Rigorous Electromagnetic Theory Research Articles

Multiple Bloch surface wave excitation with gratings

We study the coupling of a finite number of Bloch Surface Waves (BSWs) propagating in different directions at the surface of a dielectric multilayer. These surface waves arise from a set of diffraction orders associated to a grating on the bottom surface of the substrate that is illuminated by a normally incident beam. Simultaneous excitation of multiple BSWs is possible with a set of diffraction orders having the same radial spatial frequency. Using rigorous electromagnetic theory, we design gratings for simultaneous excitation of two, four and six BSWs propagating in directions separated by π, π/2 and π/3 azimuthal intervals, respectively.

Accurate Morphology-Related Diffraction Behavior of Light-Induced Surface Relief Gratings on Azopolymers

Holographic relief gratings can be fabricated directly on the surface of azobenzene-containing materials (or simply azomaterials) without additional development steps. Despite often being described to have ideal sinusoidal profiles, the developing surface morphology in large amplitude gratings can affect the light distribution of the writing interferogram, causing profile deformations and deviations in the expected diffraction behavior. In this work, we characterize the temporal evolution of the surface relief grating (SRG) morphology fabricated by means of interference lithography on azopolymer films, quantitatively relating the results of a Fourier analysis of their surface profiles to the accurate measurement of efficiencies in the transmitted diffraction orders. A reliable surface structuration dynamics is empirically extracted from the analysis and used to formulate a simple but detailed diffraction model that, within the scalar diffraction theory, exhaustively describes the diffraction behavior of real SRGs without the need of complex rigorous electromagnetic theories. Our results add a deeper insight in the quantitative description of the morphology and the diffraction behavior of SRGs, which can contribute to their adoption for operating high-performance, reconfigurable, compact, and lightweight diffractive optical devices.

Enhancing near-field optical tweezers by spin-to-orbital angular momentum conversion

Near-field patterns of light provide a way to optically trap, deliver, and sort single nanoscopic particles in a wide variety of applications in nanophotonics, microbiology, and nanotechnology. Using rigorous electromagnetic theory, we investigate the forces and trapping performance of near-field optical tweezers carrying spin and orbital angular momenta. The trapping field is assumed to be generated by a total internal reflection microscope objective at a glass–water interface in conditions where most of the transmitted light is evanescent. We discover aspects of these tweezers, including the possibility to rotate and stably trap nanoscopic beads. More importantly, we show that, under near-field conditions, the contributions of spin and orbital angular momenta to the rotation of small particles are almost equivalent, opening the possibility to cancel each other when they have an opposite sign. We show that these conditions result in optimal optical trapping, giving rise to extremely effective optical tweezers for nanomanipulation, with both circular symmetry and relatively weak rotation.

A simple and comprehensive electromagnetic theory uncovering complete picture of light transport in birefringent crystals

Birefringence production of light by natural birefringent crystal has long been studied and well understood. Here, we develop a simple and comprehensive rigorous electromagnetic theory that allows one to build up the complete picture about the optics of crystals in a friendly way. This theory not only yields the well-known refraction angle and index of ellipse for birefringence crystal, but also discloses many relevant physical and optical quantities that are rarely studied and less understood. We obtain the reflection and transmission coefficient for amplitude and intensity of light at the crystal surface under a given incident angle and show the electromagnetic field distribution within the crystal. We derive the wavefront and energy flux refraction angle of light and the corresponding phase and ray refractive index. We find big difference between them, where the phase refractive index satisfies the classical index of ellipse and Snell’s law, while the ray refractive index does not. Moreover, we disclose the explicit expressions for the zero-reflection Brewster angle and the critical angle for total internal reflection. For better concept demonstration, we take a weak birefringent crystal of lithium niobate and a strong birefringent crystal tellurium as examples and perform simple theoretical calculations. In addition, we perform experimental measurement upon z-cut lithium niobate plate and find excellent agreement between theory and experiment in regard to the Brewster angle. Our theoretical and experimental results can help to construct a clear and complete picture about light transport characteristics in birefringent crystals, and may greatly facilitate people to find rigorous solution to many light–matter interaction processes happening within birefringent crystals, e.g., nonlinear optical interactions, with electromagnetic theory.

