Dispersive perfectly matched layers and high-order absorbing boundary conditions for electromagnetic quasinormal modes.

Resonances, also known as quasinormal modes (QNMs) in the non-Hermitian case, play a ubiquitous role in all domains of physics ruled by wave phenomena, notably in continuum mechanics, acoustics, electrodynamics, and quantum theory. The non-Hermiticity arises from the system losses, whether they are material (Joule losses in electromagnetism) or linked to the openness of the problem (radiation losses). In this paper, we focus on the latter delicate matter when considering bounded computational domains mandatory when using, e.g., finite elements. We address the important question of whether dispersive perfectly matched layer (PML) and high-order absorbing boundary conditions offer advantages in QNM computation and modal expansion of the optical responses compared with nondispersive PMLs.

Finite element analysis of electromagnetic waves in two-dimensional transformed bianisotropic media.

We analyze the wave propagation in two-dimensional bianisotropic media with the Finite Element Method (FEM). Starting from the Maxwell-Tellegen's equations in bianisotropic media, we derive some system of coupled Partial Differential Equations (PDEs) for longitudinal electric and magnetic field components. These PDEs are implemented in FEM using a solid mechanics formulation. Perfectly Matched Layers (PMLs) are also discussed to model unbounded bianisotropic media. The PDEs and PMLs are then implemented in a finite element software, and transformation optics is further introduced to design some bianisotropic media with interesting functionalities, such as cloaks, concentrators and rotators. In addition, we propose a design of metamaterial with concentric layers made of homogeneous media with isotropic permittivity, permeability and magnetoelectric parameters that mimic the required effective anisotropic tensors of a bianisotropic cloak in the long wavelength limit (homogenization approach). Our numerical results show that transformation based electromagnetic metamaterials can be extended to bianisotropic media.

Phase retrieval of reflection and transmission coefficients from Kramers-Kronig relations.

Analytic and passivity properties of reflection and transmission coefficients of thin-film multilayered stacks are investigated. Using a rigorous formalism based on the inverse Helmholtz operator, properties associated with the causality principle and passivity are established when both the temporal frequency and spatial wave vector are continued in the complex plane. This result extends the range of situations where the Kramers-Kronig relations can be used to deduce the phase from the intensity. In particular, it is rigorously shown that the Kramers-Kronig relations for reflection and transmission coefficients remain valid for all fixed angles of incidence. Possibilities for exploiting the new relationships are discussed and numerically tested.

Surface plasmon hurdles leading to a strongly localized giant field enhancement on two-dimensional (2D) metallic diffraction gratings.

An extensive numerical study of diffraction of a plane monochromatic wave by a single gold cone on a plane gold substrate and by a periodical array of such cones shows formation of curls in the map of the Poynting vector. They result from the interference between the incident wave, the wave reflected by the substrate, and the field scattered by the cone(s). In case of a single cone, when going away from its base along the surface, the main contribution in the scattered field is given by the plasmon surface wave (PSW) excited on the surface. As expected, it has a predominant direction of propagation, determined by the incident wave polarization. Two particular cones with height approximately 1/6 and 1/3 of the wavelength are studied in detail, as they present the strongest absorption and field enhancement when arranged in a periodic array. While the PSW excited by the smaller single cone shows an energy flux globally directed along the substrate surface, we show that curls of the Poynting vector generated with the larger cone touch the diopter surface. At this point, their direction is opposite to the energy flow of the PSW, which is then forced to jump over the vortex regions. Arranging the cones in a two-dimensional subwavelength periodic array (diffraction grating), supporting a specular reflected order only, resonantly strengthens the field intensity at the tip of cones and leads to a field intensity enhancement of the order of 10 000 with respect to the incident wave intensity. The enhanced field is strongly localized on the rounded top of the cones. It is accompanied by a total absorption of the incident light exhibiting large angular tolerances. This strongly localized giant field enhancement can be of much interest in many applications, including fluorescence spectroscopy, label-free biosensing, surface-enhanced Raman scattering (SERS), nonlinear optical effects and photovoltaics.

Finite frequency external cloaking with complementary bianisotropic media.

