and scattering of SPP's into waves propagating away from the interface, are studied with respect to the dielectric constant of the metal and the height of the scatterer above the interface. In the case where the light wavelength is close to the SPP resonance, the SPP-to-SPP scattering cross section can be orders of magnitude larger compared to the extinction cross section of a particle in free space, whereas in the case of a nearly perfect conductor, the SPP-to-SPP cross section tends to 0. The efficiency of SPP-to-SPP scattering is calculated and, e.g., for the metal dielectric $\mathrm{constant}\mathrm{ }\ensuremath{-}100$ (order of magnitude for gold at the light wavelength 1500 nm) it is found to be above 60% for the optimum scatterer-surface distance.

Surface modes at the interface of conventional and left-handed media

Surface p- and s-polarized stationary waves propagating along the interface between left-handed electromagnetic meta-material with three types of conventional materials: dielectrics, metals, and magnetic media with negative magnetic permeability μ( ω) are studied. The constraints for the existence of surface modes are identified. It is shown that the frequency domains of existence for p- and s-modes do not overlap and they are quite different for different types of interfaces. The Poynting vector and the density of energy associated with surface mode are calculated. Depending on the system parameters either p- or s-surface mode has the time-averaged Poynting vector directed opposite to the mode phase velocity.

New Pockels field sensor with ferroelectric liquid-crystal phase modulator

A new optical field sensor for measuring the electric field close to an electrical discharge has been developed. The new system that uses both P- and S-polarized light-division and azimuth angle modulation methods has been devised and investigated. By using a ferroelectric liquid-crystal phase modulator instead of an azimuth angle modulator, it has been possible to eliminate noise from the optical field measurement system, specifically, the birefringence effects in a long optical fiber cable. The optical cable is used for connecting a Pockels field sensor located close to the discharge with the main system located at the ground. Furthermore, it has been possible to compensate for the sensitivity difference between two optical detectors for converting P- and S-polarized light waves to an electrical signal. From this, it is found that by using a light reflection technique, the measurable minimum field strength is reduced from 100 kV/m to 1.0 kV/m in the discharge region. If the smallest phase change in the system is set to be less than 10−3 [rad], the measurable minimum field strength is reduced to 0.1 kV/m. The possible use of the probe is also considered for checking for damage caused by cosmic rays to the insulating skin of a spacecraft.

Optical near field in nanometallic slits

The propagation and the distribution of the optical near field in nanometallic slits are measured by a near-field scanning optical microscope. The optical near field for the p-polarized wave is confined to the middle of the slit. In contrast, the near field for the s-polarized wave is located at the edges. Asimulation by the finite-difference time-domain method verifies that the near-field distribution for the s-polarized wave is due to the propagation of the surface plasmon wave (SPW) at the air-metal surface. The existence of the SPW also accounts for the extraordinary transmittance of s-polarized light, which is one order of magnitude larger than that of p-polarized light.

On calculation of ohmic losses at metallic surface with sharp edges

We discuss the applicability of the perturbation theory in electrodynamic problems where the local impedance boundary conditions are used to calculate the ohmic losses at the metallic surface. As an example, we examine a periodic grating formed from semi-infinite rectangular plates exposed to the s-polarized electromagnetic wave. Two different ways of calculation are presented: (i) the calculation of the reflection coefficient obtained with the aid of the perturbation theory (the impedance is the small parameter) and (ii) the direct calculation of the energy flux through the metallic surface. In the case (ii) to get the answer only the tangential magnetic field at the surface of a perfect conductor of the same geometry has to be known. The results (i) and (ii) differ noticeably. The same difficulty is inherent in all the problems where the metallic surface has rectangular grooves. We show that in this problem the standard first-order perturbation theory is not applicable. The point is that beginning from a number n the first corrections to the modal functions φ n used to calculate the fields, are of the same order as the zero-order modal functions (the impedance is equal to zero). Basing on the energy conservation law we show that the accurate value for the ohmic losses is obtained with the aid of the approach (ii).

Dispersion relation of guided-mode resonances and Bragg peaks in dielectric diffraction gratings.

We present the dispersion relation of guided-mode resonances in non-dissipative dielectric diffraction gratings, both for s-polarized (TE mode) and p-polarized (TM mode) incident waves. We present a simple approximate theory as well as a rigorous calculation within the so-called coupled-wave theory. We discuss the dependence of the positions and the lifetimes of the resonances on the thickness of the gratings and on the strength of its modulation. We find that the diffraction efficiency of the different orders show peaks at different Bragg orders.

Electromagnetic wave scattering from conducting self-affine surfaces: an analytic and numerical study.

We derive an analytical expression for the scattering of an s-polarized plane wave from a perfectly conducting self-affine one-dimensional surface in the framework of the Kirchhoff approximation. We show that most of the results can be recovered by means of a scaling analysis. We identify the typical slope taken over one wavelength as the relevant parameter controlling the scattering process. We compare our predictions with direct numerical simulations performed on surfaces of varying roughness parameters and confirm the broad range of applicability of our description up to very large roughness. Finally we verify that a nonzero electrical resistivity, provided that it is small, does not invalidate our results.

