Efficient optical elements to generate intensity weighted spot arrays: design and fabrication

Predictive search algorithm for phase holography

We present an algorithm for generating high-quality holograms for computer generated holography: holographic predictive search. This approach is presented as an alternative to traditional holographic search algorithms such as direct search (DS) and simulated annealing (SA). We first introduce the current search-based methods and then introduce an analytical model of the underlying Fourier elements. This is used to make prescient judgments regarding the next iteration of the algorithm. This approach is developed for the case of phase-modulating devices with phase-sensitive reconstructions. When compared to conventional iterative approaches such as DS and SA on a multiphase device, holographic predictive search offered a fivefold improvement in quality as well as up to a 10-fold improvement in convergence time. This comes at the cost of an increased iteration overhead.

Improving holographic search algorithms using sorted pixel selection

Traditional search algorithms for computer hologram generation such as Direct Search and Simulated Annealing offer some of the best hologram qualities at convergence when compared to rival approaches. Their slow generation times and high processing power requirements mean, however, that they see little use in performance critical applications. This paper presents the novel sorted pixel selection (SPS) modification for holographic search algorithms that offers mean square error reductions in the range of 14.7-19.2% for the test images used. SPS operates by substituting a weighted search selection procedure for traditional random pixel selection processes. While small, the improvements seen are observed consistently across a wide range of test cases and require limited overhead for implementation.

easySLM-STED: Stimulated emission depletion microscopy with aberration correction, extended field of view and multiple beam scanning

We demonstrate a simplified set-up for STED microscopy with a straightforward alignment procedure that uses a single spatial light modulator (SLM) with collinear incident excitation and depletion beams to provide phase modulation of the beam profiles and correction of optical aberrations. We show that this approach can be used to extend the field of view for STED microscopy by correcting chromatic aberration that otherwise leads to walk-off between the focused excitation and depletion beams. We further show how this arrangement can be adapted to increase the imaging speed through multibeam excitation and depletion. Fine adjustments to the alignment can be accomplished using the SLM only, conferring the potential for automation.

Highly efficient multicolor multifocus microscopy by optimal design of diffraction binary gratings

Multifocus microscopy (MFM) allows sensitive and fast three-dimensional imaging. It relies on the efficient design of diffraction phase gratings yielding homogeneous intensities in desired diffraction orders. Such performances are however guaranteed only for a specific wavelength. Here, we discuss a novel approach for designing binary phase gratings with dual color properties and improved diffraction efficiency for MFM. We simulate binary diffraction gratings with tunable phase shifts to explore its best diffraction performances. We report the design and fabrication of a binary array generator of 3 × 3 equal-intensity diffraction orders with 74% efficiency, 95% uniformity and dual color capability. The multicolor properties of this new design are highlighted by two-color MFM imaging. Finally, we discuss the basics of extending this approach to a variety of diffraction pattern designs.

Analysis of grating doublets for achromatic beam-splitting

Achromatic beam-splitting grating doublets are designed for both continuous phase and binary phase gratings. By analyzing the sensitivity to lateral shifts between the two grating layers, it is shown that continuous-profile grating doublets are extremely difficult to fabricate. Achromatic grating doublets that have profiles with a constant first spatial derivative are significantly more resistant to lateral shifts between grating layers, where one design case showed a 17 times improvement in performance. Therefore, binary phase, multi-level phase, and blazed grating doublets perform significantly better than continuous phase grating doublets in the presence of a lateral shift between two grating layers. By studying the sensitivity to fabrication errors in the height of both grating layers, one grating layer height can be adjusted to maintain excellent performance over a large wavelength range if the other grating layer is fabricated incorrectly. It is shown in one design case that the performance of an achromatic Dammann grating doublet can be improved by a factor of 215 if the heights of the grating layers are chosen to minimize the performance change in the presence of fabrication errors.

Sensitivity analysis and optimization method for the fabrication of one-dimensional beam-splitting phase gratings

A method to design one-dimensional beam-spitting phase gratings with low sensitivity to fabrication errors is described. The method optimizes the phase function of a grating by minimizing the integrated variance of the energy of each output beam over a range of fabrication errors. Numerical results for three 1x9 beam splitting phase gratings are given. Two optimized gratings with low sensitivity to fabrication errors were compared with a grating designed for optimal efficiency. These three gratings were fabricated using gray-scale photolithography. The standard deviation of the 9 outgoing beam energies in the optimized gratings were 2.3 and 3.4 times lower than the optimal efficiency grating.

