The detailed theoretical analysis of the fine optical phenomena
caused by surface plasmon polariton (SPP) excitation in a metallic
film with weakly modulated dielectric permittivity is made for
both symmetrical and nonsymmetrical dielectric arrangements. SPP
modes in the film are close to those existing at an interface
between metal and dielectric half spaces (these polaritons are
weakly coupled under the symmetrical surrounding), and the effect
of enhanced light transmission (ELT) caused by photon-SPP-photon
transformations can occur. The advantage of the approach used is
that we present the most interesting results in a simple
analytical form. The dispersion relation for the film SPP for both
arrangements is investigated. On this basis the comprehensive
examination of the ELT effect is performed. The parameters of the
problem (optimal film thickness, optimal modulation amplitude)
responsible for total suppression of the zeroth- and/or
nonzeroth-order reflected waves and maximal transmission are
found. The results are of essential interest for optical
nano-devices design.
An analytical treatment of optical surface plasmon-polaritons (SPP) existing on double-periodic high reflective media is presented. Periodicity, caused by the modulation of either complex dielectric permittivity or relief of the surface leads to the change of SPP dispersion relation due to coupling of the inoculating SPPs existing on the unmodulated boundary, and frequency gaps arising at the Brillouin zone edges. The SPP spectra for different types of periodicity/symmetry are investigated, in particular, the different couplings between several initial SPP are compared. Simple analytical expressions for the SPP dispersion relation are obtained using modified perturbation theory. The dependence of the dispersion relation on the parameters of the problem is examined.
Analytical examination of plane electromagnetic wave diffraction on a surface with periodically modulated impedance or a shallow profile is presented. For small absorption and high reflection there exist sharp resonances caused by excitation of surface plasmon polaritons. We consider the specific angles of incidence for in-plane geometry corresponding to simultaneous excitation of two polaritons propagating in the opposite directions. The simplest case corresponds to close-to-the-value arcsin(1/3) angle of incidence, when two diffracted orders with numbers +1 and -2 are close to the surface polaritons simultaneously and their amplitudes in the vicinity of the resonance become much greater than that of the incident wave. Scattering both of the resonance waves on the grating leads to essential changes in the amplitudes of the specular and other reflected waves, including the anti-specular reflected wave, as compared with nonresonance case for rather small the surface impedance modulation. Dependence of the amplitudes of the reflected waves and the polaritons on the parameters of the problem is examined for the arbitrary-form gratings. The characteristic values of the most relevant “inter-resonance” and “resonance” Fourier amplitudes of the grating (relating to the first-order interaction of the polaritons and to transformation of the incident wave into the polaritons, respectively) are found. It is shown that in the resonance vicinity, the results can be simplified. This allows complete analytical treatment. Existence of the wide set of the gratings that correspond to the universal self-similar behavior under double resonance conditions is demonstrated. The gratings with specific parameters relating to the given redistribution of the energy between different reflected waves and polaritons are described. A comparison between the evolved theory and the experimental results shows excellent agreement. The results obtained may be employed to smart media design.
The paper deals with diffraction on high reflecting surfaces with periodically modulated dielectric properties. Period of the structure is supposed to be close to the wavelength multiplied by an integer and, consequently, for close-to-normal incidence of a p-polarized wave there exists the resonance (Wood anomaly) caused by simultaneous excitation of two surface plasmon polaritons (SPP). We present the analytical solution of the problem using the surface impedance as the small parameter that enables us to consider variety of metals and semiconductors in red and infrared regions. The simple explicit solution obtained makes it possible to present the results in a closed analytical form and examine them in detail for arbitrary grating form. We present the dependence of the polariton, specular and other reflected waves phases and amplitudes on the angle of incidence, wavelength, and on the grating period and form. We derive the universal self-similar representation of the solution in the close resonance vicinity. This enables us to carry out a thorough investigation of the strong resonance peculiarities fine structure. There are formulated conditions on the grating parameters that correspond to the specific redistribution of the radiation flux between outgoing waves and the SPPS. In particular, we demonstrate that in spite of the geometric symmetry, excitation of one of the polaritons can be suppressed totally. The total suppression of any subset of the outgoing diffracted waves is also possible, and a variety of other energy redistributions between them is possible as well. The results are of interest both from theoretical point of view and in view of a wide field of possible applications for the novel optic and opto-electronic problems concerning light transformation and control.
