Abstract

It is often the case that when studying laser models one is confronted with the problem of stiffness: some of the variables in the problem vary much faster than others. An example of this is standard semiconductor laser models where the time scales in the problem vary from femtoseconds to nanoseconds. For such systems it is a reasonable approach to try to eliminate the fastest variables and only retain them as slaved to the slow variables in the problem. The method of choice in the optics community for realizing the slaving has mostly been standard adiabatic elimination in which the fast variables are slaved by setting the corresponding time derivative to zero and solving for the fast variables. This method has met with reasonable success, but it has been shown that it tends to remove physically relevant instabilities from the reduced mathematical description. For laser models described by ordinary differential equations an application of centremanifold techniques has been shown to retain more of the structure of the full problem. For laser models described by partial differential equations, as is the case if multimode transverse or longitudinal dynamics are studied, the application of centremanifold techniques has so far met with mixed success as it has tended to produce an equation with a singular time behavior. We have developed a new method of adiabatic elimination that is very easy to implement, that is well behaved, that is, free of unphysical instabilities and that reproduces all of the instabilities and dynamics contained in the full system.

© 1992 Optical Society of America