Rigorous Analysis Of Wave Guiding And Diffractive Integrated Optical Structures

The realization of wavelength scale and sub-wavelength scale fabrication of integrated optical devices has led to a concurrent need for computational design tools that can accurately model electromagnetic phenomena on these length scales. This dissertation describes the physical, analytical, numerical, and software developments utilized for practical implementation of two particular frequency domain design tools: the modal method for multilayer waveguides and one-dimensional lamellar gratings and the Rigorous Coupled Wave Analysis (RCWA) for 1D, 2D, and 3D periodic optical structures and integrated optical devices. These design tools, including some novel numerical and programming extensions developed during the course of this work, were then applied to investigate the design of a few unique integrated waveguide and grating structures and the associated physical phenomena exploited by those structures. The properties and design of a multilayer, multimode waveguide-grating, guided mode resonance (GMR) filter are investigated. The multilayer, multimode GMR filters studied consist of alternating high and low refractive index layers of various thicknesses with a binary grating etched into the top layer. The separation of spectral wavelength resonances supported by a multimode GMR structure with fixed grating parameters is shown to be controllable from coarse to fine through the use of tightly controlled, but realizable, choices for multiple layer thicknesses in a two material waveguide; effectively performing the simultaneous engineering of the wavelength dispersion for multiple waveguide grating modes. This idea of simultaneous dispersion band tailoring is then used to design a multilayer, multimode GMR filter that possesses broadened angular acceptance for multiple wavelengths incident at a single angle of incidence. The effect of a steady-state linear loss or gain on the wavelength response of a GMR filter is studied. A linear loss added to the primary guiding layer of a GMR filter is shown to produce enhanced resonant absorption of light by the GMR structure. Similarly, linear gain added to the guiding layer is shown to produce enhanced resonant reflection and transmission from a GMR structure with decreased spectral line width. A combination of 2D and 3D modeling is utilized to investigate the properties of an embedded waveguide grating structure used in filtering/reflecting an incident guided mode. For the embedded waveguide grating, 2D modeling suggests the possibility of using low index periodic inclusions to create an embedded grating resonant filter, but the results of 3D RCWA modeling suggest that transverse low index periodic inclusions produce a resonant lossy cavity as opposed to a resonant reflecting mirror. A novel concept for an all-dielectric unidirectional dual grating output coupler is proposed and rigorously analyzed. A multilayer, single-mode, high and graded-index, slab waveguide is placed atop a slightly lower index substrate. The properties of the individual gratings etched into the waveguide\u27s cover/air and substrate/air interfaces are then chosen such that no propagating diffracted orders are present in the device superstrate and only a single order is present outside the structure in the substrate. The concept produces a robust output coupler that requires neither phase-matching of the two gratings nor any resonances in the structure, and is very tolerant to potential errors in fabrication. Up to 96% coupling efficiency from the substrate-side grating is obtained over a wide range of grating properties

The FLAME-slab method for electromagnetic wave scattering in aperiodic slabs

The proposed numerical method, "FLAME-slab," solves electromagnetic wave scattering problems for aperiodic slab structures by exploiting short-range regularities in these structures. The computational procedure involves special difference schemes with high accuracy even on coarse grids. These schemes are based on Trefftz approximations, utilizing functions that locally satisfy the governing differential equations, as is done in the Flexible Local Approximation Method (FLAME). Radiation boundary conditions are implemented via Fourier expansions in the air surrounding the slab. When applied to ensembles of slab structures with identical short-range features, such as amorphous or quasicrystalline lattices, the method is significantly more efficient, both in runtime and in memory consumption, than traditional approaches. This efficiency is due to the fact that the Trefftz functions need to be computed only once for the whole ensemble.Comment: Various typos were corrected. Minor inconsistencies throughout the manuscript were fixed. In Section II B. Additional description regarding choice of Trefftz cell, was added. In Section III A. Detailed description about units (used in our calculation) was adde

Gratings: Theory and Numeric Applications

International audienceThe book containes 11 chapters written by an international team of specialist in electromagnetic theory, numerical methods for modelling of light diffraction by periodic structures having one-, two-, or three-dimensional periodicity, and aiming numerous applications in many classical domains like optical engineering, spectroscopy, and optical telecommunications, together with newly born fields such as photonics, plasmonics, photovoltaics, metamaterials studies, cloaking, negative refraction, and super-lensing. Each chapter presents in detail a specific theoretical method aiming to a direct numerical application by university and industrial researchers and engineers

