  Electromagnetic wave propagation in optical fiber amplifiers obeys Maxwell
equations. Using coupled mode theory, the full Maxwell system within an optical
fiber amplifier is reduced to a simpler model. The simpler model is made more
efficient through a new scale model, referred to as an equivalent short fiber,
which captures some of the essential characteristics of a longer fiber. The
equivalent short fiber can be viewed as a fiber made using artificial
(unphysical) material properties that in some sense compensates for its reduced
length. The computations can be accelerated by a factor approximately equal to
the ratio of the original length to the reduced length of the equivalent fiber.
Computations using models of two commercially available fibers -- one doped
with ytterbium, and the other with thulium -- show the practical utility of the
concept. Extensive numerical studies are conducted to assess when the
equivalent short fiber model is useful and when it is not.
