The generalized plane strain solution for anisotropic multilayer nanostructures with cubic crystal symmetry under the influence of initial strains has been derived. This solution can be used to estimate equilibrium curvature radius and strains/stresses of rolled-up anisotropic multilayer nanostructures, whose deformations are induced by crystal lattice mismatch. The solution has been applied for calculation of curvature radii and strain components of a bilayer In0.2Ga0.8As/GaAs rolled-up nanostructure. The results are in agreement with those obtained by a finite element analysis.

A closed-form solution for multilayer structures with initial strains under generalized plane strain conditions is presented. Such solutions can be useful for estimating the curvature radius and strains or stresses for self-positioning micro-and nano-structures with lattice mismatched layers. Comparison with finite element results shows that the developed solution predicts reasonable values of the curvature radius at the central part of the structure. Strains provided by the generalized plane strain solution are in agreement with those obtained by finite element analysis.

An experimental and numerical investigation of the effect of material anisotropy on the self-positioning of epitaxial nanostructures has been performed. The self-positioning occurs due to a lattice mismatch between two epitaxial material layers (GaAs and In(0.2)Ga(0.8)As) of a hinge. Both materials have cubic crystal symmetry and possess anisotropic mechanical properties. The dependence of the hinge curvature radius on the material orientation angle was obtained experimentally by creating self-positioning hinges with different angles between the hinge axis and material crystallographic axes. The same self-positioning structures were modelled by solving geometrically nonlinear problems with the help of the finite element method. Experimental and numerical values of the hinge curvature radius are in qualitative agreement. It is found that material anisotropy significantly affects the shape of self-positioning structures.

Atomic-scale modeling of self-positioning GaAs-InAs nanostructures is performed. Curvature radius values obtained by the atomic-scale finite element method are compared with a continuum mechanics solution under plane strain conditions. Atomic-scale modeling and continuum mechanics solution predict same curvature radius for structures with large thickness. However, atomic-scale modeling shows significant decrease of the curvature radius for structures with thickness less than 40 nm.

We have developed a ray-tracing simulation procedure for optically isotropic gradient refractive-index media. The procedure can take discrete points of arbitrary distribution for the definition of refractive-index distributions and lens surfaces. It is useful for simulating ray trajectories in real lens systems. The procedure is applied to a ray-tracing simulation of the Luneburg lens and a radial gradient optical fiber. The simulation results are compared with the analytical solutions, and it is shown that they are in precise agreement.