Yohei Nishidate

Ray-tracing method for isotropic inhomogeneous refractive-index media from arbitrary discrete input

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.

Ray-tracing simulation method using piecewise quadratic interpolant for aspheric optical systems

We present a new method for precise ray-tracing simulation considering form errors in the fabrication process of aspheric lenses. The Nagata patch, a quadratic interpolant for surface meshes using normal vectors, is adopted for representing the lens geometry with mid-spectral frequencies of surface profile errors. Several improvements in the ray-patch intersection calculation and its acceleration technique are also proposed. The developed algorithm is applied to ray-tracing simulation of optical disk pick-up aspheric objectives, and this technique requires 10(5) to 10(9) times fewer patches than a polygonal approximation. The simulation takes only several seconds on a standard PC.

Generalized plane strain deformation of multilayer structures with initial strains

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 nanostructures 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.

Effect of thickness on the self-positioning of nanostructures

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 those obtained by a continuum mechanics solution under plane strain conditions. Atomic-scale modeling and continuum mechanics solution predict the 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 40nm.

Curvature estimate for multilayer rolled-up nanostructures with cubic crystal anisotropy under initial strains

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.

Impact of mesh-like top p-electrode on output performance of light-emitting diode: Numerical study

Numerical model and procedure for the light-emitting diode (LED) with realistic mesh strips having square cross-section are developed and used for simulation of electrical and output optical characteristics at different dimensions of the mesh and bias voltages. Performances simulated for realistic square cross-section strips and analytical model based on the finite-radius wire approximation were compared. Comparison demonstrates the advantages of realistic model, in particular, for extraction of the mesh-like electrode parameters resulting in maximum optical output.

Modeling of light-emitting diode with nonuniform current injection

Light-emitting diode (LED) with nonuniform current injection caused by the mesh-like design of top metal electrode is studied numerically. Three-dimensional Laplace equation for electric potential is solved by finite element method. The numerical model incorporates mapped infinite element to account for potential decay far away from the LED structure and finite element model developed for boundary condition at semiconductor-air interface in the mesh opening. Simulation results demonstrate the effect of the mesh geometrical parameters on the total output power.

A generalized ray equation and its solutions for ray-tracing in anisotropic inhomogeneous media

A new form of ray equation is derived for optically anisotropic inhomogeneous media. Using the ray equation, closed-form solutions are obtained and their results are compared with those obtained by numerical calculation.

Closed-form analytical solutions for ray tracing in optically anisotropic inhomogeneous media

Closed-form analytical solutions are obtained for ray tracing in several types of optically anisotropic inhomogeneous media whose optical properties are characterized by a matrix form of the inhomogeneous dielectric tensor in principal coordinates. The first solution is for anisotropic axial media, the second solution is for meridional rays in epsilon-negative metamaterial, and the third solution is an approximate one for rectangular lenses fabricated by molding procedures. The validation of numerical ray-tracing procedures for optically anisotropic inhomogeneous media was widely ignored since the solution was not available, and thus the present solutions are also useful for the validation. Furthermore, as examples of validation, ray trajectories are calculated by the closed-form solutions, and their results are compared with those obtained by a numerical solution of the geodesic equation which can be interpreted as a generalized ray equation.

Ray-tracing simulation procedure for general GRIN media

A ray-tracing procedure has been developed for general gradient refraction index media where the distribution and the media surface position are given as discrete point sets of arbitrary distributions.