Ultracompact beam splitters based on plasmonic nanoslits

An ultracompact plasmonic beam splitter is theoretically and numerically investigated. The splitter consists of a V-shaped nanoslit in metal films. Two groups of nanoscale metallic grooves inside the slit (A) and at the small slit opening (B) are investigated. We show that there are two energy channels guiding light out by the splitter: the optical and the plasmonic channels. Groove A is used to couple incident light into the plasmonic channel. Groove B functions as a plasmonic scatter. We demonstrate that the energy transfer through plasmonic path is dominant in the beam splitter. We find that more than four times the energy is transferred by the plasmonic channel using structures A and B. We show that the plasmonic waves scattered by B can be converted into light waves. These light waves redistribute the transmitted energy through interference with the field transmitted from the nanoslit. Therefore, different beam splitting effects are achieved by simply changing the interference conditions between the scattered waves and the transmitted waves. The impact of the width and height of groove B are also investigated. It is found that the plasmonic scattering of B is changed into light scattering with increase of the width and the height of B. These devices have potential applications in optical sampling, signal processing, and integrated optical circuits.

Grid-free 3D multiple spot generation with an efficient single-plane FFT-based algorithm

Algorithms based on the fast Fourier transform (FFT) for the design of spot-generating computer generated holograms (CGHs) typically only make use of a few sample positions in the propagated field. We have developed a new design method that much better utilizes the information-carrying capacity of the sampled propagated field. In this way design tasks which are difficult to accomplish with conventional FFT-based design methods, such as spot positioning at non-sample positions and/or spot positioning in 3D, are solved as easily as any standard design task using a conventional method. The new design method is based on a projection optimization, similar to that in the commonly used Gerchberg-Saxton algorithm, and the vastly improved design freedom comes at virtually no extra computational cost compared to the conventional design. Several different design tasks were demonstrated experimentally with a liquid crystal spatial light modulator, showing highly accurate creation of the desired field distributions.

Theory of optimal beam splitting by phase gratings. I. One-dimensional gratings

We give an analytical basis for the theory of optimal beam splitting by one-dimensional gratings. In particular, we use methods from the calculus of variations to derive analytical expressions for the optimal phase function.

Aberration correction in an adaptive free-space optical interconnect with an error diffusion algorithm

Aberration correction within a free-space optical interconnect based on a spatial light modulator for beam steering and holographic wavefront correction is presented. The wavefront sensing technique is based on an extension of a modal wavefront sensor described by Neil et al. [J. Opt. Soc. Am. A 17, 1098 (2000)], which uses a diffractive element. In this analysis such a wavefront sensor is adapted with an error diffusion algorithm that yields a low reconstruction error and fast reconfigurability. Improvement of the beam propagation quality (Strehl ratio) for different channels across the input plane is achieved. However, due to the space invariancy of the system, a trade-off among the beam propagation quality for channels is obtained. Experimental results are presented and discussed.

Arbitrary structuring of two-dimensional photonic crystals by use of phase-only Fourier gratings

The computer-generated holography technique is applied to the structuring of two-dimensional (2D) photonic crystals with inherently embedded arbitrary defects. The technique uses phase-only Fourier gratings as a generator of spot arrays in the focal plane, such that a single exposure produces a 2D array of focused spots with desired defects or modifications in the lattice structure. We demonstrate several types of large-area 2D lattice structures with square, hexagonal, or hybrid lattices embedded with point and (or) line defects. Scanning the Fourier plane in the depth direction throughout multiphoton polymerization media allows 3D lattices with stacked defect layers to be formed.

High-speed holographic optical tweezers using a ferroelectric liquid crystal microdisplay

We demonstrate the advantages of a ferroelectric liquid crystal spatial light modulator for optical tweezer array applications. The fast switching speeds of the ferroelectric device (compared to conventional nematic systems) is shown to enable very rapid reconfiguration of trap geometries, controlled, high speed particle movement, and tweezer array multiplexing.

Local improvement of the signal-to-noise ratio for diffractive optical elements designed by unidirectional optimization methods

We present a straightforward method to design multilevel phase-only diffractive optical elements with a locally improved signal-to-noise ratio in the reconstruction. The method is generally applicable to all unidirectional design schemes, such as direct search, simulated annealing, or genetic optimization. As the shape and the location of the desired low noise areas are supplied by a bit map file the method allows for the design of basically any two-dimensional low noise area. The improvement in the signal-to-noise ratio that may be achieved is considerable but also entails reduced diffraction efficiency. The suggested method is applied to different beam-splitter design examples. All examples are calculated with the scalar diffraction approximation in the far field.

