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.     

Analysis of blazed diffractive optical elements formed with artificial dielectrics

A new hybrid method for the analysis of diffractive optical elements, which combines fully vectorial and scalar theories, is presented. It is suitable for use with elements of arbitrary large zone, even when the local feature size is of the order of the wavelength. To assess its applicability, we have performed cross-checking tests. The model is shown to accurately predict many optical properties of diffractive optical elements based on two-dimensional artificial dielectrics, like the useful energy diffracted into the order of interest or the deterministic loss into high diffraction orders for an illumination with a wavelength different from the design wavelength or for highly oblique incidence.     

Efficient encoding algorithms for computer-aided design of diffractive optical elements by the use of electron-beam fabrication

One of the general requirements of a computer-aided design system is the existence of efficient (in data size and running time) algorithms that are generally reliable for the broadest range of design instances. The restricted data formats of the electron-beam machines impose difficulties in developing algorithms for the design of diffractive optical elements (DOE's) and computer-generated holograms (CGH's). Issues that are related to the development of CGH algorithms for e-beam fabrication of DOE's and CGH's are discussed. We define the problems the CGH algorithms need to solve, then introduce general curve drawing algorithms for the e-beam data generation of diffractive optical components. An efficient algorithm for general aspherical DOE's is proposed. Actual design and fabrication examples are also presented.     

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.     

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%.     

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.     

Blazed-binary diffractive elements with periods much larger than the wavelength

Blazed-binary optical elements with only binary ridges or pillars are diffractive components that mimic standard blazed-echelette diffractive elements. We report on the behavior of one-dimensional blazed-binary optical elements with local periods much larger than the wavelength. For this purpose, an approximate model based on both scalar and electromagnetic theory is proposed. The model is tested against electromagnetic-theory computational results obtained for one-dimensional blazed-binary gratings with large periods. An excellent agreement is obtained, showing that the model is able to predict quantitatively the wavelength and the incidence-angle dependences of the diffraction efficiency of blazed-binary structures.     

Dual-layer blazed grating fabricated by the roll-to-roll microreplication process for chromostereoscopy

In this work we present the design and fabrication of a dual-layer blazed grating (DBG) to replace a single-layer blazed grating for chromostereoscopy. Based on the physiological and physical background, we first analyze the relationship between the performance of a grating pair and color-stereo effect. The DBG is composed of two materials of different indices and fabricated upon a polyethylene terephthalate film by two steps of a roll-to-roll microreplication process. With this dual-layer design, the fabrication tolerance in the blazed facets of the grating is three times looser and more achievable as compared with that of a grating composed of single material.     

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.     

Analytic approach for optimal quantization of diffractive optical elements

One of the most important factors that limit the performance of diffractive optical elements (DOE's) is the depth accuracy of the relief structure. A common procedure for fabricating DOE's is the binary optics procedure, in which binary masks are used for the fabrication of a multilevel relief structure. Here an analytic procedure for calculating the optimal depth levels of DOE's, the phase bias, and the decision levels is presented. This approach is based on the minimization of the mean-squared error caused by the quantization of the continuous profile. As a result of the minimization an optimal value for the etching depth of each photolithographic mask is determined. The obtained depth values are, in general, different from the depth values used by the conventional multilevel approach. Comprehensive mathematical analysis is given, followed by several computer simulations that demonstrate the advantages of the proposed procedure.     

Analysis of multimask fabrication errors for diffractive optical elements

As design algorithms for diffractive optical elements improve, the limiting factor becomes the fabrication process. It is hoped a better understanding of fabrication errors will allow elements with greater tolerance to be designed. This is important for high-power laser fiber coupling, where hot spots lead to failure. We model seven different fan-out gratings applying misetch, misalignment, and feature rounding. Our main findings are that misetch can lead to improved results, misalignment is strongly asymmetric, and both the pi and pi/2 masks can dominate misalignment. Rounding has a r(2) dependence and potentially can be incorporated into the design stage. Finally we present some experimental data for misalignment.     

Comparison of encoding methods for computer-generated diffractive optical elements

Five modern encoding methods for diffractive optical elements are compared in terms of diffraction efficiency for an f/1 focusing element. It is shown that all five produce similar results for a given value of the minimum feature size delta and number of phase levels N when the grating period is larger than N delta. In contrast, when the grating period is smaller than N delta, the analytic quantization method cannot be employed. When this condition is met, it is shown that the radially symmetric iterative discrete on-axis method can result in diffraction efficiencies as much as 30% higher than those obtained with direct sampling. It is also shown that performance advantages of iterative algorithms improve as the target region in the focal plane increases.     

High-efficiency diffractive micromachined chopper for infrared wavelength and its application to a pyroelectric infrared sensor

We have developed a diffractive micromachined chopper (DMC) for an IR wavelength of ~10 mum. This device operates mechanically by movable reflection grating beams. It modulates the diffraction efficiency by controlling the displacement of grating beams by an electrostatic force. For a CO(2) laser beam, a high modulation efficiency of 84% with an -0.8-dB small insertion loss was obtained by detecting 0th-order diffracted light. A novel pyroelectric IR microsensor with a DMC and a diffractive multilevel Si microlens was proposed and it demonstrated the detection of human existence.     

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.     

Analysis of the effects of bias phase and wavelength choice on the design of dual-wavelength diffractive optical elements

Diffractive optical elements (DOEs) are often used in pattern formation for display purposes. Constructing these images from two or more colors greatly enhances their visual effect. To achieve this with DOEs is not simple, as they are inherently wavelength specific. We discuss an algorithm for designing quantized elements that produce distinct intensity patterns in the far field for two wavelengths. The benefits of applying bias phase to the dual-wavelength problem are investigated. The difference between the best and the worst choice of bias phase is shown to produce a variation of up to 2% in the efficiency. The mean square error can vary by up to a factor of 2 between the best and the worst case. It is also critically important to understand how the values of the two wavelengths affect the result. We present an analysis of how choosing different pairs of wavelengths in the design process affects the quality of our results.     

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.     

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.     

Characterization of 1D diffractive optical elements by phase inversion

Abstract

We consider the feature dimensions of selected 1D diffractive optical elements (DOE) such that the Fourier transform based Gerchberg-Saxton (GS) iterative scalar phase retrieval algorithm, as calibrated by the results of vector coupled-wave theory, may be used for phase reconstruction. We consider examples only of continuous surface relief and binary (two level, not multi-level) phase-only DOE. Experimental phase distribution for rectangular and blazed gratings with ～ 5λ period agree within experimental limits with scalar theory, and, for the rectangular grating, were shown to agree also with the vector theory. Phase distributions are considered for a continuously varying linear blazed grating with 10λ periodicity, its sampled binary equivalent with minimum feature sizes of 0.1λ and for continuous linear blazed gratings with period varied from ～ 16λ to ～ 2λ. The vector calculations show an average linear dependence of the phase on grating period, but the vector curves are displaced to lower values from the scalar results by an increasing amount as the grating period is reduced. Grating performance is more influenced by the size of the grating period than the subwavelength size of the features in a binary representation. Reasonable equivalence is found in the prediction of correct phase distributions between scalar and vector theory for grating periods > ～ 5λ.