Fundamental Notes on Instability Analysis

In this special technical report the author presents fundamental studies on instability analysis. When an electromagnetic wave linearly interacts with an active medium or system, there can occur basically two types of instabilities. One of them, in which the wave grows indefinitely with time, is called absolute instability, and the other, in which the wave grows spatially as it travels, is called convective instability. By conformal mapping of the dispersion equation from omega onto the k plane or vice versa, the author has made a detailed analysis of these two types of instabilities. General procedures for analyzing instabilities are summarized. Effects of driving sources and the possible occurrence of branch cuts, in the k plane, of the dispersion equation are discussed.