Jan Westerholm

Kinoform Phase Relief Synthesis: A Stochastic Method

We introduce a new method of finding periodic phase relief structures, which produce the desired diffraction pattern with high light efficiency (75% to 96%) and low noise (<±1%). Use is made of explicit equations for the angular spectrum of the field immediately behind such structures and of different stochastic nonlinear optimization methods.

Optimisation and fabrication of grating beamsplitters

Optimisation of certain holographic 1 to N and 1 to N*N beamsplitters (Dammann gratings) with the aid of simulated annealing and damped least-squares algorithms is considered. Structures with N=5 to 53 uniform beams have been calculated. A photolithographic technique for fabrication of these elements is also presented, and its accuracy analysed with the aid of numerical simulations and actual test results.

Stripe-geometry two-dimensional Dammann gratings

Abstract We propose a new 2D generalization of the concept of Dammann grating [H. Dammann and K. Gortler, Optics Comm. 3 (1971) 321] which opens up the possibility of generating 2D patterns of discrete light spots with low reconstruction error and high diffraction efficiency, typically ≈ 30% in arbitrary (off-axis), and ≈ 60% in inversion symmetric (on-axis) patterns. Optimization of such interconnect hologram structures by stochastic algorithms is shown to be feasible for (arbitrary) image sizes up to about 20 X 20 to 30 X 30 on desktop computers. Experimental verification is provided by reconstructing an arbitrary pattern of 20 X 21 spots with a grating fabricated by conventional photolithographic techniques.

Optimization and fabrication of grating beamsplitters in silicon nitride

We report for the first time the generation of optimized space‐invariant fan‐out elements, so‐called Dammann gratings [H. Dammann and K. Gortler, Opt. Commun. 3, 312 (1971)] in plasma silicon nitride. Diffraction efficiencies as high as 65% have been achieved. Using simulated annealing and the greedy algorithm, grating structures with fan‐out as large as 201×201 can readily be calculated. Low absorption and high optical quality together with its ease of structuring make silicon nitride an ideal medium for the construction of phase‐only optical elements.

Multilevel grating array illuminators manufactured by electron-beam lithography

Abstract Two-dimensional multilevel grating array generators with regular M × N fan-out patterns are designed using both nonlinear optimization and an iterative phase retrieval algorithm. Ten-level designs with fan-out of 2×2, 4×4, 1×8, and 8×8, with design efficiencies of 87%, 92%, 95% and 89% are manufactured using direct electron-beam lithography on electron resist. The measured efficiencies, 79%, 84%, 84% and 84% of transmitted light, respectively, are ∼ 10% above the theoretical efficiencies of non-separable binary-phase array illuminators.

FRESNEL DIFFRACTION IN FRACTIONAL TALBOT PLANES : A NEW FORMULATION

We consider field distributions in fractional Talbot planes behind a periodic two-dimensional complex-amplitude transparency that is illuminated by a unit-amplitude plane wave. In the paraxial approximation the field in various fractional Talbot planes is expressed as a sum of contributions from a finite number of points in the plane of the transparency, yielding compact algebraic formulas for the diffracted field. Given the desired intensity distribution in the fractional Talbot plane, we synthesize the transmission function from nonlinear equations. An experimental illustration that uses a binary phase grating is given.

Storage of multiple images in a thin synthetic Fourier hologram

Abstract We show that a single thin multiple-phase Fourier-domain computer-generated hologram can be optimized to reconstruct several separate noise-free spot pattern images when replayed at different angles of incidence. This is achieved since the intensities of the diffraction orders (that form the image pattern) are highly nonlinear functions of the change of scale in the phase delay profile that occurs when the input angle is changed. The diffraction efficiencies can significantly exceed those obtainable with multiple-exposure volume holograms.

Programmable optical interconnections by multilevel synthetic acousto-optic holograms.

Reconfigurable high-fidelity, high-efficiency weighted optical interconnection patterns are demonstrated for the first time to our knowledge with the aid of optimized multilevel phase gratings achieved electronically as phase-modulated sinusoidal refractive-index variations propagating in an acousto-optic Bragg cell.

Computer-Generated Fourier-Transform Holograms For Optical Computing

We compare the performance of different types of periodic phase-only computer-generated Fourier transform holograms (Lohmann and Dammann -type binary holograms and kinoforms) as space-invariant interconnects in digital optical computing. Optical interconnects must exhibit high diffraction efficiency PE and low reconstruction error ΔR. Optimization of the hologram structure by simulated annealing and a greedy algorithm yields (in reconstruction of 2D fully arbitrary interconnection patterns) PE = 25-32% and ΔR 5% for binary holograms, and PE = 70-93% and ΔR < 1% for kinoforms. Hence the kinoform appears to be the optimal type of computer-generated holographic interconnect.

Stepped phase kinoforms

Space-invariant kinoform-type array generators with discrete phase levels high 2D diffraction efficiency 90) and low reconstruction noise are designed using a novel algorithm and their fabrication error tolerances are analyzed. L