A review of the rigorous coupled-wave analysis (RCWA) as applied to the diffraction of electromagnetic waves by gratings is presented. The analysis is valid for any polarization, angle of incidence, and for conical diffraction. Cascaded and/or multiplexed gratings as well as material anisotropy and loss can be incorporated under the same formalism. Volume and surface-relief gratings can be analyzed. Convergence analysis is presented for rectangular-groove surface-relief dielectric and metallic gratings. The role of multilevel surface-relief and holographic gratings in the substrate-mode photonic interconnect configuration is investigated. Results obtained using the RCWA are presented for 1-, 2-, 4-, 8-, and 16-level surface-relief gratings and are compared with the predictions of the simple scalar model. Two practical configurations are analyzed: (a) a silicon substrate at a freespace wavelength of 1.3 microns and (b) a glass substrate at a freespace wavelength of 0.84 microns. Equivalent holographic gratings are also designed and compared. Small period rectangular groove gratings can also be modeled using approximately equivalent uniaxial homogeneous layers (effective media). The ordinary and extraordinary refractive indices of these layers depend on the grating filling factor, the refractive indices of the substrate and superstrate, and the ratio of the freespace wavelength to grating period. It is shown how these models result from the eigenvalue equation of the boundary-value rectangular-groove grating problem. Comparisons of the homogeneous effective medium approximations with the rigorous coupled-wave analysis are presented. Antireflection designs (single-layer or multilayer) using the effective medium models are presented and compared.
Mathematical models for diffractive optics have been developed, and implemented as numerical codes, both for the “direct” problem and for the “inverse” problem. In problems of the “direct” class, the diffractive optic is specified, and the full set of Maxwell’s equations is cast in a variational form and solved numerically by a finite element approach. This approach is well-posed in the sense that existence and uniqueness of the solution can be proved and specific convergence conditions can be derived. As an example, we consider a low order metallic grating, where other approaches are known to have convergence problems, and show the variational method yields exceptionally good convergence. In problems of the “inverse” class, some information about the diffracted field (e.g., the far-field intensity) is given, and the problem is to find the periodic structure in some optimal sense. A new approach is described that applies relaxed optimal design methods to give entirely new grating structures; wave propagation is based on the Helmholtz equation. An example of an angle-optimized antireflective structure and of an ideal array generator are presented.
New systems are being developed around innovative diffractive optical components. Applications in optical interconnects, signal switching and interferometry have created a need for two-dimensional optical fanout gratings as well as complex Diffractive Optical Elements (DOE). The increasingly complex components being designed for such optical devices require specialized optimization algorithms to achieve desired performance. In this paper, we demonstrate the optimization of 1:K fanout gratings and symmetrical DOE's in a highly dimensional solution space using genetic algorithms (GA). Analytic results are presented for the optimization of an interconnect grating using different GA parameters to analyze the algorithm convergence. By means of these examples, we present design techniques for fanout gratings, radially symmetric DOE's, and polarization sensitive components.
A diffractive optical element (DOE) can correct chromatic aberration in refractive optical systems with spectral bands in the visible, mid-wavelength, and long-wavelength infrared. A DOE simplifies the optical design, improves the image quality, and lowers the cost and weight by reducing the number of lens elements and desensitizing the alignment tolerances.
A review of micro-optics technologies with special emphasis on the technology developments at Hughes Danbury Optical Systems, Inc. (HDOS) is presented. This includes both diffractive and non-diffractive techniques. As the user systems become more and more complex, the requirements imposed on micro-optic components become more demanding and, subsequently, one technology cannot presently accommodate all the system specifications. At HDOS, state-of-the-art advancements are being achieved with at least two technologies that appear to be adequate for today’s system applications.
Due to the stringent requirements on the lateral alignment and the large number of steps required to fabricate diffractive optics by typical microlithographic techniques, the need for more efficient methods to fabricate these elements has arisen. This paper discusses the use of electron beam lithography in fabricating diffractive optical elements by direct e-beam alignment and direct write into the electron beam resist. Many of the practical advantages and disadvantages of each method will be pointed out. In particular, current research and future research directions into such direct write problems as the proximity effect, hologram ruggedness, and lengthy exposure times will be addressed.
Proximity-compensated kinoforms were manufactured with direct-writing electron-beam lithography in two different resists, SAL 110 and PMMA. The kinoforms were blazed transmission gratings, with periods 4, 8, 16 pm 1 mm by 1 mm size, and a Fresnel lens, with 38 mm focal length and 3 mm by 3 mm size. The compensated gratings performed better than the uncompensated ones: for the 4 pm compensated grating the measured diffraction efficiency was 67%. It was 35% for the uncompensated grating. The Fresnel lens had diffraction limited optical performance with better than 85% efficiency. The compensation was made by repeated convolutions in the spatial domain or deconvolution in the Fourier domain using the electron-beam point-spread function.
We also present developing processes for PMMA and SAL 110 resists that are more appropriate for multilevel resist kinoforms manufactured with direct-write electron-beam lithography.
