Optical processing with vortex-producing lenses

We discuss two types of optical processing using vortex-producing angular phase plates. In the most common spatial-filtering operation, an input object is Fourier transformed (either by Fraunhofer diffraction or with a lens system). The Fourier transform is then multiplied by an angular phase pattern, and the product is again Fourier transformed. The output is a space-invariant, edge-enhanced version of the input object. Alternatively we can directly image the object using a lens multiplied by the angular phase. The space-variant image is severely distorted along the optical axis of the system. We encode the phase plates onto a liquid-crystal display and present experimental results on both systems.     

Design methods for space-variant optical interconnections to achieve optimum power throughput

Optoelectronic systems based on space-variant optics give great freedom to the system designer in terms of interconnect topologies. One feature of space-variant systems is that they can achieve a high interconnect density. However, this density is achieved by having large arrays of diffractive elements with very small apertures relative to the propagation distances involved. Thus diffraction losses from the finite apertures can significantly affect power throughput for these types of systems, regardless of the diffractive efficiencies of the optical elements involved. Therefore it is desirable that this loss be minimized. We present several space-variant optical interconnect design methods (for both one-to-one and fan-out interconnects) and compare them in terms of power throughput for diffraction-limited interconnect distances. Both numerical simulations and experimental results are presented.     

Analysis and design of variable optical attenuators based on nematic liquid-crystal cells

Variable optical attenuators based on nematic liquid-crystal cells are considered. The attenuation curves of variable optical attenuators based on the 90° twisted and the parallel-aligned liquid-crystal cells are analysed explicitly with an approximate model, and the electro-optical behaviours of parallel-aligned liquid-crystal cells with a weak surface anchoring strength are modelled. Simulation results show that a large attenuation range and a shallow attenuation slope can be achieved simultaneously by using the parallel-aligned liquid-crystal cell with appropriate surface anchoring. The attenuation is nearly wavelength insensitive in a broad range of wavelengths.     

Complex encoding of rotation-invariant filters onto a single phase-only spatial light modulator

The accuracy and flexibility of the technique proposed by Davis et al. [Appl. Opt. 35, 2488 (1996)] for the encoding of the amplitude and the phase of a filter onto a single liquid-crystal spatial light modulator operating in a phase-only regime has been exploited to implement several filter designs in a convergent optical correlator. We have selected some filters, that given their mathematical structure showing some degree of rotational invariance, or having a parameter to regulate their behavior, require amore precise encoding. We present correlation results of outstanding quality for various rotationally invariant filter designs that have never been previously implemented with a real-time optical correlator.     

Volume-consumption comparisons of free-space and guided-wave optical interconnections

We compare volume-consumption characteristics of free-space and guided-wave optical interconnections. System volume consumption is used as a fundamental measure of various point-to-point space-invariant and space-variant interconnections of two-dimensional arrays of N(1/2) x N(1/2) points. We show that, in free-space and space-invariant situations, although volume consumption for macroaperture optics is O(1)(N(3/2)), where O denotes the order, it is only O(2)(N) for microaperture optics. For free-space and space-variant operations only microaperture optics is possible without fundamental power losses. The corresponding minimum volume consumption is O(3)(N(3)). We show that single microaperture-per-channel implementations of either space-invariant or space-variant operations are, in general, more volume efficient than are their two-cascade microaperture-per-channel counterparts. We also show that, for minimizing volume consumption, the optimum relative apertures F#(opt) for space-variant optical elements are, respectively, (5N)(1/2)/4 for a single microaperture-per-channel geometry and (5N)(1/2)/2 for a two-cascade microaperture-per-channel geometry. In guided-wave or fiber interconnect cases our study shows that the volume consumption for space-invariant and space-variant operations is O(4)(N), with O(4) < O(2), and O(5)(N(3/2)), respectively. Thus an important conclusion of the study is that free-space optics is less volume efficient than is guided-wave optics in both space-invariant and space-variant interconnect applications.     

