Rigorous Electromagnetic Analysis Research Articles

Polarization modulation by surface plasmons in Young's double-slit setup

A simple phenomenological model, justified by rigorous electromagnetic analysis, is used to examine far-field polarization modulation introduced by a metallic screen with two subwavelength slits in uniform, partially polarized illumination. The accuracy of this intuitive model is assessed numerically, by employing the Fourier modal method, as regards the wavelength, the screen metal, and the slit depth, width, and separation. The Stokes parameters and the degree of polarization are evaluated paraxially in the far zone of the slits. We demonstrate that a uniform, partially linearly polarized incident beam can be rendered unpolarized by the nanoslits. Our work provides insight into the pivotal role that surface plasmons have in polarization modulation in photonics.

Cascade domino lithography for extreme photon squeezing

Squeezing photons into deep sub-wavelength volumes and few-nanometer gaps has led to the investigation of interesting phenomena, including strong coupling, quantum plasmonics, nonlinearity enhancement, nonlocality, and molecular junctions. The common configuration of bowtie nanoantennas has been extensively studied owing to the great enhancement of the localized electromagnetic field. The enhancement rapidly increases as the tips become sharper and the gap becomes narrower. However, reliable fabrication of nanoantennas that are extremely sharp with sub-10 nm gaps is statistically prohibited due to the fundamental limitation of the proximity effect of electron beam lithography. Here, an intuitive “fall-to-rise” scheme is proposed and experimentally validated using a new concept of cascade domino lithography. In this report, we successfully establish a controllable lithography method of making extremely sharp bowtie nanoantennas with sub-1 nm radius of curvature reaching the size of a gold nanocluster as well as single-digit-nanometer gaps between such sharp tips. In addition, a proof-of-concept application of surface enhanced Raman spectroscopy is demonstrated along with rigorous full-wave electromagnetic simulations and numerical analysis. This control of falling nanostructures opens up an unexplored gateway towards conquering the limitations of experimentally exploring the realm of plasmonics down to the sub-nanometer regime.

A mode-matching solution for the study of cylindrical waveguide bifurcation via closed-form coupling integrals

In this paper, we present a mode-matching technique formulation for the rigorous electromagnetic analysis of a circular waveguide bifurcated into circular and coaxial domains. A generalized scattering matrix is obtained for relating the modal field amplitudes in each of the waveguides, and we were able to obtain closed-form solutions for all the associated coupling integrals. We present a series of validation results showing that the technique introduced in this work can model accurately and efficiently a class of cylindrical waveguide devices.

Engineering the Eigenspace Structure of Massive MIMO Links Through Frequency-Selective Surfaces

We propose an efficient finite-difference time-domain (FDTD) computational paradigm to estimate the channel matrix of generic massive multiple-input–multiple-output (MIMO) systems. Working with a practical scenario with 196 base station (BS) elements and 6 equispaced user-equipment devices, we compute the dominant eigenspace for the uplink channel. The full-wave results are compared to conventional ray-tracing methods, with emphasis laid upon observing and understanding the electromagnetic (EM) impact of interelement mutual coupling and spherical wavefront illumination on the wireless MIMO channel properties. In particular, we investigate EM manipulation of massive MIMO channel structures by utilizing, especially, engineered wire-grid frequency-selective surfaces placed in the vicinity of the BS massive MIMO array. Using the in-house FDTD code, we demonstrate the capability of such passive structures to redistribute the illumination Poynting vector magnitude over the BS array aperture, as well as modifying the dominant eigenspace at certain design frequencies. This letter demonstrates the advantage of the synergy between rigorous EM analysis and stochastic communication theories and techniques, with expected applications in emerging wireless technologies (5G and beyond).

Passive synthesis rules of coupled-cavity quantum cascade lasers

A new approach to passive electromagnetic modelling of coupled–cavity quantum cascade lasers is presented in this paper. One of challenges in the rigorous analysis of such eigenvalue problem is its large size as compared to wavelength and a high quality factor, which prompts for substantial computational efforts. For those reasons, it is proposed in this paper to consider such a coupled-cavity Fabry-Perot resonant structure with partially transparent mirrors as a two-port network, which can be considered as a deterministic problem. Thanks to such a novel approach, passive analysis of an electrically long laser can be split into a cascade of relatively short sections having low quality factor, thus, substantially speeding up rigorous electromagnetic analysis of the whole quantum cascade laser. The proposed method allows to determine unequivocally resonant frequencies of the structure and the corresponding spectrum of a threshold gain. Eventually, the proposed method is used to elaborate basic synthesis rules of coupled–cavity quantum cascade lasers.

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.

Highly-efficient THz generation using nonlinear plasmonic metasurfaces

Nonlinear metasurfaces loaded with multi-quantum-well (MQW) heterostructures constitute a rapidly progressing class of optical devices that combine high nonlinear generation efficiency with an ultrathin profile. Here, we introduce and discuss terahertz (THz) difference-frequency generation (DFG) using MQW-based plasmonic metasurfaces and present a comprehensive theory for their rigorous electromagnetic analysis. We explicitly take into account complex phenomena associated with the local intensity saturation of intersubband transitions and identify fundamental upper-bounds for DFG conversion efficiency. Using this framework, we design and analyze a nonlinear DFG metasurface providing giant DFG nonlinear response and conversion efficiency up to 0.01% at 5.8 THz. Such metasurface can be used to generate 0.15 mW of THz power using pump intensities in the kW cm−2 range. We envision that such DFG metasurfaces can become a platform for uncooled, compact, and highly-efficient continuous-wave THz sources.

