Thick Holograms Research Articles

Use of dynamic theory to describe experimental results from volume holography

The general applicability of dynamic theory to the description of the recording and readout characteristics of volume (thick) hologram gratings is indicated. In dynamic theory (as opposed to static theory), the volume nature of the thick holographic grating allows the interference of an incident light beam with its own diffracted beam inside the recording medium. This effect causes the continuous recording of another grating that alters the initial one, producing a resultant grating that is not uniform through the thickness of the recording material and a grating whose writing and reading characteristics may vary dramatically depending on the recording material and the experimental conditions. A large number of diverse types of writing, reading, and angular selectivity behavior have been reported in the published literature. The dynamic theory of thick hologram writing and reading is shown to predict qualitatively all of these various types of experimental behavior.

Modulation transfer function of phase holograms

The frequency characteristics were determined for the diffraction of light by a phase hologram with a sinusoidal distribution of the refractive index. For the range intermediate between the Raman-Nath (thin holograms) and Bragg (thick holograms) diffraction mechanisms the characteristics were calculated on a computer and plotted as the frequency dependences of the intensity of light in the first positive, zeroth, and first negative orders for different modulation depths. These graphs could be used conveniently to determine the parameters of holograms needed to ensure a specified diffraction efficiency and uniformity of the modulation transfer function.

Theory of diffraction of guided optical waves by thick holograms

A theory is developed which describes the diffraction of guided optical beams into the same or other modes of the waveguide structure. Expressions are derived for the coupling constants connecting the incident and diffracted beams. Numerical calculations on a hypothetical waveguide structure indicate that, for holograms written at the intersection of two guided beams, the effects of modal dispersion are weak as long as neither the incident nor the diffracted modes are near cutoff. In the converse case, where one of these beams is near cutoff, strong effects of modal dispersion appear.

Volume holograms in photochromic materials

Theoretical expressions are derived describing the process of writing volume (or thick) hologram gratings in photochromic materials. The theory includes the effects of the saturation of the material response, scattering of the writing beams by the partially written hologram, and the refractive index changes that accompany the photoinduced absorption changes. Results of representative numerical calculations are presented and interpreted in terms of simpler models and approximations. Use of the results is illustrated by the calculation of the holographic characteristics of an actual material. The results are also related to model photochromic systems to estimate the range of achievable holographic characteristics and to obtain an approximate procedure to estimate the absorption spectra of materials that would give specified holographic characteristics.

Explanation of the diffraction fine-structure in overexposed thick holograms

The far-field diffraction patterns of overexposed thick holographic gratings often contain circular or arcuate structures. The geometrical properties of these patterns were explained earlier. This letter explains the fine-structure of the rings using an extension of the kinematical theory of X-ray diffraction.

On the theory of diffraction by holographic gratings

The well-known results given by the theory of coupled waves for the diffraction of light by volume holograms are shown to go over into Born’s first approximation in the case of low diffraction efficiency. They are, therefore, valid over the whole range of thick and thin holograms with and without Bragg incidence.

Diffraction efficiency of thick holograms in coloured sodium-chloride crystals

Diffraction efficiency of thick holograms in coloured sodium-chloride crystals

Diffraction of a narrow laser beam by a thick hologram: Experimental results

Results are reported on an optical effect observed with a thick, two-beam holographic transmission grating. Illumination of the grating with a narrow laser beam (beam waist much smaller than grating thickness) results in the emergence of four diffracted beams at the rear surface of the hologram. The results are in qualitative agreement with the theory of Chu and represent an optical analogue of an X-ray diffraction effect predicted by Kato and observed by Authier.

Unique Properties of SBN and Their Use in a Layered Optical Memory

Holographic storage experiments using crystal Sr(0.75)Ba(0.25)Nb(2)O(6) (SBN 75/25) as a volume-phase holographic medium show that this material is the most sensitive crystalline storage medium yet discovered. An exposure level of 0.003 J/cm(2) at 0.488 microm produces a 1% diffraction efficiency in a 5-mm length of crystal. In addition to high recording sensitivity, SBN 75-25 exhibits interesting electric-field induced effects that include electric-field enhanced recording sensitivity and voltage-switchable latent-to-active holographic reconstruction efficiency. These effects are explained in terms of drift and diffusion of photoionized carriers coupled with the nonlinear electrooptic behavior characteristic of this low Curie temperature ferroelectric crystal. Detailed measurements of the holographic recording and reconstruction properties of thick phase-volume holograms stored in SBN 75/25 are reported. A mechanism is proposed that correlates the observed electrically controlled holographic response with the dielectric behavior of the crystal. These interesting effects are used to implement a novel, layered optical memory having no moving parts and having electrical access for writing or reading selected layers. An experimental model of the layered memory was constructed to demonstrate the interrelation of the several phenomena involved in the layered concept.

