Rigorous Electromagnetic Analysis Research Articles

68.2: Using Rigorous Electromagnetic Analysis in Modeling OLEDs with Gratings

AbstractWe present a stable and efficient electromagnetic analysis for the influence of grating on light extraction in organic light emitting diodes. By this approach, the trend of the output power and mode distribution variance with the change of structure parameters could be predicted before the experiments.

Vector-vortex Bessel–Gauss beams and their tightly focusing properties

We demonstrate that the amplitude of vector-vortex beams has a Bessel-Gauss (BG) distribution through a rigorous vector electromagnetic analysis. We also investigate the intensity profiles in the focal plane of vector-vortex beams that are focused by a high numerical-aperture lens obeying the Helmholtz condition. Although the intensity of a vector-vortex BG beam with a topological charge n=1 is nonzero along the axis in the focal plane, the beams with n≠1 show discrete multiple spots which can be useful for optical trapping.

Optical Focusing by Planar Lenses Based on Nano-scale Metallic Slits in Visible Regime

A kind of planar metallic lenses is proposed to realize optical focusing in the visible wavelength through a metallic film with nano-scale slit arrays, which have the same depth but tuning widths. Due to the subwavelength and aperiodic nature of planar metallic lenses, we present the rigorous electromagnetic analysis by using two dimensional finite difference time domain method. The electromagnetic wave transports through the tuning slits in the form of surface plasmon polaritons, and gets the required phase retardations to focusing at the focal plane. We analyze the focusing characteristics of planar dielectric lens and metallic lens with tuning widths that are obtained by generalizing the relevant phase delay, for different incidence polarization waves (TM polarized case and TE polarized case). The computational calculation results show that, extraordinary optical transmission of surface plasmon polaritions through non uniform nano-scale metallic slits is observed, and it has contributions to the optical focusing, but cannot increase the focal energy compared with dielectric planar lens with the same profile, and the metallic lenses are more sensitive to the polarization of incidence wave than that of dielectric lenses. The influence of metallic lenses’ thickness on the focal characteristics has been analyzed also.

Dosimetry of an in vitro exposure system for fluorescence measurements during 2.45 GHz microwave exposure

An in vitro system for 2.45 GHz microwave (MW) exposure with real-time fluorescence measurements is proposed. This system is specifically designed for the measurement of those biophysical parameters of living cells or membrane models which can be quantified by spectrofluorometric methods (e.g. membrane generalized polarization (GP), membrane fluidity, membrane potential, etc.). The novelty of the system consists in the possibility to perform fluorescence measurements on the biological samples simultaneously with their exposure to MW. The MW applicator is an open ended coaxial antenna which is dipped into a cuvette. The distribution of electromagnetic field and specific absorption rate (SAR) in the cuvette are provided from a rigorous electromagnetic numerical analysis performed with a finite difference-time domain (FDTD) based tool. With this system, fluorescence measurements were used to calculate the membrane GP values of giant unilamellar vesicle suspensions that were acquired during exposure to a 1.2 W incident power. For this power, the SAR distribution and mean SAR value for the whole volume were calculated based on temperature measurements made at different positions inside the cuvette.

The Impact of Spectral and Spatial Exciton Distributions on Optical Emission From Thin-Film Weak-Microcavity Organic Light-Emitting Diodes

We present an analytical model for the optical emission produced by sources located in a thin-film weak-microcavity formation and study the effects of the ensemble spectral and spatial distribution on the device emission properties. However derived for a general stratified media configuration, the formulation results are highly applicable for the study of nanometric organic light-emitting devices. Rigorously developed into closed-form analytical expressions using the device's thin-film weak-microcavity characteristics, they enable clear observation of the underlying physical processes that determine the emission properties of the device, as well as the impact of the exciton ensemble spectral and spatial distributions on these properties. For the sake of simplicity and clarity, we focus on a 2-D canonical configuration excited by impulsive (line) sources. Our results show that the spectral distribution of the ensemble diminishes interference effects originated in the weak microcavity formed between the substrate/air and cathode/active layer interfaces, while the spatial distribution can only impact the slow-varying component of the emission pattern, which is the consequence of the source-image interference near the highly reflecting cathode. For a typical device, the quasi-Lambertian emission pattern reported experimentally is reproduced. It should be pointed out that the incorporation of both rigorous electromagnetic analysis and the source spectral and spatial broadening effects is addressed in our report, to the best of our knowledge, for the first time. This results in a precise model capable of repeating and interpreting experimental and simulated data.