Electromagnetic diffraction theory of refractive axicon lenses.

We study the field that is produced by a paraxial refractive axicon lens. The results from geometrical optics, scalar wave optics, and electromagnetic diffraction theory are compared. In particular, the axial intensity, the on-axis effective wavelength, the transverse intensity, and the far-zone field are examined. A rigorous electromagnetic diffraction analysis shows that the state of polarization of the incident beam strongly affects the transverse intensity distribution, but not the intensity distribution in the far zone.

Diffraction efficiency sensitivity to oblique incident angle for multilayer diffractive optical elements.

The relationship between diffraction efficiency of multilayer diffractive optical elements (MLDOEs) and arbitrary incident angle was numerically analyzed with the effective area method. The method is based on the shield effect between two elements of MLDOEs; a generalized diffraction efficiency formulation was obtained in a wide range of tilt angles, which overcame the limitations of scalar diffraction theory when the period width of MLDOEs is taken into account. A detailed comparison of the proposed effective area method with the scalar diffraction theory is numerically presented for MLDOEs. The validity of the proposed method is verified by comparison with the rigorous electromagnetic analysis method, especially the finite-difference time-domain method. The analysis results show that the shield effect augments with the increase of the incident angles; the effect of incident angles on MLDOEs with finite period widths is more noticeable than that with large period widths.

Optimal design of multilayer diffractive optical elements with effective area method.

The effective area method is described to design high-efficiency multiplayer diffractive optical elements (MLDOEs) with finite feature sizes for wide wave band. This method is presented with consideration of the shield effect between two elements of MLDOEs, and the optimal surface relief heights of MLDOEs are calculated with the effective area method. Then the comparisons of diffraction efficiency and polychromatic integral diffraction efficiency for MLDOEs with different period widths are described and simulated with the effective area method and scalar diffraction theory (SDT). Finally, the design results of MLDOEs obtained by SDT and the effective area method are compared by a rigorous electromagnetic analysis method, specifically, the finite-difference time-domain method. These results show that the limits of SDT for MLDOEs, ascertain and quantify the greatest sources of the diffraction efficiency loss due to the shield effect. The design results of the effective area method can obtain higher polychromatic integral diffraction efficiency than that of the SDT when the period width of MLDOEs is taken into account.

Computationally-efficient FDTD modeling of supercontinuum generation in photonic crystal fibers

It is shown in this paper that a finite-difference time-domain method can be successfully applied to rigorous electromagnetic analysis of supercontinuum generation in photonic crystal fibers. Large computational requirements of the method are alleviated by the use of a hybrid procedure where, at first, vector two-dimensional simulation is applied in order to determine mode properties of the fiber. Subsequently, one-dimensional simulation of a pulse propagating in a transmission line filled with effective material is performed. The parameters of the line take into account nonlinear characteristics of the filling material as well as the previously computed mode dispersion. It is depicted that the proposed novel hybrid approach opens the way for rigorous, yet, computationally-efficient modeling of third order nonlinear processes in optically long fibers. The example investigated in this paper shows very promising results as compared with experiments and approximate numerical simulations of a nonlinear Schrodinger equation performed with the aid of the split-step Fourier method.

Hybrid FDTD analysis of two- and four-level atomic systems

A hybrid algorithm, which couples rigorous time-domain electromagnetic analysis with rate equations representing a multi-level atomic system, is presented in this paper. It is explicitly shown that the rate equations can be decoupled from Maxwell curl equations, provided that the evolution of both systems is ongoing on different time scales. Consequently, the proposed algorithm allows substantially speeding up electromagnetic analysis of absorbing and lasing materials with no deteriorating impact on accuracy. Several computational examples, pointing out major properties of the proposed hybrid FDTD algorithms, are presented in this paper.

Optical phase front control in a metallic grating with equally spaced alternately tapered slits

A technique capable of focusing and bending electromagnetic (EM) waves through plasmonic gratings with equally spaced alternately tapered slits has been introduced. Phase resonances are observed in the optical response of transmission gratings, and the EM wave passes through the tuning slits in the form of surface plasmon polaritons (SPPs) and obtains the required phase retardation to focus at the focal plane. The bending effect is achieved by constructing an asymmetric phase front which results from the tapered slits and gradient refractive index (GRIN) distribution of the dielectric material. Rigorous electromagnetic analysis by using the two-dimensional (2D) finite difference time domain (FDTD) method is employed to verify our proposed designs. When the EM waves are incident at an angle on the optical axis, the beam splitting effect can also be achieved. These index-modulated slits are demonstrated to have unique advantages in beam manipulation compared with the width-modulated ones. In combination with previous studies, it is expected that our results could lead to the realization of optimum designs for plasmonic nanolenses.

