NCSA NEWS

Central to Hess and Klein's method is something called the Green's function. Lasers concentrate light by trapping it within a cylinder of reactive semiconducting material and bouncing it back and forth between mirrors placed at both ends. The beam is amplified with each pass as photons -- the individual packets of light energy -- induce atoms in the reactive material to emit photons that are clones of the original; that is, they radiate at exactly the same frequency, energy, phase, and direction. The extraordinary intensity of lasers owes to the uniformity of this emission.

The majority of researchers designing VCSELs rely on analytical studies that approximate the lasers' geometry and physics. While suitable for conceptual designs, theoretical modelers such as Hess argue that these methods lack the precision required for optimizing microtechnology.

But simulating laser behavior requires solving two complicated sets of equations -- one for light (the optics) and the other for the behavior of the electrical current that initiates lasing (the electronics). They must be solved almost simultaneously so that the results from each set continually feeds into the other. Sophisticated methods exist for modeling the electronics. What remains to be tackled are the optics. "What makes Karl's work unique," says Shun-Lien Chuang, an electrical engineering professor at Illinois, "is that he's found an efficient way of combining both."

Here's where the Green's function comes in. For most VCSEL models, researchers place a computational mesh, or grid, over the entire laser diode and define the field at each point on this matrix with a linear relationship: the field at point A equals the field at point B plus the field at point C, and so on. They then solve the resulting set of equations to obtain a solution for the system at all of the points. When the engineers are refining a laser design, their code races through the calculations that generate the equations defining the mesh points. It slows to a grind, though, when it has to actually solve these equations. This must be done simultaneously, with the computer's processors exchanging data back and forth about the state of these millions of equations. This is the step that takes 12 hours. And that is assuming the data are a constant for the electronically conducting portion of the equation. If they calculate this portion as well, they're up to 600 hours.