A Symbolic Method in Geometrical Optics

A Fast Method for Linear Waves Based on Geometrical Optics

We develop a fast method for solving the one-dimensional wave equation based on geometrical optics. From geometrical optics (e.g., Fourier integral operator theory or WKB approximation) it is known that high-frequency waves split into forward and backward propagating parts, each propagating with the wave speed, with amplitude that is slowly changing depending on the medium coefficients, under t...

Matrix Methods in Geometrical Optics

As well as the geometrical methods used for solving lens problems, and locating the size and position of images in optical systems, there is an alternate, perhaps more versatile, method involving matrix manipulation. Many of you will be familiar with the use of simple 2x2 matrices. Firstly, however, before I consider the use of matrices in optics, I will review the matrix solution of two simult...

Multiphase Computations in Geometrical Optics

In this work we propose a new set of partial diierential equations (PDEs) which can be seen as a generalization of the classical eikonal and transport equations, to allow for solutions with multiple phases. The traditional geometrical optics pair of equations suuer from the fact that the class of physically relevant solutions is limited. In particular, it does not include solutions with multipl...

Electromagnetic Scintillation I. Geometrical Optics

Geometrical optics and chessboard pebbling

Recently Chung. Graham, Morrison and Odlyzko [l] studied some combinatorial and asymptotic enumeration aspects of chessboard pebbling. In this problem, we start with a single pebble, placed at the origin (0,O) of an infinite chessboard. At each step we remove a pebble from (i,j) and repIace it with two pebbles at positions (a + 1,j) and (i.j + I). provided the latter are unoccupied. After m ste...