Space-variant interconnections based on diffractive optical elements for neural networks: architectures and cross-talk reduction

Optical architectures for fully connected and limited-fan-out space-variant weighted interconnections based on diffractive optical elements for fixed-connection multilayer neural networks are investigated and compared in terms of propagation lengths, system volumes, connection densities, and interconnection cross talk. For a small overall system volume the limited-fan-out architecture can accommodate a much larger number of input and output nodes. However, the interconnection cross talk of the limited-fan-out space-variant architecture is relatively high owing to noise from the diffractive-optical-element reconstructions. Therefore a cross-talk reduction technique based on a modified design procedure for diffractive optical elements is proposed. It rearranges the reconstruction pattern of the diffractive optical elements such that less noise lands on each detector region. This technique is verified by the simulation of one layer of an interconnection system with 128 x 128 input nodes, 128 x 128 output nodes, and weighted connections that fan out from each input node to the nearest 5 x 5 array of output nodes. In addition to a significant cross-talk reduction, this technique can reduce the propagation length and system volume.     

Diffractive optical elements for the formation of "light bottle" intensity distributions

Application of the two-photon polymerization (2PP) technique for the fabrication of binary radial diffractive optical elements (DOEs) to form a bottle-like intensity distribution, or "light bottle," is studied. Computer modeling and fabrication of a binary DOE for the formation of the desired light distributions are realized. The results of scanning electron microscopy analysis of the diffractive relief produced by the 2PP technique and an investigation of the optical properties of the fabricated elements are presented.     

遗传算法用于衍射光学元件的优化设计

提出了一种基于遗传算法的衍射光学元件优化设计方法;在衍射光学元件设计中遗传算法运行参数对遗传算法性能有一定的影响:采用较大的群体规模,遗传算法越容易获得最优解;交叉算子越大,遗传算法全局搜索能力越强;选择算子对遗传算法的影响不是太大;如果要进一步提高解的精度,可选取较大的终止代数。数值计算结果表明,用遗传算法优化设计的衍射光学元件,其误差小于 5.2%,衍射效率达到 91.2%。遗传算法很适合衍射光学元件的优化设计。     

Investigation of computer-generated diffractive beam shapers for flattening of single-modal CO(2) laser beams

A full cycle was realized of the photolithographic development and detailed testing of a diffractive optical element that transforms the diverging Gaussian beams of CO(2) lasers into a uniformly filled-in rectangle. The zone feature size of the beam shaper, the diffractive efficiency and accuracy, the focus depth, and the stability with respect to the size and the divergence of incident Gaussian beams are studied by computer modeling. Calculated flattop intensity distributions are presented in the same form of gray-level pictures and three-dimensional plots as the corresponding results measured by an IR camera.     

New Design of High NA Photolithographic Lens Using Diffractive Optical Element

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Replication of continuous-profiled micro-optical elements for silicon integration

A novel scheme for the integration of diffractive optical elements onto silicon is presented. The processing is made in reverse order, meaning that the process of structuring the optical elements on the wafer precedes the silicon microstructuring. The first processing step on the wafer is the hot embossing of the optical microstructures into an amorphous fluorocarbon polymer spin coated on the wafer. The cured polymer forms a highly stable material with excellent optical properties. The remaining silicon processing is thus performed with the diffractive optical elements already in place. Two different diffractive structures were used in the development of the method-a (Fresnel) lens with a rather low f-number and a diffractive element producing a fan-out of a large number of paraxial beams.     

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.     

Programmable optical logic systems using free-space optical interconnections

A free-space optical logic technique is presented that utilizes a two-dimensional array of diffractive optical elements. Each optical element focuses light to multiple, separate positions in the output focal plane. The focal spots from different optical elements are allowed to overlap spatially, resulting in interference. By changing the phase shift between the optical elements, one can create different optical logic operations in the focal plane. The technique is demonstrated by the use of two input beams incident onto a multiplexed optical element written onto a programmable spatial light modulator. The optical element simultaneously creates both AND and XOR logic functions in the output plane.     

Diffractive optical elements with modulated zone sizes

Abstract

The standard design for phase-only diffractive optical elements comprises a transformation of the continuous phase function into a surface relief by means of wrapping the phase into regular intervals of M2π. This results in a structure with diffractive zones aligned in a horizontal plane. We present an alternative design concept with modulated zone sizes leading to non-periodic boundary positions and non-aligned surface structures. The diffractive properties are compared to those of conventional diffractive optical elements. It can be shown that they are fully equivalent for the design wavelength, but exhibit a different spectral behaviour for deviating wavelengths. These properties are exploited for the improvement of the optical performance of blazed gratings and diffractive lenses under conditions of deviating wavelengths. Special emphasis is put on the optimization of the ratio between diffractive efficiencies of the design order and other orders for blazed gratings and focusing diffractive lenses, as well as the suppression of interference effects within Gaussian beams collimated with diffractive lenses.     

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.     

Iterative optimization of diffractive phase elements simultaneously implementing several optical functions

The design of diffractive optical elements that incorporate several optical functions in a single element is discussed. The technique used involves iterative optimization. Aprevious paper is continued, in which initial results with few sampling points were reported. Here new results that involve a large number of sampling points are reported. Because the algorithm is computationally intensive with a large number of data points, the parallel implementation of the algorithm on a MASPAR machine is described. MASPAR is a single-instruction multiple-data machine with 16,384 processors. The computer simulations discussed involve simultaneous wavelength demultiplexing, focusing, and the filtering out of a particular wavelength component. It is shown that satisfactory designs of diffractive optical elements can be achieved by the assignment of only a small number of sampling points on the output plane that adequately specify what is required at each wavelength.     

