The small signal dynamic behavior of the linear optical amplifier (LOA) is described by using small signal analysis to evaluate both gain and rate equations. Analytical results are obtained for both horizontal and vertical emissions that delineate the difference between the LOA region of maximum gain and gain compression. Crosstalk is calculated by adding a second gain equation to represent the output in a parallel channel. The analytical approach is based on the representation of the laser gain with the concept of the frequency dependent stimulated lifetime. This model is especially useful to represent multiple channels in the LOA. Experimental data are found to be well matched by the calculated results.