High-efficiency blazed diffractive optical elements for the violet wavelength fabricated by electron-beam lithography

Blazed diffractive optical elements (DOEs) were studied for the violet wavelength by electron-beam lithography. By optimizing electron-beam writing parameters and electron-dose distributions, we fabricated eight kinds of grating (period A = 10-0.54 microgm) with excellent blazed structure. It has been demonstrated that the measured diffraction efficiency values agreed well with the rigorous theoretical ones. For the fine period of 0.54 microm, we confirmed a peak appearance of 75.6% (TE) experimentally. A wave aberration as small as approximately 0.01 lambda (rms) was obtained for the first-order diffracted wave from the fabricated DOEs. Blazed DOEs for the violet wavelength could be used as key devices in a high-density optical disk pickup of the next generation.     

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%.     

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.     

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.     

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.     

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.     

Analysis and optimization of fabrication of continuous-relief diffractive optical elements

The fabrication of continuous-relief diffractive optical elements by direct laser beam writing in photoresist is analyzed. The main limitation and tolerances are identified, and their influence on optical performance is quantified. Fabricated structures show rounded profile steps resulting from the convolution of the desired profile with the writing beam. This leads to a reduction in diffraction efficiency. Optimization techniques are presented to minimize this effect. Scaling the profile depth by a factor of mu > 1 increases the first-order diffraction efficiency for blazed elements. This method is also applied to suppress the zeroth diffraction order in computer-generated holograms. A nonlinear compensation of the exposure data for the Gaussian beam convolution results in an 18% increase of the diffraction efficiency for a blazed grating with a 10-mum period to a value of 79%.     

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.     

Phase-only diffractive optical elements with subdiffraction-limited depth of focus

Abstract

Phase-only subdiffraction-limited depth of focus (DOF) elements are proposed and a relatively simple method is given which reduces the number of design parameters to four. A diffractive optical element with subdiffractive-limited DOF was experimentally demonstrated for the first time. Experimental results are in close agreement with numerical prediction. Several calculated examples show that the DOF for subdiffraction-limited elements can decrease by an amount, ranging from 37% to 71% compared to the DOF for a diffraction-limited element when ρ is chosen close to zero. The reduction is determined by the focal length of the element and the required distance between the primary peak (focal plane) and the secondary peak, both in units of wavelength. The latter, i.e. the peak-to-peak distance, determines the maximum applicable DOF. The influence of input laser beam parameters, such as phase distribution and beam size, on the focusing performance have also been investigated.     

Polarization-selective diffractive optical elements with an index-matching gap material

Highly polarization-selective diffractive optical elements for use in optical interconnection and routing systems have been fabricated by the wet etching of pairs of calcite substrates and characterized experimentally. We show that when an index-matching polymer is used to fill the gap between the two substrates, substrate alignment problems are eliminated and efficiency is greatly increased. This has resulted in first-order diffraction efficiencies of 40.5% and polarization contrast ratios of 450:1 for several off-axis binary-phase elements, allowing these components to be used for practical applications.     

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.     

Design of two-dimensional polarization-selective diffractive optical elements with form-birefringent microstructures

We describe a design methodology for synthesizing polarization-sensitive diffractive optical elements based on two-dimensional form-birefringent microstructures. Our technique yields a single binary element capable of producing independent phase transformations for horizontally and vertically polarized illumination. We designed two elements for operation at 10.6 microm and fabricated them in silicon. Qualitative experimental results agree with design predictions.     

Beam shaping for multicolour light-emitting diodes with diffractive optical elements

An improved particle swarm optimization method is proposed for the design of ultra-thin diffractive optical elements (DOEs) enabling multicolour beam shaping functionality. We employ pre-optimized initial structures and adaptive weight strategy in the algorithm to achieve better and identical shaping performance for multiple colours. Accordingly, a DOE for shaping light from green and blue LEDs has been designed and fabricated. Both experiment and numerical simulations have been conducted and the results agree well with each other. 15.66% average root mean square error (RMSE) and 0.22% RMSE difference are achieved. In addition, the parameters closely related to the performance of the optimization are analysed, which can provide insights for future application designs.     

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.     

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.     

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.     

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.     

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.     

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.