We investigate the twofold functionality of a cylindrical shell consisting of a negatively refracting heterogeneous bianisotropic (NRHB) medium deduced from geometric transforms. The numerical simulations indicate that the shell enhances their scattering by a perfect electric conducting (PEC) core, whereas it considerably reduces the scattering of electromagnetic waves by closely located objects when the shell surrounds a bianisotropic core. The former can be attributed to a homeopathic effect, whereby a small PEC object scatters like a large one as confirmed by numerics, while the latter can be attributed to space cancellation of complementary bianisotropic media underpinning anomalous resonances counteracting the field emitted by small objects (external cloaking). Space cancellation is further used to cloak a NRHB finite size object located nearby a slab of NRHB with a hole of same shape and opposite refracting index. Such a finite frequency external cloaking is also achieved with a NRHB cylindrical lens. Finally, we investigate an ostrich effect whereby the scattering of NRHB slabs and cylindrical lenses with simplified parameters hide the presence of small electric antennas in the quasi-static limit.

Negative-index materials: a key to "white" multilayer Fabry-Perot.

The use of negative-index materials is highly efficient for tailoring the spectral dispersion properties of a quarter-wavelength Bragg mirror and for obtaining resonant behavior of a multilayer Fabry-Perot cavity over a very large spectral range. An optimization method is proposed and validated on some first promising devices.

Artificial dispersion via high-order homogenization: magnetoelectric coupling and magnetism from dielectric layers.

We investigate a high-order homogenization (HOH) algorithm for periodic multi-layered stacks. The mathematical tool of choice is a transfer matrix method. Expressions for effective permeability, permittivity and magnetoelectric coupling are explored by frequency power expansions. On the physical side, this HOH uncovers a magnetoelectric coupling effect (odd-order approximation) and artificial magnetism (even-order approximation) in moderate contrast photonic crystals. Comparing the effective parameters' expressions of a stack with three layers against that of a stack with two layers, we note that the magnetoelectric coupling effect vanishes while the artificial magnetism can still be achieved in a centre-symmetric periodic structure. Furthermore, we numerically check the effective parameters through the dispersion law and transmission property of a stack with two dielectric layers against that of an effective bianisotropic medium: they are in good agreement throughout the low-frequency (acoustic) band until the first stop band, where the analyticity of the logarithm function of the transfer matrix ([Formula: see text]) breaks down.

Focusing light in a bianisotropic slab with negatively refracting materials.

We investigate the electromagnetic response of a pair of complementary bianisotropic media, which consist of a medium with positive refractive index (+ε, +µ, +ξ) and a medium with negative refractive index(-ε, -µ, -ξ). We show that this idealized system has peculiar imaging properties in that it reproduces images of a source, in principle, with unlimited resolution. We then consider an infinite array of line sources regularly spaced in a 1D photonic crystal (PC) consisting of 2n layers of bianisotropic complementary media. Using coordinate transformations, we map this system into 2D corner chiral lenses of 2n heterogeneous anisotropic complementary media sharing a vertex, within which light circles around closed trajectories. Alternatively, one can consider corner lenses with homogeneous isotropic media and map them into 1D PCs with heterogeneous bianisotropic layers. Interestingly, such complementary media are described by scalar, or matrix valued, sign-shifting parameters, which satisfy a new version of the generalized lens theorem of Pendry and Ramakrishna. This theorem can be derived using Fourier series solutions of the Maxwell-Tellegen equations, or from space-time symmetry arguments. Also of interest are 2D periodic checkerboards consisting of alternating rectangular cells of complementary media which are such that one point source in one cell gives rise to an infinite set of images with an image in every other cell. Such checkerboards can themselves be mapped into a class of 3D corner lenses of complementary bianisotropic media. These theoretical results are illustrated by finite element computations.

Discrete dipole approximation in time domain through the Laplace transform.

We present a form of the discrete dipole approximation for electromagnetic scattering computations in time domain. We show that the introduction of complex frequencies, through the Laplace transform, significantly improves the computation time. We also show that the Laplace transform and its inverse can be combined to extract the field inside a scatterer at a real resonance frequency.

Magneto-optical circulator designed for operation in a uniform external magnetic field.