Real-time optical image subtraction and edge enhancement using ferroelectric liquid-crystal devices based on speckle modulation

We carried out real-time optical image subtraction and edge enhancement based on a speckle modulation technique by using ferroelectric liquid-crystal polarization switches and a ferroelectric liquid-crystal spatial light modulator. A ferroelectric liquid-crystal spatial light modulator is employed as a real-time and multiple-exposure optical device, and successful results are obtained from three-exposure images modulated by speckles. Thus, image subtraction and edge enhancement are realized in real time. The whole operation is performed within several milliseconds with modest operating conditions. Because the spatial light modulator has a high resolution of greater than 100 line pairs/mm and can store fine speckle patterns, the image qualities we obtained are quite satisfactory.     

Space-variant optical correlator based on the fractional Fourier transform: implementation by the use of a photorefractive Bi(12)GeO(2(a)) (BGO) holographic filter

A space-variant optical correlator is proposed on the basis of the fractional Fourier transform. The optical device uses as a recording medium for the holographic filter a photorefractive Bi(12)GeO(2) (BGO) crystal. The experimental results confirm the shift-variance properties. Some limitations that arise from the volume diffraction are also considered.     

Electrically controllable in-line-type polarizer using polymer-dispersed liquid-crystal spliced optical fibers

The polarization-dependent transmission of light through an electrically controllable in-line-type polarizer that is made from polymer-dispersed liquid-crystal spliced optical fibers is discussed experimentally and theoretically. This in-line-type optical splicing method has the advantage of low transmission loss when it is applied in optical fiber communication systems. An anomalous diffraction approach is used to compute the scattering cross section of polymer-dispersed liquid-crystal droplets. The experimental results are supported by a theoretical analysis. This device can be employed in electrically controllable in-line-type polarizers and has the potential to yield electrically controllable polarization-dependent loss compensators.     

Encoding amplitude information onto phase-only filters

We report a new, to our knowledge, technique for encoding amplitude information onto a phase-only filter with a single liquid-crystal spatial light modulator. In our approach we spatially modulate the phase that is encoded onto the filter and, consequently, spatially modify the diffraction efficiency of the filter. Light that is not diffracted into the first order is sent into the zero order, effectively allowing for amplitude modulation of either the first-order or the zero-order diffracted light. This technique has several applications in both optical pattern recognition and image processing, including amplitude modulation and inverse filters. Experimental results are included for the new technique.     

Parallel optical negabinary arithmetic based on logic operations

On the basis of signed-digit negabinary representation, parallel two-step addition and one-step subtraction can be performed for arbitrary-length negabinary operands. The arithmetic is realized by signed logic operations and optically implemented by spatial encoding and decoding techniques. The proposed algorithm and optical system are simple, reliable, and practicable, and they have the property of parallel processing of two-dimensional data. This leads to an efficient design for the optical arithmetic and logic unit.     

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.     

A scheme of developing frequency encoded tristate-optical logic operations using semiconductor optical amplifier

The ever increasing demand for very fast and agile optical networks requires very fast execution of different optical and logical operations as well as large information handling capacities at the same time. In conventional binary logic based operations the information is represented by two distinct states only (0 and 1 state). It limits the large information handling capacity and speed of different arithmetic and optical logic operations. Tristate based logic operations can be accommodated with optics successfully in data processing, as this type of operation can enhance the speed of operation as well as increase the information handling capacity. Here in this communication the author proposes a new method to implement all-optical different logic gates with tristate logic using the frequency-encoding principle. The frequency encoding/decoding based optical communication has distinctly great advantages because the frequency is the fundamental character of an optical signal and it preserves its identity throughout the communication. The principle of the rotation of the state of polarization of a probe beam through semiconductor optical amplifier (SOA), frequency routing property of an optical add/drop multiplexer (AD) and high frequency conversion property of reflecting semiconductor optical amplifiers (RSOA) have been exploited here to implement the desired AND, OR, NAND and NOR logic operations with tristate logic.     

Application of a wire-grid-mirror liquid-crystal light valve in a nonlinear joint transform correlator

We describe the operation of a wire-grid-mirror liquid-crystal light valve and its use for optical pattern recognition. The nonlinear characteristic of the wire-grid-mirror liquid-crystal light valve is used to implement the nonlinear joint transform correlator. Experimental results and computer simulations show that the nonlinear characteristic of the wire-grid-mirror liquid-crystal light valve can produce a well-defined correlation peak and low output background. The performance of the nonlinear joint transform correlator obtained when the wire-grid-mirror liquid-crystal light valve is used is compared with that of the binary joint transform correlator.     

