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.     

Analysis of phase sensitivity for binary computer-generated holograms

A binary diffraction model is introduced to study the sensitivity of the wavefront phase of binary computer-generated holograms on groove depth and duty-cycle variations. Analytical solutions to diffraction efficiency, diffracted wavefront phase functions, and wavefront sensitivity functions are derived. The derivation of these relationships is obtained by using the Fourier method. Results from experimental data confirm the analysis. Several phase anomalies were discovered, and a simple graphical model of the complex fields is applied to explain these phenomena.     

Effect of spurious diffraction orders in arbitrary multifoci patterns produced via phase-only holograms

We analyze the effect of spurious diffraction orders when generating functional multifoci patterns produced by illuminating a phase-only hologram with a single Gaussian beam. Using a practical device for encoding a hologram generates an undesirable zero order and high-diffraction orders at the Fourier plane. This translates to the fact that a significant fraction of the incident light does not necessarily convert to functional multifoci patterns. In most applications, the zero order can be avoided by generating foci patterns shifted off the optical axis, which further increases the amount of light distributed to spurious high-diffraction orders owing to the reduction of light directed to the desired foci pattern. We analyze the amount of light dispersed to spurious orders and show that these unwanted orders can be a major limiting factor for most applications based on arbitrary multifoci patterns.     

Analysis of the disturbing diffraction orders of computer-generated holograms used for testing optical aspherics

Aspheric surfaces are increasingly used in the design of high-quality optical imaging systems. Therefore accurate testing methods for aspherics are also necessary. One possibility is to use a computer-generated hologram (CGH) as a part of a null lens in an interferometric testing device. However, CGHs normally have more than one diffraction order, thus causing disturbing areas in the interferogram. Here a simple approximative analytical expression is given for the spatial frequencies of the disturbing light in the interferogram coming from the different diffraction orders of the CGH. This expression also enables one to calculate the size and the shape of the disturbing areas in the interferogram. Some design examples for CGHs are given in an application of the expression.     

Copying low spatial frequency diffraction gratings in photopolymer as phase holograms

Abstract

Photopolymers are studied as holographic recording materials for recording computer-generated phase holograms. The recording was performed using a holographic copying process, in which the master is produced by means of a high resolution graphic device. To our knowledge it is the first time a photopolymer has been used to obtain copies with this technique. As it does not work in real time, it is possible to store the diffractive optical element for a long time because the dye is finished during exposition and no wet processing is needed after exposition. The photopolymer used in these experiments was composed of acrylamide and triethanolamine as the co-initiator, photo-initiated with a dye, yellow eoxine. Components were supported by a film of poly-(vinylalcohol) (PVA). The resulting thickness of the film was 70 & plusmn; 5 μm, symmetrical and asymmetrical diffraction gratings were obtained as phase holograms by index and thickness modulation, monitored with an electron microscope, and the low spatial frequency response of the photopolymer was studied. Diffraction efficiency achieved for copied gratings was about 30%. With this study we get a complete characterization of the photopolymer for the full range of the typical spatial frequencies that can be recorded with the high resolution graphic device used.     

Real-time binary phase holograms on a reflective ferroelectric liquid-crystal spatial light modulator

A ferroelectric liquid-crystal spatial light modulator with an active silicon backplane is used to implement reconfigurable reflective phase holograms. Optical results are presented for an optimized computergenerated Fourier hologram.     

Suppression of higher diffraction orders in the extreme ultraviolet with a trapezoidal nano-mirror array

ABSTRACT

Higher diffraction orders from a grating introduce harmonic contamination in ‘monochromatic’ output beams processed by grating monochromators at synchrotron radiation facilities, resulting in imprecise calibration of optical elements and detectors. Suppressing these orders can be achieved with a quasi-random nano-hole array, but its fabrication can be a significant limiting factor for implementation. Here, an advanced type of grating is demonstrated that contains a periodic array of several hundred million trapezoidal nano-mirrors with a grazing-incidence reflection geometry that suppresses higher diffraction orders. Moreover, it reduces the difficulty of fabrication to the level of a traditional grating. It has great potential for harmonic suppression in synchrotron radiation, spectral diagnostics of plasmas, and astrophysics.     

Infrared metamaterial phase holograms

As a result of advances in nanotechnology and the burgeoning capabilities for fabricating materials with controlled nanoscale geometries, the traditional notion of what constitutes an optical device continues to evolve. The fusion of maturing low-cost lithographic techniques with newer optical design strategies has enabled the introduction of artificially structured metamaterials in place of conventional materials for improving optical components as well as realizing new optical functionality. Here we demonstrate multilayer, lithographically patterned, subwavelength, metal elements, whose distribution forms a computer-generated phase hologram in the infrared region (10.6 μm). Metal inclusions exhibit extremely large scattering and can be implemented in metamaterials that exhibit a wide range of effective medium response, including anomalously large or negative refractive index; optical magnetism; and controlled anisotropy. This large palette of metamaterial responses can be leveraged to achieve greater control over the propagation of light, leading to more compact, efficient and versatile optical components.     

Study of the pH dependence of diffraction efficiency of phase holograms in dye sensitized dichromated gelatin

Dichromated gelatin is thought to be a good substitute for photographic emulsions in some uses. The results of a systematic study of the effect of the pH of the developer on the diffraction efficiency of volume holographic gratings recorded in dye sensitized dichromated gelatin are presented.     