Analysis of a diffractive microlens using the finite-difference time-domain method

The finite-difference time-domain (FDTD) method is used as rigorous electromagnetic analysis model to calculate the field for a diffractive microlens (DML). The FDTD is used for the entire solution rather than using a near- to far-field propagation method to obtain the far-field energy distribution; thus, all the results are vector based. We derived a formula to calculate the magnitude of electric field, which is time dependent and can be used to graphically show the light wave propagation and focusing process through a DML. Both the comparison and the integral methods are presented to obtain wave amplitude in full solution space, and the distribution of light energy behind a DML is illustrated based on the wave amplitude. The formula of diffractive efficiency of the DML is derived from a time-averaged Ponyting vector, which can indicate the propagation direction of light energy. Application of these formulations in the analysis of a DML example demonstrates the high accuracy and efficiency of our method.

Rigorous electromagnetic analysis of metallic cylindrical focusing micromirrors with high diffraction efficiency, achromatic aberration and long focal depth

In this paper, we propose a kind of metallic cylindrical focusing micromirrors (MCFMs) with parabolic profiles, and the focal performance is investigated based on rigorous electromagnetic theory and the boundary element method (BEM). Numerical results by the BEM show that the proposed MCFM possesses a high diffraction efficiency and axially achromatic aberration. In addition, through designing a modulating phase function, the MCFM holds long focal depth and high transverse resolution simultaneously. It is believed that the MCFM should have wide application prospects in micro-optical systems, such as micro solar concentrators.

Vector fuzzy control iterative algorithm for the design of sub-wavelength diffractive optical elements for beam shaping

The vector fuzzy control iterative algorithm (VFCIA) is proposed for the design of phase-only sub-wavelength diffractive optical elements (SWDOEs) for beam shaping. The vector diffraction model put forward by Mansuripur is applied to relate the field distributions between the SWDOE plane and the output plane. Fuzzy control theory is used to decide the constraint method for each iterative process of the algorithm. We have designed a SWDOE that transforms a circular flat-top beam to a square irradiance pattern. Computer design results show that the SWDOE designed by the VFCIA can produce better results than the vector iterative algorithm (VIA). And the finite difference time-domain method (FDTD), a rigorous electromagnetic analysis technique, is used to analyze the designed SWDOE for further confirming the validity of the proposed method.

Rigorous electromagnetic analysis of two dimensional micro-axicon by boundary integral equations

The focal performance of the micro-axicon and the Fresnel axicon (fraxicon) are investigated, for the first time, by the rigorous electromagnetic theory and boundary element method. The micro-axicon with different angle of apex and the fraxicon with various period and angle of apex are investigated. The dark segments of the fraxicon are explored numerically. Rigorous results of focal performance of the micro-axicon and the fraxicon are different from the results given by the approximation of geometrical optics and the scalar diffraction theory. The scattering effects are dominant in the fraxicon with small size of feature. It is expected that our study can provides very useful information in analyzing the axicon in optical trapping systems.

Electromagnetic Radiation from Organic Light-emitting Diodes

An analytical prototype model for the electromagnetic radiation emitted from a nanometric organic light-emitting diode device is presented and thoroughly investigated herein. The results are obtained via asymptotic evaluation of the resultant radiation integral in con- junction with coherence considerations, resulting in closed-form analytical expressions. For the sake of simplicity and clarity, we focus on a two-dimensional canonical conflguration excited by impulsive (line) sources. The resultant expressions can be most efiectively utilized by engineers for improved design, as they enable the calculation of the device's physical parameters, such as electrical to optical conversion e-ciency and emission angular distribution, as a function of de- vice structure. It should be pointed out that the incorporation of both rigorous electromagnetic analysis and coherence efiects is addressed in our report, to the best of our knowledge, for the flrst time. This results in a precise model capable of repeating and interpreting experimental and simulated data.

