4 research outputs found
Transformation-optics modeling of 3D-printed freeform waveguides
Multi-photon lithography allows to complement planar photonic integrated
circuits (PIC) by in-situ 3D-printed freeform waveguide structures. However,
design and optimization of such freeform waveguides using time-domain Maxwell's
equations solvers often requires comparatively large computational volumes,
within which the structure of interest only occupies a small fraction, thus
leading to poor computational efficiency. In this paper, we present a
solver-independent transformation-optics-(TO-) based technique that allows to
greatly reduce the computational effort related to modeling of 3D freeform
waveguides. The concept relies on transforming freeform waveguides with curved
trajectories into equivalent waveguide structures with modified material
properties but geometrically straight trajectories, that can be efficiently fit
into rather small cuboid-shaped computational volumes. We demonstrate the
viability of the technique and benchmark its performance using a series of
different freeform waveguides, achieving a reduction of the simulation time by
a factor of 3-6 with a significant potential for further improvement. We also
fabricate and experimentally test the simulated waveguides by 3D-printing on a
silicon photonic chip, and we find good agreement between the simulated and the
measured transmission at .Comment: 23 pages, 8 figure
A Survey of Spatial Deformation from a User-Centered Perspective
The spatial deformation methods are a family of modeling and animation techniques for indirectly reshaping an object by warping the surrounding space, with results that are similar to molding a highly malleable substance. They have the virtue of being computationally efficient (and hence interactive) and applicable to a variety of object representations.
In this paper we survey the state of the art in spatial deformation. Since manipulating ambient space directly is infeasible, deformations are controlled by tools of varying dimension - points, curves, surfaces and volumes - and it is on this basis that we classify them. Unlike previous surveys that concentrate on providing a single underlying mathematical formalism, we use the user-centered criteria of versatility, ease of use, efficiency and correctness to compare techniques
Procesado de geometr铆a en CAGD mediante S-series
El dise帽o geom茅trico asistido por ordenador (CAGD) se basa en la representaci贸n de entidades geom茅tricas en el est谩ndar nurbs, por lo que se debe obtener una aproximaci贸n polin贸mica o racional de aquellas funciones trascendentes, entidades que no pueden ser expresadas en la base de Bernstein. En principio se podr铆a pensar en una aproximaci贸n mediante series de Taylor truncadas. De esta forma se obtendr铆a una buena aproximaci贸n alrededor de un punto, pero se precisar铆an grados muy elevados para errores peque帽os y los programas de CAD tienen limitado el grado maximo admisible. Una forma de evitar estos grados elevados seria conectar varios desarrollos de Taylor, pero en este caso aparecer铆an huecos en la uni贸n de dos expansiones, algo inaceptable en una representaci贸n para CAD.
En esta tesis se introduce la herramienta matem谩tica b谩sica empleada en este trabajo, las s-series. Estas series resultan de la base s-monomial, basada en expansiones de hermite en un intervalo unitario de la variable. Asimismo, se describen las estrategias para calcular de manera eficiente la aproximaci贸n de una entidad mediante s-series. Seguidamente, se comparan las aproximaciones mediante s-series con las basadas en series de poisson. A continuaci贸n, se aproxima la clotoide como ejemplo de aplicaci贸n de las estrategias de aproximaci贸n mediante s-series expuestas.
Finalmente, se aplican las s-series a las t茅cnicas de deformaci贸n. El objetivo de este cap铆tulo consiste en conseguir una aproximaci贸n polin贸mica Bernstein-Bezier de los objetos deformados