Diffractive optical elements (DOEs) assimilate optical functionality within thin (≤100 μm), lightweight films. With the recent advent of high dynamic range two-stage photopolymers, gradient-index volume DOEs can now achieve diffraction efficiencies competitive with conventional surface-relief DOEs, while also offering the advantages of contact-free, selfprocessing optical recording into a flat film that can be laminated between protective sheets. Here we design and fabricate Fresnel lenses with what we believe to be the highest reported diffraction efficiencies achieved to date using this gradientindex DOE approach. Our analysis demonstrates that these high diffraction efficiencies are crucially enabled by the high index modulation of the photopolymer, Δn < 0.01. Another factor enabling high diffraction efficiency is the pixel count of the recording exposure. Thus, we use a photolithographic chrome mask with 9000 × 9000 pixels of 2.5 μm diameter, significantly exceeding the pixel count available from spatial light modulators. The mask is imaged onto photopolymer films of 50 μm thickness, and Fresnel patterns of up to 23 mm diameter are recorded in one-shot exposures. The resulting lenses range from f/44 – f/79 with diffraction efficiencies up to 83%. The performance of various lens designs is validated by an analysis showing that, for a given Δn, there is a fundamental trade-off between low f/# and high diffraction efficiency. This high performance represents an important step toward practical applications, ranging through solar energy concentrators, customized vision optics, integrated photonics, heads-up displays, and hybrid lenses.
Two-stage holographic photopolymers capable of high refractive index modulation (Δn) on the order of 10<sup>–2</sup> enable the fabrication of a myriad of optical elements. While there are commercial products available that meet these requirements, researchers often want the flexibility to customize both the form factor of the samples as well as the mechanical and chemical properties for their specific applications. We present a novel high refractive index acrylate writing monomer in a low refractive index urethane matrix as a model material for customization for optical applications. We discuss the achievable Δn of this custom monomer, 1,3-bis(phenylthio)-2-propyl acrylate (BPTPA) in the urethane matrix as a function of solubility, along with a comparison to a commercially available high refractive index monomer, 2,4,6- tribromophenyl acrylate. Formulations with BPTPA exhibit a peak-to-mean Δn ≈ 0.029 in transmission holograms without any obvious deficiencies in transparency, color, or scatter. This writing monomer and the synthetic processes present a promising platform for the fabrication of high-performance holographic photopolymers for a wide range of research applications.
We show the design and fabrication of high diffraction efficiency, optically recorded gradient-index Fresnel lenses in a two-stage photopolymer. A design analysis reveals that lens <i>f</i>/# is limited by the material refractive index contrast, motivating use of recent high contrast polymers. The number of pixels required for the optical exposure is typically well beyond available spatial light modulator resolutions, motivating the use of a photolithographic mask. Thus, we present a photolithographic technique by which a single exposure into a self-developing photopolymer can directly print single custom high efficiency DOEs with freeform phase profiles, in contrast to holographic optical elements that are limited to the interference of two propagating fields. We use a dithered binary chrome mask with 9000 x 9000 pixels of 2.5 μm diameter to write lenses up to 23 mm in diameter. Lenses down to <i>f</i>/44 with 76% diffraction efficiency and <i>f</i>/79 with 83% diffraction efficiency are demonstrated.
Holographic photopolymers capable of high refractive index modulations (Δn) on the order of 10<sup>-2</sup> are integral for the fabrication of functional holographic optical elements (HOEs) for use in a range of optical applications. A novel high refractive index liquid writing monomer suitable for two-stage photopolymer systems was designed and synthesized. This monomer exhibits facile synthetic procedure, low viscosity, high refractive index as well as excellent solubility in a low refractive index urethane matrix. The solubility limit, refractive index change and reaction kinetics/conversion were studied against a commercial reference high refractive index monomer, 2,4,6-tribromophenyl acrylate (TBPA). Superior performance in solubility to TBPA is shown with similar reaction kinetics and final conversion as confirmed by realtime Fourier transform infrared spectroscopy (FTIR) and real-time monitoring of diffraction grating growth. We demonstrate the ability to load substantial amounts of these writing monomers enabling a straightforward path to higher achievable Δn values (peak-to-mean Δn ~ 0.03) without sacrificing optical properties (transparency, color or scatter) as validated through recording ~100% efficiency volume transmission holograms in sub-15 μm thick films.
