Incident Plane Electromagnetic Wave Research Articles

Photonic clusters formed by dielectric microspheres: Numerical simulations

We show through rigorous calculations that dielectric microspheres can be organized by an incident electromagnetic plane wave into stable cluster configurations, which we call photonic molecules. The long-range optical binding force arises from multiple scattering between the spheres. A photonic molecule can exhibit a multiplicity of distinct geometries, including quasicrystal-like configurations, with exotic dynamics. Linear stability analysis and dynamical simulations show that the equilibrium configurations can correspond with either stable or a type of quasi-stable states exhibiting periodic particle motion in the presence of frictional dissipation.

Some properties of the angular power distribution of electromagnetic waves multiply scattered in a collisional magnetized turbulent plasma

A study is made of oblique incidence of a small-amplitude plane electromagnetic wave on a semi-infinite slab of a collisional turbulent plasma in an external uniform magnetic field. In the small-angle scattering approximation, the condition for neutralizing the effects of oblique incidence and plasma anisotropy on the statistical properties of radiation multiply scattered in the absorbing plasma medium is determined by using the methods of geometrical optics. The validity of this condition was confirmed by numerical calculations based on the statistical modeling technique. The effect of the shape of the spectrum of the electron density fluctuations on the shape of the angular power distribution of a multiply scattered radiation is investigated.

Frozen light in periodic stacks of anisotropic layers

We consider a plane electromagnetic wave incident on a periodic stack of dielectric layers. One of the alternating layers has an anisotropic refractive index with an oblique orientation of the principal axis relative to the normal to the layers. It was shown recently that an obliquely incident light, upon entering such a periodic stack, can be converted into an abnormal axially frozen mode with drastically enhanced amplitude and zero normal component of the group velocity. The stack reflectivity at this point can be very low, implying nearly total conversion of the incident light into the frozen mode with huge energy density, compared to that of the incident light. Supposedly, the frozen mode regime requires strong birefringence in the anisotropic layers--by an order of magnitude stronger than that available in common anisotropic dielectric materials. In this paper we show how to overcome the above problem by exploiting higher frequency bands of the photonic spectrum. We prove that a robust frozen mode regime at optical wavelengths can be realized in stacks composed of common anisotropic materials, such as YVO(4), LiNbO(3), CaCO(3), and the like.

Inverse Medium Scattering Problems for Electromagnetic Waves

Consider a time-harmonic electromagnetic plane wave incident on a medium enclosed by a bounded domain in $\mathbb{R}^3$. In this paper, existence and uniqueness of the variational problem for forward scattering are established. An energy estimate for the scattered field with a uniform bound with respect to the wavenumber is obtained in the case of low frequency on which the Born approximation is based. A continuation method for the inverse medium scattering problem, which reconstructs the scatterer of an inhomogeneous medium from boundary measurements of the scattered wave, is developed. The algorithm requires multifrequency scattering data. Using an initial guess from the Born approximation, each update is obtained via recursive linearization on the wavenumber k by solving one forward problem and one adjoint problem of Maxwell's equations.

Uniqueness and local stability for the inverse scattering problem of determining the cavity

Considering a time-harmonic electromagnetic plane wave incident on an arbitrarily shaped open cavity embedded in infinite ground plane, the physical process is modelled by Maxwell's equations. We investigate the inverse problem of determining the shape of the open cavity from the information of the measured scattered field. Results on the uniqueness and the local stability of the inverse problem in the 2-dimensional TM (transverse magnetic) polarization are proved in this paper.

Propagation of an Electromagnetic Wave in a Mixing of Plasma-dense Neutral Gas

The propagation of a normal incident electromagnetic plane wave in a mixture of rare plasma and dense neutral gas is investigated by one dimensional model. The numerical results show that the amplitude of wave electric field is decayed dramatically and its phase is modulated obviously in a distance of a few wave lengthes due to the frequent collisions between electrons and neutrals (the collision frequency νc is near or even larger than the wave frequency ω0).

Analysis of nonuniform nonlinear distributed feedback structures using a simple numerical approach

A simple numerical approach previously proposed for calculating the input-intensity dependence of the reflectivity and transmissivity of a nonlinear dielectric slab for incident plane electromagnetic waves is adopted for analyzing nonuniform nonlinear distributed feedback (NLDFB) structures. The method is first validated by checking with the analytic solution for the bistability characteristics of a strictly periodic, uniform NLDFB structure as well as the reported transmission characteristics of linear structures based on transfer matrix method calculation. The method is then applied to determine the transmission bistability characteristics of linearly tapered and linearly chirped NLDFB structures. The results are found to be different in some cases from those based on a generalized transfer matrix calculation in which the nonuniform structure is approximated by a set of strictly periodic, uniform segments.