Thick holograms: a survey

Many workers are turning away from holograms made with thin photographic emulsions and are investigating ‘thick’ holograms, with their exciting potential of high diffraction efficiency, increased information storage capacity, reduced noise, and increased spectral or angular discrimination. This article discusses the principles of thick hologram theory, and describes some of the materials which can be used as thick recording media. Advantages and limitations of thick holograms are illustrated by experimental examples. The article concludes with a survey of the existing and future applications for thick holograms.

Thick phase holograms in colour centre materials

Thick holograms have been recorded in single crystals of KCl and NaF containing colour centres introduced by electron irradiation. Diffraction efficiencies up to 4.2% are reported and near an absorption band there is a characteristic ‘M’ shaped variation of efficiency with wavelength. These observations show that there is a strong phase contribution to the diffraction efficiency and a simple model is used to describe the properties of such mixed holograms.

The Imaging Properties and Aberrations of Thick Transmission Holograms

Expressions are derived for the amplitude and phase variations across the reconstructed wavefront of a thick transmission hologram. The expressions can be used to describe the field variations in the region of the Gaussian image point or, alternatively. to describe the wavefront as it emerges from the hologram surface. Comparison with the ideal, Gaussian ‘reference’ sphere centred on the image point allows a pupil function to be defined. This differs from the pupil function of lens aberration theory in that it possesses spatial amplitude variations, as well as phase variations. Some predictions of the theory are illustrated by graphical examples. Experimental results are given.

Explanation of the “Venetian blind” effect in holography, using the Ewald sphere concept

The Ewald sphere construction of X-ray diffraction theory is used to describe the “Venetian blind” effect which occurs in holography when changes in geometry occur between hologram formation and image reconstruction. The limitations on information storage in thick holograms, due to the existence of the effect, are pointed out. Experimental results are given.

Calculation of diffraction efficiency in hologram gratings attenuated along the direction perpendicular to the grating vector

A thick hologram grating with modulation that decreases along the direction perpendicular to the grating vector has been analyzed using coupled-wave theory developed by Kogelnik. General solutions of two predominant waves, undiffracted and first-order diffracted waves, are given for transmission and reflection types of hologram gratings. Calculated efficiency of diffraction for some special cases is compared with that for the uniform grating. The influence of the attenuation of grating modulation upon the validity of the theory when applied to the Bragg reflection is also discussed.

Thick holograms by KBr single crystrals containing colour centres

A helium-neon laser has been used to record holograms in KBr single crystals containing colour centres introduced by electron irradiation. Holograms recorded in crystals with coloured layers between 6 and 500 μm thick have diffraction efficiencies up to 2.3% and show marked orientation sensitivity.

Volume holograms in photographic emulsions of extended thickness

Methods for recording true volume holograms in photographic silver halide emulsions have been developed. The layers are swollen in an immersion of water or organic solvents to about the sevenfold of their dry thickness. After exposure and processing, the extended thickness is stabilized by forming a hardened polymer in or on the swollen layer. These thick holograms in the highly sensitive silver halide layers are needed where exposure restrictions disqualified other thick recording materials as in holography of biological objects and in holographic high-speed cinematography.

Multiple storage of thick phase holograms in LiNbO3

Multiple storage of thick phase holograms in LiNbO₃

Effect of Emulsion Thickness on the Diffraction Efficiency of Amplitude Holograms

The diffraction efficiency of amplitude holograms recorded on photographic emulsions is shown to be independent of the thickness of the emulsion layer. This can be explained theoretically under the assumption that the exposure modulation is not too high, i.e., for high and moderate beam ratios K. With this assumption it is possible to demonstrate the equivalence of Kogelnik’s equation using a coupled-wave theory for thick holograms and the equations derived by Kaspar and Lamberts for thin holograms. This is true even though the former contains an explicit dependence on thickness and the latter equation includes only the MTF of the emulsion and the slope of the amplitude-transmittance log-exposure characteristic of the emulsion. This conclusion is demonstrated experimentally by measuring the diffraction efficiency for two series of very-fine-grain emulsions, which differ only in the thickness of the emulsion layer.

Compensation of Aberrations due to a Wavelength Shift in Holography

A shift in wavelength between the recording and reconstruction beams of a hologram introduces aberrations in the image wavefront and decreases the diffraction efficiency. The holograms investigated in this paper are recorded on dichromate gelatin film with either plane waves or point sources and are designed to image to a point source when illuminated with a plane wave. A computer program is employed to calculate the aberrations present in the image wavefront and to determine an optimized recording geometry necessary for minimum aberrations. It is shown that the computer program, which was designed for surface-type holograms, has some application in thick transmission-type phase holograms. The experimental results are in close agreement with the computed results indicating that compensation for the wavelength shift may be obtained by using a computer program to calculate the proper recording geometry.

On the diffraction efficiency of transmittance storage holograms

In the present paper the total diffraction efficiency of single exposure holograms, multiple exposure holograms, and thick holograms formed by multiplexing is evaluated via a space-dependent contrast function. Diffuse objects and arrays of equipspaced coherent radiators are considered, and diagrams of the results are presented.