Mode spectra of magnetic and dielectric plasmon spheres obtained from Mie scattering and free oscillation theories

This paper presents Mie scattering theory as compared to rigorous electromagnetic theory of free oscillations in magnetic and electric plasmon spheres. It is shown that the maxima of Mie scattering and absorption spectra well correspond to resonance frequencies of plasmon modes occurring in dielectric and magnetic spheres, similarly as it takes place for ordinary dielectric resonator modes. Mie theory is well applicable to determine resonance frequencies and scattering parameters of spherical plasmons. However, this theory cannot be applied to determine intrinsic properties of modes induced in the object by the incident plane wave, like quality factors. On the contrary, rigorous electromagnetic theory of free oscillations allows one to determine the complex resonance frequency of each mode that can occur in a given object, and the corresponding quality factor accounting for various kind of losses, including medium and radiation losses. The advantage of the free oscillations theory, as shown in this paper, is in the determination of the quality factors of modes occurring in magnetic plasmon spheres made of a strongly dispersive magnetic medium.Graphical

Plasmonic mode coupling and thin film sensing in metal\u2013insulator\u2013metal structures

Optical sensors based on surface plasmon resonance (SPR) in the attenuated total reflection (ATR) configuration in layered media have attracted considerable attention over the past decades owing to their ability of label free sensing in biomolecular interaction analysis, and highly sensitive detection of changes in refractive index and thickness, i.e. the optical thickness, of thin film adsorbates (thin film sensing). Furthermore, SPR is highly sensitive to the refractive index of the medium adjacent to the bare metal, and it allows for bulk sensing as well. When deposited at the metal/air interface, an adsorbed layer disturbs the highly localized, i.e. bound, wave at this interface and changes the plasmon resonance to allow for sensing in angular or wavelength interrogation and intensity measurement modes. A high degree of sensitivity is required for precise and efficient sensing, especially for biomolecular interaction analysis for early stage diagnostics; and besides conventional SPR (CSPR), several other configurations have been developed in recent years targeting sensitivity, including long-range SPR (LRSPR) and waveguide-coupled SPR (WGSPR) observed in MIM structures, referred here to by MIM modes, resulting from the coupling of SPRs at I/M interfaces, and Fano-type resonances occurring from broad and sharp modes coupling in layered structures. In our previous research, we demonstrated that MIM is better than CSPR for bulk sensing, and in this paper, we show that CSPR is better than MIM for thin film sensing for thicknesses of the sensing layer (SL) larger than 10 nm. We discuss and compare the sensitivity of CSPR and MIM for thin film sensing by using both experiments and theoretical calculations based on rigorous electromagnetic (EM) theory. We discuss in detail MIM modes coupling and anti-crossing, and we show that when a thin film adsorbate, i.e. a SL), is deposited on top of the outermost-layer of an optimized MIM structure, it modifies the characteristics of the coupled modes of the structure, and it reduces the electric field, both inside the SL and at the SL/air interface, and as a result, it decreases the sensitivity of the MIM versus the CSPR sensor. Our work is of critical importance to plasmonic mode coupling using MIM configurations, as well as to optical bio- and chemical-sensing.

Flat metal-dielectric grating with 100% retro-diffraction efficiency: rigorous theory

We have recently designed a new type of a flat metal-dielectric grating which is supposed to replace blazed diffraction gratings, providing very high −1st reflected diffraction order efficiency within a broad wavelength band, high durability, and relative ease of fabrication. In this communication we present a rigorous electromagnetic theory of the grating in the approximation of infinitely thin perfect metal and show that the properly designed grating can reach 100% diffraction efficiency in the Littrow configuration for either transversal electric (TE or s) or transversal magnetic (TM or p) polarizations. Properties of the grating are analysed and discussed in detail.

A 2D Waveguide Method for Lithography Simulation of Thick SU-8 Photoresist.

