Three-dimensional analysis of subwavelength diffractive optical elements with the finite-difference time-domain method

We present a three-dimensional (3D) analysis of subwavelength diffractive optical elements (DOE's), using the finite-difference time-domain (FDTD) method. To this end we develop and apply efficient 3D FDTD methods that exploit DOE properties, such as symmetry. An axisymmetric method is validated experimentally and is used to validate the more general 3D method. Analyses of subwavelength gratings and lenses, both with and without rotational symmetry, are presented in addition to a 2 x 2 subwavelength focusing array generator.     

Computer-generated stratified diffractive optical elements

We present what is to our knowledge a new type of diffractive optical element (DOE), the computer-generated stratified diffractive optical element (SDOE), a hybridization of thin computer-generated DOEs and volume holograms. A model and several algorithms for calculating computer-generated SDOEs are given. Simulations and experimental results are presented that exhibit the properties of computer-generated SDOEs: the strong angular and wavelength selectivity of SDOEs makes it possible to store multiple pages in a computer-generated SDOE, which can be read out separately (multiplexing). The reconstruction of an optimized SDOE has a higher quality than the reconstruction of optimized one-layer DOEs. SDOEs can be calculated to have only one diffraction order.     

Multi-wavelength optical pickup with diffractive optical elements

Abstract

A novel, to our knowledge, multi-wavelength diffractive optical pickup is presented. The pickup enables multi-focus imaging and increases the data transfer rate considerably. Parallel reading of two or more memory layers is possible. The different spots can be controlled independently. The optical pickup consists of different diffractive optical elements (DOEs). The measured full-width at half-maximum (FWHM) spot intensity for the DOE-pickup is 0.76 μm—close to the diffraction limited predicted value of 0.71 μm—indicating good optical performance. The measured highest diffraction efficiencies of the realized DOEs are about 92%.     

Interference effects in far-field diffractive optical elements

The effects of interference between closely packed diffraction orders in the far field are studied for a number of different scalar-domain diffractive optical elements (DOE's). We demonstrate that there are specific order separations that minimize the observed degradation in the far-field output uniformity. Finally, a DOE that is designed to ensure that the order separation lies near one of these minima is compared with a more general design that produces an equivalent far-field output.     

Multilayer technology for diffractive optical elements

The proposed multilayer technology makes it possible to approximate a continuous phase distribution by discrete phase steps. Compared with binary techniques, a higher diffraction efficiency can be achieved. In most known processes a bulk substrate is used and etched directly; therefore it is difficult to control the height of the phase steps. We propose applying layers of a well-known thickness and structuring them with a selective etching process. In this new multilayer process for reflecting elements a system of metal and dielectric layers is used that can easily be produced by standard methods.     

A method of designing diffractive optical elements focusing into plane areas

Abstract

We propose a numerical method for designing phase function of diffractive optical elements (DOE_s) aimed at focusing into a plane area of complex shape. The method is applied to factorable intensity distribution in the domain of focusing and factorable illuminating beam of arbitrary cross-section. The diffraction analysis of a direct problem of focusing into the plane region is carried out. Based on a specially developed software, the numerical experiment was carried out, which allowed us to find that the theoretical power efficiency of typical DOE_s is no less than 85%.     

Polarization-multiplexed diffractive optical elements with liquid-crystal displays

We show experimental results for programmable polarization multiplexing of diffractive optical elements (DOEs) onto two liquid-crystal displays (LCDs). The first LCD encodes the two multiplexed phase-only diffractive optical elements. The second LCD acts as a pixelated polarization rotator to change the polarization state for each of these two DOEs. Although the system requires precise alignment, the DOE's and polarization angles are fully programmable.     