The electromagnetic inverse-scattering problem for partly coated Lipschitz domains

We consider the inverse-scattering problem of determining the shape of a partly coated obstacle in R3 from a knowledge of the incident time-harmonic electromagnetic plane wave and the electric far-field pattern of the scattered wave. A justification is given of the linear sampling method in this case and numerical examples are provided showing the practicality of our method.

The inverse electromagnetic scattering problem for a mixed boundary value problem for screens

We consider the inverse scattering problem of determining the shape of mixed perfectly conducting-impedance screens from a knowledge of the incident time harmonic electromagnetic plane wave and the electric far field pattern of the scattered wave. We adapt the linear sampling method invented by Colton and Kirsch (Inverse Problems 12 (1996) 383) for the case of scattering by obstacles with nonempty interior. Numerical examples are given for mixed screens in R 3 .

Reconciliation of the forward scattering and wave theories of electric-field-gradient-induced birefringence

We consider propagation of a linearly polarized, harmonic, plane electromagnetic wave incident on a dilute gas subject to a non-uniform electrostatic field. We work to electric quadrupole–magnetic dipole order. In general, the wave is distorted to include a perpendicular component induced by the electrostatic field gradient, and the resultant is not a plane wave. Although the induced component is small, its contribution to the polarization-dependent refractive index of the gas in Buckingham's quadrupole experiment is significant. We show that distortion of the incident wave accounts exactly for the present discrepancy between wave theory and forward scattering theory of electric-field-gradient-induced birefringence in a gas: both theories yield the result obtained originally by Buckingham and Longuet-Higgins.

Complete Transmission Through a Two-Dimensional Diffraction Grating

The propagation of a normally incident electromagnetic plane wave through a two-dimensional metallic grating is modeled and analyzed. The period of the structure A is on the order of the incident wave length $\lambda$, but the height of the channel H separating the blocks is very small. Exploiting the small parameter H/A, an approximate transmission coefficient is obtained for the grating. For a fixed frequency this coefficient is O(H/A) except near resonant lengths where it is O(1). That is, for certain widths the structure is transparent. Similarly, for a fixed length the transmission coefficient has the same resonant features as a function of frequency.

Oblique frozen modes in periodic layered media.

We study the classical scattering problem of a plane electromagnetic wave incident on the surface of semi-infinite periodic stratified media incorporating anisotropic dielectric layers with special oblique orientation of the anisotropy axes. We demonstrate that an obliquely incident light, upon entering the periodic slab, gets converted into an abnormal grazing mode with huge amplitude and zero normal component of the group velocity. This mode cannot be represented as a superposition of extended and evanescent contributions. Instead, it is related to a general (non-Bloch) Floquet eigenmode with the amplitude diverging linearly with the distance from the slab boundary. Remarkably, the slab reflectivity in such a situation can be very low, which means an almost 100% conversion of the incident light into the axially frozen mode with the electromagnetic energy density exceeding that of the incident wave by several orders of magnitude. The effect can be realized at any desirable frequency, including optical and UV frequency range. The only essential physical requirement is the presence of dielectric layers with proper oblique orientation of the anisotropy axes. Some practical aspects of this phenomenon are considered.

Coherent backscattering of light by a layer of discrete random medium

We consider the problem of backscattering of light by a layer of discrete random medium illuminated by an obliquely incident plane electromagnetic wave. The multiply scattered reflected radiation is assumed to consist of incoherent and coherent parts, the coherent part being caused by the interference of multiply scattered waves. Formulas describing the characteristics of the reflected radiation are derived assuming that the scattering particles are spherical. The formula for the incoherent contribution reproduces the standard vector radiative transfer equation. The interference contribution is expressed in terms of a system of Fredholm integral equations with kernels containing Bessel functions. The special case of the backscattering direction is considered in detail. It is shown that the angular width of the backscattering interference peak depends on the polar angle of the incident wave and on the azimuth angle of the reflection direction.

