Reflecting the growing importance of multi-mode transmission media in communications, radar, sensors, remote sensing, and many other industrial applications, this work presents analytic methods for calculating the transmission statistics of microwave and optical components with random imperfections. The emphasis here is on multi-mode waveguides, optical fibers, and directional couplers-described by the coupled line equations with random parameters-as well as multi-layer optical coatings used as windows, mirrors, or filters. The author clearly explains how to calculate the transmission statistics of these devices in terms of their coupling or optical thickness statistics, in both the time and frequency domains. This unique resource for engineers and researchers involved in the design of multi-mode transmission media:* Focuses on matrix techniques and the various types of problems to which they can be applied* Incorporates many new results developed by the author* Discusses applications to problems of significant practical interest* Demonstrates a purely analytical approach-not using Monte Carlo or other simulation methods