In recent years surface-relief Diffractive Optical Elements (DOEs), a specialized class of diffractive optical elements, have revolutionized design of optical systems and instruments. Surface-relief diffractive optical components improve performance of the existing optical systems and increase systems compactness and reliability. Surface-relief DOEs can be fabricated as multilevel binary optical elements, or as continuous surface-relief optical elements. A surface-relief DOE is being designed such that incident light interacts with the topography of the surface-relief microstructure including the size and shape characteristics of surface profile features such as indentations and projections as well as their dimensional relationship, to perform a desired optical function. Binary optical elements are being made by the same microlithographic and ion etching techniques used to produce VLSI circuits. Computer-generated continuous surface-relief DOE is recorded by direct laser-beam or e-beam writing in photoresist. Continuous surface-relief DOE can be also recorded in photoresist by interferometric (holographic) technique. After development recorded in photoresist surface-relief microstructures are being ion-beam etched into quartz or other inorganic optical substrates.
There are a number of possible sources of scattering in diffractive optics: sloping walls, pattern depth errors, line edge errors, quantization errors, roughness, and the step wise approximation to the ideal surface. These sources of scattering can be systematic (deterministic) or random. In this paper scattering formulas for both systematic and random errors are derived using Fourier optics. These formulas can be used to explain the results of scattering measurements and computer simulations.
Recent advances in design, analysis and fabrication have made diffractive optical elements (DOEs) an attractive and viable choice for a number of applications , such as optical interconnects, laser diode optics, and military imaging systems. However, in military and aerospace applications, ambient air temperatures can vary greatly and in some cases, these systems must operate over an 80°C temperature range. Nor is it uncommon for commercial products to perform over a significant temperature range. To properly design and evaluate such systems, a detailed understanding of thermal behavior is required.
Subwavelength structured surfaces have a multitude of applications. These include antireflection suppression, fabrication of polarization components, narrowband filters, and phase plates. All of these applications offer advantages over conventional components. With advances in manufacturing technologies, the fabrication of these surfaces for visible and infrared portions of the spectrum is increasingly feasible.
Free-space digital optical systems represent a novel interconnection technology that exploits the volume surrounding an electronic circuit substrate. The potential advantage of free-space optical systems is the creation of high density, energy efficient, parallel, high bandwidth interconnections. A photonic switching network, whose function is to connect high bandwidth channels, is a natural vehicle for exploring and developing this technology. Diffractive optical components play critical roles in these free-space systems as optical power array generators and interconnection holograms. In this paper, we will examine how these diffractive elements have served in realized photonic switching demonstration systems and explore some of the issues that determine their successes and limitations.
We will identify the varieties of diffractive optics and computer generated holograms needed in single- and multi-stage optoelectronic interconnection networks, discuss their design issues and present fabricated examples.
Microoptical devices (including diffractive and refractive microlenses) fabricated using integrated circuit technology have recently received considerable attention. This scientific achievement offers new options for optical system design and has the potential to create a revolution in optical technology. Microoptic devices have been used for infrared focal plane array efficiency enhancement, beam splitters, and miniature optical scanners. What makes this technology attractive to industry is its potential low cost owing to its compatibility with VLSI batch processing and volume production, and low-cost replication techniques.
In parallel with this development in optics, researchers have been pursuing micro-electro-mechanical (MEM) technology. MEM technology enables the development of many applications for sensors and actuators in automotive, machine tools, robotics, and medical instrumentation. This paper discusses the potential for merging microoptics with micromechanics to create a new class of micro-opto-electromechanical (MOEM) devices, a few examples of which are laser scanners, optical shutters and dynamic micromirrors. Both key MOEM device technologies (microoptics and MEM) employ similar batch processing methods, making low-cost, commercial applications highly feasible. Recent developments and achievements in microoptics and MEM are discussed. Then several very attractive MOEM devices that have recently been proposed and are being developed at different laboratories are introduced.
Advanced-technology-based electro-optical sensors of minimum size and weight require miniaturization of optical, electrical, and mechanical devices with an increasing trend toward integration of various components. Micro-optics technology has the potential in a number of areas to simplify optical design with improved performance. Applications of micro-optics technology for sensor subsystems include internally cooled apertures/windows, hybrid optical design, electronically controlled optical beam steering, and microscopic integration of microoptics, detectors, optical interconnects, and signal-processing layers. Typical components are spherical, aspherical, and dispersive microlenses which simultaneously focus and disperse light. Arrays of dispersive microlenses have potential applications in multicolor focal planes. We discuss the theory, analytical design programs, analog and Fresnel microlens design options, and photolithographic fabrication technologies for micro-optics. Sample results of several microlens types are reported. We also present results of laboratory evaluations of several microlens types that have been fabricated at Lockheed Research and Development Division (R and DD). The microlenses include both wideband and dispersive types, in isolation and in arrays. Different geometries are considered, including square, hexagonal, and skewed microlenses. Results of point-spread-function measurements from our unique micro-optics testbed facility are compared to design predictions.
The use of optical interconnections for communicating between chips or boards of a computer has been hampered by the lack of practical packaging schemes for free-space optics. In order to solve this problem, the concept of "planar optics" was proposed. This approach is based on the use of computer aided design and standard fabrication techniques adapted from semiconductor processing. Microoptical components are placed on the surfaces of a single optical substrates. Optoelectronic chips are integrated using hybrid techniques such as flip chip solder bump bonding. In this review article, we present the idea of planar optics, show several demonstration experiments, and discuss various aspects related to manufacturability. For our considerations, emphasis will be put on interconnection applications.