High-diffraction-efficiency pseudorandom encoding

Pseudorandom encoding (PRE) is a statistics-based procedure in which a pure-phase spatial light modulator (SLM) can yield, on the average, the prescribed diffraction pattern specified by the user. We seek to combine PRE with the optimization of an aperture-based target function. The target function is a fully complex input transmittance, unrealizable by a phase-only SLM, that generates a prescribed light intensity. The optimization is done to increase the diffraction efficiency of the overall process. We compare three optimization methods-Monte Carlo simulation, a genetic algorithm, and a gradient search-for maximizing the diffraction efficiency of a spot-array generator. Calculated solutions are then encoded by PRE, and the resulting diffraction patterns are computer simulated. Details on the complexity of each procedure are furnished, as well as comparisons on the quality, such as uniformity of the output spot array.

Modified minimum-distance criterion for blended random and nonrandom encoding

Two pixel-oriented methods for designing Fourier transform holograms--pseudorandom encoding and minimum-distance encoding-usually produce higher-fidelity reconstructions when combined than those produced by each method individually. In previous studies minimum-distance encoding was defined as the mapping from the desired complex value to the closest value produced by the modulator. This method is compared with a new minimum-distance criterion in which the desired complex value is mapped to the closest value that can be realized by pseudorandom encoding. Simulations and experimental measurements using quantized phase and amplitude modulators show that the modified approach to blended encoding produces more faithful reconstructions than those of the previous method.

Two-deformable-mirror concept for correcting scintillation effects in laser beam projection through the turbulent atmosphere

A two-deformable-mirror concept for correcting scintillation effects in laser beam projection through the turbulent atmosphere is presented. This system uses a deformable mirror and a Fourier-transforming mirror to adjust the amplitude of the wave front in the telescope pupil, similar to kinoforms used in laser beam shaping. A second deformable mirror is used to correct the phase of the wave front before it leaves the aperture. The phase applied to the deformable mirror used for controlling the beam amplitude is obtained with a technique based on the Fienup phase-retrieval algorithm. Simulations of propagation through a single turbulent layer sufficiently distant from the beacon observation and laser beam transmission aperture to cause scintillation shows that, for an ideal deformable-mirror system, this field-conjugation approach improves the on-axis field amplitude by a factor of approximately 1.4 to 1.5 compared with a conventional phase-only correction system.

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.

Design, implementation, and characterization of an optical power supply spot-array generator for a four-stage free-space optical backplane

The design and implementation of a robust, scalable, and modular optical power supply spot-array generator for a modulator-based free-space optical backplane demonstrator is presented. Four arrays of 8 x 4 spots with 6.47-mum radii (at 1/e(2) points) pitched at 125 mum in the vertical direction and 250 mum in the horizontal were required to provide the light for the optical interconnect. Tight system tolerances demanded careful optical design, robust optomechanics, and effective alignment techniques. Issues such as spot-array generation, polarization, power efficiency, and power uniformity are discussed. Characterization results are presented.

Integrated waveguide diffractive doublet for guided-wave manipulation

An integrated waveguide diffractive doublet consisting of a uniform grating coupler and a diffractive optical element is proposed. Design of this waveguide diffractive doublet for guided-wave manipulation is described in detail. Experimental results for a fabricated waveguide diffractive doublet are also presented to demonstrate the device principles. It was found that this waveguide diffractive doublet can enhance device functionality while remaining simple and compact and having a planar structure. Furthermore, this device can be fabricated by use of all-optical lithography.

Design and characterization of a microchannel optical interconnect for optical backplanes

The design, modeling, and experimental characterization of a microchannel-based free-space optical interconnect is described. The microchannel interconnect was used to implement a representative portion of an optical backplane that was based on field-effect transistor, self-electro-optic device smart-pixel transceivers. Telecentric relays were used to form the optical interconnect, and two modes based on two different optical window clusterings were implemented. The optical system design, including the optical geometry for different degrees of clustering of windows supported by a lenslet relay and the image mapping associated with a free-space optical system, is described. A comparison of the optical beam properties at the device planes, including the spot size and power uniformity of the spot array, as well as the effects of clipping and misalignment for the different operating modes, is presented. In addition, the effects of beam clipping and misalignment for the different operating modes is presented. We show that microchannel free-space optical interconnects based on a window-clustering scheme significantly increase the connection density. A connection density of 2222 connections/cm(2) was achieved for this prototype system with 2 x 2 window clustering.