We propose an approach for the design of resonant cavities employed in magnetophotonic crystal (MPC) circulators and isolators. Starting from the analysis of a model circularly symmetric cavity, we show how to obtain a significant splitting of the eigenfrequencies of the two counterrotating cavity modes without introducing subdomains magnetized in opposite directions. Using the multiple-scattering method extended to handle uniaxial gyrotropic materials, we demonstrate numerically an MPC circulator working in a uniform external magnetic field.

Antireflection gratings for a photonic-crystal flat lens.

A dielectric structure with effective permittivity and permeability close to -1 operating for propagative waves at optical wavelengths is proposed. This structure is a two-dimensional photonic crystal with refractive index -1, coated by appropriate antireflection gratings. Numerical simulations involving a flat lens made of this optimized crystal illustrate the improvements that antireflection gratings can bring. In particular, following Veselago's proposition, this lens "can focus at a point the radiation from a point source" with negligible reflection losses. The proposed design takes into account the fabrication requirements and can be used for optical devices integrated in planar waveguides.

Solutions of Maxwell's equations in presence of lamellar gratings including infinitely conducting metal.

Modal methods often used to model lamellar gratings that include infinitely or highly conducting metallic parts encounter numerical instabilities in some situations. In this paper, the origin of these numerical instabilities is determined, and then a stable algorithm solving this problem is proposed. In order to complete this analysis, the different geometries that can be handled without numerical instabilities are clearly defined. Numerical tests of the exact modal method implemented with the proposed solution are also presented. A test of convergence shows the efficiency of the method while the comparison with the fictitious sources method shows its accuracy.

Singularity of the dyadic Green's function for heterogeneous dielectrics.

For heterogeneous media with piecewise constant complex permittivity on regular domains, we show that the dyadic Green's function has the same singular part as the corresponding free space dyadic Green's function on every domain of constant permittivity. We give two important applications of this property, namely the distorted-wave Born approximation for composite media and the calculation of the single photon decay rate in spontaneous emission.

Towards -1 effective index with one-dimensional metal-dielectric metamaterial: a quantitative analysis of the role of absorption losses.

We propose a theoretical study of the optimization of one dimensional metal-dielectric metamaterials in order to approach -1 effective optical index. Taking into account actual values of dielectric constants of metal (silver) and dielectrics (HfO(2), GaP), and taking advantage of the dispersion relation of Bloch modes, we get a silver/HfO(2)metamaterial with suitable parameters that possesses a near -1 effective optical index for all angles of incidence at a visible wavelength for H-polarized light (i.e. the magnetic field is parallel to the interfaces). The absorption losses of materials appear to be a crucial factor that affects the effective properties of the metamaterial. We show that the losses not only decrease the transmission of the stack, but also change the negative refraction effect. Then, we propose another silver/GaP structure design that is less sensitive to losses. When considering finite thickness structures, and with adequate thickness for the terminating layers, it is possible to achieve a high transmittance of the structure. A near -1 effective index and high transmittance metal-dielectric metamaterial may pave the way to the realization of negative refraction in the visible or ultraviolet wavelength range.

Thermal radiation scanning tunnelling microscopy.

In standard near-field scanning optical microscopy (NSOM), a subwavelength probe acts as an optical 'stethoscope' to map the near field produced at the sample surface by external illumination. This technique has been applied using visible, infrared, terahertz and gigahertz radiation to illuminate the sample, providing a resolution well beyond the diffraction limit. NSOM is well suited to study surface waves such as surface plasmons or surface-phonon polaritons. Using an aperture NSOM with visible laser illumination, a near-field interference pattern around a corral structure has been observed, whose features were similar to the scanning tunnelling microscope image of the electronic waves in a quantum corral. Here we describe an infrared NSOM that operates without any external illumination: it is a near-field analogue of a night-vision camera, making use of the thermal infrared evanescent fields emitted by the surface, and behaves as an optical scanning tunnelling microscope. We therefore term this instrument a 'thermal radiation scanning tunnelling microscope' (TRSTM). We show the first TRSTM images of thermally excited surface plasmons, and demonstrate spatial coherence effects in near-field thermal emission.

Perfect corner reflector.