Photonic gap in amorphous photonic materials

Two-dimensional amorphous photonic materials are created, which do not possess any long-range order but have only short-range order. Our calculation of the multiple-scattering method shows that, for S-polarized waves, these materials have photonic gap that is independent of incident directions. Even though the detailed structures of amorphous photonic materials are different with each other, they possess a common photonic gap, if only they have the same short-range order. Based on our studies it may be confirmed that, for S-polarized waves, the first band gap of photonic crystals comes mainly from the short-range order, while the higher-order band gaps are related to the long-range order. The measured transmission spectrum of an amorphous photonic material agrees perfectly with the calculation.

Scattering of s-polarized electromagnetic plane waves from a film with a shallow random rough surface on a perfect conductor

Scattering of s-polarized electromagnetic planes waves from a film, with a shallow random rough one-dimensional surface, bounded by vacuum and a perfect conductor is calculated. An integral equation that relates the amplitude of the scattered field to the incident wave is found by use of the Rayleigh hypothesis. The integral equation is solved numerically and by use of the perturbation theory, up to the fourth order in the surface profile function. In the angular dependence of the incoherent part of the differential reflection coefficient, the backscattering peak and two additional satellite peaks are observed, owing to two guided waves supported by the film. Analysis of the perturbation solution reveals that the background scattering exhibits minima and maxima as functions of the thickness. By studying the behavior of the scattering as a function of the absorption index of the film, it is shown that the amplitudes of the peaks are low when k approximately 10(-2) and high when k approximately 10(-4).

Optically Nonlinear s-Polarized Electromagnetic Waves in Multilayered Symmetric Dielectrics

A theory is presented for the nonlinear s-polarized electromagnetic waves in multilayer systems with an arbitrary number of planar interfaces. Each of the individual layers may be characterized by either a linear or a Kerr-type nonlinear dielectric constant, and we examine the coupled nonlinear waves at both linear/nonlinear and nonlinear/nonlinear interfaces. An analysis of the phase trajectories (in terms of an electric field amplitude and its spatial derivative) is employed to enumerate the modes of the system in a systematic manner and to facilitate the derivation of dispersion relations. In particular, numerical examples are given for two-interface systems (for example, a thin film sandwiched between two semi-infinite media) and for periodic superlattices (with effectively infinite interfaces), thereby extending previous calculations.

OPTICALLY NONLINEAR S-POLARIZED ELECTROMAGNETIC WAVES IN MULTILAYERED SYMMETRIC DIELECTRICS

A theory is presented for the nonlinear s-polarized electromagnetic waves in multilayer systems with an arbitrary number of planar interfaces. Each of the individual layers may be characterized by either a linear or a Kerr-type nonlinear dielectric constant, and we examine the coupled nonlinear waves at both linear/nonlinear and nonlinear/nonlinear interfaces. An analysis of the phase trajectories (in terms of an electric field amplitude and its spatial derivative) is employed to enumerate the modes of the system in a systematic manner and to facilitate the derivation of dispersion relations. In particular, numerical examples are given for two-interface systems (for example, a thin film sandwiched between two semi-infinite media) and for periodic superlattices (with effectively infinite interfaces), thereby extending previous calculations.

S-Polarized surface electromagnetic waves in inhomogeneous media: exactly solvable models

The spectral properties and the spatial structure of S-polarized surface electromagnetic waves propagating near the interface of an inhomogeneous solid plasma are examined by means of an exact analytical solution of Maxwell equations for a smooth density profile, characterized by two free parameters. The drastic differences between these waves and traditionally considered P-polarized surface plasmons are emphasized. The spectral parameters, the depth of localization, and the energy flux of such waves are shown to depend essentially upon the profile of carrier density in the plasma.

Simulations of Two-Dimensional Photon Scanning Tunneling Microscope by Boundary Integral Equation Method: p-polarization

Accurate simulations of a two-dimensional photon scanning tunneling microscope (2D-PSTM) for incident p-polarized waves (TM-mode) have been performed by the boundary integral equations called guided-mode extracted integral equations. The method used in this paper is a global method and the case of uncoated dielectric probe is treated. Complete and rigorous integral equations for a given configuration of 2D-PSTM have been solved numerically by the conventional boundary-element method with high accuracy. Using three universal laws, i.e., the optical theorem, the energy conservation law and the reciprocity relation for incident p-polarized waves, numerical results have been confirmed. The basic physical characteristics of interaction between probe-tip and near-field for incident p-polarized waves are compared in detail with those of incident s-polarized waves (TE-mode) which are previously reported.

Scattering and extinction of evanescent waves by small particles

Expressions have been obtained for the total cross sections for extinction and scattering of evanescent waves by small spherical particles. Due to the different structure of p- and s-polarized waves, cross sections for both extinc- tion and scattering of p-polarised evanescent waves exceed those for s-polarised waves, as long as the Mie coefficients for magnetic multipoles are smaller than those for electric mul- tipoles for each multipolar order, i.e. for sufficiently small particles. The difference increases with the angle of incidence of the totally reflected wave. The definition of cross sections for evanescent-wave excitation with variable intensity over the cross-sectional area of the particle allows quantitative comparison with the case of plane-wave excitation. For ex- ample, within the dipole approximation the cross sections for plane-wave excitation lie between those for p- and s-polarised evanescent-wave excitation, respectively. Due to the inhomo- geneity of the evanescent field higher multipole contributions are strongly enhanced as compared to plane-wave excitation and increase further with the angle of incidence, resulting in corresponding changes in the scattering and extinction spec- tra. These effects are demonstrated in the specific case of scattering of evanescent waves by small silver particles.