Insight of limitations of effective media theory for metal–dielectric multilayer metamaterials

Effective media theory (EMT) is usually used in the simulations and descriptions of one type of metamaterials which are composed of metal–dielectric multilayer films because of its simplicity and intuitiveness. It is consistent with the rigorous electromagnetic field analysis when the approximation conditions are strictly satisfied. However, there are several noticeable, and sometimes significant failures for the predicted properties that are caused by the approximation dealing with the finite layer of metal/dielectric multilayer structures. These inaccuracies and errors including surface plasmon polaritons (SPPs) spreading angles, reflection properties and interference patterns for SPPs lithography, originate from the differences of isofrequency contours between ideal hyperbolic multilayer structures and the actually fabricated multilayer structures with finite layer of films. Simulation results of EMT with metal/dielectric multilayer structures are analyzed and compared with the rigorous field analysis approach. Being aware of these issues can help to reduce the errors and improve the designs of the plasmonic devices for many applications.

Plasmonic planar lens based on stack of metal–insulator–metal waveguides with height tuning

We introduce a technique capable of focusing electromagnetic (EM) waves through plasmonic nanoslits symmetrically arranged along the indented semi-circular surface in silver background. The EM transports through the tuning slits in the form of surface plasmon polaritons (SPPs), and gets the required phase retardations to focus at the focal plane. Due to the subwavelength nature of planar metallic lens, we present the rigorous electromagnetic analysis by using two dimensional (2D) finite difference time domain (FDTD) method. These height-modulated slits with uniform width are demonstrated to have unique advantages in beam manipulation. In combination with previous studies, it is expected that our structure with small number of slits could lead to realization of optimum designs of plasmonic nano-lens.

The Focusing Property of Immersed Plasmonic Nanolenses Under Radially Polarized Illumination

The focusing property of immersed plasmonic nanolenses was theoretically studied by a rigorous electromagnetic numerical analysis method. The immersed plasmonic nanolens consists of a through central hole surrounded by a set of concentric slits with a period of plasmonic wavelength. The computational results show that the focusing property of immersed plasmonic nanolenses is, in general, similar to that of traditional immersion lenses. Normally, for the given incident wavelength, the higher the refractive index of the immersed medium, the smaller the focusing spot. For different wavelengths, the focusing property of immersed plasmonic nanolenses shows the similar focusing property, in comparison with traditional lenses, as well. A focal length of around half of the incident wavelength and the smallest focusing spot of less than a quarter of the incident wavelength have been achieved. The physical explanation of the different focusing behavior of immersed nanolenses is also given. The reported immersed plasmonic nanolens with a quasi-far-field focal length, as well as a superfocusing spot, can find applications in areas including nanolithography, data storage, super-resolution imaging, and so on.

Electromagnetic Analysis of Apodized Annular-Aperture Logarithmic Axicons in Wave Imaging Systems

An apodized annular-aperture logarithmic axicon (3ALA) can be applied potentially to improve imaging resolution in quasi-optical and/or millimeter wave imaging systems, due to its property of long depth of field (DOF). Electromagnetic analyses of forward and backward 3ALAs are conducted respectively at mm- and submm-wavebands. Their lateral and axial intensity distributions are evaluated by rigorous electromagnetic analysis method. And the comparative conclusions are drawn at last in our present work

Study on Refractive-Diffractive Logarithm Axicons in mm/submm Range

Large depth of field and uniform axial intensity distributions are important in many practical applications. Lots of optical elements have been proposed for this end, such as full-aperture logarithmic axicons (LAs), annular-aperture LAs and apodized annular-aperture LAs. In millimeter/submillimeter (mm/submm) range, the refractive-diffractive behaviors (including transverse and longitudinal intensity distributions) behind these axicons illuminated by a plane wave are calculated by rigorous electromagnetic analysis method in our paper. Many important features of these axicons are concluded by comparing their refractive-diffractive field distributions

Study on Refractive-Diffractive Logarithm Axicons in mm/submm Range

Large depth of field and uniform axial intensity distributions are important in many practical applications. Lots of optical elements have been proposed for this end, such as full-aperture logarithmic axicons (LAs), annular-aperture LAs and apodized annular-aperture LAs. In millimeter/submillimeter (mm/submm) range, the refractive-diffractive behaviors (including transverse and longitudinal intensity distributions) behind these axicons illuminated by a plane wave are calculated by rigorous electromagnetic analysis method in our paper. Many important features of these axicons are concluded by comparing their refractive-diffractive field distributions

New fast and memory-sparing method for rigorous electromagnetic analysis of 2D periodic dielectric structures

A method is presented that performs the exact electromagnetic analysis of 2D periodic dielectric structures of arbitrary profile or index distribution and possibly large period. The generalized source method is used to formulate the problem of light diffraction in the form of a volume integral equation reduced to a linear equation system, which is solvable by known fast algorithms. The calculation time and required memory are linearly proportional to the total number N o of considered diffraction orders instead of N o 3 typical for conventional methods. Numerical examples are provided to demonstrate the potential of the method for the analysis of complex periodic structures.