We numerically investigate the electromagnetic field radiated by a line source within a perfect lens [Phys. Rev. Lett. 85, 3966 (2000)] consisting of two orthogonal planes delimiting positive and negative index media. Use of a coordinate transformation [J. Phys. Condens Matter 15, 6345 (2003)] together with a well-adapted transfer-matrix method permits rigorous calculation of the vector field. We find that two negative corners combine to make a cavity that traps light along closed trajectories. Finally, we numerically show that the field presents some spatial oscillations with a period that is proportional to absorption sigma inside the negative materials as 1/ln sigma and that it is associated with an infinite density of states when sigma tends toward 0.

Enhanced transmission due to nonplasmon resonances in one- and two-dimensional gratings.

Enhanced transmission through subwavelength slit gratings and hole arrays is studied in view of its application in the far-infrared and microwave domains. Because for perfectly conducting gratings, plasmon resonances are not expected to produce an enhanced transmission, other kinds of resonance, such as Fabry-Perot, waveguide-mode, and cavity-mode resonances, are studied. The possibility of reaching 100% transmittivity for some particular wavelengths is established when two superimposed identical gratings are used while each of them transmits approximately 1% off resonance. A similar transmission is obtained with hole arrays. The study of the field map inside the groove region allows our establishing the nature of the resonance, that is involved. Comparison of the bandwidth with respect to the wavelength or incidence given by various kinds of resonance is presented.

Theoretical study of photonic band gaps in woodpile crystals.

We investigate numerically the existence of photonic band gaps in woodpile crystals. We present a numerical method specifically developed to solve Maxwell's equations in such photonic structures. It is based upon a rigorous mathematical formulation and leads to a considerable improvement of the convergence speed as compared to other existing numerical methods. We tested our method by comparing the calculated reflectivity with measurements on an actual sample, i.e., a silicon woodpile photonic crystal designed for 1.5 microm wavelength. Excellent agreement is obtained, provided the main structural imperfections of the sample are taken into account. We show that the existence of photonic band gaps in woodpile crystals requires an index contrast higher than 2.05 +/- 0.01. The effects of imperfections of such structures with an index contrast equal to 2.25 are also investigated. Thus, the relative band gap width falls from 3.5% to 2.2% with structurals imperfection similar to those of the sample.

From scattering or impedance matrices to Bloch modes of photonic crystals.

The dispersion relation of Bloch waves is derived from the properties of a single grating layer. A straightforward way to impose the Bloch condition leads to the calculation of the eigenvalues of the transfer matrix through the single grating layer. Unfortunately, the transfer-matrix algorithm is known to be unstable as a result of the growing evanescent waves. This problem appears again in the calculation of the eigenvalues, making unusable the transfer matrix in numerous practical problems. We propose two different algorithms to circumvent this problem. The first one takes advantage of scattering matrices, while the second one takes advantage of impedance matrices. Numerical evidence of the efficiency of the algorithms is given. Dispersion diagrams of simple cubic and woodpile photonic crystals are obtained by using, respectively, the scattering and impedance matrices.

Staircase approximation validity for arbitrary-shaped gratings.

An electromagnetic study of the staircase approximation of arbitrary shaped gratings is conducted with three different grating theories. Numerical results on a deep aluminum sinusoidal grating show that the staircase approximation introduces sharp maxima in the local field map close to the edges of the profile. These maxima are especially pronounced in TM polarization and do not exist with the original sinusoidal profile. Their existence is not an algorithmic artifact, since they are found with different grating theories and numerical implementations. Since the number of the maxima increases with the number of the slices, a greater number of Fourier components is required to correctly represent the electromagnetic field, and thus a worsening of the convergence rate is observed. The study of the local field map provides an understanding of why methods that do not use the staircase approximation (e.g., the differential theory) converge faster than methods that use it. As a consequence, a 1% accuracy in the efficiencies of a deep sinusoidal metallic grating is obtained 30 times faster when the differential theory is used in comparison with the use of the rigorous coupled-wave theory. A theoretical analysis is proposed in the limit when the number of slices tends to infinity, which shows that even in that case the staircase approximation is not well suited to describe the real profile.