Modifications of detour phase computer-generated holograms

The detour phase method for the design of computer-generated holograms can be modified to achieve multichannel reconstruction along various diffraction orders. It is shown how a single hologram can be used to display two patterns of different intensities along two diffraction orders. This is achieved by the release of any requirement on the phase distributions of these patterns, thus leaving them as free parameters. Various algorithms are suggested to make possible nonidentical reconstructions along two different off-axis diffraction orders. The two reconstruction orders can be chosen arbitrarily. The case of four-channel reconstructions for generating four different images is discussed as well. Computer simulations and optical experiments were carried out to demonstrate the capabilities of the proposed approaches.     

Off-Bragg analysis of the diffraction efficiency of transmission photorefractive holograms

Formulas for calculating the diffraction efficiency of gratings recorded in a photorefractive medium are given. The analysis uses coupled-wave theory for photorefractive hologram gratings and takes into account the photorefractive phase shift and fringe-bending effect. General solutions for diffracted (signal) and undiffracted (reference) waves are derived in a closed-form expression. By use of the derived formulas the diffraction efficiency for angle mismatch from the Bragg condition can easily be evaluated as compared with numerical-analysis methods. The diffraction efficiency is also quantified in terms of medium parameters and recording and reconstruction conditions.     

Off-Bragg analysis of the diffraction efficiency of reflection photorefractive holograms

Formulas are given for the calculation of diffraction efficiency of reflection-type gratings recorded in a photorefractive medium. The analysis incorporates the coupled-wave theory that was developed for photorefractive hologram gratings. This analysis takes into account grating slant with respect to the medium surface, light absorption during reconstruction, any incident angle of the reference beam, and any photorefractive phase shift. General solutions for signal and reference wave functions are given in a closed-form expression by use of a hypergeometric function. The optimum media parameters and recording conditions for high diffraction efficiency are obtained by the derived formulas. The diffraction properties for off-Bragg conditions are also discussed.     

Comparison of diffraction efficiencies for single-exposure and unity-contrast multiple-exposure holograms

The diffraction efficiency for a single-exposure holographic recording is compared with that of a multiple-exposure hologram recorded with maximum signal-to-bias ratio. For the multiple-exposure recording the object is illuminated point by point, and the reference wave amplitude for each subexposure is adjusted to produce a unity-contrast interferogram in the holographic recording plane. It is shown that, for the same M-point object and the same average exposure, the ratio of the single-exposure diffraction efficiency to the mulitple-exposure diffraction efficiency is proportional to M/R, where R is the reference-to-object beam ratio in the single-exposure case. This result is compared with that obtained in the multiple-exposure case when the reference wave amplitude assumes a constant value. Application areas include optical interconnects, holographic data storage, and volumetric multiplexed holograms for display.     

Design of binary diffraction gratings of liquid crystals in a linearly graded phase model

We report on a linearly graded phase model for the design of binary diffraction gratings of liquid crystals (LCs) associated with the periodic interfacial effect. The binary nature of the LC grating is produced by use of periodic striped domains in an alternating homeotropic and hybrid geometry. In our graded phase model the diffraction patterns and the diffracted intensities of the LC binary grating is primarily governed by three length scales: the cell thickness and two distortion parameters scaled by the grating period at two domain boundaries. The experimental data agree well with theoretical predictions made in our linearly graded phase model as well as the elastic continuum theory.     

Duplication of phase key for random-phase-encrypted volume holograms

Holographic memory encrypted by an optical random-phase key and decrypted by either the original phase key or a duplicate key is proposed and demonstrated. The duplicate key is made by recording the encryption wave front with angle multiplexing during writing of the hologram. The amount of three-dimensional shifting that is tolerable in the duplicate key is analyzed.     

Light wave diffraction on reflection holograms in a cubic piezoelectric crystal

Analytical expressions for the electric field strength in a signal wave formed during the interaction of opposite waves in a cubic photorefractive piezoelectric crystal are obtained in the given grating approximation. As a result of the optical activity of the medium, the amplification coefficient and the diffraction efficiency of a hologram in the \(\left( {\bar 1\bar 1\bar 1} \right)\) cut crystals may exceed the analogous values for the \(\left( {00\bar 1} \right)\) cut crystals.     

Nonlinear effects of phase blurring on Fourier transform holograms

Liquid-crystal light valves can have intensity-dependent resolution. We find for a nematic liquid-crystal light valve that this effect is well modeled as a phase that has been blurred by a linear space-invariant filter. The phase point-spread function is measured and is used in simulations to demonstrate that it introduces intermodulation products to the diffraction patterns of computer-generated Fourier transform holograms. Also, the influence of phase blurring on a pseudorandom-encoding algorithm is evaluated in closed form. This analysis applied to a spot array generator design indicates that nonlinear effects are negligible only if the diameter of the point-spread function is a small fraction of the pixel spacing.     

X-ray diffraction patterns from nanocrystalline binary alloys

X-ray diffraction powder patterns of a random nanocrystalline material containing two atomic species were calculated by evaluation of the Debye function. Atoms of different types were positioned to produce stoichiometric compound, CsCl, and grain boundary segregation in copper-iron alloys. Radial strain fields of the type associated with point or boundary defects were introduced into the structure and the x-ray powder patterns were calculated. Grain boundary defects of different composition than the bulk were introduced and combined with radial strain fields. The diffraction signatures of the “gas-like” and crystalline grain boundaries are calculated and compared.