Sensitivity analysis for grating reconstruction

Periodic structures, called diffraction gratings, play an important role in optical lithography. The diffraction of the incident field in multiple diffraction orders provides a way to accurately determine a position on a wafer on one hand and on the other hand it provides a test method to determine the quality of the photolithographic process. For both applications it is crucial to be able to find the actual shape of the structure to correct for damages or imperfections. When besides the incident field also the shape of a diffraction grating is known, we can compute the diffracted field by using the rigorous coupled-wave analysis (RCWA) or the C method. These methods solve Maxwell’s equations for time-harmonic fields directly, which is required because such a grating typically has a period smaller than the wavelength of the incident field. The basic idea of both methods is that they transform Maxwell’s equations into algebraic eigensystems, which have to be solved in order to obtain the diffracted field. The reconstruction of the grating shape is carried out by first making an initial guess of its shape. Next the computed diffracted field is compared to actual measurements and the difference between them determines how the shape parameters should be adjusted. For the reconstruction we make use of standard optimization techniques such as quasi-Newton methods to find local optima. We assume that the initial guess of the grating shape is close enough to its actual shape such that the optimum that is found is the actual shape and take more angles of incidence to make the optimization more robust. The focus of this thesis is finding the first-order derivative information of the diffracted field with respect to the shape parameters. This is possible using finite differences where the diffracted field is computed again for a neighbouring value of the shape parameter under consideration. However, straightforward differentiation of the relations within RCWA or the C method gives a more accurate, but also faster way to find this derivative information. When straightforward differentiation is used, we also have to find eigenvalue and eigenvector derivatives, but to determine these derivatives no additional eigenvalue systems have to be solved. This implies that the reconstruction process can be performed faster and more accurate. Besides the speed-up of the reconstruction, we also provide a firm mathematical basis to this sensitivity theory. The sensitivity of RCWA is tested for some specific grating structures, such as the binary grating, the trapezoidal grating and more advanced structures as the coated trapezoid and a stacked grating of multiple trapezoids. The simulations show that for the most simple structure, the binary grating, we have the derivatives with respect to shape parameters up to twice as fast as obtained with finite differences, depending on the truncation number of the Fourier series. When the number of physical shape parameters increases, the analytical method becomes increasingly faster than finite differences. For the stacked trapezoids, the analytical method is more than 10 times faster than finite differences. In practice, the grating shapes will be more and more complex and therefore, the analytical approach offers a more and more significant speed increase in the computations of the derivatives without loss of accuracy

Comparison of simplified theories in the analysis of the diffraction efficiency in surface-relief gratings

In this work a set of simplified theories for predicting diffraction efficiencies of diffraction phase and triangular gratings are considered. The simplified theories applied are the scalar diffraction and the effective medium theories. These theories are used in a wide range of the value Λ/λ and for different angles of incidence. However, when 1 ≤ Λ/λ ≤ 10, the behaviour of the diffraction light is difficult to understand intuitively and the simplified theories are not accurate. The accuracy of these formalisms is compared with both rigorous coupled wave theory and the finite-difference time domain method. Regarding the RCWT, the influence of the number of harmonics considered in the Fourier basis in the accuracy of the model is analyzed for different surface-relief gratings. In all cases the FDTD method is used for validating the results of the rest of theories. The FDTD method permits to visualize the interaction between the electromagnetic fields within the whole structure providing reliable information in real time. The drawbacks related with the spatial and time resolution of the finite-difference methods has been avoided by means of massive parallel implementation based on graphics processing units. Furthermore, analysis of the performance of the parallel method is shown obtaining a severe improvement respect to the classical version of the FDTD method.This work was supported by the “Ministerio de Economía y Competitividad” of Spain under projects FIS2011-29803-C02-01 and FIS2011-29803-C02-02 and by the “Generalitat Valenciana” of Spain under project PROMETEO/2011/021

Gratings: Theory and Numeric Applications, Second Revisited Edition

International audienceThe second Edition of the Book contains 13 chapters, written by an international team of specialist in electromagnetic theory, numerical methods for modelling of light diffraction by periodic structures having one-, two-, or three-dimensional periodicity, and aiming numerous applications in many classical domains like optical engineering, spectroscopy, and optical telecommunications, together with newly born fields such as photonics, plasmonics, photovoltaics, metamaterials studies, cloaking, negative refraction, and super-lensing. Each chapter presents in detail a specific theoretical method aiming to a direct numerical application by university and industrial researchers and engineers.In comparison with the First Edition, we have added two more chapters (ch.12 and ch.13), and revised four other chapters (ch.6, ch.7, ch.10, and ch.11

A microscopic view of the electromagnetic properties of sub-wavelength metallic surfaces