Generating doughnut-shaped beams with large charge numbers by use of liquid-crystal spiral phase plates

Liquid-crystal spiral phase plates with cell gaps of 7 and 20 microm have been used to generate doughnut-shaped beams (doughnut beams) with charges of 1 and 4, respectively. Stacking these liquid-crystal spiral phase plates yielded doughnut beams with charge numbers up to 8. High efficiency and flexibility are the advantages of generating doughnut beams by stacking liquid-crystal spiral phase plates. Interference of doughnut beams generated by liquid-crystal spiral phase plates and plane waves has been studied. Fingerlike interference patterns were obtained with a doughnut beam tilted from a Gaussian beam; spiral fanlike patterns were obtained with a doughnut beam and a Gaussian beam collimated coaxially. The experimental results are supported qualitatively by simulation. By rotating a glass slide in the path of the Gaussian beam, one can rotate the fanlike interference pattern in a controlled fashion. With the liquid-crystal display technology that we have developed and report here, these liquid-crystal spiral phase plates should find applications in optical tweezers.     

Phase-aberration correction with dual liquid-crystal spatial light modulators

A phase-aberration-correction system that uses high-resolution, twisted nematic liquid-crystal spatial light modulators in a Mach-Zehnder interferometer is presented. A correction algorithm is described and experimentally verified by use initially of one liquid-crystal panel. Phase aberrations are successfully removed by a single liquid-crystal panel, but unacceptably high amplitude variation is introduced into the wave front because of the phase-amplitude coupling of the spatial light modulator. A second panel is used to remove the amplitude modulation. The modified optical system with a multiplicative architecture is described, and results are presented that show the correction of phase aberrations with an amplitude variation of less than 10%.     

Optical configuration of a horizontal-switching liquid-crystal cell for improvement of the viewing angle

We propose an optical configuration of a horizontal-switching liquid-crystal cell, consisting of a splayed liquid-crystal cell and uniaxial films, to improve the viewing angle characteristics by compensating for the phase dispersion in a diagonal direction. The optical design of the proposed configuration was performed on a Poincaré sphere with geometric calculations. By fabricating in-plane switching cells with the introduced configuration, we demonstrated their optical performances. As a result, we found that the diagonal viewing angle of the proposed horizontal-switching cell could be increased by 80% compared to a symmetrical viewing cone.     

Properties of Output Signal Moments of Optical Processors

General results for the output signal moments are given for both linear and bilinear systems and both space-variant and space-invariant processing. As an example of a bilinear system, a partially coherent system is considered. The properties of intensity moments for a Fourier optical processor and an imaging system with partially coherent illumination are also investigated.     

Angular motion point spread function model considering aberrations and defocus effects

When motion blur is considered, the optics point spread function (PSF) is conventionally assumed to be fixed, and therefore cascading of the motion optical transfer function (OTF) with the optics OTF is allowed. However, in angular motion conditions, the image is distorted by space-variant effects of wavefront aberrations, defocus, and motion blur. The proposed model considers these effects and formulates a combined space-variant PSF obtained from the angle-dependent optics PSF and the motion PSF that acts as a weighting function. Results of comparison of the new angular-motion-dependent PSF and the traditional PSF show significant differences. To simplify the proposed model, an efficient approximation is suggested and evaluated.     

Encoded Multichromophore Response for Simultaneous Label‐Free Detection

The self‐assembly of molecularly precise nanostructures is widely expected to form the basis of future high‐speed integrated circuits, but the technologies suitable for such circuits are not well understood. In this work, DNA self‐assembly is used to create molecular logic circuits that can selectively identify specific biomolecules in solution by encoding the optical response of near‐field coupled arrangements of chromophores. The resulting circuits can detect label‐free, femtomole quantities of multiple proteins, DNA oligomers, and small fragments of RNA in solution via ensemble optical measurements. This method, which is capable of creating multiple logic‐gate–sensor pairs on a 2 × 80 × 80‐nm DNA grid, is a step toward more sophisticated nanoscale logic circuits capable of interfacing computers with biological processes.