NCSA NEWS

Following a suggestion by Dennis Deppe, an electrical engineer at the University of Texas at Austin, Hess and Klein adopted an entirely different way of calculating the matrix elements so that most of the heavy-duty computing shifts from the step that requires simultaneous computing to the first step, which can be run in parallel because each calculation is independent of the others. (Robert Dutton, a member of the Alliance's Nanomaterials Application Technologies team from Stanford University, helped them eliminate many preliminary designs.) Instead of meshing the entire diode and using linear equations to define each point in the matrix, Hess and Klein meshed only the gain region -- the area where the light beam is bouncing back and forth -- and defined mesh points with a Green's function, a tricky mathematical "operator" that describes, or integrates, how the points on a computational mesh interact with each other by taking into account how a change in the field at one point affects all fields at every other point. It incorporates into their smaller number of matrix elements all the behavior that would have happened had they meshed the entire laser.

The result is that each of Hess and Klein's matrix elements is more difficult to calculate, but there are fewer of them to generate and they can be computed at the same time. Hess and Klein used all 128 nodes of the SGI CRAY Origin2000 at NCSA. The step that had been so time-consuming before -- solving the matrix that represents the laser's structure -- is now much faster because the number of mesh points, and hence the number of equations, is much smaller. Therefore the endless renditions required for fine tuning a design can be done in 30 seconds to 5 minutes...on a workstation.

"Our method is faster because we've increased the portion of the equation that can be solved in parallel and decreased the part that must be solved sequentially," says Klein.

For now, Hess and Klein's method only works for optimizing designs. Engineers must know something about the structure of the laser; say, that it is an oxide-confined laser. When designing VCSELs from scratch, they're back to 12 to 600 hours per idea. Overcoming this obstacle will be Hess and Klein's next goal.