We review the properties of the surface waves that are scattered by two-dimensional sub-wavelength indentations on metallic surfaces. We show that two distinct waves are involved, a surface plasmon polariton (SPP) and a quasi-cylindrical wave (quasi-CW). We discuss the main characteristics of these waves, their damping characteristic lengths and their relative excitation weights as a function of the separation distance from the indentation and as a function of the metal conductivity. In particular we show that derive a closed-form expression for the quasi-CW, which clarifies its physical origin and its main properties. We further present an intuitive microscopic model, which explains how the elementary SPPs and quasi-CWs exchange their energies by multiple-scattering to build up a rich variety of near- and far-field optical effects.Comment: Review article, 98 references. Sur. Sc. Rep. (in press

Directional Thermal Emission and Absorption from Surface Microstructures in Metalized Plastics

Thermal emission, exhibiting antenna-like directivity, has been generated by a wide variety of both simple and complex micro-structures. The basic demonstrations of directional emission, and specific device performance evaluations, have been conducted at elevated temperatures, typically several hundred degrees Celsius. The most common applications for these high-temperature designs are thermal photo-voltaic and spectroscopic sources. A wide range of lower temperature applications, such as spacecraft thermal management and mid- to far-infrared optical train stray light management, are precluded by the cost and complexity of the fabrication processes employed. In this work, a novel fabrication and physical surface optimization of a seminal directionally emitting structure is conducted in metalized plastic. The fabrication method is derived from the high-throughput compact disc manufacturing process and exploits the advantageous surface electromagnetic properties of aluminium, at the expense of forgoing high-temperature operation. Then, a novel directionally emitting structure, exhibiting a broader angular response, is design and fabricated by the same methods. The performance of both structures is evaluated through reflectance and self-emission measurements, and compared to rigorous modeling results. The necessity of conducting low-temperature emission and reflectance measurements, on instruments designed for radiometry rather than scatterometry, requires consideration of the longitudinal spatial coherence of field incidence on the surface. To this end, a well-developed modeling method was extended to include finite longitudinal spatial coherence excitation

Investigation of passive atmospheric sounding using millimeter and submillimeter wavelength channels

Progress by investigators at the Georgia Institute of Technology in the development of techniques for passive microwave retrieval of water vapor, cloud, and precipitation parameters using millimeter- and sub-millimeter wavelength channels is reviewed. Channels of particular interest are in the tropospheric transmission windows at 90, 166, 220, 340, and 410 GHz and centered around the water vapor lines at 183 and 325 GHz. Collectively, these channels have potential application in high-resolution mapping (e.g., from geosynchronous orbit), remote sensing of cloud and precipitation parameters, and retrieval of water vapor profiles. During the period from 1 Jan. 1993 through 30 Jun. 1993 the Millimeter-wave Imaging Radiometer (MIR) completed data flights during a two-month long deployment in conjunction with TOGA/COARE. Coincident data was collected from several other ground-based, airborne, and satellite sensors, including the NASA/MSFC AMPR, MIT MTS, DMSP SSM/T-2 satellite, collocated radiosondes, ground- and aircraft-based radiometers and cloud lidars, airborne infrared imagers, solar flux probes, and airborne cloud particle sampling probes

Designing and optimizing gratings for soft X-ray diffraction efficiency

The diffraction efficiency is critical to the speed and sensitivity of grating-based spectroscopy instruments. This becomes particularly important for soft x-ray instruments, used on material science beamlines at synchrotrons around the world, where the low reflectivity of materials makes it challenging to create efficient optics. The efficiency of soft x-ray gratings is examined from a rigorous electromagnetic approach using the differential method, adapted for deep gratings using the S-matrix propagation algorithm. New software is written to provide an open-source implementation with fast performance on cluster computing resources. Trends in diffraction efficiency are examined as a function of grating materials, coatings, groove geometry, and incidence conditions; these trends are used to provide recommendations for instrument design, including the identification of a new principle of optimal incidence angle. Efficiency calculations and optimizations are applied to the design of a high-performance soft x-ray emission spectrometer for the REIXS beamline at the Canadian Light Source. The process produces an innovative design that exploits an efficiency peak in the third diffraction order to offer higher resolution than would otherwise be possible given the space constraints of the machine. Finally, the spectrometer's actual gratings are measured for diffraction efficiency as a function of wavelength. Although the real-world efficiencies differ substantially from the nominal calculations, the differences are explained by incorporating real-world effects: geometry errors, groove variation, oxidation, and surface roughness. A fitting process is proposed to match the calculated to the measured efficiency spectra. The geometry parameters predicted by the fitting process are found to agree exactly with atomic force microscopy (AFM) measurements for all the gratings studied. Because each grating parameter affects the shape of the efficiency spectrum in a different way, the spectrum can be considered as a unique "fingerprint" or "hash"; we conclude that this might be extended to use efficiency measurements and fitting calculations to characterize grating parameters that are difficult or impossible to measure directly