We present new experimental and fitting methods that describe Bragg selectivity of distorted holograms in soft photopolymers. These are used to study the mechanical response of holograms that shrink when exposed. An inelastic response is identified which can be exploited to reduce fringe distortion even in the presence of shrinkage.
The Bragg selectivity of a volume hologram is a crucial characterization metric, but distorted Bragg selectivity curves obtained from holograms in soft media cannot be evaluated by existing analysis techniques. We demonstrate that distorted Bragg curves arise from mechanical strain within the polymer network, causing non-uniform distortion of the grating fringe spacing. We then present a method for obtaining spatially resolved Bragg selectivity curves and for evaluating the local and global hologram fidelity.
The Bragg selectivity of holograms recorded in polymers often fits poorly to theory derived for perfectly rigid hosts. We present closed-form and numerical solutions of the coupled-mode equations for distorted holograms in soft hosts. Fits extract index contrast, thickness and distortion from Bragg selectivity that strongly deviates from existing theory.
The current surge of interest in holographic photopolymers is motivated by display applications that often call for holograms in reflection geometry. However, the geometry of reflection holograms is uniquely sensitive to problems that arise from non-instantaneous recording, including volume shrinkage and off-target index development during exposure. Here we leverage a high-powered recording laser to compare holograms of varying writing power and exposure time pairings (with a consistent exposure intensity), showing improved hologram quality with shorter (higher-powered) exposures. Shorter, higher-powered reflection hologram exposures result in lower haze and higher diffraction efficiency.
The geometry of refraction and interference of two plane laser beams into a flat recording package is sufficiently simple that analytic expressions can be derived for the beam and sample angles to write a given transmission or reflection hologram. The accessible range of grating vectors is constrained only by the coherent transfer function determined from the cut-off angle of writing ray vectors. To reach a larger portion of the grating space, as is typically required for materials testing and applications such as augmented reality waveguide couplers, one must add prisms to one or both sides of the sample. The constraints on possible grating vectors in this case are a complex interplay of the cut-off angle, the clear aperture of the prism faces, hologram position in the sample, and the limits of the motion system that positions the recording medium and writing beams. Further, the number of possible writing geometries jumps from two in the planar case (that is, reflection and transmission) to the square of the number of entry facets or 16 in the case of triangular prisms on both sides of the sample. Determining the best prism, writing beam, and stage configuration to write a required set of gratings at a multiplicity of locations in the sample thus becomes analytically intractable.
We present a graphical method of solving this inverse problem. The foundation is a highly parallel, non-sequential ray tracer that solves for all possible holographic gratings given a specific sample geometry consisting of a film, substrates, and triangular prisms on one or both sides. The tool graphically presents the allowable grating vectors as a function of writing beams entering surfaces in all possible combinations, hologram position in the sample, and motion control such as writing beam and sample rotation and translation. Constraint regions due to the cut-off angle, surface clear apertures, and stage motion are illustrated to guide design modifications that would reach different regions of grating space. Finally, we show how this supports writing into curved films.
The transition from exploring holographic photopolymer dynamics to designing a holographic display presents several challenges, including the need to create phase-matched holograms over large areas using high-intensity exposure conditions. High-intensity recording conditions result in low haze and highly diffraction efficient holograms, but such exposures are typically limited to a relatively low writing area. Here we demonstrate a method by which a high-intensity writing beam is rastered across a large region of holographic material in a manner which locks the phase of the hologram grating vector across the entirety of the exposed region.
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