Self-adjusting dynamic binary phase holograms

An optical system constructed around a dynamic diffractive optic element, a ferroelectric liquid-crystal spatial light modulator in binary phase-only modulation mode, is investigated. The spatial light modulator is successively adjusted according to the direct binary search technique to diffract an incoming laser light beam into a predecided intensity distribution by use of feed back from the diffracted light. It was found that the feedback signal was noisy and that vibrations and limited bistability in the spatial light modulator's pixels were the main noise sources. The final diffraction efficiency depends on the degree of noise in the feedback signal, but even under fairly noisy conditions the iterations were found to converge properly.

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.

Performance of an optoelectronic neural network in the presence of noise

Optoelectronic neural networks must not only be highly parallel but also fast to compete with electrical systems. Receiver noise becomes an important consideration at high data rates; so the limits set by noise to network size and speed are analyzed. A network incorporating an array of high-speed multi-quantum-well modulators was constructed. It employed a general method for optical representation of bipolar values, which required only a minimal increase in network dimensions and gave the network immunity to common-mode parameter variations. Different ways of partitioning pattern-recognition problems were compared, and the accuracy of one configuration was tested with the experimental network over a range of noise levels.

Very-large-scale-integration fabrication technique for binary-phase gratings on sapphire

An efficient, high-yield process for the production of binary-phase holograms is presented by controlled deposition of silicon nitride over a sapphire substrate with the binary structure formed by plasma etch of the silicon nitride. Optical results are presented for a 16 × 16 transmission fanout element that shows near-optimal performance.

Approximating fully complex spatial modulation with pseudorandom phase-only modulation

Any desired diffraction pattern can be produced in the Fourier plane by the specification of a corresponding input-plane transparency. Complex-valued transmittance is generally required, but in practice phase-only transmittance is used. Many design procedures use numerically intensive, constrained optimization. We instead introduce a noniterative procedure that directly translates the desired but unavailable complex transparency into an appropriate phase transparency. At each pixel the value of phase is pseudorandomly selected from a random distribution whose standard deviation is specified by the desired amplitude. We also derive statistical expressions and use them to evaluate the approximation errors between the desired and achieved diffraction patterns.

Scale-invariant binary phase-only matched filter using a ferroelectric-liquid-crystal spatial light modulator

We describe the implementation of a scale-invariant binary phase-only matched filter using a 128 × 128 ferroelectric spatial light modulator. A 5-dB discrimination was obtained between a 10-image training set of highly correlated characters (E's and F's) over a scale range of 1.0 to 1.5.

Handling of quasi-Gaussian beams by phase plates: far-field simulation

Effects of phase plates on focused laser beams are studied numerically. Gaussian beams are simulated when they pass through several kinds of phase device (random phase plates, phase gratings, etc.). Partially coherent and aberrated beams are also considered. Their control by phase devices is analyzed. In particular this work is devoted either to reducing the intensity transverse modulations on the spot region, which are able to excite filamentation instability in plasmas, or to producing such modulations in a controllable way in order to investigate filamentation accurately.

Dynamic holographic interconnects that use ferroelectric liquid-crystal spatial light modulators

<p>Dynamic interconnect holograms are designed by the use of a simulated annealing algorithm and written to a 128 × 128 pixel ferroelectric spatial light modulator that is used in a binary-phase mode. Dynamic holograms are used to implement a 2 × 2 crossbar with single-mode fiber inputs and outputs, which function with as high as 27 dB of isolation between output ports. The principle is extended to two-dimensional interconnection holograms, and arbitrary fan-out to as high as 64 points is demonstrated with good performance.</p><p>Images of interconnection holograms are transferred from the spatial light modulator to an optically addressed spatial light modulator that is used in a binary-phase mode. The addition of a fixed array generator computer-generated hologram permits replication of the hologram image, thus creating a larger hologram with a high space-bandwidth product on the optically addressed spatial light modulator.</p><p>Results of a preliminary experiment are presented.</p>

Design of an optoelectronic cellular processing system with a reconfigurable holographic interconnect

The design of an optoelectronic parallel processing system is presented. In this system a reconfigurable computer-generated hologram is used to perform a shift-invariant optical interconnection operation. Scalability issues are investigated, and simple cellular processing operations are experimentally demonstrated.