Crossed phase gratings with diffractive optical elements

Orienting two identical or complementary diffractive gratings with a small angle between the grating grooves allows a new crossed-grating device to be constructed. This device has an effective profile that varies locally. For understanding the effects of this variation and the diffraction efficiency of the gratings, the local profiles were correlated with the moiré period of the crossed-grating system by use of various techniques. Asymmetric intensity behavior in the first order of the crossed gratings was seen. Effectively, the diffraction efficiency of the crossed gratings yielded a response equivalent to that of a grating with variable blaze that could be useful in optical computing as a passive optical switching device. One of several models is described that creates greater asymmetric behavior.     

Stray-light effects of diffractive beam-shaping elements in optical microsystems

The use of diffractive beam-shaping elements in hybrid or monolithic microsystems is investigated. Compact optical systems require diffractive structures with small grating periods for creating large deflection angles. Such elements are difficult to fabricate while a low stray-light level is maintained. In addition, because of the small geometrical dimensions and the short propagation lengths in an optomechanical microsystem, any stray light generated by the diffractive structure critically affects the overall optical performance. A model for the estimation of the interference effects between the designed and the unwanted diffraction orders is developed and applied to an example of a collimating diffractive optical element. On the basis of theoretical and experimental results, design rules for the application of diffractive beam-shaping elements in microsystems are derived.     

Application of an interferometric phase contrast method to fabricate arbitrary diffractive optical elements

A novel approach for the fabrication of diffractive optical elements is described. This approach is based on an interferometric phase contrast method that transforms a complex object wavefront into an intensity pattern. The resulting intensity pattern is used to expose a photoresist layer on a substrate. After development, a diffractive phase object with an on-axis diffraction pattern is achieved. We show that the interferometric phase contrast method allows a precise control of the resulting intensity pattern. An array of blazed Fresnel lenses is realized in photoresist by using kinoform or detour-phase computer holograms for the interferometric phase contrast setup.     

Optimal design method for multi-layer diffractive optical elements with consideration of antireflection coatings

An optimal design method for multi-layer diffractive optical elements (MLDOEs) is put forward with consideration of antireflection coatings in actual applications of hybrid optical systems. Taking this method into account for optimal design, it can ensure 100% diffraction efficiency at the designed wavelengths and maximum polychromatic integral diffraction efficiency over the whole waveband. In addition, it can be obtained not only for mechanical durability of soft polymers improvements but increase antireflection coatings functions for hybrid optical systems. Finally, an example for optimal design algorithm process and simulation of MLDOEs used in visible waveband is presented. The results show that this optimal method perfects the MLDOEs design on the basic theory with great practicability for MLDOEs design.     

Polarization-multiplexed diffractive optical elements fabricated by subwavelength structures

Polarization-multiplexed phase-only diffractive optical elements with subwavelength structures are proposed and fabricated. The differences among the phase modulations result from the differences among the effective indices exhibited in the subwavelength structures with various filling factors and surface profiles, and the phase retardations are obtained by the relief depth of the structures. The polarization-selective property is achieved by the polarization dependence of the effective indices exhibited in the one-dimensional subwavelength structures and the polarization independence exhibited in the two-dimensional structures. Additionally, the polarization contrast of our polarization-multiplexed elements, defined as the cross talk between the two polarization incidences, is independent of the relief depth. The principle of the polarization multiplexing by use of the subwavelength structures is described, and the fabrication results for the polarization-multiplexed computer-generated holograms are demonstrated.     

Modeling considerations for rigorous boundary element method analysis of diffractive optical elements.

Critical modeling issues relating to rigorous boundary element method (BEM) analysis of diffractive optical elements (DOEs) are identified. Electric-field integral equation (EFIE) and combined-field integral equation (CFIE) formulations of the BEM are introduced and implemented. The nonphysical interior resonance phenomenon and thin-shape breakdown are illustrated in the context of a guided-mode resonant subwavelength grating. It is shown that modeling such structures by using an open geometric configuration eliminates these problems that are associated with the EFIE BEM. Necessary precautions in defining the incident fields are also presented for the analysis of multiple-layer DOEs.     

Design of diffractive optical elements for multiple wavelengths

A method for producing diffractive optical elements (DOE's) for multiple wavelengths without chromatic aberration is described. These DOE's can be designed for any distinct wavelength. The DOE's are produced from two different optical materials, taking advantage of their different refractive indices and dispersions.     