We present a general strategy for characterizing the reaction and diffusion kinetics of polymeric holographic recording media by which key processes are decoupled and independently measured. The separate processes are combined into a predictive model that is shown to make accurate quantitative predictions of index response over three orders of exposure dose (~1 to ~10<sup>3</sup> mJ/cm<sup>2</sup>) and feature size (0.35 to 500 microns) for a model material similar to commercial media. Several critical performance concepts also emerge from the model, including a prediction of a formulation’s maximum potential index response, insight into why a particular material may not achieve this maximum and the process that limits the recording resolution.
Two-chemistry polymer systems are attractive platforms for a wide range of optical and mechanical applications due to the orthogonal chemistries of the initial thermoset matrix and the subsequent photo-initiated polymerization. This scheme allows the mechanical and optical properties of the materials to be individually addressed. However, the mechanical properties of both the initial matrix and the photopolymer system affect the performance of these materials in many applications from holography to optically-actuated folding. We present a mechanical model along with experimental demonstrations of a two-chemistry holographic photopolymer system. A three-dimensional finite element model is used to simulate the mechanical and chemical responses in time. The model uses standard material measurements to predict both large-scale deformation and more localized stress and strain. To demonstrate the magnitude of mechanical stresses possible in these materials, we show bending of thin strips with UV light activation using an optical absorber to create an intensity gradient in depth. The resulting non-uniform polymerization causes shrinkage and bending toward the light followed by swelling and bending away from the light caused by monomer diffusion. In addition to this large-scale bending, we demonstrate that the model can be used to qualitatively predict surface deformations that can be used for surface relief optical elements. The mechanical model enables understanding of shrinkage and swelling properties of a material system that affect the performance of that system over a wide range of illumination conditions.
Optically-driven diffusion of high refractive index molecules within a transparent thermoset polymer matrix is a promising platform for hybrid optics that combines a wide range of optical structures from large scale holograms to micron-scale gradient index waveguides in a single integrated optical system. Design of such a system requires characterization of the optical response of the material at a wide range of spatial scales and intensities. While holographic analysis of the photopolymers is appropriate to probe the smaller spatial scales and lower intensity optical response, quantitative phase mapping of isolated structures is needed to probe the response to the higher intensities and lower spatial frequencies used in direct write lithography of waveguides. We apply the transport of intensity equation (TIE) to demonstrate quantitative refractive index measurements of 10 μm-scale localized gradient index structures written into diffusive photopolymer materials using both single- and two-photon polymerization. These quantitative measurements allow us to study the effect of different exposure conditions and material parameters such as writing beam power, exposure time, and wt% loading of the writing monomer on the overall profile of the refractive index structure. We use these measurements to probe the time scales over which diffusion is significant, and take advantage of the diffusion of monomer with a multiple-write scheme that achieves a peak refractive index contrast of 0.025.
Two-beam holographic exposure and subsequent monitoring of the time-dependent first-order Bragg diffraction is a common method for investigating the refractive index response of holographic photopolymers for a range of input writing conditions. The experimental set up is straightforward, and Kogelnik’s well-known coupled wave theory (CWT) can be used to separate measurements of the change in index of refraction (Δn) and the thickness of transmission and reflection holograms. However, CWT assumes that the hologram is written and read out with a plane wave and that the hologram is uniform in both the transverse and depth dimensions, assumptions that are rarely valid in practical holographic testing. The effect of deviations from these assumptions on the measured thickness and Δn become more pronounced for over-modulated exposures. As commercial and research polymers reach refractive index modulations on the order of 10<sup>-2</sup>, even relatively thin (< 20 μm thick) transmission volume holograms become overmodulated. Peak Δn measurements for material analysis must be carefully evaluated in this regime. We present a study of the effects of the finite Gaussian write and read beams on the CWT analysis of photopolymer materials and discuss what intuition this can give us about the effect other non-uniformities, such as mechanical stresses and significant absorption of the write beam, will have on the analysis of the maximum attainable refractive index in a material system. We use this analysis to study a model high Δn two-stage photopolymer holographic material using both transmission and reflection holograms.