A UNIQUENESS THEOREM FOR AN INVERSE ELECTROMAGNETIC SCATTERING PROBLEM IN INHOMOGENEOUS ANISOTROPIC MEDIA

AbstractWe show that the support of a (possibly) coated anisotropic medium is uniquely determined by the electric far-field patterns corresponding to incident time-harmonic electromagnetic plane waves with arbitrary polarization and direction. Our proof avoids the use of a fundamental solution to Maxwell’s equations in an anisotropic medium and instead relies on the well-posedness and regularity properties of solutions to an interior transmission problem for Maxwell’s equations.AMS 2000 Mathematics subject classification: Primary 35R30; 35Q60. Secondary 35P25; 78A45

Maxwell's equations in periodic chiral structures

AbstractConsider a time–harmonic electromagnetic plane wave incident on a biperiodic structure in ℝ3. The periodic structure separates two homogeneous regions. The medium inside the structure is chiral and heterogeneous. In general, wave propagation in the chiral medium is governed by Maxwell's equations together with the Drude– Born–Fedorov (constitutive) equations. In this paper, the diffraction problem is formulated in a bounded domain by introducing a pair of transparent boundary conditions. It is then shown that for all but possibly a discrete set of parameters, there is a unique quasi–periodic weak solution to the diffraction problem. Our proof is based on the Hodge decomposition, a compact imbedding result, and the Lax–Milgram Lemma. In addition, an energy conservation for the weak solution is also shown.

Analysis of the electromagnetic scattering from a cavity

Consider a time-harmonic electromagnetic plane wave incident on a cavity in a ground plane. Inside the cavity, the medium may beinhomogeneous. In this paper, variational formulations in TE and TM polarizations are studied. Existence and uniqueness of the solutions for the model problems are established. The variational approach also forms a basis for numerical solution of the model problems.

Two-dimensionally-periodic diffractive optical elements: limitations of scalar analysis.

The range of validity of the scalar diffraction analysis is quantified for the case of two-dimensionally-periodic diffractive optical elements (crossed gratings). Three canonical classes of two-dimensionally-periodic grating structures are analyzed by using the rigorous coupled-wave analysis as well as the scalar diffraction analysis. In all cases the scalar-analysis diffraction efficiencies are compared with the exact diffraction efficiencies. The error in using the scalar analysis is then determined as a function of the grating-period(s)-to-wavelength ratio(s), the minimum feature size, the grating depth, the refractive index of the grating, the incident polarization, and the number of phase levels. The three classes of two-dimensional (2-D) unit cells are as follows: (1) a rectangular pillar, (2) an elliptical pillar, and (3) an arbitrarily pixellated multilevel 2-D unit cell that is representative of more complicated diffractive optical elements such as computer-generated holograms. In all cases a normally incident electromagnetic plane wave is considered. It is shown that the error of the scalar diffraction analysis in the case of two-dimensionally-periodic diffractive optical elements is greater than that for the corresponding one-dimensionally-periodic counterparts. In addition, the accuracy of the scalar diffraction analysis degrades with increasing refractive index, grating thickness, and asymmetry of the 2-D unit cell and with decreasing grating-period-to-wavelength ratio and feature size.

Transformation of the Angular Power Spectrum of Scattered Radiation in a Turbulent Absorbing Magnetoactive Plasma

We consider the oblique incidence of a small-amplitude plane electromagnetic wave on a layer of turbulent absorbing plasma in a uniform external magnetic field. The equations for the first two statistical moments of the angular power spectrum of scattered radiation are derived in the geometrical-optics approximation. We show that two asymmetry factors of the problem, i.e., the oblique incidence and the influence of the anisotropic medium, compensate for each other along a certain direction and impede the appearance of the effect of displacement of the power-spectrum maximum and the effect of anomalous spectrum broadening. We find the condition at which such a case of wave propagation is realized. The dependence of the angular-spectrum shape on the distance from the plasma-layer boundary is studied numerically without using the small-angle approximation. The calculations confirm the results obtained using the geometrical-optics approximation.

Mathematical Modeling of Near-Field Optics

Consider a time-harmonic electromagnetic plane wave incident on a periodic (grating) structure. An inhomogeneous (subwavelength) object is placed inside the periodic structure. The scattering problem is to study the electromagnetic field distributions. The problem arises in the study of near-field optics and has many physical and biological applications. This work is devoted to modeling and analysis of a near-field optics problem. An integral representation approach is presented to solve the problem. It is shown particularly that the perturbation due to the object decays exponentially along the periodic direction of the structure, provided that no surface waves occur. Based on the approach, a general solution method is discussed and the well-posedness of the model problems are established.

Maxwell's Equations in a Perturbed Periodic Structure

The paper is concerned with electromagnetic wave propagation in a perturbed periodic structure. Consider a time-harmonic electromagnetic plane wave incident on a biperiodic (grating) structure. A single inhomogeneous object is placed inside the biperiodic structure. The scattering problem is to study the electromagnetic field distributions. The problem arises in the study of near-field optics and has recently found many applications in physics and biology. In this paper, an integral representation approach is presented to solve the problem. Using the approach, well-posedness of the model problem is established. In addition, it is shown that the perturbation due to the object is exponentially decaying along the periodic directions of the structure, provided that no surface waves occur.