On the zero-thickness model of diffractive optical elements

In a recent paper [J. Opt. Soc. Am. A 16, 113 (1999)] a thin-element approximation of diffractive optical elements was used to describe diffraction of oblique incident wave fronts. This expression motivated by a ray optical analysis is shown to be incorrect. I discuss how the thin-element approximation can be generalized to arbitrary diffraction geometries. This includes an intuitive interpretation of the results.     

Asymptotic analysis and design of diffractive optical elements

The problem of light diffraction by a micro-optical diffractive element is investigated. The method of stationary phase is applied to obtain approximate values of the integrals in the Kirchhoff approximation. The accuracy of the asymptotic approximation is studied in detail. As an application, the obtained approximate formulas are used to solve a design problem of constructing a diffractive optical element with a desired intensity distribution.     

Laser beam relaying with phase-conjugate diffractive optical elements

A diffractive optical element is used to relay complex laser beam profiles by phase conjugation. It has the advantage over a conventional afocal system of avoiding light concentration at the intermediate focal point. Theoretical and experimental results show that the image quality is a function of alignment errors and mode-size changes. When the optical system is within the calculated tolerances, the diffractive optic reproduces images of high quality.     

Optimal quantization method for uneven-phase diffractive optical elements by use of a modified iterative Fourier-transform algorithm

A method based on an iterative Fourier-transform algorithm (IFTA) with phase optimization for phase-only multilevel diffractive optical elements (DOEs) is presented. Phase optimization by minimizing the mean-squared error composed of an amplitude-weighted probability-density function is performed in the IFTA iterations to ensure that the wavefront difference is minimized and thus to improve the DOEs' performance. Using the proposed method, we obtained a small standard deviation of diffraction efficiency of 20 uneven-phase DOEs, showing that DOEs with high diffraction efficiency did not vary significantly with the initial conditions. The simulation results of even- and uneven-phase four-level DOEs designed by use of direct and stepwise quantization IFTA methods are compared.     

Speckle reduction in laser projection systems by diffractive optical elements

In laser projection systems the observer in the far field of the image points on the screen will recognize serious speckle noise. There are many methods to reduce or eliminate speckles in the near field by reducing or eliminating temporal or spatial coherence of the laser. But for the far field it is hardly possible to change the coherence properties of laser sources so that speckles will disappear. We propose a new method for eliminating speckles in the far field by using a diffractive optical element. The intensity modulation depth in the far-field speckle pattern can be reduced to a few percent while good beam quality is preserved.     

Two-dimensionally-periodic diffractive optical elements: limitations of scalar analysis

The range of validity of the scalar diffraction analysis is quantified for the case of two-dimensionally-periodic diffractive optical elements (crossed gratings). Three canonical classes of two-dimensionally-periodic grating structures are analyzed by using the rigorous coupled-wave analysis as well as the scalar diffraction analysis. In all cases the scalar-analysis diffraction efficiencies are compared with the exact diffraction efficiencies. The error in using the scalar analysis is then determined as a function of the grating-period(s)-to-wavelength ratio(s), the minimum feature size, the grating depth, the refractive index of the grating, the incident polarization, and the number of phase levels. The three classes of two-dimensional (2-D) unit cells are as follows: (1) a rectangular pillar, (2) an elliptical pillar, and (3) an arbitrarily pixellated multilevel 2-D unit cell that is representative of more complicated diffractive optical elements such as computer-generated holograms. In all cases a normally incident electromagnetic plane wave is considered. It is shown that the error of the scalar diffraction analysis in the case of two-dimensionally-periodic diffractive optical elements is greater than that for the corresponding one-dimensionally-periodic counterparts. In addition, the accuracy of the scalar diffraction analysis degrades with increasing refractive index, grating thickness, and asymmetry of the 2-D unit cell and with decreasing grating-period-to-wavelength ratio and feature size.