Due to the increasing complexity of microelectromechanical system (MEMS) devices, the accuracy and precision of two-dimensional microstructures of SU-8 negative thick photoresist have drawn more attention with the rapid development of UV lithography technology. This paper presents a high-precision lithography simulation model for thick SU-8 photoresist based on waveguide method to calculate light intensity in the photoresist and predict the profiles of developed SU-8 structures in two dimension. This method is based on rigorous electromagnetic field theory. The parameters that have significant influence on profile quality were studied. Using this model, the light intensity distribution was calculated, and the final resist morphology corresponding to the simulation results was examined. A series of simulations and experiments were conducted to verify the validity of the model. The simulation results were found to be in good agreement with the experimental results, and the simulation system demonstrated high accuracy and efficiency, with complex cases being efficiently handled.

Surface plasmon dispersion engineering for optimizing scattering, emission, and radiation properties on a graphene spherical device.

We present a dispersion engineering method based on the rigorous electromagnetic theory to study the scattering properties of a double graphene layer spherical structure. The localized surface plasmons (LSPs) supported by the structure provide resonance channels that lead to an enhancement of the electromagnetic cross section. The method is used to find conditions under which two different multipolar LSP resonances occur at the same frequency value. The superscattering feature under these conditions is revealed by an extraordinary enhancement of the scattering cross section when the structure is illuminated by a plane wave field. Moreover, by studying the behavior of a single emitter localized near the graphene sphere, we show that the spontaneous emission and radiation efficiencies are also largely enhanced when the two different LSP resonances overlap.

Understanding diffraction grating behavior, part II: parametric diffraction efficiency of sinusoidal reflection (holographic) gratings

With the widespread availability of electromagnetic (vector) analysis codes for describing the diffraction of electromagnetic waves by periodic grating structures, the insight and understanding of nonparaxial parametric diffraction grating behavior afforded by approximate methods (i.e., scalar diffraction theory) is being ignored in the education of most optical engineers today. We show that the linear systems formulation of nonparaxial scalar diffraction theory enables the development of a scalar parametric diffraction grating model [for transverse electric (TE) polarization] for sinusoidal reflection gratings with arbitrary groove depths and arbitrary nonparaxial incident and diffracted angles. This scalar parametric analysis is remarkably accurate as it includes the ability to redistribute the energy from evanescent orders into the propagating ones, thus allowing the calculation of nonparaxial diffraction efficiencies to be predicted with an accuracy usually thought to require rigorous electromagnetic theory. These scalar parametric predictions of diffraction efficiency are compared to paraxial scalar and rigorous electromagnetic (vector) predictions for a variety of nonparaxial diffraction grating configurations, thus providing quantitative limits of applicability of nonparaxial scalar diffraction theory to sinusoidal reflection gratings as a function of the grating period-to-wavelength ratio (λ / <italic>d</italic>).

Оптические свойства отечественного сетчатого стеклоуглерода и его основы

The paper presents the results of experimental studies and mathematical modeling of the optical properties of glassy carbon and domestic reticulated foam materials based on it. Since the optical properties of the surface are studied on dense samples, dense samples were previously created, identical in physical properties to glassy carbon - the basis of highly porous cellular carbon materials. From the experimentally measured the spectral hemispherical reflectivity of the surface of the samples under its normal illumination and by the Kramers-Kronig relations the spectra of optical constants of glassy carbon - the refractive indices and absorption, as well as a number of their derivative characteristics were determined. For them, simple approximating relations are given in the paper. The obtained spectral data was incorporated into the previously developed optical statistical simulation model of ultra-porous reticulated foam materials, which is based on a rigorous electromagnetic theory and allows you to take into account both the features of their microstructure and physical processes that occur in such systems at different spa-tial and temporal scales. The results of the calculation of local spectra, the scattering phase function, and radiation thermal conductivity are presented for the reticulated glassy carbon foam, which has wide prospects for use as a structural and heat-shielding material. Some additional features of the mathematical model are demonstrated also.