Sapphire-GaN-based planar integrated free-space optical system

We report on the design and fabrication of a planar integrated free-space optical system working on the basis of binary phase diffractive optical elements (DOEs) realized in GaN on a sapphire substrate. Group III-nitride/sapphire substrates enable the parallel monolithic integration of passive microoptical elements like lenses and gratings as demonstrated here and optoelectronic devices like light emitters and photodetectors on a single wafer. We present an approach for the simultaneous optimization of the efficiency of transmissive and reflective diffractive optical elements processed in a single lithographic etching step.     

Implementation of phase-shift patterns using a holographic projection system with phase-only diffractive optical elements

We proposed a method to implement spatial phase-shift patterns with subdiffraction limited features through a holographic projection system. The input device of the system displayed phase-only diffractive optical elements that were calculated using the iterative Fourier-transform algorithm with the dummy-area method. By carefully designing the target patterns to the algorithm, the diffractive optical elements generated the Fourier-transformed images containing the phase-shift patterns in which the widths of dark lines were smaller than the diffraction limit. With these demonstrations, we have successfully shown that the near-field phase-shift lithographic technique can be realized through an inexpensive maskless lithographic system and can still achieve subdiffraction limited images.     

Diffractive phase elements for beam shaping: a new design method

A design method based on the Yang-Gu algorithm [Appl. Opt. 33, 209 (1994)] is proposed for computing the phase distributions of an optical system composed of diffractive phase elements that achieve beam shaping with a high transfer efficiency in energy. Simulation computations are detailed for rotationally symmetric beam shaping in which a laser beam with a radially symmetric Gaussian intensity distribution is converted into a uniform beam with a circular region of support. To present a comparison of the efficiency and the performance of the designed diffractive phase elements by use of the geometrical transformation technique, the Gerchberg-Saxton algorithm and the Yang-Gu algorithm for beam shaping, we carry out in detail simulation calculations for a specific one-dimensional beam-shaping example.     

Diffractive light attenuators with variable transmission

Abstract

A new application of diffractive optical elements (DOEs) for continuous or multistage adjustment of optical radiation intensity is described. The diffractive attenuators are linear or circular gratings (amplitude or phase) with constant period and diffraction efficiency that varies across the grating. The zero order of diffraction is used as the output and transmitted through the grating without angular deviation. The diffractive attenuators, in distinction to conventional analogues, allow one to change the intensity of the light beam according to predetermined function and have no limitations for power of the regulated light beam. These elements can be used in optical systems as a beam splitter with adjusted splitting coefficient. The experimental results on a circular diffractive attenuator fabricated by direct laser writing on a chromium film are presented. The range of transmission variation was 20 times within a 340° angle of attenuator turn. The possibility to use a phase diffractive attenuator as a light radiation modulator for a powerful technological laser is discussed.     

Design considerations of stacked multilayers of diffractive optical elements for optical network units in optical subscriber-network applications

The detailed design process and experimental results of stacked multilayer diffractive optical elements are reported for an optical network unit used in optical subscriber-network applications. The optical network unit accepts two incoming light beams of 1.3- and 1.55-mum wavelengths through a single-mode optical fiber. A laser diode is also placed for bidirectional communications. The optical network unit consists of five diffractive optical elements that perform the following functions: collimation of incoming beams, focusing of the outgoing 1.55-mum beam, 3-dB splitting of the 1.3-mum beam, focusing of the 1.3-mum beam onto the photodiode, and collimation of the light emitted from a laser diode. Possible cost reductions as a result of mass production and the ease of alignment of the stacked diffractive optical elements could be ideal for constructing low-cost optical network units.     

Achromatic fan-out diffractive system for white-light free-space optical interconnects

Abstract

A simple and versatile white-light fan-out diffractive system based on the achromatization of the fractional Talbot effect is proposed. This achromatic configuration is able to interconnect a single polychromatic point source with a 2-D array of optoelectronic microdevices with low residual chromatic aberration even for white light. The whole broadband beamsplitter system is formed by two simple diffractive optical elements, a periodic diffractive lenslet array and a diffractive lens, that are made with a direct laser writing technique giving high light efficiency. The focal amplitude distribution corresponding to the lenslet array produces, by free-space propagation, self-replicas with different density of light points. These patterns, in conjunction with the achromatization process carried out by the additional diffractive lens, are, in short, the key to achieving a set of undistorted white-light spots at the output plane with high uniformity and variable separation between them. Experimental results are also shown.     

Achromatic fourier processor with holographic optical lenses

An optical Fourier processor that allows the use of broadband light sources and colored inputs is designed, fabricated, and tested. We develop a design technique based on phase manipulation in the Fourier plane to construct an image processor that provides a chromatically corrected image making use of the good aberrations behavior of symmetrical optical systems. Only a small number of diffractive lenses and one achromatic refractive lens are required to obtain a real image. We verify our design experimentally using holographic lenses, which are presented, owing to their versatility, as a good alternative to expensive blazed diffractive elements.     

Single-point diamond turning and replication of visible and near-infrared diffractive optical elements

High-fidelity diffractive surfaces have been generated with single-point diamond-turning techniques. A key to the success of this technique is the ability to shape the diamond tool tip to provide the optimum phase-relief profile, given manufacturing constraints. Replication technology is used to transfer the phase-relief surface into a thin epoxy or photopolymer layer on a glass substrate. Diffraction efficiency results for a wide range of zone widths are presented to provide the reader with a baseline of expected performance for replicated visible and near-infrared diffractive optical elements. In addition, a new method for analyzing diffractive surface structures is presented. The ray-trace algorithm quickly provides accurate results of predicted diffraction efficiency for arbitrary zone profiles, which is extremely valuable in predicting manufacturing errors.