Surface-emitting electroholographic SAW modulator.

We report the design and operation of a surface-emitting surface acoustic wave (SAW) acousto-optical modulator which behaves as a cm-scale linear hologram in response to an applied electronic waveform. The modulator is formed by an optical waveguide, transducer, and out-coupling surface grating on a 1 mm-thick lithium niobate substrate. We demonstrate the ability to load and illuminate a 9-region linear hologram into the modulator's 8 mm-long interaction region using applied waveforms of 280-320 MHz. To the best of the authors' knowledge, this is the first demonstration of a monolithically-integrated, surface-emitting SAW modulator fabricated using lithographic techniques. Applications include practical implementations of a holographic display.

Sawtooth structure formation under nonlinear-regime ion bombardment.

Linear-regime Ar+ bombardment of Si produces symmetrical ripple structures at ion incidence angles above 45° measured off-normal (Madi 2009 J. Phys.: Condens. Matter 21). In the nonlinear regime, new behaviors emerge. In this paper, we present experimental results of ion bombardment that continues into the nonlinear regime until pattern saturation at multiple ion incidence angles, showing the evolution of their grazing incidence small-angle x-ray scattering (GISAXS) spectra as well as atomic force microscopy topographs of the final, saturated structures. Asymmetric structures emerge parallel to the direction of the projected ion beam on the sample surface, constituting a height asymmetry not found in the linear regime. We then present simulations of surface height evolution under ion bombardment using a nonlinear partial differential equation developed by Pearson and Bradley (2015 J. Phys.: Condens. Matter 27 015010). We present simulated GISAXS spectra from these simulations, as well as simulated scattering from a sawtooth structure using the FitGISAXS software package (Babonneau 2010 J. Appl. Crystallogr. 43 929-36), and compare the simulated spectra to those observed experimentally. We find that these simulations reproduce many features of the sawtooth structures, as well as the nearly-flat final GISAXS spectra observed experimentally perpendicular to the sawtooth structures. However, the model fails to reproduce the final GISAXS spectra observed parallel to the sawtooth structures.

Distinguishing physical mechanisms using GISAXS experiments and linear theory: the importance of high wavenumbers.

In this work we analyze GISAXS measurements of the structure factor of Si surfaces evolving during 1 keV Ar+ ion bombardment. Using newly-developed methods sensitive to the full range of experimentally-available wavenumbers q, we extract the linear amplification rate R(q) governing surface stability over a range of wavenumbers 4-5 times larger than has previously been obtained. Comparing with theoretical models also retaining full wavenumber-dependence, we find an excellent fit of the experimental data over the full range of irradiation angles and wavenumbers. Moreover, the fitted parameter values represent experimental evaluation of the magnitudes of most physical mechanisms currently believed to be important to the pattern-formation process. In all cases, the extracted values agree well with direct observations or atomistic simulations of the same quantities, suggesting that GISAXS analysis may allow more powerful comparison between experiment and theory than had previously been thought.

Designing steep, sharp patterns on uniformly ion-bombarded surfaces.

We propose and experimentally test a method to fabricate patterns of steep, sharp features on surfaces, by exploiting the nonlinear dynamics of uniformly ion-bombarded surfaces. We show via theory, simulation, and experiment that the steepest parts of the surface evolve as one-dimensional curves that move in the normal direction at constant velocity. The curves are a special solution to the nonlinear equations that arises spontaneously whenever the initial patterning on the surface contains slopes larger than a critical value; mathematically they are traveling waves (shocks) that have the special property of being undercompressive. We derive the evolution equation for the curves by considering long-wavelength perturbations to the one-dimensional traveling wave, using the unusual boundary conditions required for an undercompressive shock, and we show this equation accurately describes the evolution of shapes on surfaces, both in simulations and in experiments. Because evolving a collection of one-dimensional curves is fast, this equation gives a computationally efficient and intuitive method for solving the inverse problem of finding the initial surface so the evolution leads to a desired target pattern. We illustrate this method by solving for the initial surface that will produce a lattice of diamonds connected by steep, sharp ridges, and we experimentally demonstrate the evolution of the initial surface into the target pattern.