Influence of Surface Morphology on Absorptivity of Light-Absorbing Materials

Absorptivity of three kinds of surface morphology, i.e., V-type groove surface, sinusoidal surface, and random distribution, is investigated using a rigorous electromagnetic theory and a finite element method. Influences of surface contour parameters (span distance, intersection angle, and height) and light wave parameters (incident angle and wavelength) on absorptivity are numerically simulated and analyzed for the three kinds of surfaces, respectively. Absorbing spectra about three silicon wafers with different surface roughness are recorded, and the results are coincident with simulated results.

Understanding diffraction grating behavior: including conical diffraction and Rayleigh anomalies from transmission gratings

With the wide-spread availability of rigorous electromagnetic (vector) analysis codes for describing the diffraction of electromagnetic waves by specific periodic grating structures, the insight and understanding of nonparaxial parametric diffraction grating behavior afforded by approximate methods (i.e., scalar diffraction theory) is being ignored in the education of most optical engineers today. Elementary diffraction grating behavior is reviewed, the importance of maintaining consistency in the sign convention for the planar diffraction grating equation is emphasized, and the advantages of discussing “conical” diffraction grating behavior in terms of the direction cosines of the incident and diffracted angles are demonstrated. Paraxial grating behavior for coarse gratings (<italic>d</italic> ≫ λ) is then derived and displayed graphically for five elementary grating types: sinusoidal amplitude gratings, square-wave amplitude gratings, sinusoidal phase gratings, square-wave phase gratings, and classical blazed gratings. Paraxial diffraction efficiencies are calculated, tabulated, and compared for these five elementary grating types. Since much of the grating community erroneously believes that scalar diffraction theory is only valid in the paraxial regime, the recently developed linear systems formulation of nonparaxial scalar diffraction theory is briefly reviewed, then used to predict the nonparaxial behavior (for transverse electric polarization) of both the sinusoidal and the square-wave amplitude gratings when the +1 diffracted order is maintained in the Littrow condition. This nonparaxial behavior includes the well-known Rayleigh (Wood’s) anomaly effects that are usually thought to only be predicted by rigorous (vector) electromagnetic theory.

Electromagnetic Fields Due to the Wake of a Moving Slender Body in a Finite-Depth Ocean with Density Stratification

Weak electric currents are induced in moving seawater by cutting the geomagnetic fields. These electric currents can produce measurable electromagnetic fields that may be used for some purposes such as monitoring of ocean internal waves. This article is aimed at presenting the procedure to calculate the electromagnetic fields owing to the wake raised by an undersea moving slender body. A pair of Havelock point sources are introduced to model the moving body, which generate the similar wake at places far from the body. The ocean is taken to be of finite-depth with density stratification due to thermocline. Three distinct forms of water-flow wake can be identified, the free-surface Kelvin wake, the internal interfacial wake, and the localized volume wake. The electric currents evoked by the motional wake may produce observable electromagnetic fields, which may be solved using rigorous electromagnetic field theory. At the sea level, the magnitudes of the induced electric field and magnetic field are on the order of a few microvolts per meter and one nano-Tesla, respectively, which are appreciable in terms of nowadays marine electric and magnetic sensors.

Cloaking design for arbitrarily shape objects based on characteristic mode method

In the framework of characteristic mode method (CMM) we develop a theoretical approach for achieving invisibility and illusion of three-dimensional arbitrary-shaped objects. Starting from rigorous electromagnetic theory, electromagnetic wave interaction with arbitrarily shape scatterers is modelled by discrete-dipole approximation (DDA) method. By exploiting the characteristic mode analysis, it is theoretically shown that scattered field is tightly related to generalized eigenvalues of the matrix in the DDA method. A theoretical formulation for designing thin homogeneous cover is derived to achieve invisibility and illusion image of the irregularly shaped objects. It is demonstrated by numerical simulations that the proposed cloaking design provides a significant scattering reduction and optimal illusion performance.