Rigorous Electromagnetic Analysis of Domestic Induction Heating Appliances

In this paper the developed analytical electromagnetic model of induction heating system is presented. The model was built up assuming equivalent electric and magnetic currents ∞owing in each planar element of the typical structure used for an induction heating system: the load disk represents the pan steel bottom, the copper inductor, and ferrite ∞ux conveyor. A system of integral equations system was then obtained enforcing the boundary conditions on each element of the structure for the electric and magnetic flelds, produced by the equivalent currents. The numerical solution of the system is a matrix equation with a known voltage vector in the left-hand side, and product of impedance coe-cients matrix and unknown electric and magnetic currents vector in the right-hand side. Since the feeding voltage is known, and impedance coe-cients are calculated using of geometry and material parameters, currents vector can be also calculated. Thus, the whole model is solved and it gives a detailed picture of currents distribution in the system, which in its turn allows to analyze heating process in the load. Each step of developing of the model was verifled by appropriate experimental measurements. Achieved results give a possibility to analyze and develop improvements to increase e-ciency, safety and to reduce the cost.

PROPERTIES OF APPROXIMATE BESSEL BEAMS AT MILLIMETER WAVELENGTHS GENERATED BY FRACTAL CONICAL LENS

An axicon, which images a point source into a line along the optic axis, is used widely to generate an approximation to a Bessel beam. More recently many novel axicons, such as Fresnel axicons, Fractal axicons and fractal conical lenses (FCLs), have been proposed. Understanding the properties of Bessel beams generated by these axicons is very helpful to research their applications. However, in optical region, all of them are calculated approximately by the scalar theory. To accurately analyze FCLs when illuminated by a plane wave at millimeter wavelengths, the rigorous electromagnetic analysis method, which combines a two-dimension finite-difference time-domain (2-D FDTD) method and Stratton-Chu formulas, is adopted in our paper. By using this method, the properties of approximate Bessel beams generated by FCLs are analyzed and the conclusions are given.

Investigation on the Frequency Range of Validity of Electroquasistatic RC Models for Semiconductor Substrate Coupling Modeling

Electroquasistatic analysis is currently the dominant approach for the modeling of semiconductor substrate noise coupling. The electroquasistatic (EQS) approximation is considered acceptable for frequencies such that the distances over which substrate interactions are considered are a small fraction of the wavelength. Yet, with clock bandwidths in state-of-the-art and future designs extending to multiple tens of gigahertz, it is necessary to accurately investigate and quantify the range of validity of the EQS approximation. This investigation is carried out in this paper by means of a rigorous electrodynamic model for the induced surface voltage due to an elementary dipole source in various types of commonly used semiconductor substrates for digital and radio-frequency integrated circuits. In addition to enabling a quantitative assessment of the frequency range of the validity of the electroquasistatic approximation and, hence, the RC models used commonly in computer-aided design tools for substrate noise coupling, the proposed electrodynamic model is used to investigate the prominence of inductive-like characteristics in noise propagation through the substrate. Through these investigations, it is demonstrated that the electrodynamic model used in this paper provides for a unified rigorous electromagnetic analysis of substrate noise coupling over the entire frequency bandwidth of interests to practical applications, from DC to multiple tens of gigahertz.

Rigorous electromagnetic analysis of dual-closed-surface microlens arrays

In this paper, we investigated the focal performance of the dual-closed-surface microlens arrays (DCSMAs) based on rigorous electromagnetic theory and boundary element method (BEM) in the case of TE polarization. The DCSMAs are designed with different substrate thickness and different distance between microlenses. DCSMAs designed according to different wavelengths are surveyed. The DCSMAs with different incident angles are also studied. Several focusing performance measures, such as the focal spot size, the focal position on the preset focal plane, the diffraction efficiency and the normalized transmitted power, are presented. Numerical results indicate the DCSMAs with different parameters can implement focusing beams and the focal performance of DCSMAs is easily influenced by the substrate thickness and the incident wavelength. Furthermore, the optimal thickness for the maximal diffraction efficiency of the DCSMAs is given. It is expected that the DCSMAs may be used as a parallel processing device in micro-optics systems.

