G. Michael Morris

Highly improved convergence of the coupled-wave method for TM polarization

The coupled-wave method formulated by Moharam and Gaylord [ J. Opt. Soc. Am.73, 451 ( 1983)] is known to be slowly converging, especially for TM polarization of metallic lamellar gratings. The slow convergence rate has been analyzed in detail by Li and Haggans [ J. Opt. Soc. Am. A10, 1184 ( 1993)], who made clear that special care must be taken when coupled-wave methods are used for TM polarization. By reformulating the eigenproblem of the coupled-wave method, we provide numerical evidence and argue that highly improved convergence rates similar to the TE polarization case can be obtained. The discussion includes both nonconical and conical mountings.

Antireflection behavior of silicon subwavelength periodic structures for visible light

We describe subwavelength surfaces etched into silicon wafers that exhibit antireflection characteristics for visible light. The wafers are fabricated by holographically recording a crossed-grating in a photoresist mask followed by reactive-ion etching to transfer the primary mask onto the silicon substrate. The dependence of reflectivity on the wavelength and angle of incidence is measured. The overall antireflection performance of the corrugated silicon wafers is compared with that of standard thin-film stacks, and is interpreted with the effective medium theory and with simulation results obtained from rigorous computations.

Resonant scattering from two-dimensional gratings

A theoretical investigation of resonant scattering from two-dimensional gratings is presented. Abrupt changes of diffraction efficiency over a small parameter range have been observed by rigorous coupled-wave analysis. The peak reflection or transmission efficiencies can approach unity. This phenomenon is explained in terms of the coupling between the incident plane wave and guided modes that can be supported by the two-dimensional-grating waveguide structure. Because of the double periodicity, the incident field can be coupled into any direction in the grating plane. The guided modes supported by two-dimensional gratings are found by rigorous solution of the homogeneous problem associated with the scattering (inhomogeneous) problem. The complex propagation constants for the guided modes provide estimates of both the resonance angle and width. In addition, to illustrate the implication of the radical change in the phase and amplitude of the propagating waves, we report a study of finite-beam diffraction in the resonant scattering region. Applications for the structures include polarization-independent narrow-band filters and bandwidth-tunable filters. It is shown that, because of the double resonance, the polarization-independent narrow-band filters have a large angular tolerance.

Diffractive superresolution elements

Superresolution phase-only pupil filters designed to utilize the degrees of freedom made available by diffractive optics technology are investigated theoretically. These so-called diffractive superresolution elements improve the quality of the superresolved diffraction pattern from the point of view of Strehl ratio, reduction of the spot size, control of the sidelobe effects, optimization procedures, and fabrication tolerances. The performance of these elements is studied, and the nature of the solutions obtainable with binary and multiple-phase structures is analyzed. Design considerations and solutions for applications such as confocal scanning microscopy and optical data storage are presented. Optimization of the degrees of freedom to satisfy desired constraints is discussed and compared with other methods.

Efficient implementation of rigorous coupled-wave analysis for surface-relief gratings

A computationally efficient implementation of rigorous coupled-wave analysis is presented. The eigenvalue problem for a one-dimensional grating in a conical mounting is reduced to two eigenvalue problems in the corresponding nonconical mounting. This reduction yields two n × n matrices to solve for eigenvalues and eigenvectors, where n is the number of orders retained in the computation. For a two-dimensional grating, the size of the matrix in the eigenvalue problem is reduced to 2n × 2n. These simplifications reduce the computation time for the eigenvalue problem by 8–32 times compared with the original computation time. In addition, we show that with rigorous coupled-wave analysis one analytically satisfies reciprocity by retaining the appropriate choice of spatial harmonics in the analysis. Numerical examples are given for metallic lamellar gratings, pulse-width-modulated gratings, deep continuous surface-relief gratings, and two-dimensional gratings.

Images of cone photoreceptors in the living human eye

Though the photoreceptor mosaic has been imaged through the intact optics of the eyes of several species, it has not been clear whether individual photoreceptors can be resolved in the living human eye. We have constructed a high-resolution fundus camera and have resolved cones with a spacing as small as 3.5 microns in single images of the fundus. The high contrast of these images implies that almost all the light returning from the retina at this wavelength (555 nm) has passed through the apertures of foveal cones. The average power spectra of our retinal images show that it is possible to recover spatial frequencies as high as 150 c/deg in eyes with normal optical quality, a conclusion that was confirmed with estimates of the optical quality of these eyes obtained with a Hartmann-Shack wavefront sensor. These results emphasize the superiority of the eyes optics over the spatial sampling limits of the retina when the eyes optical quality is optimized. They also show that it would be possible to routinely resolve retinal structures as small as photoreceptors in the normal living eye if its aberrations could be corrected.

Coupled-mode theory of resonant-grating filters

An approximate closed-form expression for the loss in a planar phase grating is derived by using coupled-mode theory. It is shown that this loss expression can be used to determine the spectral and angular width of a resonant-grating filter. A resonant-grating filter is a free-space optic that takes advantage of grating resonances to create narrow-band reflection peaks. Design characteristics, such as bandwidth, have previously been determined by profiling the resonance in reflectivity with the use of numerically intensive vector-diffraction methods such as rigorous coupled-wave analysis. The coupled-mode approach described here, however, gives the resonant-filter width directly, without the need to profile the resonance. Therefore computation time and hence design time are reduced. In addition, it is shown that the coupled-mode approach provides physical insights into the factors contributing to filter bandwidth.

Effects of source correlation on the spectrum of light

Abstract Experiments that illustrate the influence of source correlations on the spectrum of light detected in the far field are reported. It is demonstrated that source correlations which violate the scaling law [E. Wolf, Phys. Rev. Lett. 56 (1986) 1370] produce a normalized spectrum in the far field that is different from the normalized spectrum of the light at the source.

Controlling the spectral response in guided-mode resonance filter design

Techniques for controlling spectral width are used in conjunction with thin-film techniques in the design of guided-mode resonance (GMR) filters to provide simultaneous control over line-shape symmetry, sideband levels, and spectral width. Several factors that could limit the minimum spectral width are discussed. We used interference effects for passband shaping by stacking multiple GMR filters on top of one another. A design is presented for a 200-GHz telecommunications filter along with a tolerance analysis. Compared with a conventional thin-film filter, the GMR filter has fewer layers and looser thickness tolerances. Grating fabrication tolerances are also discussed.

Diffractive optics applied to eyepiece design

Eyepieces often limit the overall optical performance of visual instruments and, because of the wide field-of-view and high-performance requirements, they present a well-known difficult design problem. Improvement of existing eyepieces is limited with the use of conventional design variables. We have designed and fabricated a hybrid diffractive-refractive wide-field (>60°) eyepiece that offers significant improvements over existing conventional eyepieces. The hybrid eyepiece consists of only three common-crown refractive elements and weighs 70% less than an Erfle-type eyepiece, while having enhanced optical performance such as a 50% decrease in pupil spherical aberration and a 25% reduction in distortion. Experimental modulation transfer function results are in excellent agreement with the theoretical performance.