Breaking the efficiency limit for high-frequency blazed multilayer soft x-ray gratings: Conical vs classical diffraction

High-frequency multilayer-coated blazed diffraction gratings (HFMBGs) are most promising elements for ultrahigh resolution soft x-ray spectroscopy. As it has been demonstrated recently [Voronov et al., Opt. Express 23, 4771 (2015)], the efficiency limit for in-plane diffraction can exceed 2–3 times, in higher orders too, when the period of a HFMBG is shorter than an attenuation length for soft x-rays and a bilayer asymmetry is designed. In this letter, using numerical experiments based on the rigorous electromagnetic theory, a possibility of off-plane diffraction and symmetrical multilayer coatings to enhance the efficiency of soft-x-ray high-order HFMBGs very closely to the absolute limit, i.e., 0.92–0.98 of the reflectance of the respective W/B4C multilayer, has been demonstrated.

Predicting radiative transport properties of plasma sprayed porous ceramics

The typical yttria-stabilized zirconia material for making the thermal barrier coatings (TBCs) is intrinsically semitransparent to thermal radiation, and the unique disordered microstructures in TBCs make them surprisingly highly scattering. To quantitatively understand the influence of disordered microstructures, this paper presents a quantitative prediction on the radiative properties, especially the transport scattering coefficient of plasma sprayed TBC based on microstructure analysis and rigorous electromagnetic theory. The impact of the porosity, shape, size, and orientation of different types of voids on transport scattering coefficient is comprehensively investigated under the discrete dipole approximation. An inverse model integrating these factors together is then proposed to quantitatively connect transport scattering coefficient with microstructural information, which is also validated by available experimental data. Afterwards, an optimization procedure is carried out based on this model to obtain the optimal size and orientation distribution of the microscale voids to achieve the maximal radiation insulation performance at different operating temperatures, providing guidelines for practical coating design and fabrication. This work suggests that the current model is effective and also efficient for connecting scattering properties to microstructures and can be implemented as a quantitative tool for further studies like non-destructive infrared imaging as well as micro/nanoscale thermal design of TBCs.

Partial coherence and polarization of a two-mode surface-plasmon polariton field at a metallic nanoslab.

Rigorous electromagnetic theory is utilized to characterize the partial spatial coherence and partial polarization of a two-mode field consisting of the long-range and the short-range surface-plasmon polariton at a metallic nanofilm. By employing appropriate formulations for the spectral degrees of coherence and polarization, we examine the fundamental limits for these quantities associated with such a superposition field and explore how the degrees are influenced when the media, frequency, and slab thickness are varied. It is in particular shown that coherence lengths extending from subwavelength scales up to thousands of wavelengths are possible and their physical origins are elucidated. In addition, we demonstrate that for ultra-thin films the generally highly polarized two-mode field can be partially polarized in close vicinity of the polariton excitation region. The results could benefit cross-disciplinary electro-optical applications in which near-field interactions between plasmons and nanoparticles are exploited.

Geometrical optics in the near field: local plane-interface approach with evanescent waves.

We show that geometrical models may provide useful information on light propagation in wavelength-scale structures even if evanescent fields are present. We apply a so-called local plane-wave and local plane-interface methods to study a geometry that resembles a scanning near-field microscope. We show that fair agreement between the geometrical approach and rigorous electromagnetic theory can be achieved in the case where evanescent waves are required to predict any transmission through the structure.

Long-range higher-order surface-plasmon polaritons

Besides the two fundamental symmetric and antisymmetric modes, a thin metal slab surrounded by a dielectric medium supports an infinite number of other modes whose propagation distances, however, are extremely short. We show that such a higher-order mode, normally not regarded to be useful, can turn into a long-range surface-plasmon polariton in circumstances where the fundamental long-range mode does not exist and the propagation length of the single-interface surface-plasmon polariton is negligible. This transition, which is an electromagnetic near-field phenomenon not previously observed, occurs with a broad range of bandwidths and materials, especially in the context of high-index semiconductors. The long-range behavior of the higher-order surface-plasmon polaritons does not originate from the coupling between the polaritons supported by the individual boundaries, and in some situations it comes with increased field confinement, which is the opposite of what occurs for the fundamental long-range surface mode. Our results, which follow from rigorous electromagnetic theory, provide deeper insight into the foundations of thin-film plasmonics and suggest avenues for enhanced properties of nanophotonic devices involving modern polaritonic media.