Design method for small-f-number microlenses based on a finite thickness model in combination with the Yang-Gu phase-retrieval algorithm

We present a fast and general iterative design method for both diffractive and nondiffractive two-dimensional optical elements. The method is based on a finite-thickness model in combination with the Yang-Gu phase-retrieval algorithm. A rigorous electromagnetic analysis (boundary element method) is used to appraise the designed results. We calculate the transverse-intensity distributions, diffraction efficiency, and spot size of the designed microlenses at the focusing plane for microlenses designed using the presented method and the conventional zero-thickness model. The main findings show the superiority of the presented method over the conventional method, especially for nondiffractive optical elements.

Rigorous electromagnetic analysis of the common focusing characteristics of a cylindrical microlens with long focal depth and under multiwavelength illumination

The common focusing characteristics of a cylindrical microlens with a long focal depth and under a given multiple-wavelength illumination are analyzed based on the boundary element method (BEM). The surface-relief profile of a finite-substrate-thickness microlens with a long focal depth is presented. Its focusing performances, such as the common extended focal depth (CEFD), the spot size, and the diffraction efficiency, are numerically studied in the case of TE polarization. The results show that the CEFD of the microlens increases initially, reaches a peak value, and then decreases with increasing preset focal depth. Two modified profiles of a finite-substrate-thickness cylindrical microlens are proposed for enlarging the CEFD. The rigorous numerical results indicate that the modified surface-relief structures of a cylindrical microlens can successfully modulate the optical field distribution to achieve longer CEFD, higher transverse resolution, and higher diffraction efficiency simultaneously, compared with the prototypical microlens. These investigations may provide useful information for the design and application of micro-optical elements in various multiwavelength optical systems.

Electromagnetic analysis of coupling and guiding phenomena in elliptical cross-section parallel waveguides with rotated symmetry planes

Rigorous electromagnetic analysis methods, based on the Green's function method along with the method of moments, are utilized to analyze coupling, guiding, and polarization phenomena in elliptic cross-section parallel waveguides. The analysis is carried out for the general case of closely spaced elliptic fibers of arbitrary orientation of the ellipses' axes. Numerical results are presented for the cases of 0 degrees and 45 degrees angles between axes, as well as for the single elliptical fiber and closely spaced circular dielectric waveguides. The possibility of using this type of coupling structure in quantum signal processing applications is examined.

Rigorous analysis of the coupling between two nonparallel optical fibers

The rigorous electromagnetic analysis of the coupling between two nonparallel optical-fiber waveguides is developed for the first time. Green's theorem, involving the dyadic Green's function of the fiber guiding the incident mode, is used to formulate the electric-field integral equation inside the second fiber. By applying the entire-domain Galerkin technique and by utilizing the generalized addition theorem for cylindrical waves for nonparallel axis translation, which is derived by the authors, this equation is analytically transformed into a system of coupled integral equations for the spectral weights of the field on the basis of TE and TM cylindrical vector wave functions. The Neumann-series iterative procedure is adopted to solve this system and obtain analytical expressions for the field scattering coefficients, which are sufficiently accurate for weakly coupled fibers

Design and Evaluation of Color Separation Grating Using Rigorous Coupled Wave Analysis

In this study, we focused on a small and light grating that is capable of converting efficiently white light into only the three primary colors red, green, and blue with a high saturation level. To evaluate its diffraction characteristics properly, we performed a rigorous electromagnetic analysis based on the rigorous coupled wave analysis (RCWA). We designed the grating such that diffraction efficiency higher than 70% and a color gamut higher than 65% were obtained. On the basis of our numerical results, we then fabricated a grating by laser drawing and determined its color separation efficiency. The grating was etched into quartz and had a six-level surface relief, a maximum groove depth of 5.75 µm, and a period of 50 µm. Furthermore, we calculated the tolerances of fabrication errors in the depth and width directions that satisfy optimal design conditions for establishing guiding principles for the accurate fabrication of multilevel color separation gratings with deep grooves.

Fabrication of blazed gratings by area-coded effective medium structures

Area-coded effective medium structures (ACES) are a recently presented novel type of diffractive structure. Because of their higher stability compared to 2D binary blazed gratings, they have the potential of a broader use in micro-optics applications. The first fabrication with electron-beam lithography validate the theoretical model of blazed ACES. The measured diffraction efficiencies are in very good agreement with the values obtained from rigorous electromagnetic analysis.