The results of analytical and numerical investigation of the surface plasmon-polaritons (SPP)dispersion relation on double periodical high reflecting surfaces (two-dimensional photonic crystals)are presented. The formalism is developed for gratings formed by the modulation of either optical properties or the relief of the medium. The coupling between SPP existing on the non-modulated boundary leads to the mini-gaps arising at the Brillouin-zone boundaries. The dependence of the dispersion relation upon the parameters of the problem (amplitude of
the modulation, an angle between the elementary translations,etc.) is calculated for different types of symmetry that corresponds to the coupling from two to six polaritons. The specific values of the parameters corresponding to existence of the standing polariton modes, vanishing of the polariton group velocity are found. The distribution of surface charges for corresponding polariton modes is presented. The ratio between the polariton dispersion relation and the light diffraction under the condition of the polariton excitation is discussed as well. The results obtained can be used to design the two-dimensional photonic crystals with specific and given properties.
The paper deals with the theoretical investigation of plane, normally incident electromagnetic wave transmission through the flat metal folm whose dielectric constant has small periodical sinusoidal modulation in one dimension parallel to the projection of the electric field onto the film surface. The dependencies of the film transmittancy on the parameters of the problem (frequency, modulation depth and absorption) are examined. It is shown that the film transmittancy increases considerably when the conditions for resonance interaction of an incident electromagnetic wave with surface plasmon polaritons (SPPs) are met. It is found that for small but finite absorption there are two frequencies in the vicinity of which the transmittancy can achieve the values of the order of unity due to resonances on symmetric and antisymmetric (relative to the mean plane) SPP modes. It is shown that for each value of absorption there exists a certain optimal modulation depth, which maximizes the
resonance transparency.
As it is well known, the diffraction of p- polarized wave on metal gratings may be accompa-nied by Wood type anomalies, caused by resonance excitation of surface plasmon polaritons. In the report we present the results of the analytical and numerical investigation of the reso-nance diffraction for grazing incidence on the gratings with period larger than the wavelength. In this case a number of diffracted orders, corresponding to evanescent waves may be close to the resonance simultaneously, i.e., we have multiple resonance case.
We consider the high conducting plane surface with harmonically modulated surface impedance, presenting small parameter of the theory. Contrary to the case of single or double resonance case, the infinite set of the linear algebraic equations for the diffracted wave ampli-tudes cannot be reduced to one or two equations for the resonance wave amplitudes. But for the harmonic grating, the matrix of the system is Jacobi one and thus the solution may be presented in the continued fractions form. The results are analyzed as functions of the wavelength to grating period ratio 0.1...0.0003, and grazing angle 0...30 deg. It is shown that a number of evanescent wave am-plitudes can exceed amplitude of the incident wave and possess complicated behavior as func-tion of parameters. The specular reflectivity is of complicated behavior also and in some cases it is similar to the one obtained in numerical calculations and experiments for deep profile gratings.
An overview of results concerning diffraction by periodic structures under conditions of surface plasmon polaritons excitation is presented. The possibility of the detailed analytical investigation of the problem is based upon the restriction for the case of weak scattering. In spite of this restriction, it is shown that resonance may be strong. The simple analytical approach based upon the modified perturbation theory allows presenting results in explicit analytical form. We consider both the in-plane diffraction (i.e., the wavevector of the periodic structure is parallel to the plane of incidence) and diffraction in general geometry (conical mounting). The systematization of the resonances is presented for diffraction from the grating on the surface of high reflecting media. It is shown that the behavior of the complex amplitudes of all diffracted waves in the resonance vicinity possesses universality, namely, the results may be presented in a scaled form and thus are self-similar. The difference between various media consists in the resonance position and scaling factors. For the conical mounting, the dependence of the diffracted wave intensities, amplitudes and phases on the parameters of the incident wave and media properties are investigated. The theoretical results obtained show good agreement with the experimental data. The possibilities of new experiments based on the theoretical predictions and possible generalizations are discussed.
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